Using Instructional Routines to Inspire Deep Thinking

We want students to think about math deeply. Creatively. Analytically. Instead, what often happens is that students race towards quick solutions. So what can we do to support this other kind of thinking in class—the slow, deep kind?

One way is through instructional routines like “Which One Doesn’t Belong” and “Notice and Wonder.” These routines give structure to time and interactions. Within the structure, there are opportunities to have time to think deeply and a predictable way to share and deepen thinking with partners and the whole class. 

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Making Authentic Modeling Possible


The first thing you have to understand is that asking people to model with mathematics makes them mad. Not in all contexts, though! At a social gathering with a generally amiable and curious group of people, you might try floating a question like:

  • I wonder if graduates of more expensive universities tend to earn more in their careers?
  • Do you think the time it takes a pendulum to swing back and forth depends on how heavy it is?
  • What do you think is the most efficient way to get 2,000 calories a day?

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Which Vertex is the Center of a Triangle?

I am sometimes asked what is the secret to the success of our curriculum, what is the special property that sets it apart from other curricula. That question is like the one in the title of this blog post, “Which vertex is the center of a triangle?” It doesn’t have an answer. None of the vertices is the center of a triangle; all three are equally necessary for it to exist. Similarly, all three vertices of the instructional triangle—students, teachers, and content—need equal attention in the work of teaching mathematics. And not only the vertices but the arrows between them, which “represent the dynamic process of interpretation and mutual adjustment that shapes student learning [and] instructional practice.”1 If there is something special about what we do in writing curriculum it is to pay equal attention to all parts of the instructional triangle. 

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Updates to Supports for Students with Disabilities and English Language Learners in IM 6–8 Math

At Illustrative Mathematics we are committed to creating a world where learners know, use, and enjoy mathematics. We believe that every student can learn grade-level mathematics with the right opportunities and support. Our approach is to remove unnecessary barriers and provide teachers with options for additional support so that every student can engage in rigorous mathematical content. We’ve been busy this year working on some exciting enhancements to the teacher tools and supports to empower teachers to deliver instruction that meets the specialized needs of English learners and students with disabilities.

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Preparing for the School Year, Updated with Tips for Staying on Pace

Last year, we put together some reading to help people get started planning their year with IM 6–8. Now, we have another year’s worth of blog posts to choose from, plus a shiny, new high school curriculum! So once again, we’ve gathered some posts from IM’s blog with different purposes to help get your year off to a good start.

Before we dive into the links, if you are new to the IM curriculum, here are some tips to help you stay on pace

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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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Realizing the promise of open resources, part II

In my first post on the topic of realizing the promise of open educational resources, I described the IM Certified program. Our partners offer multiple versions, including a free online version and enhanced versions with different options for users. This is IM’s way of reaching teachers and students from a wide variety of districts who may be looking for those different options, while assuring that, as these versions evolve, they will stay true to the original design. However, by the terms of the CC BY license, anybody can use the curriculum with or without certification. This freedom further supports our mission to get these carefully crafted materials into the hands of as many students and teachers as possible.

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Building a Supportive Home/School Partnership

DOWNLOAD 9–12 FAMILY NIGHT RESOURCE 

While families arrive with different school experiences and perspectives on what “doing math” means, they often share common questions: What do I need to know to set my child up for success in math this year? and How can I continue to support them throughout the school year? Hosting a family math night can answer these questions and help bring a school community together.

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Explicit Classroom Norms to Teach Kids How to Learn From Solving Problems

This blog post is the fourth in a series of four blog posts exploring the student experience of problem-based learning. The first three posts are available here: (1) “How Do Students Perceive Problem-Based Learning?” (2) “Inviting Students to the Mathematics” (3) “Concrete Representations that Give Students a Way to Get Started.”

Okay, so the kids can get started and represent their thinking. But are they really learning? Am I really teaching? What are we doing here?

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