CLASSROOM PROJECTS with ENVIRONMENTAL APPLICATIONS
Faculty
Classroom Guide
This project is funded by
The National Science Foundation #
DUE-9952568
The
With additional support from
Written by
Professor of Mathematics,
All
rights reserved. Manual may be printed
for classroom use only. No part of this guidebook may be reproduced, in any
form or by any means, without the permission in writing from the authors.
The Earth Math project
provides you with a new way to integrate environmental science data and real
life problems into your classroom.
Whether you are familiar with the authors of the Earth Algebra texts or
new to this project, this faculty classroom guide is designed to help you in
several ways. You will want to use the
guide because you…
want to become familiar with the Earth Math web site and
tools.
are preparing for instruction with the Earth Math
modules.
need to take note of the ways you might want to use the
Earth Math modules as you teach your class.
want to learn to use the Earth Math demonstration
materials, modules, and applets.
wish to use the guide as a reference throughout the term
and beyond.
We would suggest you print this guide to have a hard
copy reference to the site materials and uses.
It will provide you a map to the materials, descriptions, and
directions.
Notes to the Instructor
The content of this handbook reflects
the third version of the Earth Math modules.
This guidebook will be updated to reflect the changes made to the
modules and applets as the project evolves.
There may be minor differences in the directions given in this guidebook
compared to the web site as the project is continued. Faculty designed this guidebook for faculty
and we welcome your suggestions and comments, so that we may improve the
training manual. Send all suggestions
and comments, as well as ask assistance when you need it, to:
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Please
contact |
Table of Contents
Welcome to the Earth Math Projects
Notes to the Instructor
History of the Earth Math Project
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Chapter
1 |
Home Page and Site Map Instructor Materials …………………………..… 1-1 Course Materials ……………….………………... 1-3 Evaluation ..………………………………...…..... 1-7 Button Links ….………………………………….. 1-8 |
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Chapter 2 Using
Earth Math Modules |
Learning to Use Earth Math Modules Starting the Modules …………………………..… 2-1 Website Windows
………………………………... 2-3 Using Review Topics
.…………………..….…..... 2-7 Using the Applets ………………………..…..…... 2-9 |
Chapter 3 |
Instruction Preparation Introductory Module: Your First
Module ……… 3-1 Modules Available ………………………………… 3-11 Review Topics
……………………………………… 3-16 Tool Chest
…..………………………………………. 3-31 |
Chapter 4 |
Inquiry in the Math Classroom Introduction to Inquiry-based Instruction ……..
4-1 Good Questions
………………………………….... 4-4 Assessment and Adaptation
……………………... 4-5 Web Sites and Bibliography ……………………… 4-7 |
History of the Earth Math Projects
The Earth Math Projects are an exciting
extension of the previous mathematics textbooks and materials produced with
applications to Environmental Science.
Over the past 12
years, the Earth Math Projects have produced unique materials that teach
mathematics through the study of environmental issues and problems. The materials are appropriate for use in
mathematics courses ranging from beginning algebra through calculus.
All Projects are
directed by Dr.
Three textbooks have
resulted from these projects, Earth
Algebra (algebra), Addison/Wesley, Earth
Angles (pre-calculus), Addison/Wesley, and Earth Studies (applied calculus), Kendall/Hunt. The applications
are based on real environmental problems that effect students’ lives and
therefore generate more interest in the use of mathematics as a tool that can
be used to analyze real situations. The
materials have been tested and formally evaluated and have shown that the use
of mathematics to study real problems that are interesting to students
significantly improves interest in, understanding and appreciation of the role
of mathematics in science and society.
As a spin-off,
special class notes based on water availability for a growing community were
developed for
Current Project Activities
The National Science
Foundation and the U.S. Dept. of Education, FIPSE have funded Schaufele and
Zumoff, for a curriculum development project which was an extension of the work
described above. The goal is to produce versatile, technology-intensive
materials for classroom use and teacher training. Reform-based applications are
incorporated into platform-independent software to make them accessible to
anyone with a computer. The versatility of these materials will allow an
instructor to use them regardless of textbook or underlying curricula.
Environmental applications
from the previous projects and new applications are designed for courses from
beginning algebra through calculus. The project features an inquiry-based
format, web-based interactive materials, seamless interface with
state-of-the-art technology, use of real data, interesting applications of
mathematical concepts, and flexibility of classroom use.
Materials
Each module, or
study, is presented on the Web (also available on CD-Rom) and can be used as an
in-class or lab project that illustrates real applications of mathematics to
students. Students are able to access data provided on the website or download
relevant data from the Internet.
Software applets are written that can perform mathematical operations reflecting
concepts learned in the classroom or be used for demonstration purposes. These
tools are available from the Web and packaged on the CD. Review topics of related prerequisite skills
are linked to the modules to provide a quick, easy view of content necessary to
complete the study.
Resources
Resources for the
faculty using the Earth Math modules include links to data, other related
projects, references, announcements of user activities, as well as contact with
authors and others involved in the project consortium.
Chapter
1 Web Site Specifics
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Home
Page and Site Map This
section of the guidebook gives an overview of infor-mation
regarding the web site, using the web site buttons, and all its materials. |
FAQ
What does the web site include? Becoming Familiar with the
Earth Math Web Site Instructor
Materials ……………………… 1-1 Course
Materials ………………………… 1-4 Evaluation …………….…………………… 1-8 Button Links ..…..………………………….
1-9 |
Instructors using Earth Math modules
will find a description of the Earth Math homepage and the site for easy
reference and use. In this first
chapter, the instructor materials and course materials will be discussed, as
well as the site evaluation and links for resources and use in the classroom. The next chapter will describe the content of
the modules and the use of each of the site tools.
Starting the Modules
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Standard
Formatting of the Earth Math Modules Introduction A
standard format and methods are used in the analysis of the data and solution
of problems that are presented in Earth Studies. The Studies will all be presented in a
somewhat structured format that is demonstrated in the Introductory Module
described in depth in Chapter Three. The Earth Studies Introductory Module
demonstrates the basic format and how to integrate the website
materials. We recommend you use the
introduction modules as a starting point for students (and instructors) to
learn to use the Earth Studies. The
standard format should make the implementation of any of the modules easy –
use all or any part of a module, along with the appropriate applets and
review. Click on the Course level page
and module name. The page opened will
be written in the standard format, with components as follows. |
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Study Components Each
Study will have three components:
The
text will be presented in four sections:
answers to questions raised regarding the
issue. It is in this section that the
applets will be used.
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The Tool
Chest will be the place where students can access the applets that will
perform the mathematics. Here students
can enter their data or other quantitative information and use the applets to
analyze data and construct mathematical models. The results should answer the questions
involved in the issue. A complete
listing of the Tool Chest Applets can be found in Chapter 3, Tool Chest. |
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Journal The journal
will be the place students record their answers to questions from the text
and include the explanations of the mathematics they used. Student’s journals should be written as a
file in the word processing package on their computer; this will be the
document they turn in to you as instructor. Instructions
on selection highlighting, copy and paste of selected text and saving the
journal files should be given to students as they begin Earth Studies. It is appropriate to do this while students
work with the demonstration modules or the first module you use, if you wish
students to use a journal. |
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Using the Website Go to the
website address: http://earthmath.kennesaw.edu to the site
homepage. All Earth Math materials
available can be accessed through this address. At the Earth Math homepage, click on the
study level and scroll down to the module desired and choose the study by
clicking on the name. This will
automatically open the beginning page of the study and you are ready to
begin. You can see this is the same as
the previous image, in the CD-Rom instructions above. |
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Using the CD-Rom The CD-Rom is provided for you to
have an alternative to the website, to have a backup if you are having
problems with internet access. Contact
a project team member to request a CD-Rom version of Earth Math. Insert the disk in the drive and open
My Computer. Double-click the CD-Rom
drive (usually D:) and you will see the contents of
the CD. |
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Double-click on index
and it will open the first page of Earth Math Study materials. Once into the homepage, scroll down the page and click on the
study that you want to use and it will link automatically to all windows and
materials that are associated with that module. |
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These materials are the same as those on the website and can be
used when no internet access is available.
One caution – remember you will not have access to the websites that
are linked to the CD if you don’t have internet access, but much of the
material can be used – including the applets. |
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Using the Windows If a student clicks on Algebra with Equations they will bring up the course module listing for this level. Notice the menu map at the top of this window, which allows the student to go back to the homepage. They can then click on the Predicting Streamflow Module, to start from the beginning, or click on a particular part of the module to pick up where they left off. |
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A
listing of the available modules is included on the course level main page. Each
link is designed to go directly to that module or part of the module. Notice
the link to the Home page in blue, as well as the standard menu links on the
left of the page. You can
access any of the materials from these buttons. |
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If the student clicks on the
Predicting Streamflow Part 1 Temperature link, they
will bring up the Streamflow Temperature page, as
shown below. |
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The
student then will click on the first link, Part 1: Temperature, to begin work
in this module. They may
also access the other parts from here. Notice they can also go back to the Streamflow course main page, the Algebra with Equations
page or Home page from the top menu.
They may also access the other parts of the Streamflow
module from this top menu. The
student then will begin work on Part 1: Temperature, beginning with the
Comprehension questions, including the use of the applets. |
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Using
the Review Topics
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Review
Topics The topics provided are
for the review of the mathematical concepts and terms included in the
study. These concepts are assumed
prerequisite concepts and skills required for the successful completion of
the study. Students may access these
topics to find general information and formulas for working with the
data. Interactive applets are included
for students to explore the impact of changes on symbolic expressions, graphs,
etc. Example problems and solutions
are included to assist the student’s review of prerequisite material.
The review topics are listed on the left at the beginning of a module study, with the Tool Chest. Only those topics necessary for successfully completing that particular module of study are included. For example, when opening the Algebra with Functions Passenger Car Gasoline Consumption module, use the scroll bar to follow down the left side of the display which will reveal the following list of Menu Topics for this module. |
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When a student clicks on the topic
name, the topic opens in a new window, to be used along with the study
module. For example, if the Linear
Functions topic is opened, the following window includes embedded applets and
complete examples. |
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The student can review the material ‘just in time’ at the time needed, including working examples within the applets. The review topics include the solutions to the examples with descriptions and definitions, as well as appropriate formulas. |
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Review Topics may be accessed from
the standard menu on the left of the page by clicking on the button link
under Instructor’s Materials. The student may select to review
prerequisite material at a point that is appropriate in order to work
successfully on the Earth Math study. |
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Review Topics
The Review Topics
button is a link to prerequisite review that students can use at any
time. Embedded within the modules of
study are topics given in the left menu of the page, appropriate for each study. Students can return to the homepage to use
a topic they’ve forgotten at any time.
Available topics are listed and a description of each follows. |
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Available Review Topics ALGEBRA TOPICS § Solving Equations Graphically 1. Slope 2. Intercepts Precalculus Topics § Trigonometric Functions: Sine & Cosine § Period, Phase Shift and Amplitude of Trigonometric Functions Calculus Topics |
For
example, if a student clicks on the linear functions topic, a window begins
with the definition and an applet for reviewing the visual concepts. The general formula for slope and intercept
are defined and include examples for the student to review problems
appropriate for the topic and level.
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The applets are embedded in the
Introductory Module and some Review Topics for ease of use but may be
accessed from the standard toolbar on the left in any window. Students can choose to follow the study
step-by-step, or you may have them do selected parts of the study. You can also assign additional problems for
exploration using the applets. Internet data sites are linked within
the study, marked by the blue highlight.
Students can click on these links to obtain more data and information. |
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Using an Applet
The
Tool Chest is a set of mathematical tools for students to use in their
study. Each applet has a window with
specific directions for use below the applet window. By clicking on the applet name in the tool
chest the student brings up the applet and directions for use. Applets accessed by using a study or review
topic that has the applet embedded, do not contain the directions listed with
the applet necessarily. Most of the
directions for the applets are self-explanatory and there are groups of
applets that function in the same manner, with the various models.
To begin to use an applet, open the
applet from the Tool Chest, for example the Linear Regression Applet. Notice the window frames for entering the x
and y coordinates of the data set, the CLEAR, PLOT and ANALYZE buttons for
use. Enter the data set first, than
click on PLOT. The applets will open
in another window so the window may be resized and used with the module
window. |
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You will need to enter the X coordinates and
then the Y coordinates in the Data window.
You then click PLOT and the coordinates are
plotted in the top right window. When you click ANALYZE the ‘best fit’ linear
regression model and the resulting function is given in the lower results
window. You may clear the data to enter a new data set
by using the clear button. Students can practice entering data and using
the applet buttons, noting the resulting change from additional or new
information. |
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You will notice the graph displayed in the window on the top right and the model in the RESULTS window. |
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The linear regression applet will plot
the data points on the coordinate graph of the applet. Students will see the
data points plot in the applet. This applet result is from the
Introductory module. |
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Click ANALYZE and the best fit regression model for the entered data
set will be displayed along with the data set, with the symbolic model and
error in the RESULTS window, as shown below.
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The linear regression applet will plot
the regression line over the data points. Students will find the data model
and error in the lower window. |
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Tool Chest
The Tool Chest is
a link to applets that students can use at any time. Embedded within the modules of study and
review topics are the links to these applets, given in the left menu of the
page. Students can return to the
homepage to use an applet to graph or calculate a value at any time. Available applets are listed and a
description of each follows. A
complete set of directions for each applet are given in Chapter 3, Applets. |
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Available Applets COMPUTATION APPLETS · Math Pad INSTRUCTIONAL APPLETS · Defining Trig. Functions: Aine & Cosine · Quadratic Functions Standard Form EXPERIMENTATION APPLETS |
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example, if a student clicks on the linear regression applet, a window for
calculating the linear regression from a data set is opened. The student can then enter data and plot
the data points, then calculate the linear regression equation. The description of each applet is given in
the section on applets.
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Help
assistance is provided for each applet of the Tool Chest. Most applets are self explanatory, with
buttons and clear displays. There are
several notes regarding the use of the Math Pad and Plot Solve to consider. |
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Applet Descriptions The
descriptions below briefly identify the function of the applets
available. The list follows the same
sequence as the website TOOL CHEST. |
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Computation Applets EXPONENTIAL REGRESSION APPLET This applet has
two functions: plotting and finding the exponential function which best
approximates the user supplied data.
Using an appropriate data set, this applet
plots and data and will find the best fit exponential function for that
data. The best fit model is displayed
on the graph with the data set for comparison. The symbolic model and error is displayed
in a results window. |
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LINEAR REGRESSION APPLET This applet has
two functions: plotting and finding the linear function which best
approximates the user supplied data.
Entering an appropriate data set, the user plots the data and finds
the best fit linear function. The
function graph is plotted with the data set.
The symbolic model and associated error is displayed in the results. |
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JAVA Math Pad This applet
allows the user to evaluate mathematical expressions and functions. A
mathematical expression is made of numbers, variables, built-in and user
defined functions together with operations. It has an open screen and several
buttons. For further
information, click on the scroll down menu, under "Help Topics" to
get more detailed help on how to use this applet. You need to enter expressions including all math
symbols ( , /, ^ , etc.) in order to use the math pad. For example: Enter function
f 1(x) = 2*x Enter f1(3)
Gives answer 6.0 This will allow
students to define up to ten functions. |
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Plotting Applet The purpose of
this applet is to plot functions. It can plot up to 10 different functions at
the same time. It can also be used to solve equations numerically. Changes in window parameters and function
information, using zoom and trace buttons, can allow the user to define and
view different functions on the same graph. |
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QUADRATIC REGRESSION APPLET This applet has
two functions: plotting and finding the quadratic function which best
approximates the user supplied data. Entering an appropriate data set, the
user plots the data and finds the best fit quadratic function. The function graph is plotted with the data
set. The symbolic model and associated
error is displayed in the results. |
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Instructional
Applets The The purpose of
this applet is to illustrate the relation between the unit circle and how the
trigonometric functions are defined.
As you drag a point around the unit circle, the applet displays the
coordinates and angle direction.
Choosing sine or cosine, the function’s value is displayed as the
length of the segment on the unit circle, as well as the corresponding angle. |
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The purpose of this applet is to illustrate the relationship of the slope of the tangent to the graph of y = f(x) at x = a, that can be approximated for a certain value of h where the secant line becomes the tangent to the graph of y = f(x) at x = a. This applet illustrates the concept that the slope of the secant approaches the slope of the tangent, allowing the user to enter a function, select the points (a, f(a)) and (a+h, f(a+h)), to change h so that the point (a+h, f(a+h)) gets closer to the point (a, f(a)). |
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Role of a and b in y = ab^x The purpose of
this applet is to illustrate how the values of a and
b affect the exponential function y = a b^x. Changes made to the general form
exponential function, using a scroll bar, will display the affect of the
coefficient and base on the resulting graph. |
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This applet illustrates the fact that the derivative of a function y = f(x) at x = a, denoted f'(a), is the slope of the tangent to the graph of y = f(x) a x = a. The user can plot a function, and select points on the graph. As the points are selected, the tangent to the graph at the chosen point is drawn, if desired, its slope is displayed and plotted as a new point. If the user selects enough points, the graph of the derivative will become evident. |
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Role of a, b, k and c in y = a
+ b cos(k(x - c)) The purpose of
this applet is to illustrate how the values of a, b, c and k affect the graph
of the cosine function. Plotting an appropriate data set supplied by the
user, the cosine function coefficients and constants selected are then
entered and tested by graphing with the data set to view the fit of the
function. |
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Role of a, b, k and c in y = a
+ b sin(k(x - c)) The purpose of
this applet is to illustrate how the values of a, b, c and k affect the graph
of the sine function. Plotting an appropriate data set supplied by the user,
the sine function coefficients and constants selected are then entered and
tested by graphing with the data set to view the fit of the function. |
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Understanding the Slope of a
Line The purpose of
this applet is to understand the notion of "the slope of a
line". By selecting two points
on the graph, the point coordinates and quotient rise/run is displayed, as well
as the triangle symbolizing the relationship.
Point positions can be changed and the information is updated. |
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ROLE of m and b in y = m x + b The purpose of
this applet is to illustrate how the values of m and b affect the line y = m
x + b. Using a scroll bar to change
the slope m and/or intercept b, the line position moves to reflect those
changes. |
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Role of a, b and c in y = a
x^2 + b x + c The purpose of
this applet is to illustrate how the values of a, b and c affect the parabola
y = a x^2 + b x + c. Using a scroll bar to change
the coefficients and constant, the parabola’s position moves to reflect those
changes. |
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Role of a, h and k in y = a (x
- h)^2+ k The purpose of
this applet is to illustrate how the values of a, h and k affect the parabola
y = a( x - h)^2 +k. Using a scroll bar to change the coefficients and
constant in the graphing form of a quadratic, the parabola’s position moves
to reflect those changes. |
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The The purpose of
this applet is to illustrate the relation between a point on the unit circle,
its coordinates and the angle between the x-axis and the line through the
origin and the point. By dragging a
point around the unit circle, the coordinates of the point and the angle
values will be displayed in either degrees or radians. |
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Sums and Approximating Areas This
applet allows you to experiment with Riemann sums
and approximating the area between the x-axis, the graph of y = f(x),
the vertical lines x = a and x = b. The
user specifies what kind of Riemann sum is to be used, the applet draws the graph of the function, the
rectangles corresponding to the partition, and the kind of Riemann sum being used. |
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Experimentation Applets FITTING TRIGONOMETRIC (COSINE
FUNCTION) DATA APPLET This applet has
two functions: First, it can be used to plot user supplied data. It can also
be used to test if a user supplied trigonometric (cosine) function (a
function of the form y = a + b cos(k (x - c)) ) fits the given data by plotting the
function. Plotting an appropriate data
set supplied by the user, the cosine function coefficients selected are then
entered and tested by graphing with the data set to view the fit of the
function. |
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FITTING EXPONENTIAL DATA
APPLET This applet has
two functions: First, it can be used to plot user supplied data. It can also
be used to test if a user supplied exponential function (a function of the
form y = a (b^x) ) fits the
given data by plotting the function. Plotting an appropriate data set
supplied by the user, the exponential function coefficients selected are then
entered and tested by graphing with the data set to view the fit of the
function. |
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FITTING LINEAR DATA APPLET This applet has
two functions: First, it can be used to plot user supplied data. It can also
be used to test if a user supplied linear function (a function of the form y
= m x + b) fits the given data by plotting the function. Plotting an
appropriate data set supplied by the user, the linear function coefficient
and constant selected are then entered and tested by graphing with the data
set to view the fit of the function. |
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FITTING QUADRATIC DATA APPLET This applet has
two functions: First, it can be used to plot user supplied data. It can also
be used to test if a user supplied quadratic function (a function of the form
y = a x^2 + b x + c) fits the given
data by plotting the function.
Plotting an appropriate data set supplied by the user, the quadratic
function coefficients and constant selected are then entered and tested by
graphing with the data set to view the fit of the function. |
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FITTING TRIGONOMETRIC (SINE FUNCTION) DATA APPLET This applet has
two functions: First, it can be used to plot user supplied data. It can also
be used to test if a user supplied trigonometric (sine) function (a function
of the form y = a + b sin(k (x - c)) )
fits the given data by plotting the function. Plotting an appropriate data
set supplied by the user, the sine function coefficients selected are then
entered and tested by graphing with the data set to view the fit of the
function. |
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Chapter
3 Instruction With
Earth Math
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Instruction
Preparation This
section of the guidebook gives you directions on how to get started and help you
prepare for the classes in which you will use the Earth Math modules. |
FAQ How do I teach students to
begin? Web Site Assistance To The Student …………………………………….. 3-1 Introduction
Module: Your First Module ……… 3-2 Modules
Available ………………………………… 3-8 Review
Topics ……………………………………… 3-13 Applets ………………………………………………. 3-22 |
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This
last chapter of the guide will assist you in understanding how to begin
working with the Earth Math Studies.
The Introductory Module material can be used to instruct students in
the use of the modules, integrating the applet tools and review topics. The Introduction to Applets contains step
by step instructions in the use of two applets. |
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Introductory
Material
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Introductory
Module
World Population
In this module, the student is introduced to the format and methods
that will be used in the analysis of data and solution of problems that are
presented in Earth Studies. The Studies will all be presented in a
somewhat structured format that will be outlined in this module.
Applets, or little programs, designed to be used with each Study; these will
perform the mathematical operations needed to analyze data and build
mathematical models. Also, links are included throughout each study
that will take students to explanations of mathematical terms and
methods. Here you will be guided through a study on population that
will illustrate the most common methods used in all of the Earth Math Studies
and will also illustrate the use of the applets. This demonstration
module can be used as a preliminary study to learn the use of the modules and
tools provided in the Earth Studies.
First, we outline the general structure for all the Studies. |
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Each Study will have three components: ·
Text - which will provide information about a particular issue and ask
questions; ·
Menu - lists in two parts: Tool Chest - contain the applets to perform the mathematical
operations Review Topics - contain links to explanations of relevant
mathematical topics and examples; ·
Journal - which will be the place where students can record thoughts,
answers, and mathematical solutions.
This is kept on a word processor and should be open as students record
the answers to questions. |
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The Text
will be presented in four sections: ·
Comprehension section - will provide information about the issue
and ask pertinent questions for students to think about and express their own
ideas regarding the issue. ·
The Acquisition section - will provide more detailed
information, relevant data, or direct students to a website to acquire more
information or data. ·
The Application section - will ask specific questions
which will require mathematical analysis that will lead to a mathematical
model. The model should be able to provide answers to questions raised
regarding the issue. It is in this section that the applets will be
used. ·
The Reflection section - will ask questions regarding
the reasonableness or validity of a student’s model. |
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The
Tool Chest will be
the place where students can access the applets that will perform the
mathematics. Here they can enter data or other quantitative information
and use the applets to analyze data and construct mathematical models.
The results should answer the questions involved in the issue. |
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The Journal
will be the place students record their answers to questions from the text
and include the explanations of the mathematics used. The journal
should be written as a file in the word processing package on the computer;
this will be the document turned in to you as instructor. |
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Your First Module |
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EARTH
STUDY: WORLD POPULATION |
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Comprehension
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In
this section, questions are posed that are designed to stimulate thoughts and
observations regarding population increase/decrease, reasons for studying
population change, and methods that might be used. At this point,
students should open a blank document in their word processor and record the
answers to these questions. Copy each question into the journal (Ctrl-C to copy
and Ctrl-V to paste) and type their response below the question in a
different color or font. Be sure to remind them to write in
complete sentences and express their ideas so that others can
understand. Students should save their work and keep this window open
throughout this study so they can easily record other questions and answers. Each of the applets is embedded in this
first module and an additional applet display follows with the correct
result. The applet tools are embedded in this first Introductory Module only. Questions
A. Do
you think that the population of the World is increasing or decreasing? B. What
have you noticed recently that led you to your answer to A? C.
How do you think population change in the world might influence your
life? D.
How do you think mathematics can be used to study population change? E. What are
some reasons for studying population change? |
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Acquisition
In
this section, students will be given information about population increase,
real data is provided, and links to websites that contain more information
and updated data are also included. Estimates of world
population before the twentieth century vary widely, but most sources put the
number of people in the world in 1750 at about 750 million. By
mid-nineteenth century the population reached 1 billion and until 1930 the
growth was never more than 1%; however, since 1950 the increase has never
fallen below 1.6%. Current patterns of population growth and the
accompanying changes in consumption are placing increasing stresses on
ecosystems through environmental degradation, deforestation, loss of biological
diversity, over harvesting, and accumulation of toxic wastes. |
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The Table below
gives the United Nations estimates of the world population (in billions)
every five years from 1950 -1995. Students producing a model for
prediction of population will use this table of information.
World Watch 1996 In this section, objectives and
assumptions are stated; these will determine the mathematical model for
population. Students will use relevant mathematical tools that are
provided, the applets, to perform an analysis on the data and build an
appropriate model. Students will develop a model for world measure of
population growth. Applets can be accessed by clicking “Tool Chest” on the Menu to the left of the screen
in the demonstration module. Instructors and students should follow the steps outlined after each question to familiarize themselves with the techniques used and the applets available. Record answers in the student journal. |
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The objectives and assumptions are
listed below. Objectives
To determine: 1. a
linear model for world population; 2. the annual rate of change of world population. Assumption
The current
trends for world population continue. |
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Application
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Linear Models
In this part, students will find a linear
function to approximate data for world population and use this to • estimate
annual population growth, • estimate the
population for years other than those in the data set, and • forecast
future population size. (Note
the link to a Topic for review, if the student needs to review linear
functions.) (Students
should round off to three places for this work.) Problem
Set
The applets needed to
complete this problem are provided in the text for this demonstration module.
Usually, students will need to follow the following steps. ·
Scroll down to “Tool Chest” on the applet menu to the
left of the screen. ·
Click “linear regression” (since we are looking for a
linear function). The linear regression
applet will open in a separate screen. Students will enter the data in the
applet. 1. Plot
the points corresponding to the data in Table 1. The first coordinate
is year; denote this by t with t = 0 in year 2000. The second
coordinate is population in billions. Enter the data
provided in Table 1; enter the t value for each year (t = -10 for 1990, t =
-5 for 1995, etc.) in the “x” column, then enter the population figures in
the “y” column. Click
“Plot”. |
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The linear regression applet will plot their data points
on the coordinate graph of the applet. Students will see the data points plot
in the applet. |
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2. Determine
the linear regression
function that best fits these data; call this function P(t).
Graph the function P(t) on the same coordinate
system as the plot of the data points.
Click “Analyze”. The screen shown below should appear. |
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The linear regression
applet will plot the regression line over the data points. Students will find
the data model and error in the lower window. |
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Students should obtain the linear function P(t)
= 0.072t + 5.952. Here, the variable x has been replaced by t, and the
variable y has been replaced by the function notation P(t);
coefficients are rounded to three places according to instructions. The
graph is shown on the applet screen. 3.
What is the slope of P(t)? Students can give a verbal interpretation of
the answer; make sure they identify the units clearly. The slope is
m = 0.072; this means that the world population is growing at the rate of
0.072 billion (72,000,000) people each year. (There is not an applet
for this!) Use the
function P(t) to answer the following questions. 4.
What is the annual population growth? The annual
population growth is 72,000,000 people (see #3) The next
computations can be done using the "Java Math Pad" applet in the Tools Menu. Usually,
students will need to follow these steps. Scroll down
to “Tool Chest” on the menu to the left of the screen. Click “Java Math Pad”. This applet performs mathematical evaluations. 5.
How much will the population grow in 10 years? Six months? One week? Type 10*72000000 then press enter. Your answer will appear in scientific notation,7.2E8 which is 720,000,000 people. Or, you can type
10*.072, press enter. Here your answer will be .72 billion people. Type .5*72000000 then press enter. Type
(1/52)*72000000 then press enter. In 10 years
the population will grow by 10x72,000,000 =
720,000,000 people; in 6 months, 0.5x72,000,000 = 36,000,000 people; in one
week, (1/52)x72,000,000 = 1,384,615 people. |
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The screen shown below should appear.
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The Java Math Pad
applet will perform mathematical evaluations. Students will find the value of
basic computation and evaluation of expressions with this applet. |
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6.
Estimate the population in the year 2005. In the year 2005,
t = 5. You can continue using the “Java Math Pad”. Type in P(t) = 0.072*t + 5.952, then “Enter”. Next type P(5), then “Enter”. You should see the value of the
function P at t = 5:
P(5) = 6.312 (rounded to 3 decimal places). In the year 2005,
there will be approximately 6.312 billion (6,312,000,000) people in the
World. 7. Predict
when the population will reach 8,000,000,000. To make this
prediction, you can solve the linear equation
P(t) = 8. Students can do this prediction by hand algebraically
fairly easily but we illustrate an applet that will instead do this
graphically. This will make a
student’s work easier for more complicated equations. The graphical
solution will be the intersection of the graphs of P(t)
and the horizontal line y = 8. Scroll down the menu to the “Tool Chest”, then
click Plot-Solve. (First, read the "help" section.) Enter the first
function P(t), then enter the second function as the
constant 8. Click "plot". Then click on the screen to see a red
point on the graph of one of the functions. Click on "right" or
"left" to move the point to the intersection of the two graphs. You
may want to zoom in for more accuracy. The coordinates of the point can be
read on the screen. |
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The
screen shown below should appear.
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The Plot-Solve applet
will plot functions, given window parameters and the expression that defines
the function. Students will find the applet will plot several functions on
the same coordinate plane and can use zoom and trace to find the
intersections of the given functions. |
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In the year 2028 (t = 28.4), there will be
approximately 8 billion people in the World. |
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Reflection
In this section, students will examine
their model, solutions, and implications. Students will think about the
validity and reasonableness of their answers. How closely does the function
fit the data? Relevant questions are provided although students may
raise questions of their own. Record student answers to these questions and thoughts of
their own in the student journal. Students return their
journals to you upon completion of the module. Questions A.
Do you think that a linear function is good to
use for this study? Are there other functions that you think might
provide a better model? Why? B.
How long do you think this model will be
accurate; i.e., what is a reasonable domain for the
function? C.
How do you think the predicted increase
in world population might affect future life in the World? In the |
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MODULES
AVAILABLE
|
|
Introductory Studies |
Tutorial Demonstration Studies
The following
demonstration studies are available to both the instructor and the student
for use while learning to use the Earth Studies modules. A demonstration study, a practice study,
and an applet demonstration are included in the learning modules. |
|
This first note to the student is a discussion of
the student perception and real application of mathematics to modeling. It includes the relevance of the topic and
important issues presented in the modules. |
|
This sample study on World population is designed to assist the instructor in working with the Earth Math materials, both for their own reference and to use with the students as a first, directed and step-by-step introduction to the format of the modules. All components of the study have directions for using the data and applets. A practice study is included for use after students complete the demo module. |
|
This module is a demonstration in the use of the
applets. Specific directions to the
use of the applets in the Tool Chest menu are given, using the Java Math Pad
and the Plot-Solve applets as an example. |
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This sample study on |
|
Earth Studies |
|
Earth
studies are provided for different levels of mathematical study. Levels of study are for foundation
mathematics Algebra with Equations, intermediate level Algebra with
Functions, Pre-calculus and Calculus. |
|
Levels Available These Modules are appropriate for foundation mathematics: introductory and intermediate level algebra. They emphasize linear, quadratic, piecewise, and prediction from these models. Fuel
Economy This is a study of the
fuel economy rates for two different vehicles and the cost of fuel for each
over a given time period. A comparison
of the miles driven and fuel used for each vehicle leads to the cost analysis
of the vehicle driven. |
|
Predicting Streamflow This
study looks at streamflow rates for the foundation
algebra level. The three parts
together make up a complete study on predicting streamflow.
However, each part is designed so that it can be done independently. Relevant
answers from preceding parts are included in each part as needed. Temperature
In this module we will construct a model for average temperatures for spring
through fall. Precipitation In this module we will construct a model
which gives the rate of precipitation in a certain region of the country. Snowmelt
In this module, we will determine the streamflow
for a river. It will first be necessary to find out how much snow
contributes to the flow, then the volume of water distributed over the
watershed for the river. |
|
These Modules are appropriate for college algebra level
mathematics. They emphasize linear,
quadratic, piecewise, and prediction from these models. Carbon
Dioxide Concentration (linear) The study is in two parts. In the first
part you will model atmospheric carbon dioxide concentration. In the second
part you will use this model to predict the impact of changes in
concentration on global temperature and ocean level. Carbon Dioxide Concentration This study will model the CO2 concentration
with a linear model for the last forty years and predict the future levels. Impact:
Temperature This module examines the possible impact of changes in
atmospheric carbon dioxide concentration on the global temperature. CO2
Emission from Passenger Vehicles This Earth Math Study is written in
three parts. The three parts together make up a complete study on predicting
carbon dioxide emission from passenger vehicles. However, each part is
designed so that it can be done independently. Relevant answers from
preceding parts are included in each part as needed. Passenger
Car Gasoline Consumption In this
first part you will study the factors that affect passenger car gasoline consumption
including the number of vehicles, annual mileage, and average fuel
efficiency. CO2
Emission from Passenger Cars In the second part you will model gasoline consumption
for passenger vehicles in the Reducing
Emissions from Passenger Cars In
part three you devise a plan to decrease emissions. Streamflow The three parts together make up a complete study
on predicting streamflow. However, each part is
designed so that it can be done independently. Relevant answers from
preceding parts are included in each part as needed. Temperature
This module is the first of three
that are designed to lead to the prediction of streamflow
for a river in a particular region. Precipitation
In this module we will construct a
model which gives the rate of precipitation in a certain region of the
country. Snow
Melt and Streamflow In this module, we will
determine the streamflow for a river. Population
This sample study on World
population is designed to construct a linear model and predict the world
population values. It explores the
patterns in slope and the linear function, as well as the accuracy of
prediction. |
|
These Modules are appropriate for
pre-calculus level mathematics. They
emphasize rate of change, exponential, trigonometric functions, and
prediction from these models. These studies are designed to cover the same
data and questions that the Algebra version does but it assumes the student
has completed the foundation courses of Algebra. Carbon
Dioxide Concentration (Exponential) This study is in two parts. In the
first part you will model atmospheric carbon dioxide concentration. In the
second part you will use this model to predict the impact of changes in
concentration on global temperature and ocean level. Concentration
This study will model the CO2 concentration with a linear model for the last
forty years and predict the future levels. Impact This module examines the possible impact of
changes in atmospheric carbon dioxide concentration on the global temperature. Population
This sample study on World population is designed to construct an exponential
model and use rate of change to predict the world population values. Streamflow The three
parts together make up a complete study on predicting streamflow.
However, each part is designed so that it can be done independently. Temperature
This module is the first of three that are designed to lead to the prediction
of streamflow for a river in a particular
region. It looks at how temperature
and amount of precipitation affect the amount of water in a river. Precipitation
This module is the second of three that are designed to lead to the
prediction of streamflow for a river in a
particular region. A model for average
precipitation for the region is constructed using the previous model for
temperature. Snow Melt
and Streamflow This module is the third of
three that are designed to lead to the prediction of streamflow
for a river in a particular region. Results from the previous parts are
combined with area to compute monthly streamflow
figures. The Gas-Mileage
Bill and The Arctic National Wildlife Refuge This
module explores the efficiency of automobile gasoline consumption and the
feasibility of drilling in the Artic National Wildlife Refuge to relieve this
nation’s dependency on foreign oil.
Students use earlier explorations on gasoline consumption to extend
this into a prediction equation for oil consumption. Water
Consumption in the This
module explores the water consumption in the |
|
These
Modules are appropriate for calculus level mathematics. They emphasize rate of change, integrals,
derivatives, demand functions and prediction from these models. World Coal
Supply In this module we will study availability and world use of coal.
In particular, we will determine the current usage rate and how long the coal
supply will last at this rate of consumption. World
Grain The three parts together make up a complete study on world grain
supply and demand. However, each part is designed so that it can be done
independently. Relevant answers from preceding parts are included in each
part as needed. Grain Supply
This part of the study looks at the area of the land cultivated and the world
grain supply yield. Supply
versus Demand This part looks at
the worldwide demand for grain and when the demand will equal the supply. Per
Capita Supply This part derives a function that describes the per capita
grain supply. Students predict how
much grain will actually be available per person. World
Population The world population
growth rate is revisited as the rate of change described as a percent of the
population. Students see what affect the change in growth rate has on the
population and prediction. In
this study we will examine oil supply and gasoline demand in a small
(fictional) community. In connection with this we analyze the economics
involved in the sale of oil and the purchase of gasoline. Specifically, we
will be concerned with cost, revenue and profit associated with the
production and sale of a product. Cost of oil This
part explores the factors affecting the cost of a barrel of oil. Fixed, variable and marginal costs are included
in the discussion to develop a cost function. Revenue
and profit Students examine the
revenue and profit for a company and use a cost function to see how the
selling price influences the profit. Supply curve Students examine the
relationship between selling price of oil and the amount of oil the company
is willing to extract. Supply,
demand and equilibrium Now we assume that currently the market
is in equilibrium. You have derived the oil supply curve (step three),
and will determine the current quantity of oil demand, the current
price, and the demand equation The
Gas-Mileage Bill and The Arctic National Wildlife Refuge This
module explores the efficiency of automobile gasoline consumption and the
feasibility of drilling in the Artic National Wildlife Refuge to relieve this
nation’s dependency on foreign oil.
Students use earlier explorations on gasoline consumption to extend
this into a prediction equation for oil consumption. Water Consumption in United States This module explores the
water consumption in the This study is the
investigation of available resources for a growing village. It is divided into three parts: Population;
Food, Coal and Electricity; and Water.
Models are used to predict the natural and human consumption of
resources for the village, as well as when the water source will be totally
depleted. Other Modules The
authors have other planned modules that will be available on-line in the
future. Keep watching the site for
updates. |
changes
as the values of the coefficients m and b change. Note any useful
observations in your journal.
.
The
solution is given below. 
Figure
2
can
be factored, then we
that
has real solutions can be solved by the quadratic formula
is
called the 
,
the equation has two real solutions.
,
the equation has no real solutions.
,
we see that 
Substituting
these values into the quadratic formula we get
Substituting
these values into the quadratic formula, we get
.
.
Round your answers to three decimal places.
and
the right-hand side, 
on
the same coordinate axes. See Figure 1.
(accurate
to one decimal place).
,
the range is the set of all real numbers except 0.
for
all 
. 
.
,
the radian measure of an angle. Also, given any real 
.
Tool Chest
AppletsThe
Tool Chest is a link to applets that students can use at any time. Embedded within the modules of study and
review topics are the links to these applets.
Students can return to the homepage to use an applet and graph or
calculate a value at any time. Available Applets |
|
|
COMPUTATION
APPLETS INSTRUCTIONAL
APPLETS
EXPERIMENTATION
APPLETS |
For
example, if a student clicks on the linear regression applet, a window for
calculating the linear regression from a data set is opened. The student can then enter data and plot
the data points, then calculate the linear regression equation. The description of each applet is given in
the section on applets.
Help
assistance is provided for each applet of the Tool Chest. Most applets are self explanatory, with
buttons and clear displays. There are
several notes regarding the use of the Math Pad and Plot Solve to consider. |
|
Applet Descriptions Tool Chest Computation
Applets |
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EXPONENTIAL REGRESSION APPLET This applet has two functions:
plotting and finding the exponential function which best approximates the
user supplied data. Using an
appropriate data set, this applet plots and data and
will find the best fit exponential function for that data. The best fit model is displayed on the
graph with the data set for comparison.
The symbolic model and error is displayed in a results window. Use it as follows: 1.
Put the data to plot and
analyze in the Data section. Though the variables default to x (the
independent variable) and y (the dependent variable), they can be renamed.
Renaming them will cause the graph to be updated. The values are entered one
per line. 2.
The buttons work as follows: CLEAR
will clear the data, the plot area and the RESULTS area. PLOT will
plot the data as points. ANALYZE will find the exponential function
which best approximates the data, plot it and display its equation in the
RESULTS area. 3.
The plot area (top, right) will show the plot. 4.
The RESULTS area is used to communicate with the user. Errors will be
displayed there, for example if the number of values is not the same for both
variables. Information will also be displayed there. For example, when the
user clicks on ANALYZE, the equation of the regression function will
appear there, as well as the error associated with this function. |
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|
LINEAR REGRESSION APPLET This
applet has two functions: plotting and finding the linear function which best
approximates the user supplied data.
Entering an appropriate data set, the user plots the data and finds
the best fit linear function. The
function graph is plotted with the data set.
The symbolic model and associated error is displayed in the results. Use
it as follows: 1.
Put the data to plot and analyze in the Data section. Though the
variables default to x (the independent variable) and y (the dependent
variable), they can be renamed. Renaming them will cause the graph to be
updated. The values are entered one per line. 2.
The buttons work as follows: CLEAR will clear the data, the
plot area and the RESULTS area. PLOT will plot the data as points. ANALYZE
will find the linear function which best approximates the data, plot it and
display its equation in the RESULTS area. 3.
The plot area (top, right) will show the plot. 4.
The RESULTS area is used to communicate with the user. Errors will be
displayed there, for example if the number of values is not the same for both
variables. Information will also be displayed there. For example, when the
user clicks on ANALYZE, the equation of the regression function will
appear there, as well as the error associated with this function. |
|
|
Chapter 3 Instruction With Earth Math: Tool Chest 3-24
|
|
|
JAVA Math Pad This applet allows the user to
evaluate mathematical expressions and functions. A mathematical expression is
made of numbers, variables, built-in and user defined functions together with
operations. It has an open screen and several buttons. For further information, click on
the scroll down menu, under "Help Topics" to get more detailed help
on how to use this applet. You
need to enter expressions including all math symbols ( ,
/, ^ , etc.) in order to use the math pad. For example: Enter function
f 1(x) = 2*x Enter f1(3)
Gives answer 6.0 This will allow students to define
up to ten functions. |
|
|
Plotting Applet The purpose of this applet is to
plot functions. It can plot up to 10 different functions at the same time. It
can also be used to solve equations numerically. Changes in window parameters and function
information, using zoom and trace buttons, can allow the user to define and
view different functions on the same graph. It functions as follows: 1.
The Viewing Window
Parameters area is used to set the area of the graph the user wishes to
see. Use it as follows: Specify the desired
values for XMin, XMax, YMin, YMax.
The applet will do basic error checking. If a entry
other than a number is typed in, an error will be displayed, and the focus
will remain in the field which caused the error. When Use y-range
is checked, the supplied values for the y-range will be used Otherwise, the
applet will find YMin and YMax
from the supplied functions. Any change in this
area will take effect only after the Plot button is pressed. 2.
The Function Information
area is where the functions to be plotted are entered. Use this area as
follows: To enter a new
function, always press the New Function button. Then, enter the
expression defining the function. The syntax is similar to the syntax used in
the Java Math Engine. For example, to defines the
sine function, you would type in sin(x). Make sure you use x for the variable
in your definition. A maximum of 10
functions can be defined at the same time. Checking Active
means the function will show on the graph. Unselecting it means the function
will not show. Use the + and -
buttons to scroll through the list of defined functions. Each defined function
has a different color assigned to it. The selection is automatic. When a function is
defined, it is automatically assigned a name of the form fi
where i is a number which
starts at 1 and is incremented every time a new function is defined. The name
a function will be saved under appears to the left of the field where it is
defined. Once a function is
defined, its name can be used in the definition of other functions. For
example, if two functions have been defined, the definition of function 3
could be f1(x)+x*f2(x) Note that we use f1(x) and
not just f1. The functions defined will plot only
after Plot has been pressed. Del Function
will delete the function currently showing. When deleting a function, make
sure that it is not used in the definition of another function. An error
would occur in this case. For example, if f2(x) = x + f1(x) and f1 is
deleted, then the definition of f2 contains an unknown symbol, f1. 3.
The Zoom and Trace area is
where zooming and tracing take place. Use this area as follows: To zoom in, picture in your mind the rectangular region
you would like to zoom in. Left click on one of the corners of this imaginary
region. While holding the mouse button down, move it to the opposite corner, then release it. As you move the mouse, a rectangle will
be drawn to help you visualize the region. Once the mouse button is released,
the graph will redraw, XMin, XMax,
YMin, YMax will be
updated. To
go back to the original view (XMin = -10, XMax = 10, YMin = -10, YMax = 10), press Reset Zoom. To
trace, simply single left click in the graph area. A point will be generated
by taking the x-coordinate of the point where you clicked and the
y-coordinate on the function currently showing. To
move the point, use the Right or Left buttons. The point will
move on the function currently showing. By selecting a different function,
you can select which function you want your point to follow. The
coordinates of the point will be displayed under X: and Y:. 4.
The Control Buttons area
contains buttons which have a global effect for the applet. The
Clear All button erases all the function definitions. The
Plot button is used to update the plot area after changes in the other
areas have been made. 5.
The Messages area is
where the applet communicates with the user. Error messages as well as user
information is displayed there. Errors are displayed in red, while
information is displayed in black. |
|
|
QUADRATIC REGRESSION APPLET This
applet has two functions: plotting and finding the quadratic function which
best approximates the user supplied data. Entering an appropriate data set,
the user plots the data and finds the best fit quadratic function. The function graph is plotted with the data
set. The symbolic model and associated
error is displayed in the results. Use
it as follows: 1.
Put the data to plot and analyze in the Data section. Though the
variables default to x (the independent variable) and y (the dependent
variable), they can be renamed. Renaming them will cause the graph to be
updated. The values are entered one per line. 2.
The buttons work as follows: CLEAR will clear the data, the
plot area and the RESULTS area. PLOT will plot the data as points. ANALYZE
will find the quadratic function which best approximates the data, plot it
and display its equation in the RESULTS area. 3.
The plot area (top, right) will show the plot. 4.
The RESULTS area is used to communicate with the user. Errors will be
displayed there, for example if the number of values is not the same for both
variables. Information will also be displayed there. For example, when the
user clicks on ANALYZE, the equation of the regression function will
appear there, as well as the error associated with this function. |
|
|
Instructional Applets Instructional
applets are designed to demonstrate key concepts used in the Earth Studies
modules. They may be used by the
student to support the understanding of critical concepts or by the
instructor to demonstrate those concepts to the class, a group, or an
individual. |
|
|
The The purpose of this applet is to
illustrate the relation between the unit circle and how the trigonometric
functions are defined. As you drag a
point around the unit circle, the applet displays the coordinates and angle
direction. Choosing either
sine or cosine, the function’s value is displayed as the length of the
segment on the unit circle, as well as the corresponding angle. Use it as follows: Drag the point around the unit
circle, clockwise or counterclockwise, as many times as you want. As you do
so, the following should happen: 1.
The coordinates of the point will be updated. 2.
The point will be in green if it corresponds to a positive angle,
otherwise it will be red. 3.
Depending on which trigonometric function you have chosen (sine or
cosine), its graph will appear and the point on the unit circle will also
appear on the graph of the trigonometric function. 4.
A red line whose length is the value of the chosen trigonometric
function will be displayed on both the unit circle and the graph. 5.
If the box "Show Function Values" is checked, the the angle and the value of the chosen trigonometric
function at that angle will be displayed. 6.
As the point on the graph gets ready to leave the graph, the graph
will scroll left or right, so that the point remains visible. |
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The
purpose of this applet is to illustrate the relationship of the slope of the
tangent to the graph of y = f(x) at x = a, that can be approximated for a
certain value of h where the secant line becomes the tangent to the graph of
y = f(x) at x = a. This applet illustrates the concept that the slope of the secant
approaches the slope of the tangent, allowing the user to enter a function,
select the points (a, f(a)) and (a+h,
f(a+h)), to change h so that the point (a+h, f(a+h)) gets closer to the
point (a, f(a)). Use the applet as follows: 1.
If necessary, change the values in the Viewing Window Parameters area,
though the default values should be fine in many cases. 2.
Enter a function. Nothing can happen unless a function has been
entered. Use the same syntax as in the PlotSolve or
the Java Math Pad applets. 3.
Next, specify the point where the tangent will be drawn. 4.
Specify the second point for the secant line. 5. Change the second point defining the secant line. In doing so, the user can verify that as h approaches 0, the secant becomes the tangent. This also allows the user to evaluate the expression as h approaches 0. |
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Role of a
and b in y = ab^x The purpose of this applet is to
illustrate how the values of a and b affect the
exponential function y = a b^x. Changes made to the general form
exponential function, using a scroll bar, will display the affect of the
coefficient and base on the resulting graph. Use it as follows: 1.
Use the scroll bar to change the values of a(between
-10 and 10). The exponential function should change as a
changes. The value of a to the left of the
scroll bar should also be updated. 2.
Use the scroll bar to change the values of b(between
0.1 and 10). The exponential function should change as b changes. The value
of b to the left of the scroll bar should also be updated. |
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This
applet illustrates the fact that the derivative of a function y = f(x) at x =
a, denoted f'(a), is the slope of the tangent to the graph of y = f(x) a x = a. The user can plot a function, and select points
on the graph. As the points are selected, the tangent to the graph at the
chosen point is drawn, if desired, its slope is displayed and plotted as a
new point. If the user selects enough points, the graph of the derivative
will become evident. Use the applet as
follows: 1.
If necessary, change the values in the Viewing Window Parameters area,
though the default values should be fine in many cases. 2.
Enter a function. Nothing can happen unless a function has been
entered. Use the same syntax as in the PlotSolve or
the Java Math Pad applets. 3.
Next, specify the point where the tangent will be drawn. 4. Specify more points, until the graph of the derivative becomes evident. |
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Role of a, b, k and c in y = a
+ b cos(k(x - c)) The purpose of this applet is to
illustrate how the values of a, b, c and k affect the graph of the cosine
function. Changes made in the general
form of the Cosine equation will display graph changes of transformation:
amplitude, period and phase shift. Use it as follows: Use the scroll bar to change the
values of a, b, k and c. The graph of the cosine function should change as
these values change. The value of each parameter to the left of the scroll
bar should also be updated. The changes should happen as follows: 1.
Changing a will move the graph
up or down by |a| units. 2.
Changing b will change the
amplitude (thus the range). 3.
Changing k affects the period.
The period is 2 pi / k. 4.
Changing c will cause the graph
to be shifted left or right by |c| units. |
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Role of a, b, k and c in y = a + b sin(k(x - c)) The purpose of this applet is to
illustrate how the values of a, b, c and k affect the graph of the sine
function. Changes made in the general form of the Sine equation will display
graph changes of transformation: amplitude, period and phase shift. It will function as follows: Use the scroll bar to change the
values of a, b, k and c. The graph of the sine function should change as
these values change. The value of each parameter to the left of the scroll
bar should also be updated. The changes should happen as follows: 1. Changing
a will move the graph up or down by |a| units. 2. Changing
b will change the amplitude (thus the range). 3. Changing
k affects the period. The period is 2 pi / k. 4. Changing
c will cause the graph to be shifted left or right by |c| units. |
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Understanding the Slope of a
Line The purpose of this applet is to
understand the notion of "the slope of a line". By selecting two points on the graph, the
point coordinates and quotient rise/run is displayed, as well as the triangle
symbolizing the relationship. Point
positions can be changed and the information is updated. Use this applet as follows: 1.
If you get lost, look in the
"MESSAGES" area, you will always be told what to do next. Error
messages will also be displayed there. 2.
Double-click in the grid area
to get a first point. Note that once you have selected a point, its
coordinates will appear on the left of the applet window, under POINTS. 3.
Double-click a second time to
get a second point. Several things will then happen. First, the coordinates
of the new point will appear on the left of the applet window, under POINTS.
Then, the quotient rise / run and the value of the slope will be displayed on
the left of the applet window, under SLOPE. Finally, the line through the two
points will be drawn as well as the triangle symbolizing the rise and the
run. 4.
You can now click on either
point and drag it along the line. You will see the point move, the triangle
will be redrawn, the coordinates of the point being
dragged will be updated. The slope should remain the same. 5.
If you either click outside the
grid area, or try to drag anything other than one of the point, an error
message will be displayed. |
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ROLE of m and b in y = m x + b The purpose of this applet is to
illustrate how the values of m and b affect the line y = m x + b. Using a scroll bar to change the slope m
and/or intercept b, the line position moves to reflect those changes. Use it as follows: 1.
Use the scroll bar to change
the values of m (between -10 and 10). The line should change as m changes.
The value of m to the left of the scroll bar should also be updated. 2.
Use the scroll bar to change
the values of b (between -10 and 10). The line should change as b changes.
The value of b to the left of the scroll bar should also be updated. |
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Role of a, b and c in y = a
x^2 + b x + c The purpose of this applet is to
illustrate how the values of a, b and c affect the parabola y = a x^2 + b x + c. Using a scroll bar to change the
coefficients and constant, the parabola’s position moves to reflect those
changes. Use it as follows: 1.
Use the scroll bar to change
the values of a (between -10 and 10). The opening of the parabola should
change as a changes. The value of a
to the left of the scroll bar should also be updated. 2.
Use the scroll bar to change
the values of b and c (between -10 and 10). The parabola should change as b
and c change. The value of b and c to the left of the scroll bar should also
be updated.
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Role of a, h and k in y = a (x -
h)^2+ k The purpose of this applet is to
illustrate how the values of a, h and k affect the parabola y = a( x - h)^2
+k. Using a scroll bar to change the coefficients and constant in the
graphing form of a quadratic, the parabola’s position moves to reflect those
changes. Use it as follows: 1.
Use the scroll bar to change
the values of a (between -10 and 10). The opening of the parabola should
change as a changes. The value of a
to the left of the scroll bar should also be updated. 2.
Use the scroll bar to change
the values of h and k(between -10 and 10). The
position but not the shape of the parabola should change as h and k change.
The value of h and k to the left of the scroll bar should also be updated. |
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The The purpose of this applet is to
illustrate the relation between a point on the unit circle, its coordinates
and the angle between the x-axis and the line through the origin and the
point. By dragging a point around the
unit circle, the coordinates of the point and the angle values will be
displayed in either degrees or radians. Use it as follows: Drag the point around the unit
circle, clockwise or counterclockwise, as many times as you want. As you do
so, the following should happen: 1.
The coordinates of the point
will be updated. 2.
The value of the angle between
the x-axis and the line through the origin and the point will show only if
you have selected to display it. In this case, it will be displayed in the
chosen units (degrees or radians). 3.
The point will be in green if
it corresponds to a positive angle, otherwise it will be red. |
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Experimentation Applets The
experimentation applets are designed to allow the student to find the “best
fit” model by trying various approximated coefficients and constants in the
standard form of the selected model.
The student can adjust the model, viewing their results both
symbolically and graphically. |
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FITTING
TRIGONOMETRIC (COSINE FUNCTION) DATA APPLET This applet has two functions:
First, it can be used to plot user supplied data. It can also be used to test
if a user supplied trigonometric (cosine) function (a function of the form y
= a + b cos(k (x - c)) ) fits the given data by plotting the
function. Plotting an appropriate data
set supplied by the user, the cosine function coefficients selected are then
entered and tested by graphing with the data set to view the fit of the
function. Use it as follows: 1.
The sequence of operations must
be as follows: The user must enter the data to plot in the DATA area.
Though the variables default to x (the independent variable) and y (the
dependent variable), they can be renamed. Renaming them will cause the graph
to be updated. The values are entered one per line. Error messages will be
displayed in the MESSAGES area if the data does not have the correct format,
if the data is not a number. The user can then
plot the data by pressing the "PLOT DATA" button The user supplies
the coefficients defining the function to test. The user plots the
function by pressing the "TRY" button. 2.
The buttons work as follows: CLEAR
will clear the DATA area, the PLOT area and the MESSAGES area. PLOT DATA
will plot the data as points. TRY
will plot the trigonometric function corresponding to the coefficients
supplied by the user. 3.
The PLOT area (top, right) will
show the plot. The MESSAGES area
is used to communicate with the user. Errors will be displayed there, for
example if the number of values is not the same for both variables.
Information will also be displayed there. |
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FITTING EXPONENTIAL DATA
APPLET This
applet has two functions: First, it can be used to plot user supplied data.
It can also be used to test if a user supplied exponential function (a
function of the form y = a (b^x) )
fits the given data by plotting the function. Plotting an appropriate data
set supplied by the user, the exponential function coefficients selected are
then entered and tested by graphing with the data set to view the fit of the
function. Use
it as follows: 1.
The sequence of operations must be as follows: The user must enter the data to
plot in the DATA area. Though the variables default to x (the independent
variable) and y (the dependent variable), they can be renamed. Renaming them
will cause the graph to be updated. The values are entered one per line.
Error messages will be displayed in the MESSAGES area if the data does not
have the correct format, if the data is not a number. The user can then plot the data by
pressing the "PLOT DATA" button. The user supplies the coefficients
defining the function to test. The user plots the function by
pressing the "TRY" button. 2.
The buttons work as follows: CLEAR will clear the DATA area, the PLOT
area and the MESSAGES area. PLOT DATA will plot the data as points. TRY will plot the exponential
function corresponding to the coefficients supplied by the user. 3.
The PLOT area (top, right) will show the plot. 4.
The MESSAGES area is used to communicate with the user. Errors will be
displayed there, for example if the number of values is not the
same for both variables. Information will also be displayed there. |
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FITTING
LINEAR DATA APPLET This applet has two functions:
First, it can be used to plot user supplied data. It can also be used to test
if a user supplied linear function (a function of the form y = m x + b)
fits the given data by plotting the function. Plotting an appropriate data
set supplied by the user, the linear function coefficient and constant
selected are then entered and tested by graphing with the data set to view
the fit of the function. Use it as follows: The sequence of operations must be as
follows: 1.
The user must enter the data to
plot in the DATA area. Though the variables default to x (the independent
variable) and y (the dependent variable), they can be renamed. Renaming them
will cause the graph to be updated. The values are entered one per line.
Error messages will be displayed in the MESSAGES area if the data does not
have the correct format, that is if the data is not
a number. The user can then
plot the data by pressing the "PLOT DATA" button. The user supplies
the coefficients defining the function to test. The user plots the
function by pressing the "TRY" button. 2.
The buttons work as follows: CLEAR
will clear the DATA area, the PLOT area and the MESSAGES area. PLOT DATA
will plot the data as points. TRY
will plot the linear function corresponding to the coefficients supplied by
the user. 3.
The PLOT area (top, right) will
show the plot. The
MESSAGES area is used to communicate with the user. Errors will be displayed
there, for example if the number of values is not the same for both
variables. Information will also be displayed there. |
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FITTING QUADRATIC DATA APPLET This applet has two functions:
First, it can be used to plot user supplied data. It can also be used to test
if a user supplied quadratic function (a function of the form y = a x^2 + b x + c) fits the given data by plotting
the function. Plotting an appropriate
data set supplied by the user, the quadratic function coefficients and constant selected are then
entered and tested by graphing with the data set to view the fit of the
function. Use it as follows: The sequence of
operations must be as follows: 1.
The user must enter the data to
plot in the DATA area. Though the variables default to x (the independent
variable) and y (the dependent variable), they can be renamed. Renaming them
will cause the graph to be updated. The values are entered one per line.
Error messages will be displayed in the MESSAGES area if the data does not
have the correct format, that is if the data is not
a number. The user can then
plot the data by pressing the "PLOT DATA" button. The user supplies
the coefficients defining the function to test. The user plots the
function by pressing the "TRY" button. 2.
The buttons work as follows: CLEAR
will clear the DATA area, the PLOT area and the MESSAGES area. PLOT DATA
will plot the data as points. TRY
will plot the quadratic function corresponding to the coefficients supplied
by the user. 3.
The PLOT area (top, right) will
show the plot. 4.
The MESSAGES area is used to
communicate with the user. Errors will be displayed there, for example if the
number of values is not the same for both variables. Information will also be
displayed there. |
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FITTING TRIGONOMETRIC (SINE
FUNCTION) DATA APPLET This applet has two functions:
First, it can be used to plot user supplied data. It can also be used to test
if a user supplied trigonometric (sine) function (a function of the form y
= a + b sin(k (x - c)) ) fits the given data
by plotting the function. Plotting an appropriate data set supplied by the
user, the sine function coefficients selected are then entered and tested by
graphing with the data set to view the fit of the function. Use it as follows: The sequence of
operations must be as follows: 1.
The user must enter the data to
plot in the DATA area. Though the variables default to x (the independent
variable) and y (the dependent variable), they can be renamed. Renaming them
will cause the graph to be updated. The values are entered one per line.
Error messages will be displayed in the MESSAGES area if the data does not
have the correct format, that is if the data is not
a number. The user can then
plot the data by pressing the "PLOT DATA" button The user supplies
the coefficients defining the function to test. The user plots the
function by pressing the "TRY" button. 2.
The buttons work as follows: CLEAR
will clear the DATA area, the PLOT area and the MESSAGES area. PLOT DATA
will plot the data as points. TRY
will plot the trigonometric function corresponding to the coefficients
supplied by the user. 3.
The PLOT area (top, right) will
show the plot. 4.
The MESSAGES area is used to
communicate with the user. Errors will be displayed there, for example if the
number of values is not the same for both variables. Information will also be
displayed there. |
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Chapter
4 Inquiry with Earth Studies
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Inquiry-Based Instruction
This
section of the guidebook gives an overview of information regarding inquiry,
good questions, assessment, and web sites supporting an inquiry approach. |
FAQ
How do I use an inquiry
approach? Inquiry in the Math
Classroom Using the Earth Math Studies Introduction
to Inquiry-based Instruction ……..
4-1 Good
Questions ………………………………….... 4-4 Assessment
and Adaptation ……………………... 4-5 Web Sites
and Bibliography ……………………… 4-7 |
Instructors using Earth Math modules
will find a description of inquiry-based instruction and good questions. A discussion of the components inherent in
the approach, assessment and adaptation of the modules are included. Finally, additional web sites with
information for teachers of the inquiry approach and a Bibliography used for
this chapter complete the information in this last chapter.
Chapter
4 Inquiry-Based
Instruction
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Using Inquiry-Based Learning Introduction A philosophical and key feature of the National Standards
movement in both Mathematics and Science Education is the focus on
learner-centered and inquiry-based processes for pedagogical
enhancement. Mathematics Standards of
the NCTM, AMATYC, MAA and others emphasize the necessity for students to gain
experience with inquiry in a data rich environment. For example, the NCTM Principles and Standards for School Mathematics, Chapter 3 states “Instructional programs … should enable all students to—
(Principles and Standards for School Mathematics, Chapter 3; http://standards.nctm.org/document/chapter3/data.htm) One of the Science Standards features call for students to
engage in inquiry “to develop: · understanding of scientific
concepts, · appreciation of 'how we know' what
we know in science, · understanding of the nature of
science, · skills necessary to become
independent inquirers about the natural world, and · dispositions to use the skills, abilities, and
attitudes associated with science." (National Science Education Standards; 1996; p.105) Guidance in the meaning and
importance of inquiry in mathematics and science as a multi-faceted approach,
creating pedagogical and substantive examples showing what it looks like in
practice, and providing classroom ready resources are necessary to meet the
Standards aiding educators in understanding and implementing sound principles
of inquiry. The Earth Math Projects
fulfill these goals in both the approach and pedagogical resources created
for educators and students alike.
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A Definition of Inquiry What is Inquiry-Based Learning? Inquiry as a learner-centered process is central to its
definition – what students know and want to learn are the foundation for
learning. Several definitions of
inquiry point out this natural building of ideas:
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Inquiry-based learning is a dynamic process, encompassing
a whole range of models, including some important aspects that should be
supported in a learning environment.
Inquiry often leads to the creation of new ideas and constructively
communicating those ideas is central to the whole process. The process should include the following
concepts: ASK Meaningful questions
inspired by genuine curiosity about real-world experiences. A problem or question provides the focus
and the learner begins to define or describe what it is. Questions are redefined throughout the
learning process. INVESTIGATE Putting the curious impulse into action
and beginning to gather information: researching resources, studying,
crafting an experiment, observing, or interviewing; recasting the question,
refining a line of query, or following a new lead – a self-motivated
process that is wholly owned by the
engaged learner, CREATE The learner makes connections
and begins to synthesize meaning to form new knowledge. The learner shapes new thoughts, ideas, and
theories outside of previous experience. DISCUSS Learners share their new ideas
with others in a community-building process of shared knowledge, where the
meaning of an individual’s investigation takes on greater relevance in the
context of the learner’s society. REFLECT Taking time to look back at the
question, the research path and the conclusions made, the learner takes
inventory, makes observations, and makes new decisions. New questions come to light and so the
questions begin again. (Adapted
from Winters, Tina, & Hollweg, Karen. 2001.
Inquiry in the Standards-Based Science Classroom. ENC Focus 8(2)
p.20-22) |
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The Earth Studies modules support
this process of inquiry-based learning.
The modules are designed to facilitate the formulation of good
questioning and mathematical modeling skill, within the scientific inquiry of
the topics presented. Each Study will have
three components:
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It is in the text of each module that the student will
find questions and topic information to begin this process, the ASK and
INVESTIGATE steps are found in the beginning of the module. The text of the Earth Studies
module will be presented in four sections: Comprehension;
Acquisition; Application; and Reflection. |
Questions
A. Do you think that the population of the World is
increasing or decreasing? B. What have you noticed recently that led you to
your answer to A? C. How do you think population change in the world might
influence your life? D. How do you think mathematics can be used to study
population change? E. What
are some reasons for studying population change? |
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These questions provide a focus for the student’s
thoughts, using their experience and thinking about population, as well as
what change might be occurring in the population. The questions are designed to develop
thought regarding the use of mathematics in the study as well. |
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Reflection: Assessing the method, solution
and implications Do you think that the functions
used are appropriate? If not, what might be better? Do you think that the solution is
reasonable? Why? Do you think that the supply
function is accurate? Do you think that it is reasonable to assume that this
trend will continue? If not, what do you think might happen? Would it be appropriate to construct an alternative model?
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Planning and Strategy The Earth Studies allow easy planning for inquiry-based
and student directed learning. Questions for planning inquiry in the
classroom should include the following ideas: |
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Concepts What are the important concepts
or big ideas in the desired study or topic?
How are the concepts defined or categorized in examples? |
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Processes What are the processes needed to
collect information, analyze data, report and produce findings, and how will
you know? Which processes will you
include (collecting data, analyzing data, drawing conclusions, representing
knowledge)? |
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Generalizations Ask how the topic concepts might be
linked. What are the relevant
relationships, characteristics, similarities or differences, consequences,
conditions or contexts, and assumptions that might affect results? |
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Theory Ask how the relevant
generalizations might be formed to create a theory that is true and important
to know. |
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Products What product needs to be
designed to demonstrate the concept or support the ideas presented? What skills and knowledge must be
demonstrated and how does the product provide expected evidence? What range of possibilities and documentation
would be necessary? |
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Assessment How will you know what the students
know? What types of authentic and
alternative assessments will you allow?
What criteria will you use and what work will be included in the student’s
assessment? |
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Schedule How will you use your classroom
time effectively and optimize available time?
How will you organize the classroom or lab? Will you group the students and how? |
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Plans What resources will you
use and when will you use them? What
questions will you ask and how are the resources related to the student’s
interests and needs? |
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The module questions will form the basis for the student inquiry but additional questioning by the instructor will help the students formulate their ideas and theories. Good questions by the instructor can include the following question types. |
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Good Questions |
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A key
task for the instructor of the Inquiry Based materials is the formation of
good, meaningful questions, to assist the student in formulating ideas and
creating interest or curiosity in the student. The Earth Math materials will
begin each module with a set of questions for students to discuss and think
about, pertaining to the topic of the module.
Questions in the modules are often enough to begin a study, but
students and instructors often need to learn more about the way to ask good
questions in the inquiry format. |
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Question Types |
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Clarifying Focus on a specific idea and
provide a clear setting for the answer.
These require the student to make explicit ideas and meanings. Contextual Require the students situate
their ideas, determine the conditions for the existence of the ideas, and
factors that effect meaning. Divergent Suggest a wide range of
responses and can be answered in a variety of ways. Extending Assist students to extend their
understanding of concepts, draw conclusions, and provide reasoning to support
those concepts. Focusing Identify the “big ideas” with
concrete examples, definitions, characteristics, and categorize the
information. Open-Ended Require more than one answer or
cannot be answered with a “yes” or “no”. Organizing Determine the organization to the
events, compare and contrast, find cause and effect, and follow with a “why”
question. Shared Encourage the student to
enter a discussion or conversation with a variety of unique ideas. Thought-Provoking Require
a reasoning, engagement, and insight so these questions provide more than a
simple answer. |
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As an instructor of inquiry-based learning, always
request the student to generalize their results and draw a conclusion. Ask students for the reasoning used for the
conclusion – support (evidence) for the “why” of the idea or comparisons
made. Assist the student in finding different relationships, labeling and
identifying attributes, and focus on generalizations. This will facilitate the formulation of the
generalization, conclusion, and prediction of new connections for the
student. |
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Environment The process of learning, not just what is learned is
important in the use of the Earth Math modules. The focus of inquiry-based learning is on
the process, not the product of learning.
The environment you provide should support the questions and paths the
students choose, while you facilitate the process. Students taking responsibility, making
decisions, initiating the inquiry and learning while you as instructor
facilitate the collaboration make inquiry-based learning a dynamic
environment. The characteristics of the environment should include the
feeling of success, support, appreciation, recognition, and visible signs of
learning. The affective values of
acceptance of difference and critical awareness of political consciousness,
understanding, relationships, and societal goals should be established
throughout your classroom. As the student develops the concepts, use your questions
to guide the focus and direction of inquiry.
Include relationships and extend the thoughts beyond simple answers as
you complete analyses. Do not repeat
the student’s responses, as this could encourage others not to listen. Always as open-ended questions and listen
carefully to all responses. For focusing questions, address only one situation at a
time – simplify complex situations into several distinct steps to the final
conclusion. When a response is too
general, ask for an example to clarify the student’s understanding and
conclusion. Always ask for reasoning,
explanation that is descriptive in support of the response. |
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Interpretation of Data The interpretation of data will require students to first
recall information from past or recent experience, gleaned from the reading,
demonstrations, and assignments.
Students need to determine what is relevant in responding to the
focusing questions you provide. Ask for
a variety of information, be accepting of all responses, and ask for
clarification with specific information where necessary. Next ask students to state causes or effects of selected
datum to identify evidence or support for their inference, and establish
links or relationships. Never
establish those links yourself but allow the discussion and findings, as well
as your facilitating questions to lead the student to an appropriate, yet
open-ended conclusion. Encourage the
students to use data to establish inferences and generalizations about the
issue, testing their conceptual understanding of the relationships. Students can than establish an
understanding of the complexity and interrelatedness of the events, examining
the long-term implications. The students then draw a conclusion based on the
evidence presented. The students should then be encouraged to apply the
generalization to a prediction of future events, using their earlier
work. Predictions infer the effects of
a given situation, using facts or generalizations to form the basis of that
prediction. An objective of this
prediction is for the student to apply previously learned information to a
new situation or to solve a problem.
Students should provide factual and logical support for their prediction,
identifying conditions that make the prediction plausible. The final step in the interpretation of
data is to extend the prediction to consequences that extend from the
original situation. |
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Assessment of Learning No
chapter on inquiry-based learning would be complete without some discussion
about the assessment of learning in this environment. Assessment can be done for the individual
student or student groups, or a combination of both. The easiest assessments are done by
determining what questions the students must answer and in what format,
completed in the journal or a portfolio.
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Designing a set of points or rubric for evaluating each
part should provide assessment of evidence for conceptual change, growth,
reflection, decision-making, and understanding. Advise students to reflect on what they have come to know,
the processes and concepts developed, and what best reflects the processes
and solutions obtained. Questions you
might like students to answer are contained within the modules, but you might
also include documentation of the students’ problem-solving, individual
research or questions, and models obtained during their work. Students can make comparisons of what they like the most,
how items are similar or different and account for those similarities or
differences, what they need to know further and how they would learn it, and
document changes in processes they undertake.
You can also ask them to note the changes in their thinking that has
occurred, what influenced the change, and what they have come to know about
their “self”. They can order the
series of questions they raised and the answers determined, forming a
sequence of steps to the solution of the problem. Each of the required questions and criteria for assessment
should be clearly documented for the student as they begin the module. If you wish a complete, step-by-step
sequence of answers and solutions, this should be clearly stated with
examples, and the rubric for evaluation or points allotted each portion of
the study should be provided the student.
If the assessment will take the form of a journal or portfolio,
clearly document the required components and criteria for assessing each
part. In my experience, the more
clearly you document the assessment criteria and expectations to the student,
the better the results you obtain from the students. You can make the documentation from the student by
individual or by group. I recommend
each student have their own assessment, although a group score might be part
of that, either from other group members, or from you as an assessment of how
they have worked with their group members (their participation). All assessment should take the form of
improving learning, so you might also want to include a portion for the
student to assess themselves, or write items for improvement prior to the
next module or study undertaken. Many
students begin without knowing how to ask good questions or find related
information. The modules assist the
students in doing this, so provision should be made for including improvement
in their assessment, either by you or the student themselves. |
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Adapting Modules to Your Students All of the Earth Studies modules can be adapted to your
course and learning environment. The
modules can be given as individual or group projects in a laboratory
component, or integrated into the regular classroom time as an application of
previous learning. Modules are
designed to be done independently, so a student can self-select one of
interest, or you can design a series of labs for your students to work with
that follow your standard curriculum. One of the most interesting ways to use the Earth Math
Studies are to find different but related data from your local area (or have
your students find this data) and assign the students to conduct a similar
inquiry with the local or regional data.
For example, the population data used with World and Since the modules are written with environmental issues,
many of the studies can be easily revised to use data for the issues of the
students’ home region. You will find
it easy to replace the information and questions to those of your region, as
the questions are open-ended and merely focus on student thinking. Use the Earth Studies standard format as a
guide and replace each part with the questions, data and information, and
reflection for a local issue of your selection. Students will often find their own data as
well as questions as they work on the web site modules, so encourage extended
exploration when this occurs. |
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Web Sites for Inquiry-Based Learning The
following web sites have both information for further study and pedagogical
resources for the teacher of an inquiry-based curriculum component. |
Web Sites
Using the
Internet to Promote Inquiry-based Learning
This link provides guidance in using the internet and information for
inquiry-based learning.
http://www.biopoint.com/msla/links.html
Beyond School
Walls
Read about these inquiry and problem solving activities
that take place outside the classroom in the field. http://www.enc.org/topics/inquiry/beyond/
Classroom
Activities
Read about activities that teachers have implemented in
their classrooms to promote inquiry and problem solving. http://www.enc.org/topics/inquiry/activities/
Inquiry Page
This page provides a wealth of different topics related to inquiry
learning and activities.
http://www.inquiry.uiuc.edu/
Inquiry and the National Science Education Standards: A
Guide for Teaching and Learning will provide you with a rich resource of personal
examples and guidelines to aid you in designing and carrying out
inquiry-based science activities in your classroom. You may read the report
free of charge online (www.nap.edu/books/0309064767/html/).
The second addendum to the Standards, titled Classroom
Assessment and the National Science Education Standards, will be
available in 2001. For more information about this and other resources from
the National Research Council, contact Tina Winters at TWinters@nas.edu Disney Learning
Partnership; Concept to Classroom Resources; Inquiry-based Learning; Books,
Articles, and Websites
http://www.thirteen.org/edonline/concept2class/w6-resources.html |
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Bibliography Principles and Standards for School Mathematics, Chapter 3; http://standards.nctm.org/document/chapter3/data.htm National Science Education Standards; 1996; p.105
Inquiry in the Standards-Based Science Classroom: A New Resource for Teachers and Teacher Educators;A new guide helps teachers provide standards-based science to students of all ages. The full text is available free online.TinaWinters and Karen HollwegNational
Research Council
References
The
Research Base Supporting Inquiry Learning
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Haury, D. L. (1993). Teaching Science Through Inquiry.
ERIC CSMEE Digest (March Ed 359 048). Winters, Tina, & Hollweg, Karen.
2001. Inquiry in the Standards-Based Science Classroom. ENC Focus 8(2)
p.20-22.
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