EMAT 3500
Exploring Concepts with Technology in Secondary School Mathematics
Fall 2003

 Instructors:

 Dr. John Olive  Dr. Tanya Cofer

 Offices

 105F, Aderhold   105 P Aderhold

 Telephone

 706 - 542 - 4557  706-542-4546

 email

jolive@coe.uga.edu  cofer@math.uga.edu

Assistants : Jeong-lim Chae < jchae@coe.uga.edu >

Serkan Hekimoglu < shekimog@coe.uga.edu >


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


Office Hours :

Dr. Olive: Tuesdays 1:00pm - 3:00pm (105F)

Thursdays 1:00pm - 3:00pm (105F)

.....Or by appointment....or drop in if I'm in my office.


Assignments

 (adapted from lisa sheehy's course)

These will be updated each week
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30

 


#1 . Prepare for next class discussion (10pts)

Read Chapter 1, 2 and 3 of the Principles and Standards for School Mathematics

and also look through the Content Standards for Number and Operations, Algebra, and Statistics for grades 6-12. Find out what the Process Standards are for these grade spans. Bring 3 written questions for discussion (to be turned in at the beginning of the class period).

Due: 8/21

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#2. Investigating Integers  (10pts)

Explore the difference of two integers using the GSP4 sketch "Subtract Integers.gsp" in the 3500 folder on my Hard drive (in the Exploring Algebra folder, 1_Fundamentals folder).  Reflect on your exploration (did it help you to understand operations on integers?).  Write-up your responses to questions 8-10 on p. 8 of EA. Relate these activities to the Number and Operations Standards for 6-12.

Due: 8/26

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#3. Fun with Multiplication: (10pts)

Do the four explorations listed on p. 15 of EA with the "Mystery Machines.gsp" and the "Mystery Combos.gsp" sketches (in the 1_Fundamentals folder inside the Exploring Algebra folder on my Hard Drive). 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: 8/26

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#4 . Mathematical Adjectives: (10pts)

A. List 5 adjectives that you associate with mathematics. Then, one at a time, describe in a couple of sentences what is gained or lost in mathematics by having eliminated the missing adjective.

B. Consider the following people:

For each person, select the adjectives from your list (A) that you think that person might use to describe mathematics.

C. Consider your best high school mathematics teacher, your worst high school mathematics teacher, and an "average" high school student. From your list in (A), select adjectives you think each would choose and give reasons why an adjective would be chosen or not chosen.

Due: 8/28

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#5. Readings and Reaction Paper: (20pts)

#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. Lappin, 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 Lappin 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: 9/02

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#6. Reflections (10pts)

Read pages 1-24 in the Cooney book. Respond to Reflective problem #1 (parts 1 and 2). Be prepared to share in class (nothing to hand in).

Choose one of the 8 questions from our discussion on the NCTM Principles and Standards (click here for the list of questions) and write a one page response to the question.

Due: 9/04

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#7. Data Investigations (15pts)

Complete the three homework activities in your handout for Topic 2 (pp. 36-37) from Workshop Statistics

Respond to reflective problem #6 in Chapter One of the Cooney text

Click here to see what previous EMAT 3500 students thought...

Due: 9/09

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#8. Matching Distributions & Planetary Measurements (15pts)

Complete Activity 3.2: Matching Variables to Dotplots, Topic 3, pp. 49-50, from Workshop Statistics.

Do the first Homework activity from p.84, Topic 4 from Workshop Statistics (Activity 4-5).

Hand in or upload to your folder your results for each activity.

Due: 9/11

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#9. Relational and Instrumental Understanding (10pts)

Reflect on the article by Richard Skemp on Instrumental and Relational Understanding.  Briefly describe how you learned mathematics (instrumentally and/or relationally).  Comment on the nature of your understanding that is developing in this course (2-3 pages).  

Due: 9/16

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#10. Principles and Standards for Data Analysis and Probability (grades 6-12) and FATHOM (10pts)

Read the NCTM recommendations and 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: 9/18

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#11. Laboratory Preparation (10pts)

Click here for a list of the labs.

For Tuesday 9/23 - 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: 9/23

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

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 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

 

Predicted
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: 9/30

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Mid-Term Exam on Reasoning with Data : 9/30 (50pts)


#13. Reaction Paper on Data and Statistics (10pts)

Write a rationale for including (or not including) statistics in 6-12 mathematics curriculum. You may use the NCTM Principals and Standards and what you have learned from the class materials (Topics from Workshop Statistics, Cooney et al), along with your beliefs and experiences to support your rationale... please cite your sources.  Consider your audience to be a school board.

Suggested length: 2 pages

Due: 10/02

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#14. Reading and Reaction Paper (10pts)

Reading:

Dossey, J. (1996). Modeling with Functions. In Cooney, T. J., et. al. (Eds.), Mathematics, Pedagogy, and Secondary Teacher Education. ( only pp. 221-253). Portsmouth, VA: Heinemann.

Reaction Paper

Respond to Reflective problem #1 on pps 229 - 230 - note, there are 10 questions listed. Please select any two to write responses to.

Due 10/07

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#15. Composition of Functions Investigation (15pts)

Using the GSP Dynagraphs, investigate the composition of three functions each of which belongs to a different family (e.g, step, quadratic, and trigonometric).  Write-up your investigation, highlighting any interesting or surprizing characteristics you discovered for your particular composition (2-3 pages).

Due: 10/09

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#16. Reflection on Dynagraphs (10pts)

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: 10/14

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#17.  Reading and Mathematical Investigations (10pts)

Reading:

Dossey, J. (1996). Modeling with Functions. In Cooney, T. J., et. al. (Eds.), Mathematics, Pedagogy, and Secondary Teacher Education. ( pp. 254-280 ). Portsmouth, VA: Heinemann.

Mathematical Investigations (read all of the problems but complete the following... You may use Excel, the TI-83, word with equation editor, gsp, pencil and paper, etc... whatever you feel most comfortable with... to write-up this assignment.)

Page 255 - Exploration #6 (parts 1 & 2) 
Page 259 - Additional Explorations #8

Due: 10/17

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#18. 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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#19. Reading and Reflection (10pts)

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.

Page 29 - Reflective Problem 1 .  Bring your assigned points to class for the discussion.

Due: 10/23

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#20. Project Headlight (10pts)

Build a mathematically accurate model for the light beams emanating from a headlight (parallel beams) using GSP (see p.90 of Exploring Algebra).  I 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 your folder on my Hard Drive and notify me by email.

Due: 10/28

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#21. Mathematical Investigations (15pts)

Mathematical Investigations (read all of the problems but complete the following... Again, you may use Excel, the TI-83, word with equation editor, GSP, pencil and paper, etc... whatever you feel most comfortable with... to write-up this assignment.)

Page 40 - Exploration 1
Page 42-43 - Exploration 3 - Create a 7 x 4 table and label your column and row headings. Then write ~1 page explanation of the placement of the cells. (This is worth 10 of the 15 points for this assignment)

Due: 11/4

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#22. Reading and Mathematical Investigations (10pts)

Reading:

Cooney, T. (1996). Developing a topic across the curriculum: Functions. In Cooney, T. J., et. al. (Eds.), Mathematics, Pedagogy, and Secondary Teacher Education. (pp. 46-69). Portsmouth, VA: Heinemann.

Mathematical Investigations (read all of the problems but complete the following... Again, you may use Excel, the TI-83, word with equation editor, gsp, pencil and paper, etc... whatever you feel most comfortable with... to write-up this assignment.)

Page 62 - Exploration 6 - # 1 (with an explanation of why you placed yourself where you did)

Page 68 - Exploration 8 - # 2, 6

Due: 11/6

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#23. Reading and Mathematical Investigations (10pts)

Reading:

Cooney, T. (1996). Developing a topic across the curriculum: Functions. In Cooney, T. J., et. al. (Eds.), Mathematics, Pedagogy, and Secondary Teacher Education. (pp. 70-96). Portsmouth, VA: Heinemann.

Mathematical Investigations (read all of the problems but complete the following... Again, you may use excel, the TI-83, word with equation editor, GSP, pencil and paper, etc... whatever you feel most comfortable with... to write-up this assignment.)

Page 76 - Exploration 10 - # 1a
Page 83 - Exploration 12 - # 6

Due: 11/11

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#24. Review of the NCTM Algebra Standards (10pts)

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: 11/13

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#25. History of Functions Reading (10pts)

Read the History of Functions paper (see below). Write a one to two page reaction to this paper. Include in the reaction paper your own ideas about how the concept of function should be presented and addressed in school curriculum.

Click here to download this paper as a word document

Due 11/18

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#26. SimCalc Reflection (10pts)

Reflect on your investigations with SimCalc's MathWorlds.  Would you use this technology with your students?  If so, why?  If not, why not? (1-2 pages)

Due 11/25

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#27.  Investigating the Derivative (15pts)

Challenge problem on secant line of a quadratic from handout titled "The Dynamic Geometry of Calculus" (Assignment 11.1, p. 7)

Due: 12/02

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#28. Reflection on Integration with GSP (10pts)

Reflect on your use of the GSP sketches for exploring Integration.  In what ways did the exploration help (or hinder) your understanding of these fundamental ideas of calculus? (1-2 pages)

Due: 12/04

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#29. Reflection on EMAT 3500 (10pts)

Imagine that you will be teaching EMAT 3500 next year. What would your course look like? How would it be similar to and different from the EMAT 3500 experience you just had? What things would you emphasize/de-emphasize? include/not include? This is your chance to vent, offer suggestions, point out assignments or readings that were helpful to you, say something nice, etc... Your feedback is very valuable to me and to this department!!

Due: 12/04

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#30. Final Project (100pts)

Click here for details on this final assignment

Due: 8:00 a.m. on 12/16 (Final Exam Day)

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