Building Mathematical Comprehension - Visualizing

            

I am excited to be one of the hosts for Chapter 5 in Building Mathematical Thinking.  Thanks to   Brenda of Primary Inspired and Beth of Thinking of Teaching for getting this book study together.

Students must be able to visualize what is happening in order to comprehend what they are reading.  Therefore, we must teach students how to visualize.  It does not always come naturally to children. 

The NCTM Standards include representation as one of the Process Standards!  We must teach students to create & use representations.  Laney includes J.K. Wilhelm's seven-step sequence of activities to help students build mental images gradually.

• Create mental images of observed concrete objects.

               Show students an object. They close their eyes and try to visualize it.
               Then open their eyes and try to describe it.

• Create elaborate mental images of imagined concrete objects.

               Students recall and describe images they have previously seen.

• Envision familiar objects and settings from their own experience.

• Add familiar actions and events, then relationships and settings.

              Can begin to have students envision a math problem.

• Picture characters, settings, details, and events while listening to a story read or told about.

              I call this "Sketch to Stretch."  
              As I read aloud parts of a story, students draw what they see in their minds.

• Study text illustrations and use them to create internal images.

               As a whole group or small group activity.  

• Create mental pictures independently.

Once students are able to create and represent mental images, they are ready to see how it can help them understand math better.

Modeling & Think Alouds
To show students how to use visualization in math, teacher should model and use think alouds.
There are several different options:

• Teacher does all the modeling and thinking while students listen
• Teacher does most of the modeling with some students engagement.
• Large groups, but teacher is monitoring.
• Small groups, teacher monitors.
• Students do the modeling orally and/or in writing.  Then, compare with others.
• Students do modeling independently in a teacher conference.

"Picture Walks" to Build Capacity to Visualize

Take picture walks through math text books, math resources, or math related books to help students see multiple representations of math images.

Visualize, Draw, Share

Students listen to someone describe a mathematical idea (two plus 4, area of a square, etc) and draw a mental image of it.  Then, students share with others and compare images.  Follow up with discussion.

Multiple Representations Graphic Organizers

Practice using symbols, diagrams, models, examples, and words to express a mathematical idea.

Example:  Frayer Model - especially useful for math vocabulary

The Frayer Model:  http://scimathmn.org/stemtc/frameworks/231-shapes

(Adapted from Thompson, et al. 2008)

Math Stretches to Encourage Visualization

2 types & very brief

What do you visualize when you think about addition?

• Students use sticky notes and illustrate what they visualize.  Add it to chart.  Discuss.

What does this representation mean to you?  Sketch it.

• Students see a visual representation.  They use sticky notes to describe the math concept.  Add it to the chart.  Discuss

Use Children's Literature & Poetry that relate to math.

I absolutely love The Math Start Books, by Stuart J. Murphy.   Visit his site @ http://www.mathstart.net.

Check out this from his website.  He lists books by the NCTM Standards.  Here are his books that fall under Representation.

http://www.mathstart.net/for_teachers/nctm_standards.php

For other lists of children's book that would be great for Math, just click on the pictures below.  

And here are just a few of my other finds, I thought would go along with this chapter.

Thinking stems:

Words to use during math talk, math huddle.  

Thanks for stopping by & I hope this has been helpful!

Thompson, D. R., G. Kersaint, J. C. Richards, P. D. Hunsader, and R. N. Rubenstein.  2008.  Mathematical literacy: 
     Helping students make meaning in the middle grades. Portsmouth, NH: Heinemann.

Wilhelm, J.K.  2004.  Reading is seeing: Learning to visualize scenes, characters, ideas, and text worlds to improve   
    comprehension and reflective reading.  New York, NY: Scholastic.

Representation

Instructional programs from prekindergarten through grade 12 should enable
all students to—

• Create and use representations to organize, record, and communicate mathematical ideas
• Select, apply, and translate among mathematical representations to solve problems

• Use representations to model and interpret physical, social, and mathematical phenomena  

- See more at: http://www.nctm.org/standards/content.aspx?id=322#sthash.UciPKHrR.dpu

Instructional programs from prekindergarten through grade 12 should enable
all students to—

• Create and use representations to organize, record, and communicate mathematical ideas
• Select, apply, and translate among mathematical representations to solve problems

• Use representations to model and interpret physical, social, and mathematical phenomena 

- See more at: http://www.nctm.org/standards/content.aspx?id=322#sthash.UciPKHrR.dpuf

Representation

Instructional programs from prekindergarten through grade 12 should enable
all students to—

• Create and use representations to organize, record, and communicate mathematical ideas
• Select, apply, and translate among mathematical representations to solve problems

• Use representations to model and interpret physical, social, and mathematical phenomena  

- See more at: http://www.nctm.org/standards/content.aspx?id=322#sthash.UciPKHrR.dpuf