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Reader Reflections – December 2012 / January 2013

Readers comment on published articles or offer their own mathematical ideas.

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Media Clips: The Worst Day of the Year? – Chopsticks

Students analyze items from the media to answer mathematical questions related to the article. This month's clips discuss misrepresented formulas.

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A Graphic Organizer for Polynomial Functions

Students often view questions about polynomials—finding the zeros of a polynomial function, solving a polynomial equation, factoring a polynomial, or writing a polynomial function given certain properties—as discrete, unconnected processes. To address students' confusion about the many directions given for working with polynomial functions and to enable them to gain a true, conceptual understanding of polynomial functions, I created a graphic organizer (see fig. 1).

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Jumping to Quadratic Models

A hands-on approach to studying quadratic functions emphasizes the engineering design process.

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An Unexpected Influence on a Quadratic

Using technology to explore the coefficients of a quadratic equation leads to an unexpected result.

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Lawn and Garden//Pulp Paper

Students analyze items from the media to answer mathematical questions related to the article. This month's problems involve reading slopes from graphs, finding average rates of change, and interpreting linear graphs.

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Formative Assessment at Work in the Classroom

Assessment tools–a rubric, exit slips–inform instruction, clarify expectations, and support learning.

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Ferris Wheel Graphs

To introduce sinusoidal functions, I use an animation of a Ferris wheel rotating for 60 seconds, with one seat labeled You (see fig. 1). Students draw a graph of their height above ground as a function of time with appropriate units and scales on both axes. Next a volunteer shares his or her graph. I then ask someone to share a different graph. I choose one student with a curved graph (see fig. 2a) and another with a piece-wise linear (sawtooth) graph (see fig. 2b).

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Media Clips: The Fiancée Formula – Chocolatefinger

There seems to be a trend toward using creative terminology for mathematical properties and procedures as teachers attempt to engage their students. This short article explores potential issues and concerns related to the use of creative terminology and its effect on students' ability to meet the CCSSI standards of mathematical practice.

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Teaching Absolute Value Meaningfully

What is the meaning of absolute value? And why do we teach students how to solve absolute value equations? Absolute value is a concept introduced in first-year algebra and then reinforced in later courses. Various authors have suggested instructional methods for teaching absolute value to high school students (Wei 2005; Stallings-Roberts 1991; Friedlander and Hadas 1988), but here we focus on an investigation that will help students make meaning of the absolute value equation in the context of a practical situation. We connect absolute value to the concepts of rate, time, distance, and slope.