I often joke that my job is 50% math teacher, 50% motivational speaker because most students come into my classroom with their minds made up … they are not a math person. Don’t even get me started on the ridiculousness of that statement 😉 Other than the two periods I teach in our new math program, I teach Algebra Readiness to freshmen (and some select sophomores) that do not demonstrate a strong math foundation and I teach Financial Algebra to juniors that are not tracking towards Calculus (for whatever reason). I tell you this to illustrate that I teach a particular cross-section of students that are VERY mathematically-adverse. Many of them have felt beaten down by this beautiful subject that I love … so how do I bridge that gap?
I intentionally do a lot of “low-floor, high-ceiling” number puzzles to engage my students at the beginning of class. For example, “Use four 4s in an expression to equal any number between 1 and 20.” Everyone can engage in this type of problem, even if it is just with addition, but some will venture to include exponents, radicals and factorials. I opened up my classes with puzzles like this everyday this week and last, but never were they more engaged than when I put the numbers down and replaced them with dots. Yes. Dots.
I projected this image for about 30 seconds and asked the students to figure out how many dots are in the picture without counting each one individually.
Look at how many different ways my students saw this problem!
I used this activity to build culture and illustrate the things that I value in my math classroom:
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Everybody can “do math”. When we restrict “math” to memorizing formulas and solving equations, it is boring and so challenging. Remember the last time you had to memorize something that didn’t matter to you at all? It’s nearly impossible. Math is about finding patterns! When we show examples of math as a creative and visual subject that is all about figuring out patterns, it opens up the content to students that closed the door on it a long time ago.
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Visual math is the best math. When we teach students to see math visually they are using more pathways in their brain (think “right brain vs left brain”) and learning at a deeper level. If you are interested in reading more about the importance of visuals in mathematics, this is a great article: Seeing As Understanding: The Importance of Visual Mathematics for Our Brain and Learning
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There is more than one way to solve a problem. 12 dots and almost that many different ways of seeing the arrangement — in one class! When I showed the original dot diagram after we share strategies, the students enjoy trying to see it in the different ways their classmates saw it. There’s a lot of “Oh yeah!”’s and “I see it now!”s. Many students believe there is only one way to solve a problem — the way the teacher did it. The problem with that is if the student sees it differently than the teacher, they immediately think they are wrong,
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Listening to multiple perspectives helps everyone to have a better understanding of the problem. Have you ever looked at an optical illusion and searched for a face when all you can see is a vase? Sometimes it doesn’t matter how long you stare at something, be it an illusion or a math problem, you just. Can’t. See it. That is often what happens in math. The teacher explains one way to solve a problem and you just can’t see it that way. When we encourage students to share their thoughts and strategies, it opens up possibilities for understanding. I looked back at the 11 strategies on the board and reminded the students that if all we hear all year is 2 or 3 of these perspectives, we will be failing to make the learning accessible to everyone.
How did you see the dot diagram?
What activities or discussions do you do/have in your class to build culture at the beginning of the year?