High School and
Middle School Mathematica

Abby Brown
and Helen Papadopoulos, Austin Pogue, and Edward Zhu

Torrey Pines High School
San Diego, California

High School and Middle School Mathematica

Background

Introducing Mathematica to Students

Introducting Mathematica to Teachers

Advanced Topics in Mathematics II Class (High School)

Student Presentations

Math X Class (Middle School)

My Mathematica

Concluding Thoughts

Background

Mathematica in College

Mathematica in Teaching

Sharing Materials Online

Connected with Wolfram: Conferences, Learning Opportunities, Partnerships

Project-Based Classes

How I use Mathematica in Teaching

Calculations, Graphs, Create Problems

Solve[{3x+2y-5z==4,-2x+z==5,4x-y+6z==3},{x,y,z}]

Plot3D[Flatten@Map[(z/.Solve[#,z])&,{3x+2y-5z==4,-2x+z==5,4x-y+6z==3}],{x,-15,15},{y,-15,15},BoxRatios->{1,1,2}]

Lecture Notes Examples

a[n_]:=1/2^n;

terms=20;

Row[{
seqplotA=ListPlot[Table[{n,a[n]},{n,1,terms}],PlotStyle->{PointSize[0.03],Hue[0.65]},AxesOrigin->{0,0},PlotRange->All,PlotLabel->StyleForm[StringJoin["Sequence Plot ",ToString[TraditionalForm[a[n]]]],FontWeight->"Bold",FontSize->20],ImageSize->350],"      ",

sumplotA=ListPlot[Table[{m,Sum[a[n],{n,1,m}]},{m,1,terms}],PlotStyle->{PointSize[0.03],Hue[0]},PlotRange->All,AxesOrigin->{0,Automatic},PlotLabel->StyleForm[StringJoin["Series Plot ",
ToString[TraditionalForm[HoldForm[Sum[seq,{n,1,Infinity}]]]/.seq->a[n]]],FontWeight->"Bold",FontSize->20],ImageSize->350]
}]

Guided Computer Lab Lessons

Import["C:\\Users\\Torrey Pines 1\\Desktop\\IMUC 2008\\Presentation Files\\PolarGraphing.pdf"][[1]]

Web Site Materials

Student Presentations

Student Projects

Introducing Mathematica to Students

Oooo's and Ahhh's

First hands-on experiences: Cool, but frustrating

Common Issues: Caps, Cursors, Coding

Common Experiments

Plot[x^2 y^2+z^2=16,{x,0,10}]

N[Pi,100000000]

my name is abby brown

Manipulate and Demonstrations

Finding Balance Between Mathematica and Mathematics

Teaching with Small Examples

Buttons in Manipulate

Source

Introducing Mathematica to Teachers

Initial Reaction

Stunned Silence

Secondary Reaction

Oooo's and Ahhh's

Reflex Reaction

Fear and Panic

Thoughful Reaction

Wow! This will change everything!

Common Challenges

Understanding what they are seeing

Understanding what I do and what the computer does

Good with specific directions, but slow with technolgy

Afraid of experimentation

Uncomfortable with coding, Looking for templates

How much there is to learn

Common Concerns

Money, Time,  Availabiliy of technology, Knowing what is available

Advanced Topics in Mathematics II Class (High School)

Started in 2006-2007 School Year

Project-Based Course: Math, Interdisciplinary, Research, and Community Service

Students' Backgrounds

Student Presentations

Austin: High School Student Projects

Helen: Calculus and Geometry Demonstrations

Edward: Math Club Applications and Recreation

Advanced Topics in Mathematics II Class

www.MathematiClub.com

More Examples

Coordinate Systems

Art Paper

Pi Day: Pie and Pi Digits Visualization

Physics Application

Music Generator

Arithematica

Mathematicourt

Interactive Triangle Trig

Upcoming Activities

Math X Class (Earl Warren Middle School)

Started in 2007-2008 School Year

Project-Based Course: Exploring a Larger World of Math

Students' Backgrounds

Mathematica drove the Mathematics

"Math drives Mathematica, but Mathematica drives math."
                                                                         -- Conrad Wolfram

Math X Class - Example Projects

Early Graphics

House

Functions as Paths

Scubaman

River Rafting

City Project

City Project

Amusement Park

Tea Cups

Spinning Swings

Shooting Gallery

Ticket Booths

Skull of Terror

http://math.sduhsd.net/MathX

My Mathematica

Models for Class

Partial Derivatives

Taylor Polynomials

Fun Examples for Students

Module[{f,maxnum,polybird,shiftlist,sizelist},
f[x_]:=Sin[x];
maxnum=25;
polybird=Polygon[{{-1,-1},{0,1},{1,-1},{0,0}}];
shiftlist=Table[RandomReal[{-8,8},2],{maxnum}];
sizelist=RandomReal[{0.2,2},maxnum];
Manipulate[Show[
If[showpath,Plot[f[x],{x,-10,10}],{}],
Graphics[{
Table[
{Hue[n/5],Opacity[0.5],Scale[Translate[Rotate[polybird,ArcTan[f'[x0-shiftlist[[n,1]]]]-Pi/2],{x0+shiftlist[[n,1]],f[x0+shiftlist[[n,1]]]+shiftlist[[n,2]]}],2sizelist[[n]]]},
{n,1,nmax,1}]
}],Axes->showpath,PlotRange->15,AspectRatio->Automatic],
{{x0,-maxnum-1,"position"},-maxnum-1,maxnum+1,Animator,AnimationRate->5},{{showpath,False,"show path"},{True,False}},
{{nmax,15,"number"},1,maxnum,1},
Row[{Button["new random values",shiftlist=Table[RandomReal[{-8,8},2],{maxnum}];sizelist=RandomReal[{0.2,2},maxnum];]}]
]]

Mathematica Lessons

Pure Functions

Web Sites

www.abbymath.com

Demonstrations

Protractor Practice

NFL Quarterback Passer Rating

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Concluding Thoughts

Students and Teachers

Students who get past initial frustration enjoy Mathematica

Teachers need time and training

Mathematica in My Classroom

Visualization

Multiple Representations

Changed Conversations

Experimentation

Generalization and Automation

Interest in Mathematics

High School and Middle School Mathematica

Abby Brown and Helen Papadopoulos, Austin Pogue, and Edward Zhu

www.abbymath.com