Author Archives: David Pearce

I Didn’t Know What I Didn’t Know

I’m coming up on the two year anniversary at my current job and I’ve been reflecting on how my thinking has changed over this time. Before this job, I felt I had a good grasp on teaching math. I had just spent 20 years teaching junior high math. I faced down the torch and pitchfork crowds on a daily basis and even managed to pique an interest in some, entertain others, and teach skills to many. I was told I was a good teacher. I worked very hard at creating lessons that I felt would help make the content accessible to my students. I taught using manipulatives, graphic organizers, discussions, multiple representations, technology, games, and more. I designed my lessons incorporating activities to build what I believed was conceptual understanding. I connected the lessons to prior knowledge. I understood, better than most, the connections between the math operations of adding, subtracting, multiplying, and dividing whole numbers as well as connections between the sets of whole numbers, integers, fractions, percents, and decimals while using the math operations. Most teachers teach exactly the way they were taught, but I was constantly trying to stretch my understanding of the content and improve my teaching practices. However, I didn’t know what I didn’t know.

Even with all I tried to do, I continued to have students in my classes who struggled and were not successful. Worse, I didn’t always know why. I had junior high students who couldn’t subtract or multiply proficiently, many popping up fingers to try and determine a result. Fractions might as well have been quantum physics. I would see students in class who were taking notes, asking questions, completing homework assignments and yet continuing to struggle. Despite my best efforts, I still had students who failed to understand. As much as I learned, and as hard as I worked, I felt something was missing. Again, I didn’t know what I didn’t know.

Since joining AIMS, I have come to know, by reading and understanding research, that success in math begins with a child’s journey in the construction of an understanding of number. As adults we have forgotten our journey. It was so long ago and we have no memory of it. As a teacher, I believed my role was to teach the students skills in mathematics which they operate on numbers. Mathematics is connected ideas and these ideas are based in number. It is not isolated rules or concepts, which is why a problem can be solved multiple ways. Developing an understanding of number provides children with the ability to see and make these connections in mathematics and also develop the skills usually taught. In early education the teaching of math should be focused on the development of number, not only skills. In so doing, children will construct knowledge of mathematics in meaningful ways. I didn’t know what I didn’t know. Who knew?

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Teaching Children Fractions

“Fractions. Ugh! I’ve never been good with fractions.” I can’t count how many times I’ve heard this statement. Every teacher knows that working with fractions is an area where many kids struggle. As a middle school teacher, I saw these struggles and how they can lead to further struggles in math. In fact, mastery of… Continue Reading

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