When is a number line not a number line?

The number line is a seemingly simple object: a straight line with two points marked 0 and 1. Those two points are the seeds of great complexity, however. Whole numbers are located at positions marked off by iterating the interval. Fractions are located at equal subdivisions of the spaces between whole numbers. Flip all those numbers to the other side of 0 and you have negative rational numbers. Then, although the line is completely dense with rational numbers, you find you can sneak between them with infinite decimal expansions to define a whole universe of irrational numbers. Given all of these layers of complexity, when exactly is the right moment to introduce this marvelous object to students?

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Creating an Accessible Mathematical Community with IM K–5: the power of “yet” for students and adults

Does the perfect elementary math curriculum exist? Armed with a growth mindset and the Alpha IM K–5 curriculum, teachers in Ipswich Public Schools push their thinking to reach all mathematicians. 

I preach growth mindset daily. When my students say they can’t do something, they almost always add their own “…yet.” However, walking this walk as an elementary school teacher is another story. Creating, mastering, and modifying curricula to reach each and every student—in every content area—is a daunting expectation. We hold ourselves to near impossible standards. 

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First Impressions: The First Units in IM K–5 Math

“I’ve learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.”

― Maya Angelou 

When I think back to my 8th grade math class, I cannot recall the exact problems I struggled with or exact things the teacher said or did, but I can distinctly remember how I felt each day walking into that classroom: anxious. From the very first day of school, I struggled, and my feelings of failure and self-doubt only compounded as the year progressed. I just could not keep up. While many, many years have passed, and details have faded from my memory, I have never forgotten how badly I felt about myself as a learner of mathematics each day.  

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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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