Author Archives: David Pearce
I remember getting a Rubik’s cube when I was younger. I sat down immediately scrambled it up, put in the Def Leppard cassette on my Walkman and set out to solve the puzzle. It soon became apparent to me that it was not going to easy or quick. I would play with it for a bit and then set it down and walk away, sometimes for a short time, sometimes for days. But I would always come back to it. There were times when I’d reach a point in which I couldn’t move on no matter the combination of moves I tried and then either through some new thought of random chance I would find a way past my sticking point and progress further along towards solving the cube. I was determined and engaged by the puzzle, that with small successes propelled me along to continue working. I remember the struggle and the feelings of pride each time I was able to overcome a roadblock for me in my journey.
In NCTM’s “Principles to Actions: Mathematics Teaching Practices” one of the practice states that teachers should, “Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships”. When we sit down with children to explore and promote their mathematics, we experience many examples of students struggling productively. For the children, the situation presented to them is new for their mathematical thinking but at the edge of what is possible for their understanding. In the following video, the teacher gave the child a situation which was unknown to her, causing her to struggle. Watch what happens as she grapples with the problem.
There are several takeaways from watching her. One thing of note is that her hair is squeaky. Another is that she is one cute kid, how can we not like her? But what I would like to focus on is her productive struggle as she worked to a resolution for the situation. In providing her an opportunity with a new situation to her that is within a range that is possible for her to think about mathematically and the time to think, she accommodates her current mathematical thinking to construct new mathematics. What did it take from the teacher to provide this opportunity for her to engage in the productive struggle we see in this video? How do you provide opportunities for children to engage in productive struggle in your classroom?
There were times my frustration boiled over while working on my Rubik’s cube but I eventually worked my way entirely through it. I remember the pride and satisfaction I felt. Many people have experienced these feelings when engaging in a difficult task and completing it with success. We have seen many children engaged in a productive struggle while working with them along with the satisfaction and pride they experience when understanding mathematical ideas and solving a problem.
Which came first: the chicken or the egg? This is an age-old question based on the observation that all chickens hatch from eggs, and all chicken eggs are laid by chickens. The problem is it’s difficult to answer because it is not clear which of the two events is the cause and which is the… Continue Reading
This blog is the fourth part of a multi-part series titled “Creating Centers in the Classroom.” If you’ve missed the previous installments, you can read part 1 HERE, part 2 HERE, and part 3 HERE. In our continuing series of blog posts on creating math centers in the classroom, I began thinking about the idea… Continue Reading
“To teach mathematics well, you need to be an expert who is able to recover what it’s like to think like a novice” – Brent Davis, 2017 When students enter our classrooms, they come to us with a wide range of pre-existing knowledge, skills, beliefs, and attitudes, often referred to as prior knowledge. In the… Continue Reading
“The rabbit-hole went straight on like a tunnel for some way, and then dipped suddenly down, so suddenly that Alice had not a moment to think about stopping herself before she found herself falling down a very deep well.” ― Lewis Carroll, Alice’s Adventures in Wonderland Alice had it easy. In a recent colleague’s blog,… Continue Reading
“Sixteen!” My grandson shouts, sitting on the floor smiling, fingers extended. We had been playing with his toy cars. He counted out nine, gave them to me, and I put them behind me out of his sight. He then counted out seven more, gave them to me also, and I hid them under a nearby… Continue Reading
I am always impressed with the passion teachers have for their work. Education in general, and teachers specifically, have received a lot of negative press. The story line seems to be that the system is broken and failing our kids, so let’s throw those bums out. But if you listen to teachers talk about their… Continue Reading
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… Continue Reading
“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
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