# Linear Algebra meets the Web

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```							Linear Algebra meets
the Web
Video Footage to Follow
Question
   The purpose of this study
is to determine whether
students will apply
knowledge of algebra
acquired in teacher
directed instruction, to
effectively solve real
world problems when
given the opportunity to
make web pages and
video of their solutions.
Prior Knowledge

   Constructivist Approach with real world
problems
   Flies in the Face of Todd Oppenheimer’s
beliefs on technology
   Roy Pea is happy with our use of
affordances in the form of calculators and
computers to aid calculation and the forming
of the web pages
Research
 The TIMSS study show that internationally
higher order math skills are taught earlier and
with more rigor than programs in the U.S.
Stats
 Only 1 percent of U.S.
high school seniors
Placement calculus.
 We cannot as a nation
depend on the math
abilities of only 1% of
the population
Solve

 i               •M= monthly payments

p                 •P=amount borrowed

M        12              •i= interest rate
•N= number of payments
n
     i             •Find M when

1  1                 •P= 15,000

 12 
•i= 7.5%
•N= 60

Car Loan Calculation
Problem Based learning guide on Car Buying
P= 15,000 i= 7.5% N= 60

 i 
.075
p                 15,000        93.75
 12                        12
M               n
     i 
1  1                    .075 60             60
 12          1  (1      )  1  (1.00625) 
12
1  6.88091824  .311908

93.75
M          300.5692
.311908
Learning By Teaching

   Students are given basic instruction in Linear
Algebra
   Students then work out solutions to common
everyday problems that could be solved with
basic linear equations.
   They create video’s of verbal instructions as
well as web pages containing similar
instructions giving their solutions a multiple
learning styles twist
Research

   Bandlow’s and the TIMSS database show that US
students study algebra at a later age than foreign
students and fewer of the them go onto higher levels
of mathmatics.
   Starting sixth grade students on basic algebra
concepts is therefore not cognitively out of their reach
since students their age and younger already study
algebra routinely in other countries.
Focus Grasshopper

   Will having students create algebra solutions for everyday
problems and then building WebPages and video explaining
how to use the algebra solutions to their peers increase
student abilities to use linear equations to solve other
problems?
   If students read webpage instructions and watch video
explanations of how to do linear equations created by other
students, will this increase their ability to solve word problems
using linear equations?
   Will students better understand algebra concepts after having
created web page and video that give the solutions to common
everyday problems?
   Are the technology tools sufficiently mature
to allow students to easily build WebPages
and create video explanations of algebra
solutions
Students create video instructions
Independent Variable
Students will be able to apply knowledge of linear
equations to real world problems through video and
web creation.

Research Problem: It is the purpose of this study to determine the effects of
student video and web page creation on the understanding and application of
linear equations to real world problems.

Hypothesis: The use of student created video        and web pages will improve
the understanding and application of linear equations to real world problems.

Dependent Variable
Learning how to work linear
lecture- based classroom

Variables
Assessment
   Questionnaire All students were given a Likert- style
questionnaire. The questionnaire queried student
perception of success for math in general and specific math
concepts. Student response choice was: Never,
Sometimes, Most of the Time and Always. Students will
algebra. Students also completed a table to determine,
room assignment, gender and a question to determine
whether students were ready to start algebra instruction.
   Pretest / Posttest : All students will be given a pre-algebra
test written by middle school teachers to determine how
well students compute algebraic equations. The test is not
timed. Students could use no calculators during the test.
Instruction
   Initially, all students will have
teacher directed instruction, in
a lecture format that outlines
the basic methods of solving
problems using linear
equations. The teacher will
and the student text to present
information.
   The National Council for
Teachers of Mathematics
agrees that in order to make
connections, students must
have activities such as
translating verbal information
into symbolic expressions and
equations that often involve
functions. (NCTM)
Timeline

Timeline

Week 1-3          Week 4-8 work on simple
Week 9 student review and
Basic Instruction on   Word problems and build
Edit each others work
Linear Equations       web pages and videos
Resources

   Math book                  Internet Service
   Students white boards       Provider
   supplies for writing       Digital/Video camera
   13 computers
   WORD
   FrontPage
   Windows Movie Maker
   iMovies
Data
   Sampling method would be Comprehensive using
both of our two classes.
   Data collected would be a survey on what algebra
is and what it is used for. This survey will be
informational in looking at individual results.
   A Empire Union school district multiple measure
test will be given as a pre and post test to all
students.
   We will also look at last years algebra test and Sat
9 scores in the Algebra area and data collected in
the world research project called TIMSS.
   The TIMSS data will allow us to compare our
students with those in the world.
Go for Gold
   Each group will have a leader that is trained to save web files into
the appropriate folder on our network.
   The other student tasks will be video production, web animations,
and editing text and equations on the web pages. Everyone in the
group needs to have a definitive job that they are held
accountable for in building their overall instruction set.
   The management of these groups is crucial to the study as this is
the first place that peer to peer instruction will be utilized
intensively.
   Students will teach others in their group how to create and save
web pages.
   At this time peer tutoring in basic areas has been shown to greatly
enhance learning (ALLSOPP)
   They will become the teachers for their groups and the groups.
   Students will instruct the rest of the class.
    Each group will choose a real world problem. Students will solve
this problem using a linear equation.
Step 2
   Students will teach others in
their group how to create and
save web pages.
   At this time peer tutoring in basic
areas has been shown to greatly
enhance learning (ALLSOPP).
   They will become the teachers
for their groups and the groups
will teach the rest of the class.
   I believe the use of video will
engage students and encourage
them to refine the instruction of
others in order to produce a
clear and concise video
explanation using the equation
they create.
Discrete Skills
   My job will be to make sure I have helped
them get all the mini skills that help build the
equations. Praziale’s modeling of
sequencing skills that build and interconnect
with each other seems to exactly fit the
model I am building (Praziale 97).
   Having done previous assessments on
students we will setup objectives that help
them learn what they need to know in the
way of discrete mathematical skills.
   We will compare this phase with a pre and
post test taken in my class and my partner’s
class who is not using computer based
instruction.
   Many researchers have found that 6th grade
students aren’t ready for algebra yet in other
countries algebra is a standard subject. The
difference is thought to be preparation and
instruction (Bandlow 69) .
   Problem based learning involves students answering
question of real world applications and a choice in what
they are trying to solve.
   Both of these ideas go along with the only programs that
have shown strength and rigorous review of experts, "Full
Option Science System," developed by the Lawrence Hall
of Science, University of California-Berkeley, and "Science
and Technology Concepts for Middle School," developed by
the National Science Resources Center, Smithsonian
   These two systems use an inquiry centered activities with
fewer topics covered in direct instruction (Bandlow).
   My hope is two fold in the area of web page
publishing. One, I believe that knowing that others
are going to be reading and watching their work,
students will conscientiously review and edit their
work. Therefore students will be conscious of the
fact that their equations work and that their
instructions are easily understood. This should
lead to an internalization of information and skills
(Parizale 96). This leads to my second goal being
that they will get a cross curricular benefit in
writing. Student writing in mathematics is a sorely
overlooked area.

```
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