Linear Algebra meets Linear Algebra meets the Webthe Web

Video Footage to FollowVideo Footage to Follow

QuestionQuestion

The purpose of this study The purpose of this study is to determine whether is to determine whether students will apply students will apply knowledge of algebra knowledge of algebra acquired in teacher acquired in teacher directed instruction, to directed instruction, to effectively solve real effectively solve real world problems when world problems when given the opportunity to given the opportunity to make web pages and make web pages and video of their solutions.video of their solutions.

Prior KnowledgePrior Knowledge

Constructivist Approach with real world Constructivist Approach with real world problemsproblems

Flies in the Face of Todd Oppenheimer’s Flies in the Face of Todd Oppenheimer’s beliefs on technologybeliefs on technology

Roy Pea is happy with our use of Roy Pea is happy with our use of affordances in the form of calculators and affordances in the form of calculators and computers to aid calculation and the forming computers to aid calculation and the forming of the web pagesof the web pages

ResearchResearch

The TIMSS study show that internationally The TIMSS study show that internationally higher order math skills are taught earlier and higher order math skills are taught earlier and with more rigor than programs in the U.S.with more rigor than programs in the U.S.

StatsStats Only 1 percent of U.S. Only 1 percent of U.S.

high school seniors high school seniors elect to take Advanced elect to take Advanced Placement calculus. Placement calculus.

We cannot as a nation We cannot as a nation depend on the math depend on the math abilities of only 1% of abilities of only 1% of the populationthe population

SolveSolve

Car Loan Calculation Problem Based learning guide on Car Buying

ni

ip

M

1211

12

•M= monthly payments

•P=amount borrowed

•i= interest rate

•N= number of payments

•Find M when

•P= 15,000

•i= 7.5%

•N= 60

P= 15,000 i= 7.5% N= 60

75.9312

075.000,15

ni

ip

M

1211

12

311908.88091824.61

1.00625)(1)12

075.1(1 6060

5692.300311908.

75.93M

Learning By TeachingLearning By Teaching

Students are given basic instruction in Linear Students are given basic instruction in Linear AlgebraAlgebra

Students then work out solutions to common Students then work out solutions to common everyday problems that could be solved with everyday problems that could be solved with basic linear equations.basic linear equations.

They create video’s of verbal instructions as They create video’s of verbal instructions as well as well as web pages web pages containing similar containing similar instructions giving their solutions a multiple instructions giving their solutions a multiple learning styles twistlearning styles twist

ResearchResearch

Bandlow’s and the TIMSS database show that US Bandlow’s and the TIMSS database show that US students study algebra at a later age than foreign students study algebra at a later age than foreign students and fewer of the them go onto higher levels students and fewer of the them go onto higher levels of mathmatics.of mathmatics.

Starting sixth grade students on basic algebra Starting sixth grade students on basic algebra concepts is therefore not cognitively out of their reach concepts is therefore not cognitively out of their reach since students their age and younger already study since students their age and younger already study algebra routinely in other countries.algebra routinely in other countries.

Focus GrasshopperFocus Grasshopper

Will having students create algebra solutions for everyday Will having students create algebra solutions for everyday problems and then building WebPages and video problems and then building WebPages and video explainingexplaining how to use the algebra solutions to their peers increase how to use the algebra solutions to their peers increase student abilities to use linear equations to solve other student abilities to use linear equations to solve other problems?problems?

If students read webpage instructions and watch video If students read webpage instructions and watch video explanations of how to do linear equations created by other explanations of how to do linear equations created by other students, will this increase their ability to solve word problems students, will this increase their ability to solve word problems using linear equations?using linear equations?

Will students better understand algebra concepts after having Will students better understand algebra concepts after having created web page and video that give the solutions to common created web page and video that give the solutions to common everyday problems?everyday problems?

Are the technology tools sufficiently mature Are the technology tools sufficiently mature to allow students to easily build WebPages to allow students to easily build WebPages and create video explanations of algebra and create video explanations of algebra solutionssolutions

Students create video instructionsStudents create video instructions

VariablesVariables

Independent VariableStudents will be able to apply knowledge of linear

equations to real world problems through video and web creation.

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

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.

Dependent VariableLearning how to work linear

equations in traditional lecture- based classroom

AssessmentAssessment

QuestionnaireQuestionnaire All students were given a All students were given a LikertLikert- style questionnaire. - style questionnaire. The questionnaire queried student The questionnaire queried student perception of success for math in general and specific math perception of success for math in general and specific math concepts. Student response choice was: Never, concepts. Student response choice was: Never, Sometimes, Most of the Time and Always. Students will Sometimes, Most of the Time and Always. Students will also complete a questionnaire asking questions about also complete a questionnaire asking questions about algebra. Students also completed a table to determine, algebra. Students also completed a table to determine, room assignment, gender and a question to determine room assignment, gender and a question to determine whether students were ready to start algebra instruction. whether students were ready to start algebra instruction. Sat9 scores from 5th grade will be added by the teacher.Sat9 scores from 5th grade will be added by the teacher.

Pretest / PosttestPretest / Posttest : All students will be given a pre-algebra : All students will be given a pre-algebra test written by middle school teachers to determine how test written by middle school teachers to determine how well students compute algebraic equations. The test is not well students compute algebraic equations. The test is not timed. Students could use no calculators during the test. timed. Students could use no calculators during the test.

InstructionInstruction Initially, all students will have Initially, all students will have

teacher directed instruction, in teacher directed instruction, in a lecture format that outlines a lecture format that outlines the basic methods of solving the basic methods of solving problems using linear problems using linear equations. The teacher will equations. The teacher will utilize the overhead projector utilize the overhead projector and the student text to present and the student text to present information. information.

The National Council for The National Council for Teachers of Mathematics Teachers of Mathematics agrees that in order to make agrees that in order to make connections, students must connections, students must have activities such as have activities such as translating verbal information translating verbal information into symbolic expressions and into symbolic expressions and equations that often involve equations that often involve functions. (NCTM)functions. (NCTM)

TimelineTimeline

Timeline

Week 1-3Basic Instruction on

Linear Equations

Week 4-8 work on simple Word problems and build

web pages and videos

Week 9 student review andEdit each others work

ResourcesResources

Math bookMath book Students white boards Students white boards supplies for writingsupplies for writing

Internet Service Internet Service ProviderProvider

Digital/Video cameraDigital/Video camera 13 computers13 computers WORDWORD FrontPageFrontPage Windows Movie MakerWindows Movie Maker iMoviesiMovies

DataData

Sampling method would be Comprehensive using Sampling method would be Comprehensive using both of our two classes.both of our two classes.

Data collected would be a survey on what algebra Data collected would be a survey on what algebra is and what it is used for. This survey will be is and what it is used for. This survey will be informational in looking at individual results. informational in looking at individual results.

A Empire Union school district multiple measure A Empire Union school district multiple measure test will be given as a pre and post test to all test will be given as a pre and post test to all students. students.

We will also look at last years algebra test and Sat We will also look at last years algebra test and Sat 9 scores in the Algebra area and data collected in 9 scores in the Algebra area and data collected in the world research project called TIMSS. the world research project called TIMSS.

The TIMSS data will allow us to compare our The TIMSS data will allow us to compare our students with those in the world.students with those in the world.

Go for GoldGo for Gold Each group will have a leader that is trained to save web files into Each group will have a leader that is trained to save web files into

the appropriate folder on our network. the appropriate folder on our network. The other student tasks will be video production, web animations, The other student tasks will be video production, web animations,

and editing text and equations on the web pages. Everyone in the and editing text and equations on the web pages. Everyone in the group needs to have a definitive job that they are held group needs to have a definitive job that they are held accountable for in building their overall instruction set. accountable for in building their overall instruction set.

The management of these groups is crucial to the study as this is The management of these groups is crucial to the study as this is the first place that peer to peer instruction will be utilized the first place that peer to peer instruction will be utilized intensively.intensively.

Students will teach others in their group how to create and save Students will teach others in their group how to create and save web pages. web pages.

At this time peer tutoring in basic areas has been shown to greatly At this time peer tutoring in basic areas has been shown to greatly enhance learning (ALLSOPP)enhance learning (ALLSOPP)

They will become the teachers for their groups and the groups. They will become the teachers for their groups and the groups. Students will instruct the rest of the class.Students will instruct the rest of the class. Each group will choose a real world problem. Students will solve Each group will choose a real world problem. Students will solve

this problem using a linear equation.this problem using a linear equation.

Step 2Step 2

Students will teach others in Students will teach others in their group how to create and their group how to create and save web pages. save web pages.

At this time peer tutoring in basic At this time peer tutoring in basic areas has been shown to greatly areas has been shown to greatly enhance learning (ALLSOPP). enhance learning (ALLSOPP).

They will become the teachers They will become the teachers for their groups and the groups for their groups and the groups will teach the rest of the class. will teach the rest of the class.

I believe the use of video will I believe the use of video will engage students and encourage engage students and encourage them to refine the instruction of them to refine the instruction of others in order to produce a others in order to produce a clear and concise video clear and concise video explanation using the equation explanation using the equation they create. they create.

Discrete SkillsDiscrete Skills My job will be to make sure I have helped My job will be to make sure I have helped

them get all the mini skills that help build the them get all the mini skills that help build the equations. Praziale’s modeling of equations. Praziale’s modeling of sequencing skills that build and interconnect sequencing skills that build and interconnect with each other seems to exactly fit the with each other seems to exactly fit the model I am building (Praziale 97). model I am building (Praziale 97).

Having done previous assessments on Having done previous assessments on students we will setup objectives that help students we will setup objectives that help them learn what they need to know in the them learn what they need to know in the way of discrete mathematical skills. way of discrete mathematical skills.

We will compare this phase with a pre and We will compare this phase with a pre and post test taken in my class and my partner’s post test taken in my class and my partner’s class who is not using computer based class who is not using computer based instruction. instruction.

Many researchers have found that 6th grade Many researchers have found that 6th grade students aren’t ready for algebra yet in other students aren’t ready for algebra yet in other countries algebra is a standard subject. The countries algebra is a standard subject. The difference is thought to be preparation and difference is thought to be preparation and instruction (Bandlow 69) .instruction (Bandlow 69) .

Problem based learning involves students answering Problem based learning involves students answering question of real world applications and a choice in what question of real world applications and a choice in what they are trying to solve. they are trying to solve.

Both of these ideas go along with the only programs that Both of these ideas go along with the only programs that have shown strength and rigorous review of experts, "Full have shown strength and rigorous review of experts, "Full Option Science System," developed by the Lawrence Hall Option Science System," developed by the Lawrence Hall of Science, University of California-Berkeley, and "Science of Science, University of California-Berkeley, and "Science and Technology Concepts for Middle School," developed by and Technology Concepts for Middle School," developed by the National Science Resources Center, Smithsonian the National Science Resources Center, Smithsonian Institution/National Academies. Institution/National Academies.

These two systems use an inquiry centered activities with These two systems use an inquiry centered activities with fewer topics covered in direct instruction (Bandlow). fewer topics covered in direct instruction (Bandlow).

My hope is two fold in the area of web page My hope is two fold in the area of web page publishing. One, I believe that knowing that others publishing. One, I believe that knowing that others are going to be reading and watching their work, are going to be reading and watching their work, students will conscientiously review and edit their students will conscientiously review and edit their work. Therefore students will be conscious of the work. Therefore students will be conscious of the fact that their equations work and that their fact that their equations work and that their instructions are easily understood. This should instructions are easily understood. This should lead to an internalization of information and skills lead to an internalization of information and skills (Parizale 96). This leads to my second goal being (Parizale 96). This leads to my second goal being that they will get a cross curricular benefit in that they will get a cross curricular benefit in writing. Student writing in mathematics is a sorely writing. Student writing in mathematics is a sorely overlooked area.overlooked area.

http://imet.csus.edu/imet4/god/Algebra/index.htm