The Math Forum @ Drexel - mathforum.org Putting Research into Action Annie Fetter Kristina Lasher Suzanne Alejandre

The Math Forum @ Drexel - mathforum.org

Putting Research into Action

Annie FetterKristina 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


Brain ResearchPrimacy-Recency Effect

• Learn BEST-The FIRST

• Learn LEAST-Just Past the MIDDLE (down time)

• Learn NEXT Best-The LAST

There is some disagreement in the literature about the exact effectsof 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


Activity from Reason Together: Compare, Estimate & Refine

• Each cooperative group agrees on estimates• Record in 1st column• Clues are read aloud to groups• Groups discuss and refine estimates• Record in 2nd column• Computation clue(s) is read aloud to groups• Groups discuss and refine estimates• Record in 3rd column• Final clues are given • Groups assess the information and record their final answer in 4th

column


This resource is cataloged in the Math Forum Internet

Mathematics Library

http://mathforum.org/library/view/65118.html

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 mind in the making of the many decisions as to how mathematics is taught or learned in the Upper Moreland School District?


What can research do?

• It can inform us• It can educate us• It can answer questions• It can prompt new questions• It can create reflection and discussion• It can challenge what we currently do as

educators• It can clarify educational situations• It can help make educational decisions and

policy


Research can also fall short

• It can confuse situations• It can focus on everything but your situation• It can be hidden by its own publication style• It can be flawed• It can be boring and obtuse

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


If we think of the many things that can be investigated in mathematics education; it is easy to be overwhelmed.


Birthday Trip 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• Unlike the situation of whole numbers, a major source

of difficulty for students learning fractional concepts is the fact that a fraction can have multiple meanings—part/whole, decimals, ratios, quotients, or measures (Kieren, 1988; Ohlsson, 1988).

• Student understandings of fractions are very rote, limited, and dependent on the representational form. (Novillis, 1976). Though able to form equivalents for a fraction, students often do not associate the fractions 1/3 and 2/6 with the same point on a number line (Novillis, 1980).


Problem Solving: problem selection1. 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.

5. Whenever possible, problems should be chosen that offer opportunities for different levels of solutions.

6. Finally, students should be convinced that they can solve the problem and should know when they have a solution for it.

Most criteria apply to the full grade scale, K–12 (Nelson and Sawada, 1975).


Research on CommunicationStudents 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).


Using Technology: Triangles

•Adapted from The Geometer’s Sketchpad

•converted into “Java GSP” files

•introductory and advanced handouts

http://mathforum.org/workshops/uppermoreland/triangletypes.handout.html


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?


Professional Development1. Focus on issues or concerns identified by the

mathematics teachers themselves.

2. Be as close as possible to the mathematics teacher’s classroom environment.

3. Integrate opportunities for mathematics teachers to reflect, discuss, and provide feedback.

4. Give mathematics teachers a genuine sense of ownership of the activities and desired outcomes. (Lovitt et al., 1990)


Four key ingredients to mathresearch can be identified:

• students• teachers• content• models

( Bergeson, 2000)


• maturity

• intellectual ability

• past experiences in mathematics

• performances in mathematics

• preferred learning styles

• attitude toward mathematics

• social adjustment

KEY INGREDIENT 1: The students trying to learn mathematics— consider their:


KEY INGREDIENT 2: The teachers trying to teach mathematics—consider their:

• own understanding of mathematics

• beliefs relative to both mathematics itself and

how it is learned

• preferred styles of instruction and interaction

with students

• views on the role of assessment

• professionalism

• effectiveness as a teacher of mathematics


KEY INGREDIENT 3: The content of mathematics and its organization into a curriculum—consider its:

• difficulty level

• scope and position in possible sequences

• required prerequisite knowledge

• separation into skills, concepts, and contextual

applications


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


ReferencesBergeson, 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.

Documents

The Math Forum @ Drexel - mathforum.org Putting Research into Action Annie Fetter Kristina Lasher Suzanne Alejandre