Formal Essay: Write a 1-4 page essay based on the prompt above; include your math verb and its definition. Your essay should be 1.5-2 line spaced, written in 10-12pt Times New Roman with 1-inch margins.

PURPOSE

The purpose of this assignment is to have you reflect on your personal practice of mathematics. In particular, you should focus on what doing math looks and feels like to you. Begin by reading the three blurbs below. The instructions and writing prompt will follow.

READING 1: From Chapter 1. Mathematics as Language in Kenney, Joan M., et al. “Literacy Strategies for Improving Mathematics Instruction.” ASCD (2005).

There are over 4,000 languages and dialects in the world, and all of them share one thing in common: they have a category for words representing nouns, or objects, and a category for words representing verbs, or actions. Taking this commonality as a starting point provides an interesting way of looking at the mathematical world and its language. It is possible to identify both content and process dimensions in mathematics, but unlike many disciplines, in which process refers to general reasoning and logic skills, in mathematics the term refers to skills that are domain-specific. As a result, people tend to lump content and process together when discussing mathematics, calling it all mathematics content. However, it is vitally important to maintain a distinction between mathematical content and process, because the distinction reflects something very significant about the way humans approach mental activity of any sort. All human languages have grammatical structures that distinguish between nouns and verbs; these structures express the distinction between the objects themselves and the actions carried out by or on the objects.

A model first proposed by the Balanced Assessment Program at the Harvard Graduate School of Education (Schwartz & Kenney, 1995) suggests that we think about mathematical nouns, or objects, as being numbers, measurements, shapes, spaces, functions, patterns, data, and arrangements—items that comfortably map onto commonly accepted mathematics content strands. Mathematical verbs may be regarded as the four predominant actions that we ascribe to problem- solving and reasoning:

• Modeling and formulating. Creating appropriate representations and rela- tionships to mathematize the original problem.

• Transforming and manipulating. Changing the mathematical form in which a problem is originally expressed to equivalent forms that represent solutions.

• Inferring. Applying derived results to the original problem situation, and interpreting and generalizing the results in that light.

• Communicating. Reporting what has been learned about a problem to a specified audience.

READING 2: From page V in Barta, James, et al. “Math is a verb: Activities and lessons from cultures around the world.” Reston, VA: National Council of Teachers of Mathematics, 2014.

Mathematics is a verb! In Ute we do not have just one word to describe mathematics-rather, we name it as we use it. When we count, build, design, cook, hunt, or fish, we are doing mathematics. — Fabian Jenks, a Northern Ute elder from Fort Duchesne, Utah

For most people, the word mathematics is a noun. But as the above quote (Barta and Shockey 2006) shows, not everyone would agree. For many people in many different cultures, mathematics is not simply something they learn in school. It is instead something they do as an intrinsic part of their everyday lives.

READING 3: From page 4 of Barta, James, et al. “Math is a verb: Activities and lessons from cultures around the world.” Reston, VA: National Council of Teachers of Mathematics, 2014.

Mathematizing, or the act of mathematical thinking or doing, results from the in- teraction between the mathematician and the object or activity with which they participate.

ASSIGNMENT and INSTRUCTIONS

PROMPT

What does “doing math” look and feel like for you? Create your own verb for doing math (like Barta et al. created the word “mathematizing”) and define it.

Based on your previous experiences, can you give examples where you engaged with math as a verb and examples where you engaged with math as a noun? Is it helpful to distinguish between math as a verb and math as a noun? Should the English language be modified to include a math verb?

Fabian Jenks (the Northern Ute elder) explained that in Ute, math is a verb and that he is doing mathematics in many daily activities. Do you ever consider yourself to be doing mathematics outside of the academic framework typically used in school settings?

Bonus: If you answered YES to that last question, can you give examples? Is mathematics an activity that we might/can/should casually engage in during our daily lives? How could we alter the presentation of mathematics in K-12 to make the learning experience more true to the real-world experience of doing mathematics?