| My work with a group of teachers last week about teaching mathematics through inquiry has made me think about teaching and learning and cognitive psychology. In our zeal to help kids be automatic in arithmetic we often forget to do the groundwork that is required for automaticity rather than memorization. Automaticity is a description of how well someone can recall something. Memorization is a way of learning something. They should not be confused! |
 |
| Everyone wants the students to know their number bonds with automaticity. The question is how to learn them. Advances in cognitive psychology have taught us that memorization should not be the automatic answer! |
| First, students need to understand what addition/subtraction and multiplication/division are. They also need to see them as two sides of the same coin or, as mathematicians would say, as reciprocal operations. A student needs to really, really understand that knowing just one member of the number family, 3 + 4 = 7, gives you access to all of the rest of the family: 4 + 3 = 7, 7 – 3 = 4, 7 – 4 = 3. Really, really knowing that can reduce a lot of anxiety about the number bonds! |
| Second, we need to remember that spending time on building a good foundation about number will pay off. Children need to experiment with quantities in order to make sense of them. They need to see examples of 5ness, 6ness, 7ness, etc., in a variety of forms with a variety of materials so that they can visualize them and construct a meaning for that quantity for themselves. They need to see that 1 set of 12 and 12 sets of 1 and 3 sets of 4 and 4 sets of 3 and 6 sets of 2 and 2 sets of 6 all have 12 objects in them but they are configured differently. They need to be able to visualize how many ways 12 can be distributed equally among different sets to really, really understand what multiplication and division are all about. |
| If your inquiry is how to support this sort of learning I would suggest a glance at the work of Marilyn Burns, Mary Baratta Lorton, Kathy Richardson and John Van de Walle. They are great sources of information about how to create an environment and set of experiences for students to really, really understand addition/subtraction and multiplication/division and how numbers can be visualized. Read them! |
Ellen, I like the way you distinguish between automoticity and memorization. I learned something from reading this article about number. I will be working with 5 year olds soon and it has prompted me to reflect on how I will provide them with the multiple ways of constructing meaning for themselves.
Very interesting points you have observed , appreciate it for posting . vps hosting | best vps host |
Do we need less ‘automaticity’ in our schools, and more thoughtful working through ideas?