## What is Mathematics?

That doggoned Cathy Carroll…I have still not stopped thinking about her colloquium and podcast which pushed us to redefine “fluency”. So let’s take that even further! What is “mathematics” anyway?

If I were to ask a primary teacher, “What is mathematics?” I would expect them to say something about learning to add and subtract. Intermediate teachers might include multiplication and division. Typically, an elementary teacher’s response is something involving arithmetic and I would expect the parent of an elementary student to say the same. So is mathematics defined as arithmetic or is arithmetic just a slice of that which we call mathematics?

This is not a new concept. In 1998, the National Council of Teachers of Mathematics released its Principles and Standards for School Mathematics.

In it, they defined mathematics content as having six main areas of focus: Number & Operations, Algebra, Geometry, Measurement, and Data Analysis & Probability. In addition, NCTM defined five **process standards**: Problem Solving, Reasoning & Proof, Communication, Connections, and Representation. All of these content and process standards were expected to be incorporated into every mathematics classroom, K – 12.

Fast forward to 2010… the Common Core Standards actually built on these revolutionary NCTM Principles and Standards. The content is now delineated into 11 different domains (many of the same as NCTM) and there are now eight Standards for Mathematical Practice.

Since 1998, mathematics has been defined much broader than arithmetic, so why are we still confused? Why has our elementary curriculum put such an emphasis on arithmetic these past 20 years? (After all, a free 10-key calculator can do all of our arithmetic for us!) What is mathematics???

According to Wikipedia, “Mathematics has no generally accepted definition.” Well, that’s not very helpful…

Dictionary.com defines mathematics as, “The study of numbers, equations, functions, and geometric shapes and their relationships.” They then add in some branches and major subdivisions…

Merriam-Webster defines it as, “the science of numbers and their operations, interrelations, combinations, generalizations and abstractions, and of space configurations and their structure, measurement, transformations, and generalizations.”

So maybe Wikipedia is right but going back to my last blog post about fluency, the ability to express oneself easily and articulately, I think I know what mathematics is. Mathematics is the ability to make sense of our world. Mathematics is our way of representing our world – of expressing what we find in our world easily and accurately. Mathematics is the ability to solve problems – real problems – in our world. So, yes… arithmetic is an important aspect of mathematics, but it is not the definition of mathematics. We have to redefine mathematics for our colleagues, our administrators, our parents, and our communities. Mathematical skills are not enough if we cannot use them in our world.

I’m a big fan of Donald Duck. In 1959, Disney released “Donald in Mathmagic Land”. I showed it to my high school students every year. (I still own it in VHS format.) I’ll close with the definition put forth in this classic movie.

In the words of Galileo, “Mathematics is the alphabet with which God has written the universe.”

## Changing the Story

What is your math story? What comes to your mind when someone says the word math? Unfortunately in our society, math is unpopular. In fact, if you look at the amount of likes and retweets of the screen capture here, it would seem that the feelings shared are mutual to many. When I was a… Continue Reading

## Piaget’s Water Level Task

While it might seem obvious that living in a three-dimensional world would require a certain amount of innate spatial abilities, it is less obvious in how this spatial ability informs science and math learning. Current research in visuospatial ability does show that children who have an understanding of how shapes fit together, and can see… Continue Reading

## Episode 32 | Integrated, Creative Thought; STEAM at the Center of Versatility

Leslie Love Stone joins Chris to describe how art, and mathematics come together in her Geometric Abstract style of painting. With an incredible collection of processes, and metaphors Leslie typically collects and layers information sets upon layers. Chris and Leslie spend some time describing a series she recently painted, “California National Parks ∩ Last of… Continue Reading

## Professional Learning on Steroids

To sum up the 2017 NCTM annual conference in San Antonio, Texas takes only one word, AWESOME!! As I’ve shared before, I look forward to conferences. They provide opportunities for me to be laser focused on education, a time to reconnect and collaborate, an opportunity to be current, a time to meet other like-minded educators,… Continue Reading

## How is Reading Instruction Different from Math Instruction?

How many times do you sit in your classroom looking over fluency tests or the latest reading assessment you gave your students? I have many memories of diving into these assessments with my grade level team. We would spend time looking at our student’s scores one child at a time. By the end of our… Continue Reading

## Classroom Math vs. Math of Children

At the AIMS Center, we work with children to learn how they do math, to learn what’s in their thinking process, and to verify the results of research. It may seem like the children are learning, or at least remembering what they are being taught. Standardized test scores, though, seem to paint a bleaker picture.… Continue Reading

## Do You Possess the Math Gene?

Do you consider yourself a math minded person? Did you struggle with math in school? Do you feel stressed when calculating tips or splitting a restaurant bill? Did you choose the early learning grades to teach because of your feelings toward math? If any of these questions resonated with you, it’s okay. It’s not a… Continue Reading

## Talking Math

Allowing our students to talk to each other about mathematics is very important in today’s educational culture. Gone are the days when students sat in rows quietly working on repetitive worksheets. Instead, we want to hear what students are thinking. How are they processing information? What do they see as important? What solution pathways are… Continue Reading

## Episode 31 | Mathematics Teaching ABOUT, WITH, and FOR Social Justice, Dr. Manjula Joseph

Based on the vision of education contained with the writings of Paulo Freire and others; Dr. Joseph has studied within the field of Teaching With Social Justice. This is to say she has sought to create, within her classes, a socially just system for learning. This podcast, we discuss the three aspects of teaching with… Continue Reading