Putting Research into Action Annie Fetter Kristina Lasher Suzanne Alejandre. http://mathforum.org/workshops/uppermoreland/. Today we want to:. Do math Use technology Talk about professional development. Refer to best practices and research in each case.
Putting Research into Action
Refer to best practices and research in each case
There is some disagreement in the literature about the exact effects
of timing on retention, but it is generally accepted that timing
and sequencing matter with either the first or the most recent
information being most likely to be retained
Specifically, click on the books for classroom teachers link in
the description and then select Cooperative Math Books.
Students solving mathematical problems in small groups invokes three features that enhance the individual student’s cognitive (re)organization of mathematics:
1. The student experiences “challenge and disbelief” on the part of the other members of the group, which forces them to examine their own beliefs and strategies closely.
2. The group collectively provides background information, skills, and connections that a student may not have or understand.
3. The student might internalize some of the group’s problem solving. (Noddings, 1985)
How can research-based information support the shift from a yesterday mind to a tomorrow mindin the making of the many decisions as to how mathematics is taught or learned in the Upper Moreland School District?
Teaching and Learning Mathematics: Using Research to Shift from the “Yesterday” Mind to the “Tomorrow” Mind
Dr. Terry Bergeson,
State Superintendent of Public Instruction, Washington State
Jade's family is planning to travel to her Aunt Mazie's house to celebrate Aunt Mazie's 102nd birthday. On the first day of the trip they'll drive halfway there and then stop to set up camp for the night. On the second day of the trip they'll drive two-thirds of the remaining distance before stopping for some sightseeing and camping. On the last day they'll have 145 miles left to drive.
Question: How far is the trip to Aunt Mazie's house?
Extra: If the family averages 50 miles per hour while driving on the return trip, do you think the family will make the trip in one day? Why or why not?
Research about Fractions
Problem Solving: problem selection
1. The problem should be mathematically significant.
2. The context of the problem should involve real objects or obvious simulations of real objects.
3. The problem situation should capture the student’s interest because of the nature of the problem materials, the problem situation itself, the varied transformations the child can impose on the materials, or because of some combination of these factors.
4. The problem should require and enable the student to make moves, transformations, or modifications with or in the materials.
Most criteria apply to the full grade scale, K–12 (Nelson and Sawada, 1975).
Research on Communication
Students writing in a mathematical context helps improve their mathematical understanding because it promotes reflection, clarifies their thinking, and provides a product that can initiate group discourse (Rose, 1989).
Furthermore, writing about mathematics helps students connect different representations of new ideas in mathematics, which subsequently leads to both a deeper understanding and improved use of these ideas in problem solving situations (Borasi and Rose, 1989; Hiebert and Carpenter, 1992).
Interactive computing technologies enhance both the teaching and learning of mathematics. Great benefits occur if the technology’s power (1) is controllable by either the students or teachers, (2) is easily accessible in a way that enables student explorations, and (3) promotes student generalizations (Demana and Waits, 1990).
What does the research say about technology?
Focus on issues or concerns identified by the mathematics teachers themselves.
Be as close as possible to the mathematics teacher’s classroom environment.
Integrate opportunities for mathematics teachers to reflect, discuss, and provide feedback.
Give mathematics teachers a genuine sense of ownership of the activities and desired outcomes. (Lovitt et al., 1990)
Four key ingredients to math
research can be identified:• students• teachers• content• models
( Bergeson, 2000)
KEY INGREDIENT 1: The students trying to learn mathematics— consider their:
• maturity• intellectual ability• past experiences in mathematics• performances in mathematics• preferred learning styles • attitude toward mathematics • social adjustment
KEY INGREDIENT 2: The teachers trying to teach mathematics—consider their:
KEY INGREDIENT 3: The content of mathematics and its organization into a curriculum—consider its:
KEY INGREDIENT 4: The pedagogical models for presenting and experiencing this mathematical content — • use of optimal instructional techniques • design of instructional materials • use of multimedia and computing technologies • use of manipulatives • use of classroom grouping schemes • influences of • learning psychology • teacher requirements • role of parents and significant others • integration of alternative assessment techniques
Bergeson, Terry, Teaching and Learning Mathematics: Using Research to Shift from the “Yesterday” Mind to the “Tomorrow” Mind, Washington, 2000.
Borasi, R. and Rose, B. “Journal Writing and Mathematics Instruction.” Educational Studies in Mathematics, November 1989, 20: 347–365.
Demana, F. and Waits, B. “Enhancing Mathematics Teaching and Learning Through Technology.” In T. Cooney (ed.) Teaching and Learning Mathematics in the 1990s. Reston (VA): NCTM, 1990.
Hiebert, J. and Carpenter, T. “Learning and Teaching with Understanding.” In D. Grouws (ed.) Handbook of Research on Mathematics Teaching and Learning. New York: MacMillan, 1992.
Kieren, T. “Personal Knowledge of Rational Numbers: Its Intuitive and Formal Development.” In J. Hiebert and M. Behr (eds.) Number Concepts and Operations in the Middle Grades. Hillsdale (NJ): LEA, 1988.
Lovitt, C., Stephans, M., Clarke, D. and Romberg, T. “Mathematics Teachers Reconceptualizing Their Roles.” In T. Cooney (ed.) Teaching and Learning Mathematics in the 1990s. Reston (VA): NCTM, 1990.
Nelson, L. and Sawada, D. “Studying Problem Solving Behavior in Young Children—Some Methodological Considerations.” Alberta Journal of Educational Research, 1975, 21: 28–38.
Noddings, N. “Small Groups as a Setting for Research on Mathematical Problem Solving.” In E. Silver (ed.) Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives. Hillsdale (NJ): LEA, 1985.
Novillis, C. “An Analysis of the Fraction Concept into a Hierarchy of Selected Subconcepts and the Testing of the Hierarchical Dependencies.” Journal for Research in Mathematics Education, 1976, 7: 131–144.
Novillis, C. “Seventh-Grade Students’ Ability to Associate Proper Fractions with Points on the Number Line.” In T. Kieren (ed.) Recent Research on Number Learning. Columbus (OH): ERIC Clearinghouse, 1980.
Ohlsson, S. “Mathematical Learning and Applicational Meaning in the Semantics of Fractions and Related Concepts.” In J. Hiebert and M. Behr (eds.) Number Concepts and Operations in the Middle Grades. Hillsdale (NJ): LEA, 1988.
Rose, B. “Writing and Mathematics: Theory and Practice.” In P. Connolly and T. Vilardi (eds.) Writing to Learn Mathematics and Science. New York: Teachers College Press, 1989.