Multiplication is not Abstract

I am honored to work with dedicated, smart, and caring educators. Carmella Crawford, another AIMS Professional Learning Facilitator, is all of these and I would like to take this opportunity to introduce her to you.

Carmella lives in Charleston, West Virginia, and has been an AIMS Facilitator for some time. She has taught all grades, high school through early elementary. She likes to say she was a “misplaced elementary teacher” when she was in a high school classroom! Carmella is an integral part of our ongoing FLICC/AIMS Math project (in Florida), and you can read more about those interactions here.

Last year she worked with teachers in grades 8-9 on Algebraic Thinking. This year she is working with teachers in grades 3-5 on Number Sense and Fractions. Here are some thoughts and reflections that Carmella shared with me about her current Florida workshops.

  • While she was working on an an AIMS task called “Building Rectangles” (Click here to purchase this task) a participant said, “I get it. I can do the math because I can form the picture in my mind!” The participant made the connection between the concrete, representational, and the abstract. Being able to visualize the problem made computation easier.
  • All of the workshop participants saw the connections between solving multiplication with concrete manipulatives, drawings that represent what they had done with them, and how the abstract algorithmic procedure related to the other two methods.

As a seasoned workshop facilitator, Carmella recognized that teachers could talk ‘area model of multiplication’ but had trouble using the model when doing multiplication themselves. They had a difficult time understanding that students first need to do math using manipulatives, then drawings or representations, and eventually get to the abstract. She took that opportunity to discuss the need for using manipulatives and having students draw their work.  She helped them to see that when teachers do not use manipulatives and drawings, teachers often move too quickly to the abstract. When that happens, students sometimes never make those connections in order to fully understand the concept of multiplication. Through modeling an AIMS task that teachers can use with students, Carmella was able to delve deeply into adult content knowledge and the pedagogy of teaching these concepts to students.

Helping educators to grow both personally and professionally is what AIMS Professional Learning is committed to do for schools districts, schools, and teachers. What connections are you making in the Professional Learning opportunities you are attending?

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