On a Different Method for Solving Quadratic Equations

Published: Sunday, January 5, 2020

Solving quadratic equations (equations that can be written in the form ax2 + bx + c = 0, where a ≠ 0) is a major topic in high school Algebra. Typically, students in the U.S. learn several methods to solve them (factoring, graphing, completing the square, or using the quadratic formula). In my experience, many students not only struggle to learn four very different methods but then have to contend with determining which method works best for a given quadratic equation.

A few months ago, mathematician Po-Shen Loh published an article and video online (both can be viewed at http://www.poshenloh.com/quadratic/) that described a different way to solve quadratic equations. Although he devised it independently, other mathematicians, including the ancient Babylonians and Greeks as well as John Savage in a 1989 Mathematics Teacher article, developed similar techniques (Loh describes them in more detail at http://www.poshenloh.com/quadraticrelated/).

This year, I teach an Algebra I class of high school freshmen and sophomores, many of whom are repeating the course. I decided to teach the method outlined by Loh to my students. Along the way, I made several modifications to accommodate my students’ needs, the most notable of which was to add a visual element to the method to help students remember and understand the steps. This article describes the lessons that I would use to teach the method and how students reacted to it. (These descriptions reflect modifications that I made after initially teaching these concepts.)

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The Math Teacher's Toolbox, Coming in 2020

Published: Sunday, September 8, 2019

The Math Teacher's Toolbox, a book that I am co-authoring with my colleague Larisa Bukalov, will be released by Jossey-Bass in the spring of 2020.

The Teacher’s Toolbox series is an innovative, research-based resource providing teachers with instructional strategies for students of all levels and abilities. Each book in the collection focuses on a specific content area. Clear, concise guidance enables teachers to quickly integrate low-prep, high-value lessons and strategies in their middle school and high school classrooms. Every strategy follows a practical, how-to format established by the series editors.

The Math Teacher's Toolbox contains hundreds of student-friendly classroom lessons and teaching strategies. Clear and concise chapters, fully aligned to Common Core math standards, cover the underlying research, required technology, practical classroom use, and modification of each high-value lesson and strategy.

The book can be pre-ordered on Amazon here: https://www.amazon.com/Math-Teachers-Toolbox-Hundreds-Practical/dp/1119573297/

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Using Technology Effectively in Math Classes

Published: Wednesday, March 20, 2019

In a blog post published last week on EdWeek's Classroom Q&A with Larry Ferlazzo, I discussed ways that teachers can use technology effectively in math classes, including foster collaboration, encouraging independent work (with tools like DeltaMath), promoting guided discovery (with tools like Desmos), quickly checking student understanding, and promoting accuracy.

The complete blog post is here: http://bit.ly/2F92FC7 . I also discussed some of these ideas in a podcast available on the BAM! Radio Network at http://bit.ly/2Cn1fn8 .

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Effective Ways Students Can Teach Their Classmates

Published: Saturday, November 17, 2018

Today, my response to a question on Larry Ferlazzo's EdWeek blog about peer instruction was posted. In my response, I noted that if teachers don't create the proper classroom environment, then any cooperative learning venture will fall flat. I discussed the importance of learning students' strengths and weaknesses and starting small.

The full response is here: http://bit.ly/2Ds4j2l . A podcast on the same topic featuring me and other teachers is located here: http://bit.ly/2DauwDp .

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How to Handle a Class that Has Gotten Out of Control

Published: Saturday, October 27, 2018

I recently wrote a response for Larry Ferlazzo's Classroom Q&A blog at Edweek on the question "How do you turn around a class that you've let get out of control?" In my response, I highligted four questions I often ask myself in these situations: What else are students going through? Which students act out the most? Is the level of work appropriate? Is the work predictable? I also advised not taking student misbehavior too personally. I've had students curse at me one day and give me a friendly greeting the next day as if nothing had happened!

My full response is at http://bit.ly/2OVoGvW . A podcast on the same topic featuring me and other teachers is at http://bit.ly/2Nx6vqU .

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