Dan Finkel's Video for Teachers
Enhancing Number Sense Through the Connection of Dan's Number Activity and My Daily Math Routine
At our October staff meeting we watched the video by Dan Finkel Ted X titled “Five Principles of Extraordinary Math” and after watching the video we engaged in the game called Prime Climb.
Without a doubt, Dan Finkel makes many valid and crucial points regarding the teaching of mathematics. I differ in my opinion with regards to one of the principals, and that was not to tell students they are wrong.
I've been teaching for 25 years and despite my experience, I'm aware I don't have all the answers. I believe, however, that it is important for our young students to make mistakes and even fail at interesting problems. We are not and cannot always be right and failure can bring about great success. I tell my students they are incorrect, but it is not done rudely or in a demeaning way. We work at figuring out why the error was made and through that we often come to the right answer. And the right answer sometimes doesn’t come at that moment or during that math class. It can come a day later, a week later or a month later. It happens when children make a meaningful connection through scaffolding and practice. I know for a fact that when they do make that connection they are so proud of themselves.
Perhaps you have a difference of opinion in dealing with children's mistakes. We may have different beliefs/ideas and ways in which we teach, but I believe the most crucial factor in our classroom is to create an intellectual community that is willing to take risks and share their ideas, right or wrong, with one another. Creating this environment is not always an easy task, but the time and effort are well worth it because the outcome is incredible. Not only are the children successful in their learning, they are also loving math class. My first and foremost goal in my classroom is to get my young students to enjoy learning math. If I can do this then I can present to them many challenging and interesting problems without having to deal with the negative attitude that many students tend to have and it’s not because they are not capable, it is because they have not felt the confidence in their mathematical ability. With this said, Prime Climb, is undoubtedly one of these challenging and interesting problems to give to students.
I am going to backtrack to my staff meeting where our administration engaged us in Prime Climb. Up on the SmartBoard screen were circles with numbers 1 to 20 and each circle was color coded. We were asked to pair ourselves up and communicate our thoughts. I believe it is beneficial for teachers to engage in mathematical activities to unpack their own mathematical knowledge. However, if I would have led this activity I would have provided teachers with manipulatives, just as I would with my own students.
So, I decided to try this game with my class . On Nov. 1st, Day 39 of school. I paired my students to play Prime Climb. I provided each pair with a number line 1 to 20 and a hundreds chart. I told the students to start off by talking about their thoughts. Then I told them they can pull out their crayons and choose to use the number line and/or hundreds chart to see what they can come up with. Listening to their conversations was fascinating as these young students are only in Grade 3.
It is important to know that my daily routine, right from the first day of school, includes the learning and understanding of what the school day number is divisible by or what factors there are . For example on Day 2, you can count by 1’s two times and by 2 one time, Day 8 we determined we can count by 1 eight times, by 8 one time, by 2 four times and by 4 two times. We have determined factors of numbers from school day 1 to school day 38 using a hundreds chart. And yes, my students use the vocabulary divisibility, factors and multiples, and I also have taught them about prime and composite numbers.
So what did I hear about the circles? I heard that all the numbers you can count by two’s had orange, all the numbers you can count by 3 had green, all the numbers you can count by 5’s had blue, etc. I also heard that two was orange and 4 had 2 orange because 2 x 2 is 4 and 8 had 3 oranges because 2x4 is 8 and 15 had blue and green because 3 x5 is 15. I also heard 11, 13, 17 and 19 were red because they were prime numbers.
I then asked the students if all the numbers divisible by 5 had blue, what is the next number after 20 to be colored blue? They were able to tell me 25, 30, 35, etc. I asked them to look at the 7 and it was colored purple, where was the next purple? 14 So then where would the next purple come after 20? They used their hundreds chart and I got 21. Then I asked would 21 be solid purple or would it come with another color. Many were uncertain, but I had one little girl (who is average in ability) say it would also be green because seven 3’s is 21. Within my program we discuss groupings of 7 within our calendar routine because there are 7 days in a week.
I will definitely come back to this activity a few times so we can further solidify our understanding to 20 and then extend beyond. I would be interested in challenging them with the questions, which are the next numbers after 20 to have 1 color? 2 colors? 3 colors? 4 colors?
My students really enjoyed this activity… one of my struggling students said this is fun. Now please keep in mind that 26 out of 26 students did not figure out what was going on at this time, but about 18-20 did. We won’t have 100% success with every activity we put forth, but what every activity should do is connect and/or be a scaffolding activity to that which they are learning and also provide a challenge for them. If they can’t figure it out during one math class it is perfectly ok. My plan is to do this activity again on Day 57. I shall post again after the 2nd round.
As you can see I was granted permission by Daniel Finkel himself to post the image of the circles 1 to 20 for the purpose of this blog post. I am grateful for his permission and I believe his work is valuable.