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Learning the Language of Mathematics

Learning The Language of Mathematics

Talk Like a Mathematician

Just like any language, the language of mathematics must be used in order to be acquired. Learners need to Talk Like a Mathematician, which requires  strong conceptual understanding, and plenty of practice.

Conceptual understanding in mathematics means that learners demonstrate understanding about:

  • which mathematical ideas are key and why they are important
  • which ideas are useful in a particular context for problem solving
  • why and how key ideas aid in problem solving
  • how an idea or procedure is mathematically defensible
  • how to flexibly adapt previous experience to new problems

Learners with strong conceptual understanding must also work to have strong vocabulary usage. They must be able to demonstrate their understanding by talking about their work using appropriate math terms. Talking like a mathematician requires using higher-level skills to compare, explain and justify methods. Learners should be able to share (both orally and in writing) how they did a particular calculation, describe why and how it worked, and compare it to the methods of others. A focus on acquiring Math Vocabulary will increase overall math learning.

3 Keys to Learning the Language of Mathematics

1. Read Children’s Books About Math

  • Get Math Concept Books:   Ask a librarian for age or topic appropriate math concept books (e.g. counting, colors, shapes, measurement, addition, subtraction, fractions, division, etc.).   Enjoy these books with your learners using dialogic reading (interactive and discursive). Do activities related to the concepts in the books. Have discussions utilizing vocabulary learned. Be creative and make your own concept books to increase ownership of language and knowledge.
  • Explore More Picture Books That Promote Math Language and Concepts Don’t just read books. Discuss them, apply them to real life activities, read them again and again, retell them in your own words. Here are 5 entertaining and educational math books, starting with one of my favorites: MATH-terpieces.

2.  Develop Math Vocabulary — Focus on Fraction

Engage and increase your learner’s math vocabulary through these 14 powerful activities:

Explore / Define / Pronounce / Draw  / Give examples / Use in writing  / Use verbally  /  Read words  /  Integrate  /  Identify in real-life  /  Compare/contrast  / Visualize  /  Describe  /  Make a book

Focus on Fraction

Some examples and specific guidance regarding developing the concept and language of fractions. 

1.  Use some creative source of information like this video to learn the vocabulary of fractions. Real Life Fractions 

2.  Look up the definition in a book or online and read it, say it, write it. Then put it into your own words.

3.  Draw a real example of a fraction and label it.

4.  Talk about, describe, draw, or show other examples of fractions. Be sure to use the vocabulary you are learning.

5.  Write your own fraction story. Write about sharing things with a group of friends, or cooking something and dividing it up to eat!

6.  Explain HOW you solved a problem verbally, using as many terms as you can. Count how many math terms you can use!

7.  Make lists of vocabulary words for every lesson and use them as reading drills.

8.  Work on integrating fraction vocabulary with this specially adapted excerpt of fraction vocabulary activities from A Word About Vocabulary!

9.  Make a habit of demonstrating fraction vocabulary by identifying fractions in real life and showing off what you know!

10. Compare and Contrast fractions using fraction circles, fraction bars, fraction dominos, or other fraction games. You can also learn about comparing fractions in this videos from Math Antics.

11. Close your eyes and imagine…

Imagine your favorite pizza. Now slice it in eighths. Eat some of the pizza in your imagination. What fraction of the pizza do you have left?

Imagine you have a box of 12 cookies. Imagine 3 favorite friends. How will you divide the cookies equally between you and your friends? Share them out in your imagination. Then have another yummy snack!

What other ways can you visualize fractions?

12. Describe a fraction in as many ways as possible. 

Here’s a start:

How many fractions can you describe?

Which color has the largest fraction?What would happen if you ate all the red ones?

Which color has the smallest fraction?

13. Make a book of fractions to demonstrate all of your fraction concept understanding and vocabulary knowledge. Don’t just list facts and draw a few models. Be sure to make it creative and interesting! Here is a great list of books for fraction learning and fun. Maybe it will give you some ideas!

  1. Fraction Action by Loreen Leedy
  2. The Lion’s Share by Matthew McElligott
  3. The Wishing Club: A Story About Fractions by Donna Jo Napoli
  4. Wholey Cow: Fractions Are Fun by Taryn Souder
  5. Hershey’s Milk Chocolate Fractions Book by Jerry Pallotta
  6. My Half Day by Doris Fisher and Dani Sneed
  7. Polar Bear Math: Learning About Fractions from Klondike and Snow by Ann Nagada
  8. Apple Fractions by Jerry Pallotta 
  9.  Piece = Part = Portion by Scott Gifford
  10. Fractions are Everywhere by Sarah Naeger.  This book was created on storyjumper.com , the #1 site for creating your storybooks. 

3.    Expert! Expert! Learn all about it!

The best way to really learn something is to teach it. Ask your math learner to be the teacher and explain what they know about a new concept or math term. Encourage them to demonstrate and model what they are teaching on a piece of paper or a white board, and to ask “teacher” questions. They can also “teach” younger siblings, pets and toys. Or have them test you on your math, and then correct your work.

Example Questions to prompt the teacher: “Can you teach me how to add?”“What does ‘greater than’ mean?”“What is the difference between area and perimeter?”“Why do we have different place values in a number?”“What are the steps to solving this subtraction problem?”“Can you set up a school with your toys and teach them about geometry?”“I need to divide up my pan of brownies for my friends. Can you show me how?”

Doren Damico is a veteran education specialist who loves to read. Doren is committed to linking research, resources and wise advice to her articles.  Subscribe below to follow the Playful Minds Guide for more guidance and resources.
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