As I watched my daughter Bethany do her homework last night I had an Aha Moment. She complains almost every day that she has addition and subtraction homework. Apparently, she does not have her mother’s love of math. (I’m working on that.) Her paper had simple numeric addition and subtraction, and she decided that she would make up stories so that it would be more exciting! Her fingers became many things. They were friends that would play together or anything else she could imagine. She smiled a lot and showed me she understood Change Plus/Minus situation.
For young children, the world is their playground. We need to take that world and show them the math around them. Bethany loves to be social, so when the math had a connection to her world, the math came alive!
Douglas Hofstadter,an American professor of cognitive science whose research focues on analogy-making, discovery in mathematics, and much more and Emmanuel Sander, a Professor of Cognitive and Developmental Psychology who specializes in the study of analogy-making and categorization and their connections to education, discuss how analogies and categories (concepts) are the “fabric of cognition” (Hofstadter and Sander, 2013). Bethany was using analogies that could fit in the category Addition and Subtraction. Now I would like to help her see how three situations are in that file: Change Plus/Change Minus, Decomposing/Composing, and Comparison. (If you want to explore these categories in more depth, you can click on each situation name to view the series of posts I have written discussing them.)
Addition and Subtraction is going to go back and forth from a child’s world to the world of math. Children need to function in both worlds and see the connection between them. My son, Josiah loves the world of math, whereas my daughter Bethany loves the real world. I’m not sure about youngest Lilly, but I’m guessing it will be the real world.
I have talked to countless teachers about teaching word problems. It seems that students always seem to struggle with word problems. In my next few posts, I will explore how we can make word problems engaging for young children and how we can give our students some analogies to understand where each of the addition and subtraction situations can happen in their world. It is important to remember that concepts and categories are formed through a long series of spontaneous analogies. (Hofstadter and Sander, 2013)
I have created a few different word problems for students to role-play addition and subtraction for Change Plus/Change Minus. Click on each of the images to download a PDF.
1. Model filling in appropriate numbers for the blanks.
2. Start with small numbers at first. (You could even use 1, 2, and 3.) Once the word problems are easy to use students can use more challenging numbers.
The reason I wrote four different scenes is so that students will see connections between the different real world applications.
Where have you seen your students or kids add and subtract in their world? Stay tuned for more thoughts and tools for making word problems engaging.
Click here to see “Making Word Problems More Engaging, Part Two.”