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February 2013, Volume 106, Issue 6

FEATURES

Bundled-Up Babies and Dangerous Ice Cream: Correlation Puzzlers
Kathleen H. Offenholley
Discovering lurking variables encourages students to think critically about correlation.

Punch Up Algebra with POWs- FREE PREVIEW!
Mark Pinkerton and Kathryn G. Shafer
An action research study focuses on the teaching strategies used to facilitate Problems of the Week.

Journal Entries (PDF)
2008 NWEA mathematics status norms (PDF)

Students’ Exploratory Thinking about a Nonroutine Calculus Task
Keith Nabb
An open-ended calculus problem spurs novelties in student thinking and shows the benefits of timely teacher intervention.

An additional student solution (PDF)

Intellectual Engagement and Other Principles of Mathematics Instruction
Blake E. Peterson, Douglas L. Corey, Benjamin M. Lewis, and Jared Bukarau
What can American teachers learn about high-quality mathematics instruction from the Japanese teacher education process?

Making Sense of Extraneous Solutions
Jeremy S. Zelkowski
Do you always have to check your answers when solving a radical equation?
Second Look:
Radical Functions

Second Look - Radical Functions

A Reasonable Restriction Set for Solving Radical Equations
A method that identifies and eliminates extraneous solutions of a radical equation at the beginning of the solution process instead of at the end. It allows students to solve problems in a straightforward manner, accepting rather than rejecting solutions.

A Surprisingly Radical Problem
Interesting solutions and ideas emerge when preservice and in-service teachers are asked a traditional algebra question in new ways.

A Little-Used Art of Teaching: The Case of Storytelling
The art of storytelling as a means of introducing new mathematics topics. Two sample stories are included: one dealing with solving a radical equation, and the other with trigonometry.

Number and Operations Standard for Grades 9-12

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

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Expectations: In grades 9–12 all students should—

  • develop a deeper understanding of very large and very small numbers and of various representations of them;
  • compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions;
  • understand vectors and matrices as systems that have some of the properties of the real-number system;
  • use number-theory arguments to justify relationships involving whole numbers.

Understand meanings of operations and how they relate to one another

Expectations: In grades 9–12 all students should—

  • judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities;
  • develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices;
  • develop an understanding of permutations and combinations as counting techniques.

Compute fluently and make reasonable estimates

Expectations: In grades 9–12 all students should—

  • develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.
  • judge the reasonableness of numerical computations and their results.