MAT 517/ MAE 330: Technology in Math Education
Spring 2014
MAT 517 Schedule

### MAT 517 / MAE 330 Technology in Math Education - Fall 2014 - Schedule

• #### Unless indicated otherwise, homework should be written in Latex or html.

Week Topics and homework
1-
1/27
Math Sinc Site
Introduction
Overview of  Geogebra and Latex and Google sites.
Roots of polynomials

Hw 1 (due 2/6).
• Fill out this form.
• Make sure you have access to a computer with Geogebra and Latex.
• Start working on the  Explorations 1 handout.  Complete (and submit) the pdf and tex files of Exercise 1.
2-
2/3
The roots of a parabola.

HW 2  (due 2/13)
1. Submit a draft of the written part of your first project. You can do it in Latex or html.
2. Complete and submit Exercise 2 of Explorations 1 handout in Geogebra. Of course, the graph constructed in class has to be included. Make sure to describe all the elements of the parabola that appear (axis of symmetry, roots, minimum).  This handout actualized (from http://math247.pbworks.com/w/page/20517509/GeoGebra) might be helpful. Note that you can use Latex in Geogebra.
3. Submit a couple of short paragraphs explaining what did you learn by working on the parabola project.
4. Write down a summary of the discussions we had in class about the square root of a real number, and the solutions of the equation x2 = a, where a is a real number.
• All these files should be submitted through your Google site.
• As usual, Latex files must be submitted as Latex and pdf.
• You are encouraged to include illustrations.  You can use the explorations1.tex files at the course website as a guide.
• BlueGriffon is a free html editor. It does not include a capability to write math formulae but you can buy an inexpensive Add-on to to so.
3
2/10
Conic Sections: We will work on this handout from Thomas Hull's book "Project Origami, activities for exploring mathematics", CRC Press.
Time permits, we will work on this handout too (from the same book).
Math in Valentine's Day? Check out this!

About the presentation: The main point is to teach a math topic using technology (and not vice versa). Ideally, you should assume your students do not know anything about the topic you are about to present. You will need to make a list of topics that you will assume they already know.

HW 3  (due 2/20)

1. Exercises 3, 4 and 5 from Explorations 1 handout .
2. Make your own Math-o-gram in Desmos. Your math-o-gram should illustrate a Math point (for instance, the amplitude and period of the sine function, or the domain of the function $f\left(x\right)=\sqrt{1-{x}^{2}}$ ). This math-o-gram illustrates the a linear combination of two functions of the form Ft(x)= t.g(x)+(1-t)h(x), when t is in the interval [0,1], when t goes from 0 to 1, the graph of Ft(x) changes continuously. Here is another example. Here is a user guide for Desmos.
•  Please send me an email with your preferred email address (if you did not do so already).
• Use the guidelines for writing projects from the syllabus of our course.
• Make sure that
• Your files are named as follows: yourfirstname_hwnumber. (So, for instance, Jane Doe's homework 3 in pdf, should be named jane_hw3.pdf. If there is more than one file, add a, b, c.. e.g., jane_hw3_a.pdf or an identifier like jane_hw3_roughDraft.pdf).
• you email me your homework (instead of posting it)
• all the "pdf" part of your homework is in a single file.
• Math formulae are displayed correctly. (For instance, $\sqrt{{x}^{2}-1}$ instead of  sqrt(x^2-1) ).
• Your geogebra files are clear and correct, and all the elements that appear are explained, if that is required.
•  you give a clear and correct definition of  every term that you introduce.
• your target audience, (a reasonably educated high school student who might have forgotten some terms, like root or contour lines) will be able to understand what the demo does with your explanation.

4
2/17
Note: You can use this link to download the files you create in the Math Sinc Site.
Here is a Mathematica demonstration about Dandelin spheres and here is a very good illlustration from Wikipedia.
Here is my version of the parabola exercise.
The Mathematica demos we use are all here.

HW 4  (due 2/27)
1. Choose a topic for your next presentation.
2. Exercises 6, 7, 8, 9 and 10 from Explorations 1 handout .
3. Grade homework 1. The file is here.
4. Submit an advanced draft of your presentation.
5
2/24

This week we are going to discuss random numbers.
We will use Graphing Calculators. If you have a TI 83/84, download this app (Probability Simulations) and install it in your calculator. Here are instructions to install the app. ) This page is a good reference to start working with your graphing calculator.
Here are two questions to test your intuition for randomness.
We will work with this handout from the Texas Intrument site for education. It discusses a mathematical aspect of the episode "Double down" of Numb3rs (the math-juicy bit comes around 32 minutes after the show started).
We are going to start doing a bit of programing our graphing calculators. Here is a quick guide to write the first program.

6
3/3
Kate: What is a function?
Jamie: What is a limit?

Homework 5(due 3/13) this five problems.
Here are some of the Math-o-grams you submitted.
7
3/10
Michael: Descriptive statistics. What are the mean, standard deviation, percentiles?

Homework 6: DUE on 3/27
Submit the written part of your 2nd project. Unless exceptional circumstances, this written part will not be accepted for grading if submitted after the deadline. This draft should be an illustrated set of notes that "stand alone", and do not depend on your lecture. You can think of this draft as notes for a students who miss the class you taught that day.
3/17
Spring Recess
8
3/24
Tuesday
Kristen: What is a derivative?
Thursday
Kim: What is an integral?
Rocco: What are the extrema?

Below are the topics for the next project.  If your topic is not appearing, please send email it to me as soon as possible.  Possible topics are Newton's method,  Fitting linear functions to data, Mathematical induction. You can choose more topics from the Common Core Standards Initiative.

Kristen: Geometric constructions.
Mike: Mathematics of Running in the Rain
Kyle: Fibonacci numbers
Kate: What is $\pi$?
Rocco: Modular arithmetic
Kimberly: Area and volume
Jamie: Newton's method
Tanyalisa: TBA

Homework 7 (due 4/3)
1. Complete this worksheet (Problems 1 to 8) from the Texas Instrument material , repeating problems 1 to 7 three times each but changing the number of times the experiment is performed as indicated in the worksheet.
Compare your own results in Problem 8. The hisogram and the answer to problem 8 must be submitted Latex. Take pictures of the histograms you obtain and insert them in your  file. The rest of the answers should be submitted in this google form.
( This website can be also used to simulate roll dice. To roll N (six sided) dice, type  NE6 and click on "roll". The outcome is the number of six obtained in the simulation. )
2. Submit a geogebra file with an illustrated proof of the following statement  (this is a minor modification of the problem we discussed in class): Consider a circle of radius R. Denote by L(x) arc length of an arc of (central) angle x and by C(x) the length of the chord determined by that angle. Then  the limit when x tends to 0 of L(x)/C(x) is 1.
9
3/31
This week we will use spreadsheet to discuss certain topics in statistics. Here are some of the files we are going to use.
Some examples of distributions:
Mercury concentration in pregnant women.
Population of the US by age (from 1920 to 2005.)
Breath response to lactose in children.

Homework 8 Due 4/10
Complete this worksheet (to the end).
Complete this form.
10
4/7
Here you'll find an explanation for plotting points in Geogebra.
TanyaLisa: What is a real number and what is a rational number? Operations
Kyle: What is a complex number?

Homework 9 Due 4/22:
1. Submit a geogebra file with an illustrated proof of the following statement  (this is a minor modification of the problem we discussed in class): Consider a circle of radius R. Denote by L(x) arc length of an arc of (central) angle x and by C(x) the length of the chord determined by that angle. Then  the limit when x tends to 0 of L(x)/C(x) is 1.   You can use Calculus in your proof.
2. Create a page in your Google site explaining a math point  (or another topic that you previously cleared out with me. ). Include a proof or a math argument and one or more relevant pictures.
3. Work on your presentation. Make sure that
1. you do not exceed 15 minutes.
2. you explain a math argument (that you understand)
3. use technology in a meaningful way
4. do not use the Smartboard or the PowerPoint as a tool to write less.
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11
4/14
Here is the link to the files we will use while working on Curve Fitting and the cosine program.

Homework 10 Due 4/24:
Submit the written part of your presentation. If you are using the Smartboard, submit the Smartboard file too.
1. Define four points in Geogebra.
2. Create two sliders m and b, and  the line y=m.x+b.
3. For each point P, draw the horizontal segment between P and the line y=mx+b.
4. In the spreadsheet, for each point P, compute the horizontal distance between P and the line y=mx+b.
5. In the spreadsheet, compute the sum of the squares of those horizontal distances.
6. Find the values of (m,b) that make the sum of the squares of the horizontal distances the smallest possible. Make sure that you write down a proof of the fact that the values you found give a minimum.  (You can use Mathematica in finding the values)
7. Plot the line you found in the Geogebra document.

Extra credit: In the same Geogebra file

• Plot together the two lines (the one that minimizes squares of vertical distances and the one that minimizes squares of horizontal distances).
• Drag  your points so they are approximately in a vertical line. Which line seems the best fit? Find an explanation for your observation.
• Illustrate the fact that the line that minimizes the squares of vertical distances to a finite set of points  passes through the centroid of these points.  Extra Extra credit: Prove it!

12
4/21

We will discuss this problem as well as algorithms to compute powers.
Homework 11 Due 5/1: (from "Inside your calculator") Submit the write up of the TI 84 programs below, as well as a sample of the results (three for 1 and three for 2)
1. Write (and test) a program to find and list 27 triples of positive integers (x,y,z) satisfying 1/x =  1/y  + 1/z. (Hint: Prove that
$\frac{}{}$   and use this relationship to generate various values for x, y and z. Use For loops governed by p, q and r. Limit these values to 1 to 3).
2.  Develop and test a program to find at least 27 Pythagorean triples (x,y, z). (Hint: Use x=2pr, y=p2 - r2 and z= p2 + r2)

13
4/28
We will discuss algorithms to compute powers and logarithms.

Tuesday: Kristen.
Thursday: Jamie,  Rocco and and Michael

Homework 12 Due 5/8: Work on the homework proposed by Kristen. The problems are here. You can only use the tools that are provided in those files.
Homework for Kristen and Jamie.
Nine points can be associated with a given triangle: the midpoints of the sides, the feet of the altitudes and the midpoints of the segments joining the orthocenter of the triangle to the three vertices of the triangle.  (The orthocenter of a triangle is the point where the three altitudes intersect)
A (beautiful) theorem says that the above nine points lie in a single circle.
Problem 1 Construct a triangle and the nine points indicated in the theorem.
Problem 2 Create a tool that constructs the nine-point circle for a triangle. The input should be the three vertices of the triangle and the output, the nine points and the circle. Study how the circle varies when the triangle varies.
14
5/5

Tuesday: Kate and Kim
Thursday"Tanyalisa and Kyle
Homework 13 Due 5/15