Rigor in Proofs

Tina Cardone, Geometry Lead, & Gabriel Rosenberg, Curriculum Writer

There is no doubt that proof plays a central role in the human endeavor of mathematics, but there remains much debate on what role it should play in high school mathematics. At least two standards for mathematical practice in the common core focus on this concept. Certainly MP3, “Construct viable arguments and critique the reasoning of others”, is about the need for students to be able to write their own proofs and to analyze the proofs of others. MP6, “attend to precision” goes deeper, though, by noting the need for precision, including the use of clear definitions, when communicating their reasoning. This is what we mean by rigor in mathematical proof.

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Presenting IM Algebra 1, Geometry, Algebra 2

Kate Nowak, Director of 6-12 Curriculum

When I was teaching high school mathematics, my local colleagues and I spent a whole lot of time creating problem-based lessons. We were convinced that this style of instruction was a good way to learn, but the textbooks in use at our school simply contained definitions and theorems, worked examples, and practice problems. One day I was talking to my dad about how much time I had been spending lesson planning. His response was, “People have been teaching geometry for, what, 3,000 years? Shouldn’t the lessons be, like, already planned?”

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The IM 6–8 Math Curriculum Changed My Math Methods Experience

By Anna Polsgrove

When I first started the Math Methods course at University of California, Irvine, all of my ideas on how to learn math took a complete 180.

During the first two months, a million questions swirled in my head as I worked through problems with my classmates: We don’t just teach the algorithm anymore? What do you mean “use representations to build conceptual understanding”? What is an area diagram? What are all of the multiple strategies to solve a problem? How am I supposed to anticipate misconceptions when I have never taught the curriculum?, just to name a few. Continue reading “The IM 6–8 Math Curriculum Changed My Math Methods Experience”

Warm-up Routines With a Purpose

By Kristin Gray

As a teacher, curiosity around students’ mathematical thinking was the driving force behind the teaching and learning in my classroom. To better understand what they were thinking, I needed to not only have great, accessible problems but also create opportunities for students to openly share their ideas with others. It only makes sense that when I learned about routines that encouraged students to share the many ways they were thinking about math such as Number Talks, Notice and Wonder, and Which One Doesn’t Belong?, I was quick to go back to the classroom and try them with my students. It didn’t matter which unit we were in or lesson I had planned for that day, I plopped them in whenever and wherever I could because I was so curious to hear what students would say. Continue reading “Warm-up Routines With a Purpose”

Adapting Problems to Elicit Student Thinking

By Jody Guarino

As a teacher, I constantly wonder how I can elicit student thinking in order to gain insight into the current thinking of my students and leverage their thoughts and ideas to build mathematical understandings for the class.

First, I need a task that will make student thinking visible. Here’s a task from Illustrative Mathematics, Peyton’s Books.

Peyton had 16 books to take on his trip. He lost some. Now he has 7 books. How many books did Peyton lose?   

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