# Unit Coordination

### What Every Student Needs to Know for Multiplication (Part 4)

***This is part 4 of a series. Click the links to go back and read part 1, part 2, and part 3*** In this series, we have been discussing a progression of tasks that give students the opportunity to construct meaning for working with two types of units, the towers and the cubes that make… Continue Reading

### What Every Student Needs to Know for Multiplication (Part 3)

***This is part 3 of a series. Click the links to go back and read part 1 and part 2.*** In last week’s post, David Pearce described a modification of the Towers Task in which the students are asked to build two sets of towers and combine them. For example, the student may be asked… Continue Reading

### What Every Student Needs to Know for Multiplication (Part 2)

This post continues the Constructing Units team’s discussion about developing composite units with the goal of building children’s multiplicative reasoning. You can read part one here. In the Towers Task, the teacher uses the child’s understanding of composites as a starting point, and then provides modifications to the original task which encourage opportunities for the… Continue Reading

### What Every Student Needs to Know for Multiplication (Part 1)

The topic of the latest AIMS Center colloquium was “What every student needs to know for multiplication” (Video Archive)(Resources). This presentation highlighted the work that we have been doing around understanding how students develop multiplicative reasoning. One of the things we are doing is implementing a task with second and third grade students called the… Continue Reading

### The Power of Imagination in Mathematics

I have been reading and thinking a lot about the power of imagination in learning — specifically, learning mathematics. In this and successive blog posts, I will discuss one role imagination plays in helping children form number sense. Merriam-Webster’s definition for imagine: “to form a mental image of (something not present),” is what I mean… Continue Reading

When I taught middle school, I always found it interesting that my students could do this task: Johnny rode 34 miles on Tuesday and on Wednesday he rode 27 miles. How far did he ride over the two days? Yet they often had no idea what to do when I gave them this task: Johnny… Continue Reading

### Permission to Fail

I wrote a blog post at the beginning of the school year talking about our plans for research this semester. I’ve been reflecting on our project and the progress we have made so far, and I thought I would share a few of those reflections with you. As I mentioned previously, we have been working… Continue Reading

### Christian (Part 3)

In the August and September installments of my blog, I’ve been telling the story of Christian and our mathematical interactions with him. Christian is a second grader who came to us with mathematical skills that had been taught through his first years of schooling. He was bright, eager to work with us, and considered, by… Continue Reading

### Is Counting Really So Easy?

I have heard the claim “calculus is easy, algebra is difficult, and arithmetic is impossible,” but if that is true, then what does that make counting? We often hear little ones proudly singing the alphabet song or reciting a string of numbers from 1 to 20. Have you ever asked one of those who now… Continue Reading

### Not Another Ball!

I can’t believe it’s been a year since I embarked on this journey as a Research Associate at the AIMS Center for Math and Science Education. It has been an exciting transition for me, having the opportunity to pursue my passion for understanding how children develop their knowledge of mathematics. Over the last year, I… Continue Reading