(By Dean Ballard, Director of Mathematics, CORE, Inc.)
Numbers are all around us. Let’s teach children to embrace rather than fear numbers.
Interested in more great professional learning resources for Math? Check out another CORE blog: Getting Math Group Work to Work
My wife is a real number-phobe. Although she passed Calculus with flying colors, if you throw numbers at her she runs the other way. She is an extremely intelligent person, but from her perspective numbers are dogs and she is in constant danger of being bitten.
My daughter teaches elementary school. She knows numbers don’t bite, and she wants her students to know that as well. In her Kindergarten class she has the alphabet on display across the wall in the front of the room and under each letter is a number. The letters are numbered in order from 1 to 26. Every day the class plays a “decoding” game. My daughter puts up a space for a “secret” word or words on the board and puts the numbers for the corresponding letters underneath where each letter goes in the word. The class decodes the secret words by identifying the correct letters based on the numbers. For example, the one below decodes to, “Math is good.”
It has turned into a fun, simple, and quick activity to identify numbers, letters, and words. My daughter knows this is not the same as the students knowing what the numbers mean. It is an activity designed to help students get comfortable seeing, identifying, saying, reading, and playing with numbers, and best of all, the numbers don’t bite.
I observed another elementary teacher put numbers on the circle time rug. She taped down one number for each student. Sometimes students were randomly handed a card with a number, and they had to find their number on the rug and sit on the number. They also had to say their numbers and say the number that came before and after their numbers. Students gained familiarity with numbers while focused on finding their seats. They were more concerned with whom they were sitting next to than how they sounded saying the numbers. After all, the numbers don’t bite.
In a sixth-grade class I observed last year students were sitting at tables. Four students were at each table. The teacher asked students to work with a partner to come up with a formula for figuring out the maximum number of students who could be seated in the classroom. Given eight tables in the classroom. students came up with 8 x 4 = s, 8 x 5 = x,and some even said 8 x 6 = m, suggesting they could fit as many as six students at each table if wanted. With some teacher-facilitated discussion the students decided on the variable ‘m’ to represent the maximum number of students who could sit in the classroom and to use ‘n’ for the number of students per table. This led to the formula, 8n = m, which everyone was happy with and understood. Then a student pointed out that two extra chairs were at a side counter and were sometimes used when the teacher was mad at someone or when visitors were in the room. They decided those should be counted in the total. Thus, the formula became 8n+ 2 = m. Everyone understood this version of the formula as well. They spent another ten minutes playing with this formula. The teacher asked what the maximum number of students would be if 3 students were at each table. She also asked what the number of students per table would need to be if they had 58 students in the room (for instance, if another class came in to join them). Students used various methods to figure out the 58-student question. The teacher then asked what they would do if they had 31 students in the classroom. Notice there was no whole number solution for nthat resulted in 31 in the formula 8n + 2 = m. This led to some debates and creative ideas, all of which included students finding different combinations that worked. Since the numbers and variables were recognizable as objects in the classroom, students were able to come up with a plan for “fixing” the problem. Some students took the initiative on their own to veer from the formula, while some needed to hear that it was acceptable to be creative and change the conditions if needed. A couple of students figured out a value for nthat would work in their formula — they calculated it would be 3.625 students per table. This also led to some interesting class discussions such as, “Did they do the math right?” and “Were there any problems with this solution?” In the end the complicated math was just an interesting puzzle and numbers were just puzzle pieces.
I’ll share one more example, this one from outside the classroom. I read about a parent who often played the “I Spy” game while driving around town with her children. She incorporated numbers all the time. For example, she would say, “I spy five white cars” or “I spy two red shirts.” Her young children were having fun with mom learning and using math. They were learning that numbers were everywhere.
For any student, as well as for adults, math can be a handy tool or it can be a frightening, barking dog. I am excited to see so many examples in classrooms and at home today of teachers and parents using numbers as part of everyday activities where kids are using numbers with flexibility and understanding, not withdrawing their minds for fear of being bitten.
Links to resources with additional ideas for seeing numbers everywhere:
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