I have a beautiful baby girl, and when she was only about a month old, I came across another mom's blog that caught my attention. This mom was interested in the "Doman" philosophy for parenting and education, based on Glenn Doman.
I looked into Glenn Doman's books a little further and discovered a book about teaching math to very young babies. As a math dork, I had to check it out.
The book recommends using "dot cards" for teaching numbers to babies. It turns out that infants can look at the dots and recognize the quantity. They can identify very large numbers without knowing how to count and without knowing any numerals.
The book suggested creating or printing the dot cards (PDF available here) and showing them to the infant while saying the number. After slowly adding cards in each session, the infant has a concept of which set of dots represents each number.
Eventually, it has been proven that the infant can understand simple equations that are set up using the dot cards, such as the one in this image.
All of this is done before introducing the child to the numerals that we use to represent numbers. I really enjoyed the book and found quite a few fascinating facts and ideas in it. However, it got me thinking about using this type of visual representation for older children.
It made a lot of sense to me that these cards are a better way to introduce an equation than writing 4 + 5 = 9. The symbols that we use to represent mathematics can be abstract. We have assigned numerals to the quantities, but they are not necessarily intuitive to children. A child or baby can understand addition better visually (by seeing the dots).
I realized that we already know that this is true for many older students as well. In Algebra, we also assign symbols to quantities. I decided to try to adapt the dot cards to a similar style of visual learning cards that could be used for representing algebraic expressions.
Laws of Exponents
I realized that the Doman method was similar to the way I already like to teach the laws of exponents by rewriting each expression as a product of its factors, but instead of writing out each expression, I could use my cards. They can be put up on the whiteboard while I have students expand the expressions. The cards are a great visual representation to help show why the exponent rules work.
I started thinking of other ways to use these cards to represent different concepts. I put together a large set to stick up on the board and a small set to use as student manipulatives. I used different colors to help students remember to differentiate like terms. These will be great for teaching the distributive property and polynomial addition, because students can represent an expression, then pick up the pieces to move them and regroup them.
The Distributive Property
Here is a sample showing that "two of this quantity is really represented by two of each term."
combining like terms
When I taught middle school, I liked to color code the like terms in expressions by drawing colored boxes around the terms. I think these cards would be even better for visualizing the redistribution of the terms. Students can move the pieces around and really see that the groupings of the individual variables are changing when they combine like terms.
I am sure that there are tons of other applications for these cards. Download the cards by clicking on the picture! I have included the large cards for the board and the small set to print for your students. Combine them with the Doman dot cards (can be used to represent constants). Leave a comment to let me know if you thought up some other ways to use these in your class.
Here's the affiliate link to the book I read. Check it out if you have little ones and a math mind!
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