Author Archives: David Pearce

Takeaways from Subtraction (Part 3): The Struggle

Every elementary school teacher has seen children struggle with subtraction. From these struggles, attitudes of “I’m not good at math” emerge. Our team recently worked with students on the concept of subtraction. We presented situations in which students would count out 23 cubes, hide them, and then remove some of the cubes. The students were… Continue Reading

Takeaways from Subtraction part 2: To Take Away or Not to Take Away

In my last blog entry, I described three goals suggested by Dr. Les Steffe which support introducing subtraction as take away. Yet, there is a belief among some math teachers that thinking of subtraction as take away interferes with future mathematical development. They argue that using the words “take away” should be eliminated completely from… Continue Reading

Takeaways from Subtraction (Part 1)

Why is subtraction hard? This question can be heard from many young children, but often even from adults. Whenever adults do mental math, they tend to have an easier time with addition, multiplication, and simple division than with subtraction. For the past three months we have been engaging young children in subtraction situations while considering… 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

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

Christian – Part 2

In my previous blog I introduced Christian. He had a prescribed method for solving addition tasks, but many times his answers were not accurate. In our second session with Christian our primary goal was for him to use a counting strategy when adding two numbers. We began by presenting cards to him with the numerals… Continue Reading

Christian – Part 1

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.—Common Core State Standards for Mathematics, p. 8 CSS.MP1 Make sense of problems and persevere… Continue Reading

Brittany

In the Common Core State Standards for Math, counting-on is considered “a strategy for finding the number of objects in a group without having to count every member of the group.” Counting-on is an efficient way to add and we want children to count-on. Yet, many young children begin by counting-all. For example: Teacher [placing… Continue Reading