Master’s Thesis Research James P. Dildine, 1999

1. TECHNOLOGY-INTENSIVE INSTRUCTION WITH HIGH PERFORMING AND LOW PERFORMING MIDDLE SCHOOL MATHEMATICS STUDENTS Master’s Thesis Research James P. Dildine, 1999

2. Introduction • NCTM 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

3. 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.

4. 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.

5. 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;

6. 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

7. Two Classes • Algebra & Basic Math • Demographics

8. 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

9. 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.

10. 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

11. Survey Item Results • Percentages of favorable responses • More favorable responses on the post survey.

12. Achievement Results • Statistically Significant Gains for each class • Basic 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)

13. 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

14. 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

15. 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).

16. 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."

17. Snapshot 3 - Ashley’s 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”

18. Snapshot 4 - Michael • View 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

19. 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.

20. Snapshot 5 - Calculate Speed • Algebra students traced specific points to determine speed over an interval

21. 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

22. 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

23. 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?

24. 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?

25. Fin James P. Dildine, 1999