EMAT 3500
Secondary School Mathematics Curriculum
Fall 2001

Instructor: Professor John Olive Office 105F, Aderhold  706 - 542 - 4557 jolive@coe.uga.edu

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

Serkan Hekimoglu < shekimog@coe.uga.edu >


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


Office Hours :

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

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

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

Click here for a schedule of 111/113 hours


Assignments

 (adapted from lisa sheehy's course)

 

These will be updated each week
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#1 . Reflections (5pts)

Read pages 1-24 in the Cooney book. Respond to Reflective problem #1 (parts 1 and 2).

Due: 8/22

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#2. Journal Entry Number One (10pts)

Click here

Due: 8/27

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

Read Chapter 1 and 2 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.

Due: 8/27

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#4 . Investigating Integers  (10pts)

Explore the difference of two integers using the GSP4 sketch "Subtract Integers.gsp" in the 3500 folder on my Hard drive (or from the Exploring Algebra (EA) CD if you have it).  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.

Due: 8/27

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#5. Fun with Multiplication: (10pts)

Do the four explorations with "Mystery Machines.gsp" in the Exploring Algebra folder on my Hard Drive (or CD) listed on p. 15 of EA. Choose one of these explorations to write up and hand in.

 

Note: This assignment involves writing up investigations...for a nice description of a write up , click here. The example that Dr. Jim Wilson was referring to (which I think is really nice and helpful!) can be seen by clicking here.

Due: 8/29

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#6. Journal Entry Number Two (10pts)

Click here

Due: 9/03

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#7. 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: 9/03

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#8. Mathematical Investigations using Excel (20pts)

1. Create an Excel Spreadsheet to generate Pythagorean triples. Investigate any patterns that emerge in the triples with hypotenuse of 100 or less.

2. Generate a Fibonnaci sequence in the first column using f(0) = 1, f(1) = 1,

f(n) = f(n-1) + f(n-2) (for n>1)

a. Construct the ratio of each pair of adjacent terms in the Fibonnaci sequence. What happens as n increases? What about the ratio of every second term? etc.

b. Explore sequences where f(0) and f(1) are some arbitrary integers other than 1. If f(0)=1 and f(1) = 3, then your sequence is a Lucas Sequence. Investigate the limit of the ratio of successive terms. What do you notice?

You may do your write-up in PageMill, Word, or Excel.

Due: 9/5

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#9. Journal Entry Number Three (10pts)

Click here

Due: 9/10

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#10. Data Investigations (15-30pts)

Complete Activity 2.1 in the Topic 2 handout from Workshop Statistics using the class scrabble data rather than the names of statisticians.

For a bonus of 15 points you can complete the three homework activities in your handout for Topic 2 (pp. 36-37) from Workshop Statistics

Due: 9/10

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#11. Planetary Measurements (15pts)

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

Due: 9/12

 

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#12. Journal Entry Number Four (10pts)

Click here

Due: 9/17

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#13. Scatter Plots (12pts)

For Tuesday 9/24 - please come to class with a scatter plot of each data set from your lab experiments printed out along with your actual data sets. It would be a good idea for you to save these files as you will want to go back to them.

Click here for a list of the labs.

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#14. Journal Entry Number Five (10pts)

This assignment has been cancelled.

 

 

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

This assignment is a follow up from our class discussion/activities on 9-26. 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: 10/01

 

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#16. Reading and Reaction (15pts)

National Council of Teachers of Mathematics. (2000). Standard for grades 9 -12: Data analysis and probability (p. 324-333). In, Principles and standards for school mathematics. Reston VA: Author.

Reaction Paper

Write a rationale for including (or not including) statistics in secondary mathematics curriculum. You may use the above reading 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: 10/03

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In-class test on Reasoning with Data : 10/03 (45pts)


#17.  Project Headlight (15pts)

Build a mathematically acurate 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.  Send me your GSP file as an attachment via email or link it to your web page (and notify me by email).

Due 10/08

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#18. 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: 10/10

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#19. 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.

Due: 10/15

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#20. Cancelled

 

 


#21. Journal Entry Number Six (10pts)

Click here

Due: 10/15

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#22. Reading and Mathematical Investigations (20pts)

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... 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 255 - Exploration #6 (parts 1 & 2) 
Page 259 - Additional Explorations #8
Page 264 - Exploration #9 (parts 1, 2, and 3)
Page 266 - Additional Explorations #3
Page 268-69 - Exploration #11 or #12 (your choice)

Due: 10/17

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#23. 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: 10/22

 

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#24. 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 matrix 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 10/29

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#25. Journal Entry Number Seven 

            Cancelled

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#26. Reading and Mathematical Investigations (20pts)

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 53 - Exploration 4 - # 4
Page 62 - Exploration 6 - # 1 (with an explanation of why you placed yourself where you did)
Page 64 - Exploration 7 - # 2
Page 68 - Exploration 8 - # 2, 6

Due: 11/5

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#27.  Cancelled


 

#28. Reading and Mathematical Investigations (15pts)

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 78 - Exploration 11 - # 1
Page 83 - Exploration 12 - # 6
Just think about (you don't need to write it up) Page 95 - Exploration 15

Due: 11/12

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#29. 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.

Due 11/14

Click here to download this paper as a word document

 

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#30. Journal Entry Number Eight (10pts)

Click here

Due: 11/26

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#31.  Investigating the Derivative (15pts)

Challenge problem on secant line of a quadratic from page 7 of handout titled " Chapter 11: The Dynamic Geometry of Calculus"

Due: 11/26

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#32. Journal Entry Number Nine (10pts)

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Due: 12/03

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#33. Cancelled


#34. Journal Entry Number Ten (10pts)

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Due: 12/05

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#35. Final Project (100pts)

Click here for details on this final assignment

Due: 12/13

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