In previous posts, I encouraged parents, homeschoolers, and teachers to explore the world of math and introduced one of my favorite learning tools, the math journal.

But you may be wondering, what can my students do with their journal? How do I find good math prompts?

Here are five different ways your children can explore math through writing, classified by the type of reasoning involved.

### #1: Game Prompts

Ask your children to play a number or strategy game and then write about it.

Game prompts break through the idea that math is dull and boring. They help students develop a positive attitude toward math while practicing their number skills or strategic thinking.

For example:

“Basic Nim (two players): Draw 10–15 circles (called “stones”). On your turn, mark out one or two of the stones, removing them from play. Whoever marks the last stone wins the game.”

Game prompts can also serve as fodder for the other types of prompt questions. We might ask students to analyze the mathematics of the game, to determine whether either player has an advantage, or to explain how they make strategic decisions during game play.

### #2: Content Prompts

Ask your children about something they are learning in their math curriculum, or in a book they have read.

Content prompt questions deal with the concepts of math and the topics studied. They can range from a short summary of a recent lesson to an in-depth research report on math history. Or they may pose a number-play puzzle or a word problem for students to investigate.

For example:

“Choose any base number and investigate its powers. For example: If you choose a base of three, the powers are:

3^{1}= 3

3^{2}= 3 × 3 = 9

3^{3}= 3 × 3 × 3 = 27

3^{4}= 3 × 3 × 3 × 3 = 81, etc.

Extend the list as far as you can. What patterns do you see in the powers of your base number? What other questions can you ask?”

Content prompts help students see the bigger picture of a topic. Too often we teach by breaking a math topic into small, bite-size chunks. But writing helps students to step back and put all those little pieces in perspective.

### #3: Artistic Prompts

Ask your children to create a shape or pattern and to write about what they notice.

Artistic prompts encourage children to express their creativity in playing with mathematical designs. The prompt may propose a geometric or numerical constraint for the artwork. Or it may be open-ended, allowing the students to choose their own responses.

For example:

“Use dotty graph paper. Connect dots to create an eight-sided shape. Are all the sides of your octagon the same length? How can you tell? What kind of design can you make with octagons?”

Artistic prompts inspire children to make mental connections in a way that abstract number problems can never do. Students feel the relationships of angles and lines as they draw a shape. And these prompts may lead to informal geometry proofs, like determining whether the sides really are the same length.

### #4: Process Prompts

Ask your children to describe how they figure things out.

Process prompts explore and explain the way a student solves problems. They ask learners to organize their ideas and reflect on their problem-solving strategies. Process prompts involve *metacognition*, which means “thinking about your own thinking.”

For example:

“Describe a mistake you made in math, or a problem you missed on a quiz or test. What went wrong? How will you avoid this error the next time? Do you understand the problem now, or is there something more you need to learn about it?”

Process prompts help students recognize their own understanding. Too often, math class is about learning to follow other people’s thoughts, not about thinking for ourselves. But students already have many ideas about math, and the best way of teaching is to draw out and strengthen those ideas.

### #5: Affective Prompts

Ask your children what they think about math.

Affective prompts probe the student’s feelings and attitude toward mathematics. This includes self-assessment: How is your math comprehension growing? What is easy for you, and what is most difficult?

For example:

“Have you heard that your brain keeps growing the more you use it? And that mistakes help you learn even more than when you get things right? How do these scientific discoveries affect your attitude toward math?”

Affective prompts support students in relating math to their own personal experience. They make math seem more “real” to students, more relevant to things they care about, more meaningful. Writing helps students take ownership of their math experience.

### Bonus: Quotation Prompts

When you’re looking for ways to prompt student writing, short quotations can be a great resource. I love quotations: Everything I might possibly want to say, someone else has already said it better than I ever could.

You can share one of your own favorite quotes or search for a new quip online. You may want to sample the tidbits on my blog’s Math and Education Quotations resource page.

For example:

“There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else — but persistent.”

—Raoul Bott, via The MacTutor History of Mathematics archive

**Short-Response Prompts**

Let students choose how they want to react to the quotation. Or offer one of the following questions:

- What did the author mean? Put the thought in your own words.
- Do you agree or disagree? Why?
- Is it a general principle, or only for specific situations? Describe a time when the quote might apply, or when it might not.
- Tell a time in your life when you lived up to the quotation — or when you wish you had.
- How does the quote relate to math, science, history, or another subject?

**Research Prompts**

Short exercises are great writing practice. But occasionally you may want to assign deeper essay topics, such as:

- Look up the author’s name online. Who are/were they, and why do people care what they said?
- What have others said about the same topic? Search out a variety of quotes related to this one. How are they similar? How are they different?
- Does thinking about the quotation make you want to change anything, in yourself or in the world? How could you put that idea into action?

### Or Try a Dialogue Journal

Your student may prefer an alternate approach to math journaling.

In a dialogue journal, the child and adult alternate writing messages for the other to read. The child may ask a question, give an opinion, or react to a recent lesson. Then you might offer an answer, praise an insight, or encourage further investigation.

This process of give-and-take discussion may extend a math prompt over several days, allowing for greater depth of reasoning as you investigate the topic together. Math education is not a race. Take time to enjoy the journey of discovery.

A dialogue journal provides yet another tool in mentoring your children on their lifelong adventure of learning.

And it can be loads of fun.

*Coming in Part 4: Responding to Your Child’s Math Writing.*

*This post is an excerpt from 312 Things To Do with a Math Journal, coming next week from Tabletop Academy Press. You can get the special pre-publication ebook edition at my publisher’s store, or preorder the ebook or paperback from your favorite online retailers. Read more about my playful math books here.*

*CREDITS: Photos by Nic Rosenau (top), Santi Vedrí, and Jonathan Borba on Unsplash.com.*