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October 2011, Volume 18, Issue 3

FEATURES

Celebrate Mathematical Curiosity
Christine Redford
Spark the next generation’s natural inquisitiveness, put the Process Standards into action, and capitalize on teachable moments to foster conceptual understanding.

Appendix of student questions and student work samples
Second Look:
Focus Issue - Reasoning and Sense Making

Creating Spaces for Children’s Mathematical Reasoning
Barbara Graves
Reflect and Discuss
Learn to listen to your students’ interactions to inform your instructional decision making.

Reading Students’ Representations
Carmel M. Diezmann and Natalie T. McCosker
Students’ text, symbols, and graphics give teachers a glimpse into mathematical thinking associated with investigating the Peas problem.

A Vehicle for Instructional Transformation
Jen Munson and Tamyka S. Morant
The journey of closing the assessment-instruction loop begins with sustained, embedded professional development.

3 Ways That Promote Student Reasoning
Margaret Rathouz
Reflect and Discuss
Encourage children and their future teachers to question whether different solution methods are mathematically valid and to justify their reasoning.

Bring • Do • Leave: Nurturing Reasoning and Sense Making
Nicole R. Rigelman
This planning guide supports teachers in thinking through instructional moves prior to lesson delivery, enabling a classroom culture rich in thinking and discourse.

Completed example of the Bring - Do - Leave instructional planning guide

Number Talks Build Numerical Reasoning
Sherry D. Parrish
Strengthen accuracy, efficiency, and flexibility with these mental math and computation strategies.

Second Look - Focus Issue - Reasoning and Sense Making

How Do Children Know That What They Learn in Mathematics Is True?
How preservice teachers used interviews with elementary students to determine how the elementary students justified what they knew in mathematics to be true.

Developing Students' Mathematical Reasoning through Games
How teachers can use questions while students play games to develop their mathematical reasoning.  Games for primary as well as intermediate grades are provided, as well as questions one may ask of students who play them.

Describing Reasoning in Early Elementary School Mathematics
Examples of several ways of reasoning mathematically used by grade two students while playing games and discussing stories.

Illuminations Activity: Get the Turtle to the Pond

This activity provides opportunities for creative problem solving while encouraging young students to estimate length and angle measure. Using the Turtle Pond Applet, students enter a sequence of commands to help the turtle get to the pond. Children can write their own solutions using LOGO commands and input them into the computer. The turtle will then move and leave a trail or path according to the instructions given.


Reasoning and Proof Standard - Pre-K through Grade 12

Instructional programs from prekindergarten through grade 12 should enable all students to—