Think back to what you remember from grade school. Maybe the first things that come to mind are activities or friends or favourite teachers. Maybe you remember an embarrassing moment, a skill you took pride in, or a hard-earned life lesson.

Do you remember any of the school material you learned? Of course, there are probably skills you learned in grade school that you use all the time, such as knowing which “there” is correct in a given context or how to subtract two-digit numbers. But in terms of specific lessons, do you remember any? Chances are a few stick in your brain. Maybe it was a really compelling history analogy or an inspiringly creative art project approach.

Why do you think you remember them? Not to state the obvious, but you might be tempted to say that you remember them because, well, they were compelling, or creative, or taught in story format with an analogy. Underneath that, however, the more profound reason these lessons stuck with you is that you connected with them in some way. They resonated with you; they had some sort of meaning to you, and then you internalized the information.

The best learning happens not when we’re memorizing, but when we’re internalizing. Internalizing learning simply means to take information in to the deepest parts of your mind. It’s motivated long-term storage. There’s an element of ownership involved; you become appreciative of all the derivative implications of the new information, and it becomes a part of the way you make decisions moving forward.

If internalizing is motivated long-term storage, what motivates it? How can we unlock the power of internalization in order to help our students not only understand what they’re learning, but to appreciate it and carry it forward with them?

We’re going to take a deep-dive and see how our strategies at Mentorhood give us the best chance at fostering internalized learning.

#### Concrete Connections

One of the most basic ways that a new piece of information can feel “sticky” is if it connects with something you’re already familiar with. This is why analogies are so powerful—they model new information over an existing framework that’s already been accepted.

There are a couple of ways that we prioritize making concrete, familiar connections when it comes to math instruction, especially when it comes to the younger students. When kids are first learning math, we frame their very first questions with minimal abstraction and get them to involve as much of themselves as possible in the calculation process.

For example, when first learning to add or subtract, we use the digits on their fingers and hands to represent numbers. This may seem tediously simple; underneath that simplicity, however, we are taking advantage of the concrete nature of the visual, alongside the participatory physicality of moving one’s fingers up and down.

We also use lots of pictures and frame questions in terms of objects and real-life scenarios. Here are a couple of examples:

“If you have three apples, can you take five apples away?” “You would like to share a pie with yourself and your two siblings. How can you do that?”

By starting here, we are foundationally training our learners’ brains to see numbers as physical objects in the real world that they can relate to as much as they relate to their own hands (and snacks!).

#### Connected Complexity

Having a concrete foundation allows us to explore more complex problems strategically. When problems become more complicated, we can then break them down into bite-sized pieces that align exactly with what they’re already familiar with.

Let’s say they’ve progressed to learning two-digit addition and subtraction. While they may not have eighteen fingers to add and subtract with, they will certainly have enough to deal with each place value column separately. We break problems down as much as we can so that wherever possible, the only new part is the last step of putting everything together.

When the numbers become larger, or the concepts become more complex, it is often helpful to reference a simpler example to reinforce a framework. This is like making use of a mathematical analogy, and it’s a strategy we use frequently. You can use simple numbers off to the side to illustrate a concept—the key is to numbers small enough that students can easily verify the calculations and use multiple examples if necessary. This helps students to develop confidence and intuition regarding the new process they are practicing.

#### You Look Familiar…

As kids are growing, they are developing an appreciation for the world around them and what all the different pieces in it mean to them. When it comes to math instruction, we want to connect these calculation concepts as much as possible to those meaningful pieces of their worlds.

Focusing on concrete connections not only helps us to spark intuitive understanding in our students, but also sets them up to know the usefulness and joy that learning math can be.

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