TECHNOLOGY-INTENSIVE INSTRUCTION WITH HIGH PERFORMING AND LOW PERFORMING MIDDLE SCHOOL MATHEMATICS STUDENTS

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TECHNOLOGY-INTENSIVE INSTRUCTION WITH HIGH
PERFORMING AND LOW PERFORMING MIDDLE SCHOOL
MATHEMATICS STUDENTS

• Masters Thesis Research
• James P. Dildine, 1999

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Introduction

• NCTM recommends Utilizing technology to help all
  students learn mathematics.
• PCAST- Presidents Report on Technology in
  Education
• Learn through not the technology
• Equitable Universal Access
• Calculators put hand-held technology in all
  students hands

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Background Literature

• Steele-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.

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Background Literature

• Mevarech 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.

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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

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Research Design

• Technology Intensive Instruction in Middle School
  classrooms
• Two weeks of instruction
• Two 8th grade Math classes Basic, Algebra
• Equipment TI-82 and CBR
• Activities reading and interpreting information
  from graphs while learning about rate

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Two Classes

• Algebra Basic Math
• Demographics

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Equipment

• TI - 82 Graphing Calculator
• CBR - 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

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Instructional Activities

• Match-the-graph
• Students are presented with a graph and expected
  to match the shape of that graph by directing
  walker properly
• Match-your-graph
• Students create their own graph on paper and
  attempt to recreate it on the equipment
• Determine speed
• Students measure the change in distance over an
  interval vs. change in time.

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Data Collection

• Survey Items - Attitudes toward mathematics and
  technology
• Achievement Items - Items about knowledge of
  reading graphs and determining rate
• Classroom observations/Videos
• Interview of 4 students (each class) 3 each as
  case studies

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Survey Item Results

• Percentages of favorable responses
• More favorable responses on the post survey.

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Achievement Results

• Statistically Significant Gains for each class
• Basic Math Mean 3.53 to 4.27
• (p.02, t2.32, df14)
• Algebra Mean 8.32 to 9.11
• (p.01, t2.80, df18)

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Observations Basic Math Class

• Students actively participating
• Collaborative 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

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Observations Algebra Class

• Students 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

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Snapshot 1-Big Ideas

• Horizontal Line - No movement. Change in x but
  no change in y
• Dip 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).

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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."

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Snapshot 3 - Ashleys Bus Trip

• Math 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

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Snapshot 4 - Michael

• View of math review/useless
• in high school you do lots of algebraic word
  problems or something, and some of that youll
  never use in your life
• Chalk-Board Explanation

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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.

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Snapshot 5 - Calculate Speed

• Algebra students traced specific points to
  determine speed over an interval

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Conclusions - What did this Tell Me?

• Basic Mathematics Students were able to handle
  the technology and concepts
• Lowest tracked students performed very well
  within this type of instruction
• Most Students were motivated to learn the
  material.
• Each class attained conceptual knowledge
• Evidence of more positive attitudes during
  instruction

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Limitations

• May not generalize beyond these classes
• Achievement tests were limited to ten items and
  may not have linked directly with instruction
• Survey items may need better selection

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Implications Recommendations

• Pilot 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?

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Further Study

• More classes
• More time necessary with technology instruction -
  novelty of research environment
• More concepts
• Transfer of concepts - Do the students use the
  knowledge they may have gained later?
• Do the students retain the positive attitudes
  they may have exhibited?

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Fin

• James P. Dildine, 1999