EMAT 3500
Exploring Concepts (with Technology) in Secondary School Mathematics
Fall 2004

 (adapted from lisa sheehy's course)


 Dr. John Olive  Dr. Larry Hatfield


 105F, Aderhold   110 G Aderhold


 706 - 542 - 4557  706-542-4550


jolive@coe.uga.edu  lhatfiel@coe.uga.edu

Assistant: Serkan Hekimoglu < shekimog@coe.uga.edu >

Office Hours | Syllabus | Outline | Students | Assignments | Links

Office Hours :

 Dr. Olive (room 105 F)

 Dr. Hatfield (room 110 G)

Tuesdays 1:00pm - 3:00pm

Thursdays 1:00pm - 3:00pm

.....Or by appointment

....or drop in if I'm in my office.

Tuesdays 1:30pm - 2:30pm

Thursdays 1:30pm - 2:30pm

.....Or by appointment


Each instructor has provided a "Drop Box" on their computer in which you will place all of your electronic assignments. To do this you will need to connect to the instructor's computer via the AppleTalk network or IP address. Both computers are in the UGA Mathematics Education network. Following are the instructors' computer names and IP addresses:

   Dr. John Olive  Dr. Larry Hatfield
 Computer name:  Olive's G5  LHatfieldsMacG5
 IP address:

You will log on to the emat3500 volume as a "Guest" and when you double click on this network volume you should see the "EMAT 3500 Drop Box" for your instructor. Simply drag your file(s) into this folder. From a Macintosh computer, you will see a message indicating that you will not be able to see the results of this operation. Click the OK button to copy your file to the drop box. REMEMBER TO SEND YOUR INSTRUCTOR AN EMAIL INDICATING THAT YOU HAVE DEPOSITED A FILE IN HIS EMAT 3500 DROP BOX!

NOTE: You should use the following filename structure for all of your files:

<first intitial><last name><assignment #>.<file type>

For example: dbarnwell2.doc would be the file name for Daniel to use for his reaction paper for assignment #2.

If you decide to submit a revised assignment BEFORE the due date then append a lower case letter (starting with "b") to your updated assignment. For example, Daniel would submit dbarnwell2b.doc as his updated reaction paper for assignment #2.

NOTE: Please disconnect from the emat3500 volume when you have transferred your file (drag to the trash basket or highlight the volume and choose "Eject" from the FILE menu). This is very important as ONLY TEN people can be connected to the instructor's computer at the same time.

NOTE: If you cannot access the instructor's Drop Box you may ATTACH your file to an email to the instructor.

Click on a number in the following table to go to that assignment.

These will be updated periodically
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 August 24 (portfolio)

Read Chapter 1 and 2 of the Principles and Standards for School Mathematics

Bring 3 written questions for discussion (to be included in your portfolio).

Due: 8/24

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#2. Readings and Reaction Paper: (10pts)

#1. Borasi, R. (1995). What secondary mathematics students can do. In I. M. Carl (Ed), Prospects for school mathematics. Reston, VA: NCTM.

Click here to read about what a student did do :)

#2. Lappan, G. & Briars, D. (1995). How should mathematics be taught? In I. M. Carl (Ed), Prospects for school mathematics. Reston, VA: NCTM.

Reaction Paper: Please write a 1-2 page paper in which you react to/reflect on Readings #1 and #2. Borasi focuses on student learning while Lappan and Briars focus on teacher teaching... are they in agreement? do the authors make similar and/or different points? do you agree/disagree with the authors' discussions and suggestions? This paper is not intended to be a summary of the readings (I have read them ~ you may assume this as you write your response). I would like to know what you think about the readings.

Due: 8/26

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#3. Reflecting on Your Experiences with Mathematics Teachers: (portfolio)

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 (3-5; 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.

B. Make a short list (3-5) 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.

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.

Due: 8/31

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#4. Fun with Multiplication: (portfolio)

Do the four explorations listed on p. 15 of EA with the "Mystery Machines.gsp" and the "Mystery Combos.gsp" sketches (download or use in room 111/113: go to EMAT 3500/GSP4 files/Exploring Algebra/1_Fundamentals folder on the lab computers). Choose one of these explorations to write up and hand in. The following description of a "write-up" is adapted from Dr. Jim Wilson.

The "write-ups" 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: 9/02

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#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 the Artin Braids activity as it occured across the 3 groups in class and relate it to these 3 main points. Briefly describe how you learned mathematics (instrumentally and/or relationally).  (2-3 pages).  

Due: 9/07

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#6. Composition of Functions Investigation (10pts)

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.)  Write-up your investigations, highlighting any interesting or surprizing characteristics you discovered for your particular composition (1-2 pages). Turn in your GSP sketch along with your write-up.

Due: 9/14

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#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? (1-2 pages)

Due: 9/21

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#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: 121-149.

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: 9/23

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#9. Project Headlight (10pts)

Build a mathematically accurate model for the light beams emanating from a headlight (parallel beams) using GSP (see handout pp. 90-91 from Exploring Algebra).  You should be able to adjust your headlight to redirect the light beam and to make the beam narrower or wider.  Place your GSP file in the EMAT 3500 Drop Box on your instructor's computer (or attach to an email message) and notify your instructor by email.

Due: 9/28

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#10. Review of the NCTM Algebra Standards (portfolio)

Review the Algebra Standards for grades 6-12 in the NCTM Principles and Standards. Write a 1-2 page report on the approach to Functions taken in the Standards document.

Due: 10/05

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#11. Sorting Functions (10pts)

Sort the 28 function cards into a 7 x 4 array based on the four different kinds of representations (graph, data table, algebraic expression and verbal description) and seven distinct categories of functions that you must determine. Each function CATEGORY will have an example from each of the four different representations (but each representation will be of a different function in that category). Label each function category. Turn in a 7x4 table with rows and columns labelled appropriately and the NUMBERS of the appropriate function cards in each of the 28 cells (one card per cell). Write a one-page explanation for how you determined your seven function categories and the placement of the cards.
This activity is adapted from Cooney, T. (1996). Developing a topic across the curriculum: Functions . In Cooney, T. J., et. al. (Eds.), Mathematics, Pedagogy, and Secondary Teacher Education. (pp. 27-43). Portsmouth, VA: Heinemann.

Due: 10/07

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Mid-Term Exam on Functions : 10/19 (60pts)

#12. Reflections on your visit to GCTM Annual Meeting at Rock Eagle (10pts)

Identify sessions on Mathematical Modeling and/or Functions using technology and attend as many as you can. Write a 2-page reflection on one of these sessions, indicating the most important things you learned from it.

Due: 10/21

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#13. Data Investigations (10pts)

Problem Set 4 from page 22 of The Model Shop© by Tim Erickson. Create your own data set from at least ten different paperback books. Address all of the questions 1-6 in your write-up of this exploration. Turn in your Fathom file (you can do the write-up in your Fathom file or using a word processor).

Due: 10/26

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#14. Non-Linear Modeling (10pts)

Complete Problem Set 8: Inverse Functions: Paragraphs on page 36 of The Model Shop© by Tim Erickson. Respond to all of the questions 1-8 (including the extension). Submit your results with your Fathom file.

Due 11/02

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NOTE: All assignments from this point on are subject to change as we are using a new resource: The Model Shop© by Tim Erickson.

#15. Laboratory Preparation (Portfolio)

Click here for a list of the labs.

For Tuesday 11/09 - Discuss with your group how you intend to conduct your lab activity. Make a list of needed equipment and make plans to obtain the equipment (some equipment is avaiable from our Departmental closets). Come to class with equipment and instructions for your group's lab activity. Set up your lab activity before the beginning of class.

Due: 11/09

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#16. Approximating Best Fit Lines ~ (15 pts)

This assignment is a follow up from our class discussion/activities. Using your Pennies set of data and the line of best fit that you approximated with Fathom or GSP, calculate the signed deviation (Collected - Predicted) and absolute deviation |Collected - Predicted| of each collected data point from the predicted value given by the line of best fit.  Use the table below as a guide to calculate the different measures of error in your data.


Collected Independent Values


Collected Dependent Values


Dependent Values
(using your suggested best fit line)


Signed Error:
Sum of Signed Deviations 


Absolute Error: Sum of Absolute Deviations

The more interesting part of this assignment lies in thinking about what these error values 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 signed error, the absolute error, 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.

Due: 11/11

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#17.  Where is Mathematical Modeling from Data in the Principles and Standards? (Portfolio)

Look through the NCTM Principles and Standards for references to mathematical modeling using real-life data. What recommendations are made? Reflect on your use of FATHOM with respect to these recommendations. Write a one-page argument for or against using FATHOM based on these recommendations.

Due 11/18

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#18. Feedback for the Author of The Model Shop (portfolio)

You should approach this assignment from the point of view of a prospective teacher who might use these new curriculum materials with your students. Teachers are often asked to make curricula decisions on materials provided by publishers without having the opportunity to first use them with their students. Even though you have had only a brief time to use some of these materials, your feedback could help shape resources that could be used by your future students.

Due: 11/23


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November 23: Group and Individual Reports on Mathematical Modeling from all 5 labs (20 pts)

#19. The Biggest Box Problem (5 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 cut-out square (as a fraction of the side-length 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).

Due: 12/02

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#20. The View-Tube with GSP (10 pts)

Construct a working GSP sketch that represents the variables in the View-Tube 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.

Due: 12/09

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#21. 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. Serkan 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

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Final Project (60pts)

Click here for details on this final assignment

Due: 5:00 p.m. on Monday 12/13 (Final Exam Week)

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