TECHNOLOGY-INTENSIVE INSTRUCTION WITH HIGH PERFORMING AND LOW

PERFORMING MIDDLE SCHOOL MATHEMATICS STUDENTS

Master’s Thesis ResearchJames P. Dildine, 1999

IntroductionNCTM recommends Utilizing

technology to help all students learn mathematics.

PCAST- President’s Report on Technology in Education– Learn through not the technology– Equitable Universal Access

Calculators put hand-held technology in all students’ hands

Background LiteratureSteele-academic disidentification, “process

that occurs when people stop caring about their performance in an area, or domain that formerly mattered a great deal.”

Hill- “many intrinsic qualities of a traditional mathematics classroom offer motives for student disidentification from mathematics.”

Oakes-Low tracked classes require more rote memorization and less critical thinking than high tracked classes where teachers pursue understanding of complex themes.

Background LiteratureMevarech and Kramarsky (1997) report that

graphing involves interpretation - the ability to read a graph and gain meaning from it - and construction - building a graph from data or points.

NCTM Emphases include- appropriate calculators should be available to all students at all

times; a computer should be available in every classroom for

demonstration purposes; every student should have access to a computer for individual

and group work; Students should learn to use a computer as a tool for processing

information and performing calculations to investigate and solve problems.

Students using graphing technology

Dunham-review of calculator research (1993)

Students who use graphing calculator technology- can better read and interpret graphical information; obtain more information from graphs; have greater overall achievement on graphing items; are better at finding an algebraic representation for a graph better understand global features of functions; better understand connections among graphical, numerical, and

algebraic representations; had more flexible approaches to problem solving, were more

willing to engage in problem-solving and stayed with a problem longer; and

concentrated on math problems and not on algebraic manipulation;

Research DesignTechnology Intensive Instruction

in Middle School classroomsTwo weeks of instructionTwo 8th grade Math classes:

Basic, AlgebraEquipment: TI-82 and CBRActivities reading and

interpreting information from graphs while learning about rate

Two ClassesAlgebra & Basic MathDemographics

Basic Math Algebra

Male Female Totals Percent Male Female Totals PercentWhite 5 11 16 70 6 8 14 74Black 4 2 6 26 1 1 2 10.5Latino/a 1 0 1 4 0 0 0 0Asian 0 0 0 0 2 0 2 10.5Mid Eastern 0 0 0 0 1 0 1 5Totals 10 13 23 100 10 9 19 100Percent 43 57 100 53 47 100

Equipment

TI - 82 Graphing CalculatorCBR - Calculator Based Ranger

- Connects to calculator to act as a real-time data collection device

Distance a walker is away from sensor is plotted as a graph of distance v. time on calculator

Instructional ActivitiesMatch-the-graph

– Students are presented with a graph and expected to match the shape of that graph by directing walker properlyMatch-your-graph

– Students create their own graph on paper and attempt to recreate it on the equipmentDetermine speed

– Students measure the change in distance over an interval vs. change in time.

Data CollectionSurvey Items - Attitudes toward

mathematics and technologyAchievement Items - Items

about knowledge of reading graphs and determining rate

Classroom observations/Videos Interview of 4 students (each

class) 3 each as case studies

Survey Item ResultsPercentages of favorable responsesMore favorable responses on the post survey.

Achievement ResultsStatistically Significant Gains

for each classBasic Math Mean: 3.53 to 4.27

– (p=.02, t=2.32, df=14)Algebra Mean: 8.32 to 9.11

– (p=.01, t=2.80, df=18)

Observations: Basic Math ClassStudents actively participatingCollaborative learning environment

promoted negotiation and exploration

Students presented what they discovered and explored ideas

Related activities beyond classroom: Transfer of meters/second to miles/hour

Difficulty identifying specific points

Observations: Algebra ClassStudents worked together in

groups but consistently worked individually on the activities

Attempted to make graphs that were not possible (vertical lines)

Also transferred graphing ideas to situation beyond the classroom

Most were able to use specific end points to determine average speed over an interval

Snapshot 1-Big IdeasHorizontal Line - No movement. Change in x but no change in yDip and Peak-Represent points where walker stopped and changed direction.

Indicate specific point where no change in y (distance) but brief change in x (time).Vertical line - Not possible - requires enormous change in y (distance) with little or

no change in x (time).

Snapshot 2-Basic Math Group"woman backs up for a few feet. pauses, switches into drive, and

pulls forward for about half the distance. Pauses again and backs up a few more feet, pauses again and pulls all the way out and drives off."

Snapshot 3 - Ashley’s Bus TripMath: Boring but important to

consumers• "Going to the store, yes. Like seeing if the person

gives you the right amount of change." Evidence of identifying with ideas

• "It was fun and I think the school should get some of those calculators.”

•Now: “I think about the bus like a graph”

Snapshot 4 - MichaelView of math: review/useless

• in high school you do lots of algebraic word problems or something, and some of that you’ll never use in your life

Chalk-Board Explanation

= moving away from the motion sensor

and

= back toward the sensor

Snapshot 4 - Algebra “Cheats”Vertical Line - impossible to create“We can make it”“We just need to find a way that makes

large distance changes in almost no time”

Example of a “cheat”, student jumping in and out of the range of the sensor.

Snapshot 5 - Calculate SpeedAlgebra students traced specific points

to determine speed over an interval

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131

5.65.

5.105.160.25.2

Start TimeFinish TimeStart DistanceEnd Distance

Conclusions - What did this Tell Me?Basic Mathematics Students were able to “handle” the technology and conceptsLowest tracked students performed very well within this type of instructionMost Students were motivated to learn the material.Each class attained conceptual knowledgeEvidence of more positive attitudes during instruction

LimitationsMay not generalize beyond these classesAchievement tests were limited to ten items and may not

have linked directly with instructionSurvey items may need better selection

Implications & RecommendationsPilot included instruction to teachers and preservice teachers - can they

use this type of instruction in their classrooms?When and at What level should graphing concepts be introduced?Are lower tracked classes capable of learning complex concepts in this

environment?

Further StudyMore classesMore time necessary with technology instruction - novelty of research environmentMore conceptsTransfer of concepts - Do the students use the knowledge they may have gained later?Do the students retain the positive attitudes they may have exhibited?

Fin

James P. Dildine, 1999