LearningTip #44: 
Using Writing to Teach Mathematical Thinking

By Stefanie Kahl, B.S. 
Fourth Grade Teacher, Dunn Elementary School
Arlington, Texas

It seems today that many children have a hard time telling you what a specific math problem is asking them to do.  With time, writing can help children learn how to do this.  When a child can use writing to express how they came up with an answer to a problem, they can process it and fully understand it.  This helps them progress to another area in mathematics development.  

When I was in teacher training, one thing that really stood out for me was the concept of metacognition--the understanding of how one thinks and processes information.  This really influenced the way I thought about teaching---especially mathematics instruction.  I turned to writing to help my students learn more about how to solve mathematics problems.  These are some of my strategies:

Journaling

Write about it!

Mathematical Stories

Student-Written Story Problems

Math Buddies

1. Journaling.  This has always been a favorite strategy of mine.  Writing in journals tells me what the student knows and how s/he
   knows it.  Further, it helps the student conceptualize his/her ideas in many different areas:  problem solving, reasonableness, and in general mathematics concepts such as subtraction and multiplication.  I use journaling after the lesson to give students the opportunity to put the new information in their own words---this strengthens their learning,tells them what they understand and don't understand, and tells me what I need to do instructionally thenext time.  All mathematics writing is kept in their math journal; this creates a place to "return" to when thinking and writing about other concepts.  
   
   
2. Write about it!  I have my students write in their journals before we begin a lesson about a new math concept.  They write what they already know about the math concept .  For example, I ask them to write everything they know about fractions.   You would be surprised at the misconceptions children have about many concepts in math.  This is an excellent way to identify any misunderstandings the children have about the concept to be learned.  When I know what they're thinking, I can correct misunderstandings and use what they already know to help them learn the new information. 
   
   
3. Mathematical Stories.  We read children's books with mathematical storylines and act them out with manipulatives.   For example, I use Marilyn Burns' children's book, Spaghetti and Meatballs for All, to develop perimeter and area concepts.   Other children's books in the Marilyn Burns Brainy Day series include:

The Greedy Triangle by Marilyn Burns

A Cloak for the Dreamer by Aileen Friedman

The King's Commissioners: A Mathematical Story by Aileen Friedman

Amanda Bean's Amazing Dream: A Mathematical Story by Cindy Neuschwander

After we act out the story and expand our concept using manipulatives, the students write in their journals what they have learned from the story or activity.  In small groups, the children create another problem using the same concept in the story.  Then they trade stories and try to solve each other's problems,  This is usually done on a large sheet of construction paper or newsprint.  

1. Student-Written Story Problems. We write our own story problems.  I find that having students write their own problems and solving other students' story problems helps them recognize the code words in problems.  This increases the student's ability to comprehend the math word problems. These are written on white construction paper so we can publish our own story problem book for the classroom.  (LearningTip #35 also focuses on having children read and write mathematics story problems.) 

2. Math Buddies.  This is an online problem-solving project that will begin this fall.  It will hook classrooms up with each other for the purpose of writing about math.  Each child will receive a buddy that they will use e-mail to reply back on how they solved each problem.  The classrooms can choose a higher, same,  or lower level buddy.  Some of the story problems that my students have written will be used in the Math Buddies program.  This program will help children understand their own thinking in problem-solving and also afford them the opportunity to use the technology that they will need in the 21st century.  

Math Buddies was developed with the "journal" concept in mind.  I am hoping it will motivate the students and increase their interest in writing about what they know.  Getting to share with someone they don't know on the computer is exciting for them.  So they solve the problem first in their journal and then they get to contact their buddy and share what they think.  This also helps them pick up new ideas to help them in the future with similar problems.

The work of Marilyn Burns provides a lot of support for teachers who are using reading and writing to teach mathematics.  I use her Math by All Means: Multiplication and Math by All Means: Probability to plan relevant mathematics hands-on experiences and cooperative group activities.  I also use her book, About Teaching Mathematics: A K-8 Resource; this book explains how students understand problems and provides solid hands-on whole class and independent activities for many basic concepts in math. They can then apply their understanding to extended problems.   Her book, I Hate Mathematics, helps children understand that all of us are capable of learning mathematics.  Also, I love the published lessons on her web site.  

Putting the Pieces Together

For those who want to begin a journal program in math, I recommend that you start small and be consistent.  Write in journals at least once each week to start.  At first, make the problems or questions about things they already know.  This will give them practice and increase their level of comfort with writing about mathematics.  Don't critique their writing; just use it to understand their thinking.  This can help the teacher determine the direction to pursue a new concept.  This can also give a child with misconceptions a better understanding by knowing exactly what they are thinking and correcting it before going on with a particular concept.  Also, after you have begun writing, pick up something fun to read with a math concept in it.  Then have the students write about what they understood about the math in the story or the activity.  Next, have students write their own problems and share them with a "buddy."  This expands their own understanding while, many times, picking up new information that improves the way they approach problems that they solve in the future.  This also develops teamwork and collaboration which, in turn, gives our students the skills that they need to be successful in life.  Last, increase journaling to at least a couple of times a week.  It never should be a burden to you, so do it as time permits. I understand that some years are better than others!  I think once you see the benefits, you will love having this additional tool in teaching math!  Don't put too much pressure on yourself or the student; it takes time to get used to journaling and it takes time to develop a consistency with students' writing in math!

^
TOP

About the Author
Stefanie Kahl earned her B.S. in Elementary Education and Exercise Health and Sport Studies from the University of Texas, Arlington in 1996.  She has taught for three years.  She received the Phi Delta Kappa Award for Student Teaching in 1996.  She received the Internet Innovator Award in September, 1998 for her Math Buddies Program.  In October, 1998, she was nominated by the Arlington Independent School District to receive the Bayard Freidman Hero Award for Children.  She was the first recipient of this award.  Also, on April 19 she was inducted into the Arlington Independent School District (Arlington, TX) "Wall of Fame."  Stefanie and her husband are the proud parents of one daughter.

©KidBibs International
http://www.kidbibs.com/