In primary, students’ math knowledge can be at the concrete stage, where they may have to understand a concept using items or building a model. It may be at the representation stage where they may have to draw it out to understand a concept. Or they could just be at an abstract stage where they just know how to calculate out the answer. Whatever stage they are in, they will need modified instruction to learn that concept. Even in the upper grades, new math concepts may need to be built out or mapped out before reaching an abstract understanding.

I definitely agree with what Jan said. Using the CRA (concrete, representational, abstract) when introducing and practicing standards has done wonders for our early and elementary students. One thing though that I’ve learned as a math interventionist—while building their math capacity, you must also build up their self esteem. The lack of confidence that many of my students (especially girls) have is astounding. They phrase answers as questions instead of just saying 5. It’s more like a quiet 5?? I make them say it again but with confidence and praise the heck out of them when they do say it with confidence without my prompting.

I love this question! I’m attaching a graphic I now use regularly with my primary students. I first want to point out you must know your own math identity as a teacher. I went through an early numeracy project where we first looked at ourselves. I now use my own struggles and former lack of confidence to show students how to grow as they follow each practice in math. There is progress in the struggle. Do you use any of these strategies in your class?

I love this question. Math has traditionally been so centered around how quickly one is able to produce a correct response to simply teaching procedurally where students have no ability to make connections to the math behind the math.
The book, Building Thinking Classrooms by Peter Liljedahl, is one of my recent favorites. It shifts the focus from traditional math instruction being teacher centered to student centered. He speaks to small changes that yield high impact like defronting the classroom. Typical front facing rooms unintentionally create a learning environment that is teacher centered and implies little to no student interaction.
I also love the CRA model that has increasingly help upper grades give students the “permission” to use concrete manipulatives to develop conceptually understanding of mathematical ideas versus just teaching them an algorithm.
There are so many great strides in mathematical instruction to help students develop a strong mathematical identity.

We have a math pledge that we say together at the beginning of each math lesson that helps us reframe our thinking into mathematicians each day.
I am smart!
I can do hard things!
I can try and use different strategies!
I can persevere!
I can use math everywhere!
I am a mathematician!