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

This is a tentative
schedule of the course. It will be updated weekly as the
course progresses. It is your responsibility to check it
regularly.

Homework should be
posted every Thursday before midnight in your SB Google
site.

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.
 Practice editing your Google site.
 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)
 Submit a draft of the written part of your first project. You
can do it in Latex or html.
 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.
 Submit a couple of short paragraphs explaining what did you
learn by working on the parabola project.
 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 x^{2} = 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 Addon 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)
 Exercises 3, 4 and 5 from Explorations
1 handout .
 Make your own Mathogram
in Desmos. Your mathogram should illustrate a Math point (for
instance, the amplitude and period of the sine function, or the
domain of the function
$\textcolor[rgb]{}{}$$\textcolor[rgb]{}{f\left(x\right)=\sqrt{1{x}^{2}}}$
). This
mathogram illustrates the a linear combination of two
functions of the form F_{t}(x)= t.g(x)+(1t)h(x), when t
is in the interval [0,1], when t goes from 0 to 1, the graph of
F_{t}(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,
$\textcolor[rgb]{}{\sqrt{{x}^{2}1}}$
instead of sqrt(x^21)
).
 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)
 Choose a topic for your next presentation.
 Exercises 6, 7, 8, 9 and 10 from Explorations
1 handout .
 Grade homework 1. The file is here.
 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 mathjuicy 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
Mathograms 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
$\textcolor[rgb]{}{\pi}$$\textcolor[rgb]{}{}$$\textcolor[rgb]{}{}$$\textcolor[rgb]{}{}$?
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
 you do not exceed 15 minutes.
 you explain a math argument (that you understand)
 use technology in a meaningful way
 do not use the Smartboard or the PowerPoint as a tool to write
less.
$\textcolor[rgb]{}{{}_{\mathrm{}}^{\mathrm{}}{}^{}}$

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.
 Define four points in Geogebra.
 Create two sliders m and b, and the line y=m.x+b.
 For each point P, draw the horizontal segment between P and
the line y=mx+b.
 In the spreadsheet, for each point P, compute the horizontal
distance between P and the line y=mx+b.
 In the spreadsheet, compute the sum of the squares of those
horizontal distances.
 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)
 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
$\textcolor[rgb]{}{\frac{1}{p\cdot q\cdot r}=\frac{1}{p\cdot q\cdot (q+r)}+\frac{1}{p\cdot r\cdot (q+r)}}$$\textcolor[rgb]{}{}$$\textcolor[rgb]{}{\frac{\mathrm{}}{}}$
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=p^{2}  r^{2}
and z= p^{2} + r^{2})

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 ninepoint 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



