By William McCallum

I can’t imagine what it must feel like right now to be a teacher facing the uncharted territory that is the coming school year. Will I be teaching 100% online, or have some face-to-face interaction with my students? Will I be teaching synchronously or asynchronously for most of the school year? How will I get to know my students and how will they engage in one another’s ideas? How will I get to know my students’ families? How can I give them manageable guidance to support students this year? Most of all, where can I get help with all these questions?

By William McCallum

One of the consolations in these difficult times has been tweets and Youtube videos of parents discovering just what it takes to be a teacher. Maybe it takes a crisis like this to restore the respect that teachers deserve. There is no doubt that when schools reopen teachers will face a formidable back-to-school problem: entire classes of students returning with months of lost learning from the previous year. And there is no doubt in my mind that teachers are up to this challenge. They have always had to face this problem on a small scale; hopeful parents will be looking up to them to solve it for all.

First and most importantly, take care of yourself, your family, and your students. That might not look like doing math, or it might. To the extent that it’s useful, we have curated this list of resources recommended by our community. We understand that contexts vary widely, and there is more here than any one person can make use of, but we’ve done our best to organize these resources so you can find what is most useful. If you know of additional resources that you have found helpful, please comment on this post. Continue reading “Links to Resources for Shifting Instruction Online”

By Jenna Laib and Kristin Gray

Take a moment to think about the value of each expression below.

$\frac{1}{4}\times \frac{1}{3}$

$\frac{1}{4}\times \frac{2}{3}$

$\frac{2}{4}\times \frac{2}{3}$

$\frac{3}{4}\times \frac{2}{3}$

What do you notice? How would you explain the things you notice?

If you are like us, or the students in Ms. Stark’s grade 5 classroom, you may have noticed many things. Things such as each expression has the same denominator, or the way in which the values increased as the problems progressed. When students notice these things, we often ask, ‘Why is that happening?” but it can be challenging to explain why beyond the procedure one followed.

By 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.

Continue reading “The Power of Small Ideas”

By 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.

Continue reading “Designing Coherent Learning Experiences K-12”

By William McCallum

When I was a child, I used to get puzzle books out of the library. One of the puzzles was the twelve-coin problem, the most difficult of all coin weighing problems. My mother and I worked on it separately at the same time, and she solved it first. Some time later that evening she came into my room to find me in tears of frustration. Instead of helping me, she asked: “Do you want me to tell you the solution?” I said no and she left. I will never forget the joy when I finally figured it out.

Continue reading “What is problem-based instruction?”