Linear Algebra meets the Web

							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
  elect to take Advanced
  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
                              equations in traditional
                            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
    also complete a questionnaire asking questions about
    algebra. Students also completed a table to determine,
    room assignment, gender and a question to determine
    whether students were ready to start algebra instruction.
    Sat9 scores from 5th grade will be added by the teacher.
   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
    utilize the overhead projector
    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
    Institution/National Academies.
   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.