Instructor: 
Dr. John Olive 
Offices 
105F, Aderhold 
Telephone 
706  542  4557 

jolive@uga.edu 


All assignments should be
created electronically
and emailed as an attachment to Dr. Olive or one of the graduate
assistants.
Please use the following
file name format for each assignment: <first initial><last name><assignment
#>.<file type>. For example,
my reflection paper for assignment #1, created using Microsoft
Word, would have the file name: jolive1.doc
1  2  3  4  5  6  7  8  9  10 

11  12  13  14  15  16  17  18  19  20 
Final Project 
#1 . Prepare for next class discussion on January 13 (electronic portfolio)
Visit the NCTM web site at www.nctm.org and find the electronic version of the Principles and Standards for School Mathematics. Read through all of the Principles and study the overview of the curriculum standards for both middle grades and high school. Explore the electronic examples for both middle and high school algebra. Choose one example to respond to the "take time to reflect" questions and write up your responses to share with the rest of your class (to be included in your portfolio).
Due: 01/13
#2. Review Unit 1 of the GPS Frameworks for Math I on Function Families: (portfolio)
Download Unit 1 for Math I from the GPS Frameworks web site: http://www.georgiastandards.org/mathframework.aspx#twelve
Read through all of the tasks in Unit 1. Work the problems in Tasks 1 and 2 (Exploring functions with Fiona and Fences and Functions.) Write up your solutions and save the file in your electronic portfolio. We shall use the following GSP sketch (created by Matt Winking, the Presidential Teacher of the Year at the Phoenix School in Gwinnett County) in class to explore Fences and Functions. Make a list of the main points of this unit to share with the class. Save this list in your electronic portfolio.
Go to the web site for the new Georgia Performance Standards. Find the mathematics standards that relate to the goals of this course. You can also download the Vertical Allignment Chart for HS Math from this web page by clicking here.
Match the topics in the outline of the course with an appropriate GPS (you can copy and paste from the Outline for the course). Save these matched items in your electronic portfolio and send a copy to Dr. Olive and the TA as an email attachment. Remember to name your file: "your_name_2.doc"
(10 pts)  (8 pts)  (6 pts)  (4 pts)  (2 pts)  0  

Criteria 
Matches all outline topics to an appropriate GPS  Matches 80% of outline to an appropriate GPS  Matches 60% of outline to an appropriate GPS  Matches 40% of outline to an appropriate GPS  Matches 20% of outline to an appropriate GPS  Does
not attempt the assignment. 
Due: 01/20 (Barack Obama's Inauguration Day!)
#4. Reflecting on Your Experiences with Mathematics Teachers: (15 points)
You have been a mathematics student for most of your life! You have experienced many different teachers who taught you mathematics. These experiences have very likely influenced how you think about "mathematics teaching," and these can even affect the ways that you will behave as a beginning mathematics teacher. It can be important to reflect upon these past experiences, to take stock of some possible influences upon you and how you want to teach.
A. Make a short list (35; use initials or a pseudonym or code) of your "favorite" teachers of mathematics. For each, briefly tell why they are a "favorite." Think about them as "persons," and list any attributes that might have led you see them as a "favorite." Think about them as "teachers," and list attributes that mattered to you. Think about them in the act of teaching mathematics, and list things about their teaching that you admired. You might consider their attitudes towards students and towards mathematics, their teaching styles, and their content knowledge.
B. Make a short list (35) of your "least favorite" teachers of mathematics. For each, briefly tell why you see them this way. Think about them as "persons," and list any attributes that might have led you to see them this way. Think about them as "teachers," and list attributes that led you to see them this way. Think about them in the act of teaching mathematics, and list things about their teaching that you disliked. You might consider their attitudes towards students and towards mathematics, their teaching styles, and their content knowledge.
C. Think about the kind of mathematics teacher you want to be. List the positive attributes that would describe you, as a "person" and as a "teacher." Think about yourself in the act of teaching your mathematics students. List a few of the most important characteristics that might describe your teaching. You might consider your attitude towards students and towards mathematics, your preferred teaching style, and your content knowledge.
Email your Word document to Dr. Olive and the TA.
Due: 01/22
Rubric
Exemplary (5 pts) Proficient (4 pts) Partially Proficient (3 pts) Barely proficient (2 pts) Incomplete (1 pt) No attempt Section A
(33%)
Lists more than 3 favorite teachers and their attributes as persons and as teachers and acts of teaching Lists 2 or 3 favorite teachers and their attributes as persons and as teachers and acts of teaching Lists 1 favorite teacher and his/her attributes as a person and as a teacher and acts of teaching Lists an attribute but no characteristics of teaching Lists names of teachers only Section B
(33%)
Lists more than 3 least favorite teachers and their attributes as persons and as teachers and acts of teaching Lists 2 or 3 least favorite teachers and their attributes as persons and as teachers and acts of teaching Lists 1 least favorite teacher and his/her attributes as a person and as a teacher and acts of teaching Lists an attribute but no characteristics of teaching Lists names of teachers only Section C
(33%)
Lists more than 3 attributes of oneself as a person and as a teacher and characteristics of your teaching Lists 2 or 3 attributes of oneself as a person and as a teacher and characteristics of your teaching Lists one attribute of oneself as a person and as a teacher and characteristic of your teaching Lists an attribute but no characteristics of teaching No comments on self
#5. Relational and Instrumental Understanding (portfolio)
Read the article by Richard Skemp on Instrumental and Relational Understanding. Identify 3 main points that Skemp makes about the nature of mathematical understanding. Then reflect on your responses to assignment #4. Briefly describe how you were taught and how you learned mathematics (instrumentally and/or relationally). (23 pages). Email your reflection to Dr. Olive and the TA and save it in your electronic portfolio.
Due: 01/27
#6. Composition of Functions Investigation (10pts)
(Assignment 7.3 from Chapter 7 of Transforming Mathematics with the Geometer's Sketchpad)
Using the GSP Dynagraphs sketch, investigate the 8 mystery functions. Create three functions of your own, each of which belongs to a different family (e.g, step, quadratic, and trigonometric) and investigate the composition of your three functions. (A sketch showing compositions of several functions can be found here.) Writeup your investigations, highlighting any interesting or surprising characteristics you discovered for your particular composition (12 pages). Submit your GSP sketch along with your writeup via email attachment or file transfer to Dr. Olive. The following description of a "writeup" is adapted from Dr. Jim Wilson.The "writeups" for EMAT 3500 represent your synthesis and presentation of a mathematics investigation you have done  usually under the direction of one of the assignments. The major point is that it convincingly communicates what you have found to be important from the investigation.
The hypothetical audience might be your students, your classmates, or classroom mathematics teachers. You should present your topic in a reasonable amount of space, emphasizing the essential and eliminating the irrelevant (though sometimes interesting) side issues.
Due: 02/03
Rubric
Criteria
Exemplary
(5 pts for each part)Proficient
(4 pts for each)Partially Proficient
(3 pts for each)Incomplete (2 pts for each) Not Working (1 pt) Missing Work
(0 pts)
GSP Sketch
( 50%)
Working GSP sketch with 3 different dynagraphs and at least 3 different compositions of 2 or more functions organized on different pages Working GSP sketch with 3 different functions and 2 different compositions of 2 or more functions. Working GSP sketch but functions are not from different families or are the ones provided by the downloaded sketch. Only one or two working compositions. GSP sketch with 3 functions but no compositions. GSP sketch does not function properly. No GSP sketch. WriteUp (50%)
Functions and their compositions are fully described and surprising results are explained in terms of the properties of the composed functions, including domain and range. Functions and all compositions are fully described with reference to domain and range. Functions are listed and one or two compositions briefly described Write up describes the functions but not the compositions. Writeup does not describe the situation. No writeup.
#7. Reflection on Dynagraphs (portfolio)
Dynagraphs were very probably a new way of representing and playing with functions for you. In what ways did they enhance your own concepts and ideas about functions? Would you use these dynamic representations with your students? Why or why not? (12 pages) Email your reflections to Dr. Olive and your TA.
Due: 02/05
#8. Reading and Reflection (portfolio)
Chazan, D. (1999). On teachers' mathematical knowledge and student exploration: a personal story about teaching a technologically supported approach to school algebra. International Journal for Mathematics Learning, 4: 121149.
Reflect on how the author's approach to teaching algebra was influenced by the use of technology. Think about the role of function in the two different approaches. How might the use of GSP enhance the functions approach? Be prepared to discuss your ideas in class.
There is at least one mathematical error in this paper. See if you can find it.
Due: 02/10
#9. Dynamic Transformations of the Quadratic Function (15pts)
Complete the three Challenges on page 94 (Assignment 7.5) of Transforming Mathematics with the Geometer's Sketchpad and turn in a completed GSP sketch via email or file transfer. An extra 5 points will be possible for successfully completing the Extra Challenge.
Due: 02/17
Rubric
Criteria
All 3 complete
(15 pts)2 of 3 complete
(10 pts)1 of 3 complete
(5 pts)Attempted
(3 pts)No Attempt
(0 pts)
GSP Sketch
(100%)
Completed all three challenges with correctly working GSP sketch Completed 2 of the 3 challenges with correctly working GSP sketch Completed 1 of the 3 challenges with correctly working GSP sketch Attempted the challenges but was not successful in generating a correct function for any of the challenges. Did not attempt any of the challenges Extra Credit Successfully completed the extra credit challenge Attempted the Extra Credit but not successful Did not attempt the Extra Credit Challenge
#10. Review of the NCTM Algebra Standards (portfolio)
Review the Algebra Standards for grades 612 in the NCTM Principles and Standards. Write a 12 page report on the approach to Functions taken in the Standards document. Compare this approach to Unit 1 (Function Families) of the Math 1 GPS Frameworks and the approach we have taken in this course. Email your report to Dr. Olive and the TA.
Due: 02/19
#11. Sorting Functions (10pts)
Due: 02/24
Rubric
Criteria
Complete (10 pts) 10% errors (9 pts) 20% errors (8 pts) 30% errors (7 pts) 40% errors (6 pts) 50% errors (5 pts) 60 % errors (4 pts) 80% errors (2 pts) 90% errors (1 pt) No attempt
(0 pts)
Table entries (80%)
Explanations (20%)
MidTerm Exam on Functions : 03/03 (60pts)
#12. Probability Investigation (10pts)
Complete Task 5 of Unit 4 of the Math 1 Frameworks. Use GSP to design the spinner for question 1 that best fits the experimental data and answer all the other questions. Email your GSP sketch and the answers to the questions either in a Word document or in the GSP sketch to Dr. Olive and the TA.
Due: 03/17
Rubric:
Question 1: 3 points for a working GSP sketch with correct sectors and a spinner arrow that will move to a random position using an Action Button
2 points for a working GSP sketch with correct sectors but the spinner arrow has to be moved manually (no random action), or incorrect sectors but a randomly moving spinner arrow.Questions 24: 1 point for each correct answer.
1 point for a GSP spinner with incorrect sectors and the spinner arrow has to be moved manually (no random action)
0 points for no GSP sketch.
Question 5: 2 points for a correct answer.
Question 6: 2 points for the first part answered correctly (In the long run, would the player expect to win or loose money?).
1 Bonus point for figuring out the second part (How much they would expect to win or loose after 100 times playing the game.)
Total Points: 10 + 1 bonus
#13. Laboratory Preparation (Portfolio)
Click here
for a list of the labs.
Due: 03/26 (before class)
Once
all results have been collected for each lab
and shared with each member of your group, each individual will write a
brief
(paragraph) conclusion he/she made
from the shared class results
for
each lab. Your group's
results and your conclusions
for each lab should be emailed to Dr. Olive and the TA's.
Due: 03/31
5
labs (5 pts for each part below) 
4
labs (4 pts for each part) 
3
labs (3 pts for each part) 
2 labs (2 pts for each part) 
1 lab (1 pt for each part) 
No
results (0 pts) 


Results (50%) 
Submits group's results from all 5 labs 
Submits results from only 4 labs  Submits results from only 3 labs  Submits results from only 2 labs 
Submits results from only 1 lab 
No results submitted 
Conclusions (50%) 
Brief conclusions written up for all 5 labs
based on the shared class data for each lab. 
Brief conclusions written up for 4 labs  Brief conclusions written up for 3 labs  Brief conclusions written up for 2 labs  Brief conclusions written up for 1 lab  No conclusions 
The more interesting part of this assignment lies in thinking about what these summed deviations tell us about the 'best fit line." How can we know if we have chosen the best fit line? Which is a better predictor, the sum of the signed deviations, the sum of the absolute deviations, or the sum of the squared deviations? The following is a sketch that I created; it could be helpful in facilitating your thinking. Click here for the gsp sketch.
Write a brief
explanation (with examples) for why you would choose to use one
of the following methods for calculating the best line of fit
for your data: signed deviations, absolute deviations, squared
deviations. Attach your paper to an email to Dr. Olive and the TA.
Due: 04/07
Rubric
Exemplary (10 pts total) Proficient (8 pts) Partially Proficient (6 pts) Incomplete (4 pt) No Attempt Data ( 75%)
Has complete data set with AUTOMATICALLY CALCULATED values for Predicted data based on line of best fit, signed deviations, absolute deviations, and squared deviations Has complete data set with values for Predicted data based on line of best fit, signed deviations, absolute deviations, and squared deviations entered manually. Has complete data set with values for Predicted data based on line of best fit, but signed deviations, absolute deviations, and squared deviations are not shown, however, their sums are given Has only the collected data. Has not calculated the predicted data nor the different deviations. Has not turned in any data. Explanation (25%)
Has a rational explanation for choosing an appropriate sum to find the bestfit line.
Has chosen an appropriate sum but does not provide a rationale. Chooses an inappropriate sum based on rationale that the sum can be very small or even zero. Chooses an inappropriate sum with no explanation Does not choose a best error method and does not give any explanation
#17. Modeling Probability (10pts)
Complete Task 1: Measuring Areas of Irregular Regions using Geometric Probability: Handson Dice Activity that was begun in class. (You can download Task 1 by clicking here)
Your grade for this assignment will be based on your completion of Part B of the extension activities:
Extensions into Geometry, Algebra and Calculus using the Fathom^{TM}, Dynamic Data^{TM} software tool.
This is based on activity 7.4 from Exploring Algebra 1 with Fathom (Key Curriculum Press, 2006).
Part B: Investigating the area enclosed by a parabolic curve inscribed in a square.
1. Create a new scatterplot of y against x, where both attributes x and y have the formula random (5)
2. Add the following function to this scattterplot: y=(x2.5)^{2}
3. Create a new attribute (area_above) for the area above the parabola using your existing x and y attributes.
4. Drag your area_above attribute into the middle of your new scatter plot. You should see the area above the parabola in blue.
5. Create a summary table showing the count() of the whole collection, the count(area_above) and the ratio count(area_above)/count().
6. Create a slider and label it "a". Set a to 1.00 to start and use a to edit the function for the parabola: y=a(x2.5)^{2}.
7. Double click on the slider and set its lower limit to 0.5 and its upper limit to 1.5. Adjust the value of a using your slider until your function plot passes through the upper two corners of your square region  points (0,5) and (5,5).
8. Now edit your area_above formula to also use a so that the area is the area above your new function plot (see following screen shot from Fathom).
What do you notice about the proportion of the area of the square that is above this new parabola?Successful completion of the above will earn you 8 out of the 10 points.
For the full 10 points:
Use your knowledge of integral calculus to compute the area bounded by the parabola and the top edge of the square. Does this calculation verify your experimental results? Turn in your mathematical explanations (including details of any integration), together with your Fathom files via email attachment to Dr. Olive and the TA.
For two bonus points:
Can you generalize this result for a parabola inscribed in any square (i.e. passing through the two upper corners of the square with its vertex at the midpoint of the bottom of the square)?
Can you generalize the result for any rectangle (i.e. passing through the two upper corners of the rectangle with its vertex at the midpoint of the bottom of the rectangle)? Use Fathom sliders for the dimensions of your rectangle and edit your formulas so that the above conditions are satisfied.
Due 04/14
Target (10 pts total)  Acceptable (8 pts)  Partially acceptable (6 pts)  Incomplete (4 pts)  No Attempt  

Fathom Activities ( 80%) 
Completed all of the activities with appropriate data sets, tables, graphs, appropriate functions or formulas for the different models and summary statistics  Completed all of the activities but may not have used summary statistics or formulas in the data tables when appropriate.  Completed some of the activities but did not find appropriate functions or formulas for the models  Attempted but did not complete any of the
activities. 
No attempt at the activities 
Calculus Verification (20%) 
Provides a clear explanation
with correct integration of an appropriate function to verify the
proportion of the area of the square above the parabolic curve. 
Uses calculus to verify the proportion of the area of the square above the parabolic curve but does not provide a clear explanation.  Uses calculus but computes the
integral incorrectly or uses an inappropriate function. The calculation
does not verify the experimental results. 
Attempts but does not complete
the calculus verification. 
No attempt at the calculus
verification. 
Extra Challenge  Completed the extra challenge and found a
generalization! (2 points) 
Completed the extra challenge but did not find
a generalization! (1 point) 
Did not attempt the extra challenge 
#18. The Biggest Box Problem (10 pts)
Construct a working GSP sketch for the biggest box problem. Your sketch should include a square with variable squares cut from each corner to form the template of your box. You should link the varying size of these squares to a calculation for the volume and plot the size of cut out square (x) against volume (y) in your sketch. Derive an algebraic solution for the size of the cutout square (as a fraction of the sidelength of your square) that gives you the maximum volume. Click here to download a sophisticated GSP sketch that illustrates the problem (do not use this sketch for your assignment). Email your GSP sketch with explanations to as an attachment to Dr. Olive and the TA.
Due: 04/21
Rubric
Exemplary (10 pts total) Proficient (8 pts total) Incomplete (5 pts total) No attempt GSP Simulation (20%)
Construction for the square and the cutout corners works correctly.
Both size of square and size of cutout can be varied. The point for varying the cutout is on one half of one side of square. Size of cutout and side of square are measured.Construction works but size of square is fixed or extra objects are used for the construction to work (e.g. an extra segment to control size of square and moveable point) or moveable point goes past the midpoint of a side.
Measurements are correct.Missing measurements or measurements are not dynamic. Some aspect of the construction does not work properly. No attempt to construct the GSP simulation or just used instructor's sketch. GSP Plot
(20%)
Correctly plotted the two dynamic measurements and used plot to estimate the size of the cutout for maximum volume. Correctly plotted the two dynamic measurements. Made a plot but it was not with dynamic measurements or incorrect measurements No plot created. Algebraic Solution for fraction of side of square (40%)
Created a correct algebraic expression for the Volume based on the length of cutout and length of square. Used this expression to find the maximum using calculus and factoring of a polynomial. Determined the fraction of the side that gives the maximum volume. Created a correct algebraic expression for the Volume based on the length of cutout and length of square. Used this expression to find the maximum using calculus. Used an algorithm rather than factoring to find a solution or did not express solution as a fraction of the side length. Incorrect expression for the volume or errors in finding the maximum based on faulty calculus or arithmetic errors. Fraction of side is oncorrect. No attempt at an algebraic solution. Algebraic function for the plot
(20%)
Creates a function in GSP based on the length of the original square that coincides with the GSP plot of cutout against volume. The function still matches the plot when the size of the square is changed. Creates a function in GSP based on the length of the original square that coincides with the GSP plot of cutout against volume, but the function does not match the plot when the size of the square is changed. Function expression is not correct or does not match the plot. No attempt to create a GSP function.
#19. The ViewTube with GSP (10 pts)
Construct a working GSP sketch that represents the variables in the ViewTube experiment: Length of tube, diameter of tube, distance of tube from the screen, height of viewable portion of the screen. Use height of viewable portion of the screen as your DEPENDANT variable and plot this against each of the other variables. Derive functions for each of these relations. Copy your construction onto three pages in your GSP document and plot one function on each page, using the data generated by your sketch. Check that your functions match your data plots. Click here to download a starter GSP sketch for the view tube problem with 3 pages already created. Email your edited version of this GSP file with explanations as an attachment to Dr. Olive and the TA.
Due: 04/28
Rubric
Target
(3 pts for each part +1)Acceptable
(2 pts for each part)Incomplete (1 pt for each) No attempt Page 1 (33%)
Plots independent variable against dependent variable correctly. Creates the correct function by editing the existing f(x) to match the locus of the plotted point. Uses the other measurements in the sketch as the parameters in this function.
Correctly labels this page in terms of the independent variable.Creates the correct plotted point and function but may not use the existing f(x) or does not label the page. Correct plot but incorrect function. Does not attempt to plot the independent variable against dependent variable. No attempt to create a matching function.
May turn in the starting sketch unchanged.Page 2 (33%)
Plots independent variable against dependent variable correctly. Creates the correct function by editing the existing f(x) to match the locus of the plotted point. Uses the other measurements in the sketch as the parameters in this function. Correctly labels this page in terms of the independent variable. Creates the correct plotted point and function but may not use the existing f(x) or does not label the page. Correct plot but incorrect function. Does not attempt to plot the independent variable against dependent variable. No attempt to create a matching function.
May turn in the starting sketch unchanged.Page 3 (33%)
Plots independent variable against dependent variable correctly. Creates the correct function by editing the existing f(x) to match the locus of the plotted point. Uses the other measurements in the sketch as the parameters in this function. Correctly labels this page in terms of the independent variable. Creates the correct plotted point and function but may not use the existing f(x) or does not label the page. Correct plot but incorrect function. Does not attempt to plot the independent variable against dependent variable. No attempt to create a matching function.
May turn in the starting sketch unchanged.
#20. Reflection and Feedback on EMAT 3500 (evaluation form)
Your assignment is to complete the evaluation form that can be downloaded as a MS Word document from the above link. You can type on the form and then print it out. This will be completely anonymous. Jaehong will collect the forms and cross your name off his list as you place it in the envelope before the presentations of your Final Project on your Final Exam morning. This is your chance to reflect on YOUR contribution to EMAT 3500, the effort you put into it, the results you got out of it, how it was taught, offer suggestions, point out assignments, technologies or readings that were helpful to you, say something nice, be critical etc... Your feedback is very valuable to us and to this department!!
Due: Final Exam Day, Thursday, May 7, 2009
Click here for details on this final assignment
Post first draft by 5:00 p.m. on Monday May 4 to Dr. Olive and TA via email attachments.
Presentations on Final Exam Day, Thursday, May 7 at 8:00 a.m. in room 112.
Links for Presentations will be added here as soon as I receive them: