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Exploring the Rule of 3 in Elementary School Math Teaching and LearningPowerPoint Presentation

Exploring the Rule of 3 in Elementary School Math Teaching and Learning

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Exploring the Rule of 3 in Elementary School Math Teaching and Learning

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Exploring the Rule of 3 in Elementary School Math Teaching and Learning

Timothy Boerst

Jane Addams Elementary School, South Redford

and

The Center for Proficiency in Teaching Mathematics, University of Michigan

- “Every topic should be presented geometrically, numerically, and algebraically.” (Hughes-Hallett et al, 1994)
- Subsequent definitions have tended to emphasize graphic and verbal representations and attend less to geometric forms.
Numerical

Verbal

Geometric/GraphicAlgebraic

Numerical-Representation focuses on specific values within algorithms, equations, lists, tables and the like.

Algebraic-Representation focuses on verbal and symbolic notation to generalize, formalize, model and extend.

Graphic-Representation focuses on spatial/pictorial/ geometric/visual displays.

- In practice numerical, algebraic, graphic, and linguistic representations are often closely intertwined.

Content Sources

Classroom context

Individual case context

TRG meeting context

- National standards
- State measures
- Reformed texts
- Student learning strengths
- Subject matter rigor
- Professional growth

Try solving or communicating a solution for the following problem using numerical, algebraic, and graphic representations.

Tom wants to buy a book that costs $2.95. He can save 50 cents a week. How many weeks will he need to save enough money for the book?

a +.50 = B

.50 + .50 + .50…= $2.95

.50 W ≥ $2.95

Where W=number of weeks

.50 + .50 + .50 + .50 +.50 + .50 > $2.95

Tom wants to buy a book that costs $2.95. He can save 50 cents a week. How many weeks will he need to save enough money for the book?

Examine the student generated representations related to the following problem.

A student left Redford with her family for a well earned vacation. They traveled 50 miles per hour heading toward California. One hour after the student left, his teacher remembered an important homework assignment. She raced along the identical route on her motorcycle at a speed of 75 miles per hour to catch up. How long would it take the teacher to catch the student?

Numerical

50 › 0

50+50 › 75

50+50+50 = 75+75

Graphic

Algebraic

Geometric perception of prisms and pyramids is enhanced by:

- Numerical examination (edges (E), faces (F), vertices (V))
- Graphic organization (tables where E, F, and V are organized and also sorted by 3D shape type)
- Algebraic generalization (prisms F=B +2, F+V-2=E, pyramid Bx2=E…)

- Determining representations and meshing them with knowledge of student learning and mathematical objectives
- New instructional territory (translation, refinement, comparative utility)
- New territory for learners (leading to new sorts of instructional needs)
- Depth vs. coverage