Author Archives: Beverly Ford

The Power of Knowing the “Mathematics of Children”

Decomposing Action I have had the privilege of being a part of the AIMS Center from its birth. Having been a teacher, coach, and staff developer for the last 15 years, the world of a teacher is something I have experience with. I am now called a Research Associate and my role is to be a bridge between the educational research world and the world of a teacher. To meet this challenge, I needed to learn and understand a entirely new world.

One of the first tasks I was given was to deeply understand a line of research which includes the work of Piaget, von Glasersfeld, Steffe, Norton, and Ulrich, among others. These are mostly all new names that I have come to greatly respect.  What stands out about these researchers is their attention to the “students’ mathematics”. Throughout my career I have learned different ways to teach math concepts, but now I realize I was working out of an adult mathematical frame of mind. One of the new lenses I have acquired through my studies is the concept of the “mathematics of children”.

So what is “adult mathematics” versus “mathematics of children”? Is this important to a classroom teacher? How would having this new lens benefit a teacher? Much of what Dr. Les Steffe has published begins with a discussion around the importance of the “mathematics of children”. I wondered and reflected about this. It was through this reflection that I realized I had been working out of an adult mathematical frame of mind.  I needed to learn more about the “mathematics of children”. This is critical to the work of these researchers.

I’ve come to realize that the “mathematics of children” is about inferring what might be going on in the mind of the child. It is different than adult mathematics because an adult may have already constructed the concept. What seems completely obvious to an adult, might not be obvious to a child.

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This line of research is qualitative, which means they don’t look at statistics but instead focus on change in behavior. How does this work? In a nutshell, first the researchers observe student behaviors.  Based on what they see, they infer what might be going on in the mind of the child. They watch for trends in multiple children and then sort the gathered behavioral evidence into a developmental progression. Hopefully this progression will then provide a teacher assistance in identifying where a child is in terms of constructing their understanding.

5th-gr-6What is the journey to constructing math concepts? Research that articulates the “mathematics of children” can provide powerful tools that enable a teacher to identify where a child is in their math journey and what our next teacher step might look like. I am thrilled to be studying research that shows how children come to know certain math concepts and to discover tools that can empower teachers to be that catalyst for learning that all children deserve.

Addressing Mathematical Practice Standards Through Multiplication and Division Word Problems

Addressing Mathematical Practice Standards Through Multiplication and Division Word Problems

Have you ever given your students an experience with manipulatives and then found when you shifted over to a textbook that the students didn’t make the connection between the two experiences? As a curriculum developer and researcher, I am constantly looking for more ways for students to make connections from the concrete (manipulatives) to the… Continue Reading

Building Confidence in Math with Multiplication

Building Confidence in Math with Multiplication

Why do you teach? I remember when I first came into the profession it was because I enjoyed students and wanted to make a difference. I still love watching movies of teachers that have gone into challenging situations and inspired students to think differently. These teachers empowered the students to be all that they were… Continue Reading

Writing a Multiplication Word Problem

Writing a Multiplication Word Problem

Word problems are typically not students’ or teachers’ favorite part of the math lesson. When I talk with teachers, they are frustrated with teaching multiplication word problems. I think one of the things we have been missing is teaching students the structure of what is involved in any multiplication word problem. “Look for and make… Continue Reading

Partitioning Shapes: Is it Geometry or Fractions?

Partitioning Shapes: Is it Geometry or Fractions?

How early should we teach words like half, thirds, and fourths to children? I know that I have often heard that we give young children things they are not developmentally ready for, and I agree. But when it comes to having language identify a concrete experience, I think children can handle it. I was measuring… Continue Reading

Three Great Multiplication Posts

Three Great Multiplication Posts

How to Equip Your Students to Better Understand Multiplication, Part One As I have coached and taught in the classroom, the three most popular ways to describe multiplication is showing ______ groups of ______, using repeated addition and making arrays. Now all of these methods have their place in a student’s understanding of multiplication, but… Continue Reading

Finding Math in Unexpected Places

Finding Math in Unexpected Places

I was reading Inchworm and a Half with my 6-year-old daughter, Bethany, last night for the 40th time. She loves reading the section, “Squirmy, wormy, hoppity-hoop! We measure everything, loopity loop.” Even before she could read books she memorized this section and would “read” it. The book is about an inchworm that loves to measure… Continue Reading

Do We Really Understand What Math Is?

Do We Really Understand What Math Is?

What would you or your students say math is? Some common answers could be numbers, addition, subtraction . . . Below are the posters a group of AIMS trainers created answering that question. Most people don’t understand what math really is. If you have read some of my previous posts, you know my elementary and… Continue Reading

How to Equip Your Students to Better Understand Multiplication, Part Three

How to Equip Your Students to Better Understand Multiplication, Part Three

I never liked word problems as a student. It was difficult for me to figure out which procedure to use, but I really didn’t like problems like this: Robert is three times as old as his younger brother Mark. Mark is 7 years old. How old is Robert?  As I reflect on my experience, I… Continue Reading

How to Equip Your Students to Better Understand Multiplication, Part Two

How to Equip Your Students to Better Understand Multiplication, Part Two

Using arrays has become much more prominent in the classroom. At first glance arrays seem very straightforward and simple for students. But what are the connections that are essential for students to build understanding of the concept of multiplication through arrays? Arrays are a model of multiplication. Just because your students can build an array… Continue Reading