Post # 23 The Importance of Imagery and Simultaneous Processing

Students inspire.  They often teach us as much as we teach them.  My recent work at a school inspired me to find ways of teaching older students including some with moderate to severe disabilities.  I was tasked with coming up with a way to make the link between fractions and decimals real and the conversions between them more meaningful…not just a set of procedures based on words.  I came up with an idea based on a previous practice you will see modeled in the class, an extension so to speak.  It worked and I believe the students gained a new understanding of the link between the concrete representations. 

In the MSM I class, you will see clay used to demonstrate decimal fractions on a place value chart.  Before having the students create the decimal fractions though, I used a new and simple chart available in the supplemental materials section of your folder.  It simply has “ones” and “fractions of one” as its sections.  I asked students to use clay to model halves and fourths using our “handy dandy fraction creator tool.”  They had no difficulty in doing so.  Then we changed colors of clay and created the decimal fractions emphasizing the visual link to the based ten blocks.  We created tenths, hundredths and thousandths.  They realized that unlike the traditional fractions, they had to create fractions consistently by cutting each previous shape into tenths.  This stressed the essential differences between fractions and decimals.  We ended with applications involving whole numbers using fractions and decimals interchangeably.  At some point, I will film this lesson and post it on the website as a demonstration, but that is for another time.  We can talk about this in our video conferences. 

The second component of my demonstrations lessons involved simultaneous processing and the importance of “near point” references.  We were making the link between money and place value using the organizer in your manuals.  These were high school students in a consumer math class learning to make change.  Each student was given a hundreds chart from which we practiced counting by ten from any number:  sub-skill.  Then as we constructed quantities with real change on our place value mat, we used the hundreds chart to keep our place as we counted by tens to near 100 and the by ones to make the final change from a dollar.  Using the simultaneous processing and both hands helped the students keep their places and successfully make change with coins.  I believe it was a successful lesson and as closure at the end, one of the students remarked that it was really “neat” the link between money and place value which she finally understood.  “It really helped to see that,” she said. 

Of note:  the final piece from that lesson was later applied to a second grade class- the importance of having a counting chart within near point copy range.  The number line high on the wall does not provide the intimate access that many students need for counting.  Those who must follow with their fingers, need desk copy access to number lines and counting charts. We would call this a “near point copy.”  For many students it is an essential tool for self-monitoring and metacognition.