Below is a guest blog from author and math expert, Marian Small. Her new book,Understanding the Math We Teach and How to Teach Itis now available for preorder.

Lots of elementary teachers were not privileged to receive math instruction that built their confidence in math. As a consequence, many of these teachers feel discomfort and stress as they try to teach math in a more meaningful way to their students. They worry! What if they say the wrong thing? What if the students ask them to explain something and they can’t? What if the students say something, and they’re not sure if they are right or wrong? If you are one of the people with those feelings, you are not alone. For so long, math was taught by many as a set of rules without any attempt to make those rules make sense, and many of our teachers are products of that system.

Teachers I meet have been craving a helpful resource, broken out into digestible chunks, that they can easily return to, and understand the ideas behind the math they are teaching their students. I was motivated by their many questions to create a resource that provides just that--clear and easy-to-understand explanations of how math works the way it does and what options there are.

These are generally set out in small easy-to-manage packages.

For example, consider this bit:

But then each principle is clearly explained. For example:

This strategy would help a student to change, for example, 18 x 3 into 9 x 6, something he or she already knows.

Or

This strategy would help a student change, for example, 145 ÷ 5 into 290 ÷ 10, which is even easier.

Different approaches to procedures are explained in ways that make sense.

Notice that regrouping would never be needed with this approach. You could change, for example, 412 – 89 into 413 – 90 and then into 423 – 100.

As well, there is attention to common misconceptions with strategies to deal with them, for example:

There is attention to every part of the math curriculum K – 8, and not only is the background provided, but also lots of pedagogical suggestions and activities to use with students.

See Small, 2019. *Understanding the Math We Teach and How to Teach It.* Stenhouse. Portsmouth, NH.