How Do Students Perceive Problem-Based Learning?

Does problem-based learning mean students need to forget everything they knew about how to act in math class?

As a teacher, and then as a coach and teacher-educator, I’ve been thinking for a long time about the shifts teachers need to make when using a problem-based curriculum like the IM Math curricula. Recently, though, I’ve gotten to be in classrooms not as a coach or a teacher, but just to observe. Sitting with the students, experiencing math class from their perspective, I’ve been reflecting a lot on the demands placed on them as learners in a problem-based setting.

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Making Peace with the Basics of Trigonometry

Six months ago, I hated trigonometry.

In fact, when my daughter missed a week of school, she announced on her first day back, “Someone has to teach me trig because I missed the whole thing.” Her father jumped in, “That’ll be me. Your mother hates trig.”

At least that used to be true. I have since made peace with my least favorite topic, in large part because of my experiences with the Illustrative Mathematics Geometry course. Let me tell you ways that the IM Geometry course has helped.

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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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Storytelling in the IM K-5 Math Curriculum

Kristin Gray, Director of K–5 Curriculum & Professional Learning

Curriculum

An excellent mathematics program includes a curriculum that develops important mathematics along coherent learning progressions and develops connections among areas of mathematical study and between mathematics and the real world.

Principles to Action by National Council of Teachers of Mathematics


Developing coherent learning progressions and connections among areas of study requires crafting lessons to tell a mathematical story. Lessons must coherently build across units and grade levels and attend to many things: the mathematics, representations, activity structures, and learning trajectories, to name only a few. Each of these considerations impact how students access the mathematics and influence the belief that mathematics is a connected set of ideas that makes sense.

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The Power of Small Ideas

William McCallum, IM President

Big ideas are popular in mathematics education, and you can find many lists of big ideas on the web. Some are more thoughtful than others, and I can see how some might be useful for organizing a curriculum. But few of the ideas I see in these lists really get me excited, or really capture what I love about the subject. I am a big fan of small ideas; like intricate joints in a fine piece of carpentry, small ideas often evade the eye, but are crucial to the beauty and structural integrity of the finished product. I’d like to mention a few of my favorite small ideas.

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Making Sense of Distance in the Coordinate Plane

Linda Richard, Curriculum Writer

I used to teach my students a catchy song to memorize the distance formula. We all had fun goofily singing this song. My students hummed it to themselves during tests and successfully calculated distances. I was pleased with this outcome—but what did my students actually understand about distance in the coordinate plane? In retrospect, very little.

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Designing Coherent Learning Experiences K-12

Kristin Gray, Director of K–5 Curriculum & Professional Learning

One challenge in curriculum design is considering all we know and believe to be true about math teaching and learning and translating that into realistic and actionable pieces for teachers and students. Our recent post about the K–5 curriculum focused around our belief that each and every student should be seen as a unique person with unique knowledge and needs. And while that post centered on elementary materials, to truly design around this belief we must look past K–5 to consider each student’s unique K–12 mathematical journey. A journey that, for most students, looks very different as they move from elementary to middle to high school.

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