Building Mathematical Comprehension, Chapter 5

   
     Chapter 5 is about visualizing mathematical ideas. An advantage Sammons points out is students today are surrounded by visual images through technology and media. The disadvantage is these images are given to them-they do not have to create them on their own. Students have to create their own when reading or problem solving. Comprehension is increased when students are able to create these mental pictures automatically. The opposite is also true, students who struggle with creating mental images on their own struggle with problem solving.

     Skilled mathematicians use visualization to help them during the problem solving process. Students need explicit instruction to understand the importance of visualization in math. They need this strategy modeled through think alouds and then the opportunity to implement this strategy with teacher support before they are held responsible for using this strategy on their own.

     Students need to be able to visualize multiple representations during problem solving. Students use their background knowledge and new information when creating mental images. When their new information disagrees with their background knowledge and they are able to work through that, their understanding of math is increased. The more representations they are able to generate means the greater their ability to decide which representation best represents the problem solving situation.

     Sammons gives 7 steps you can use to teach students to create mental images from words.

• Create mental images of observed concrete objects. 
• Create elaborate mental images of imagined concrete objects.
• Envision familiar objects and settings from their own experiences.
• Add familiar acts and events, then relationships and settings. 
• Picture characters, settings, details, and events while listening to a story read or told aloud. 
• Study text illustrations. and use them to create internal images. 
• Create mental pictures independently.

     Sammons also suggests taking a picture walk through your math textbook or other math related book so students can add those mental images to their bank to recall at a later time. I think this would be great to do when introducing a new concept so as you begin to get into the specifics of of that concept students have an image to build on. She also discusses using the visualize, draw, share strategy. The teacher reads over a list of statements about a concepts, students visualize, draw their images, and then share with each other. This gives students another opportunity to stretch their understanding and add images to their mental banks by seeing and discussing each other's images. She also suggests having students use a multiple representations graphic organizer. You can grab the one I created by clicking on the image.

   
     The two suggested math stretches for visualization are:

1. What do you visualize when you think about _____________? You fill in the blank with your concept, for example: multiplication. Then students write on a sticky their image of multiplication. They could draw an array or area model. They could write that multiplication is repeated addition or a real life example: My mom bought a box of pop tarts last night. They are 4 pouches in the box and 2 pop tarts in each pouch. There are 8 pop tarts in the box. They could also write an equation 3 X 3 = 9. Emphasize that their contributions should be unique. They add their sticky to the chart, and then as a class discuss the different images for the concept. 
2. What does this representation mean to you? This is opposite of the first stretch. You draw an image on a chart and they record what the image represents. You could draw two groups of apples with 3 apples in each group. They could write 3 X 2 = 6 or 6 / 3 =2. They could write 2 girls each have 3 apples. They have six apples together, etc. 

     Sammons ends the chapter by suggesting you use children's literature and poetry to help students create mental images. She outlines a daily plan for implementing poetry in the classroom which is very similar to what I did during the poetry section of shared reading when I taught kindergarten.

• Day 1: Read, modeling fluency. Then read together for enjoyment. 
• Day 2: Focus on vocabulary, especially math vocabulary and take time to correct misconceptions.
• Day 3: Highlight a mathematics skill related to the poem.
• Day 4: Come up with and perform actions for the poem.
• Day 5: Visualization practice occurs. Students create mental images and share out. Then they illustrate their poem and add it to their poetry notebook or journal.