EMAT 3500
Exploring Concepts (with Technology) in Secondary School Mathematics
Spring 2007

 Instructor:

 Dr. John Olive

 Offices

 105F, Aderhold 

 Telephone

 706 - 542 - 4557

 email

jolive@uga.edu
Assistants: Jaehong Shin < jhshin@uga.edu > & Hyeonmi Lee <hmdoban@uga.edu>

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

Office Hours :
Dr. Olive (room 105 F)
Tuesdays & Thursdays 1:00pm - 3:00pm
Wednesdays 9:30am - 2:00pm
.....Or by appointment
....or drop in if I'm in my office.


Assignments

We shall be using LiveText as a vehicle for you to create your electronic portfolios of specific assignments in this course. (Click here to go the College LiveText web page.) All assignments should be created electronically and posted to your LiveText portfolio.  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

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 January 11 (LiveText 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: 01/11

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#2. Investigate the Georgia Performance Standards (10 points)

Go to the web site for the new Georgia Performance Standards. Find the mathematics standards that relate to the goals of this course.

Match the topics in the outline of the course with an appropriate GPS. Save these matched items in your LiveText electronic portfolio.

Due: 01/16

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#3. Research on the NCTM Standards: (portfolio)

Read Chapter 2 from A Research Companion to Principles and Standards for School Mathematics. Write a one-page response to the oft asked question: "Does research support the NCTM recommendations for curriculum reform?"

Due: 01/18

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#4. Reflecting on Your Experiences with Mathematics Teachers: (10 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 (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: 01/23

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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 your responses to assignment #4. Briefly describe how you were taught and how you learned mathematics (instrumentally and/or relationally).  (2-3 pages).  

Due: 01/25

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#6. Composition of Functions Investigation (15pts)

(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.)  Write-up your investigations, highlighting any interesting or surprising characteristics you discovered for your particular composition (1-2 pages). Submit your GSP sketch along with your write-up via LiveText. 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: 01/30

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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: 02/06

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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: 02/08

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#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 LiveText. An extra 5 points will be possible for successfully completing the Extra Challenge.

Due: 02/13

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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: 02/22

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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: 02/27

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Mid-Term Exam on Functions : 03/06 (60pts)


#12. Laboratory Preparation (Portfolio)

Click here for a list of the labs.

For Tuesday 03/20 - 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 available 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: 03/20

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#13. Lab Reports from the 4 Labs (10 points)

Each individual will turn in their own results for the 4 labs and provide these results to the appropriate group along with a brief (paragraph) conclusion they made from the group results for each lab.

Due: 03/27

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#14. Data Investigations (10pts)

We shall be using activities from Section 3, Analyzing Data with Fathom of a new curriculum resource being developed by Hollylynne Lee & Karen Hollebrands: Learning to Teach Mathematics with Technology: An Integrated Approach.

Download the PDF document for Section 3 here.

Download the Fathom data set: 2006_Vehicles.ftm here.

After working through all of the activities in Section 3, answer the Focus on Mathematics questions M-Q13 - M-Q17 on pp. 17 & 18.  Two points can be earned for each question answered.

For two bonus points, address the Pedagogical questions: P-Q11 & P-Q12 on page 18.

Upload your completed Word and Fathom files to your LiveText portfolio.

Due: 03/29

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#15. Approximating Best Fit Lines ~ (10pts)  Choose ONE of the following two options:

Option A: Using your Pennies set of data from the Experimental Labs, create a line of best fit using Fathom. Using the equation of your best-fit line, calculate the signed deviation (Collected - Predicted), absolute deviation |Collected - Predicted| and squared deviation (Collected - Predicted)^2 of each collected data point from the predicted value given by the line of best fit.  Using a Fathom Summary Table, show the sums of each of these different deviations.

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. Post your paper and any example files to your LivetText portfolio.

Option B: Assignments H-Q1 & H-Q2 from Section 4 of Learning to Teach Mathematics with Technology: An Integrated Approach. (Page 26) (Download the PDF document for Section 4 here)

Due: 04/05

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#16. Modeling Probability (10pts) 

Complete the "Geometry by Probability -- Monte Carlo Methods" activity on your handout from class. This is based on activity 7.4 from Exploring Algebra 1 with Fathom (Key Curriculum Press, 2006).

Your grade for this assignment will be based on your completion of Part B of the activity:

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=(x-2.5)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(x-2.5)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?

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 04/10

 

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#17.  Reaction Paper on Data and Statistics (Portfolio)

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, 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 04/12

 

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#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 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). Post your GSP sketch with explanations to your LiveText portfolio.

Due: 04/17

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#19. 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. Submit your completed GSP sketches to your LivetText Portfolio.

Due: 04/24

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#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 3, 2007

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Final Project (60pts)

Click here for details on this final assignment

Post first draft by 5:00 p.m. on Monday April 30 (last day of classes)
Presentation on Final Exam Day, Thursday May 3 at 8:00 a.m. in room 111/113 Aderhold Hall.

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