TED Talk Dan Finkel: 5 Ways to Share Math with Kids
Updated: Mar 11
I love watching TED talks, especially ones that are geared towards educators. I recently stumbled upon a TED talk by the mathematician Dan Finkel. According to his website Mathforlove, Mr. Finkel has his Ph.D. in mathematics and is a former college math teacher. I wish I could say that I loved math as much as Mr. Finkel does, but to put it simply, math and I are not best friends. In the past few years since I have begun teaching, we are no longer mortal enemies, but we are still not on the best of terms.
There have been three key moments in my life that have stuck out with me regarding math. The first one was when I was in fourth grade and my teacher stuck me in the low math group. She didn’t flat out tell me that it was the low math group, but I wasn’t stupid, I knew it was. She then proceeded to tell me that some kids just don’t get math and to not worry about it, I just wasn’t going to be good at it. I can’t imagine how this would go over in today’s classroom with so much discussion surrounding a growth mindset. The second moment came when I was observing a sixth-grade class while I was working on getting my teaching credential. I told the teacher that I didn’t want to teach sixth grade because I was bad at math. She looked me in the eye and said, “I’m bad at math too, but you are forgetting something. You have the answer key”. That statement had shocked me, she was right. I never thought about the fact that the teachers had answer keys. I wasn’t thinking, however, that I would still have to be able to TEACH my students HOW to solve the problem. Having an answer key is great, but they do not teach your students for you. The last moment came when I was in college, probably around the same time as the answer key comment. I had a professor who everyone hated. They made fun of him all the time and talked about him and his accent. I was scared to death to go to class because I heard how mean he was. However, it was the professor who taught me math! He has always stuck out to me, and I wish I could reach out to him now and say thank you!
Now it’s time to dive into the TED Talk from Mr. Finkel. Mr. Finkel discusses 5 different ways to share math with students.
Start your math lesson with a question.
For years now I have started out my math lesson with a question. I find that even in a virtual environment this is possible. My favorite way to start the lesson is with a technique called “Which one doesn’t belong, and why?” I will post an image and have the students tell me which one doesn’t belong and why they think it doesn’t belong. At first, they are stumped, even my student teacher gets stumped the first time we do this. My students think that they need to give the correct answer. However, I tell them that there is no correct answer, if they can justify their thinking then they are correct. When given enough time (at least 10 minutes) the students come up with lots of different reasons why they believe their image doesn’t belong. I do this either as a whole class activity or send them to breakout rooms to discuss first.
Another way I like to start out a lesson is with a number picture. I will then have the students make up their own stories based on the picture. This takes some time, again, at least 10 minutes, but given enough time the stories that the students come up with are worth it.
Mr. Finkel started the TED talk with an image of 60 different circles, of all different colors and had the audience analyze them. This is known as the Prime-Time Color Chart. Students should analyze the chart and come up with any wonderings and conjectures. Mr. Finkel doesn’t give the answer in his talk, which leads to the next two topics.
Give your students time to struggle.
Your students need time to struggle! Let me say that again, THEY NEED TIME TO STRUGGLE! Do not just give them the answer to a problem, do not assume that they need to be taught how to do a new math concept right away. Present the problem, let them think about it, let them talk to their peers about it and try to do it on their own first, and then once you have monitored their work, provide the lesson. This is a hard concept for many teachers because we are nurturers by nature. We love our students, and we don’t like to see them get frustrated, but learning is about playing around with numbers, trying it out on our own first. If we just teach the lesson first, without allowing time for the productive struggle they will always assume that they can’t do it.
I have started using metacognition thinking stems when I teach a challenging math lesson. I have the students use these stems and respond to the problem first before I have them work it out. They need that time to analyze and practice before I step in. This is not to say that you give them an advanced algebra problem and tell them to do it and never review. This means that you are giving them the opportunity to struggle for a little bit, and if you see no one is getting it, or your chats are empty when you are monitoring your breakout rooms, THEN you bring them back and start teaching. But if your chats are full of comments (on the topic of course) and students are trying to work the problem out on their own, then let them struggle! This leads me to the next topic that Mr. Finkel discusses.
Remember that you are not the answer key.
You do not need to provide answers all the time. It is okay for parents and educators to tell our students “I don’t know, let's figure this problem out together”. Teaching our children to be curious about math and exploring math problems gives them time to understand math. Instead of giving them the answer, allowing them to collaborate, explore and argue about the problem. It gives them time to show you what they really know.
I began seriously using this topic in my virtual classroom last week. I presented the students with a word problem that I did not know the answer to. I had purposely not worked it out ahead of time like I usually do. I presented the problem to them in our whole class, and we used metacognition thinking stems from what I discussed above. Students had to think about the problem and explore the problem first. After they had been given a few minutes to explore the problem we discussed it as an entire class. Being a word problem, many of my students struggled, they had no idea where to start first. There were many different numbers in the problem, and it was multi-step, meaning they had to multiply and subtract the problem.
After we discussed it as a whole class, I sent them to their breakout rooms for further discussion as I monitored the chat and helped to guide their questions. When we came back into the whole class, I felt students had a better grasp of the problem but were still struggling to figure it out. As a class, we read the question again, and I had the students draw a picture to represent their thinking. This seemed to help, as it usually does so I sent them back to their breakout rooms once again to try and solve the problem. As of this point, I still had not given them any answers, I just listened to their questions and asked guided questions of my own. As they worked in their rooms, I could see that they were still struggling, they were not multiplying like they were supposed to. So, back to the main classroom we went.
By this point, the students had a lot of time with the word problem and were much more willing to share their thoughts and ideas. I had one student who was able to answer the question right away, but instead of having her share the answer, I helped her to teach the rest of the class. I didn’t share with my students that she was correct, I just had her share her thinking. Once she came to the part of the word problem that my students were struggling with, we slowed down, and I had her carefully explain what she did. Lightbulbs went off in most of my student's heads. Back in their breakout rooms, they went to further explore. After 45 minutes on one question, my students FIGURED IT OUT! I did not give them any answers, they did it. 45 minutes for one question you may ask. Yes, 45 minutes. Was it worth every minute though to see the light bulbs go off for my students, yes, it was.
Say yes to their ideas.
Yes, students need to understand basic facts, and we do need to correct them on basic facts. The example that Mr. Finkel gives is that a student comes to you with the answer of 2+2=12. This is a time when yes, the student needs to know that 2+2 is 4. However, before you flat out tell them they are incorrect, have them prove their thinking to their peers. As Mr. Finkel says, it is more empowering to be shown you are wrong by your peers than told are wrong by your teacher. Saying yes to their ideas gives them a chance to prove their thinking and allows for debate and collaboration between their peers. According to Mr. Finkel, this is how new math is created.
When a student is incorrect, or even when they are correct, I do not give them the answer (remember, you are not the answer key). I ask them “Are you sure? Please check your work, or maybe as a peer to review your work.” This drives a few of them insane because it forces them to prove their thoughts further, which is what I want from my students. When the ones who are correct must talk to a peer about their work the student usually ends up teaching their peers how to solve the problem, which in turn makes them even more proficient at the topic. When a student is wrong, and they go back and try to prove their point, they often find where they messed up and can come back and teach a peer how to solve.
Give them time to play.
This has been a challenge virtually. Over the summer, when I thought there was still hope of returning to my classroom I had purchased the book "Math Recess: Playful Learning in an Age of Disruption". I was super excited to read it and then put it aside once I learned that we would not be returning to our classrooms anytime soon. As I am skimming through the book to write this post, I have realized that there are ideas that I could put into place in my virtual room. Things that I didn’t think were possible in an online environment. I wish I could include some of these ideas in this post but honestly have not tried them yet. Next time!
I would highly recommend watching this TED talk and checking out Mr. Finkel’s resources on his site. I am excited to read “Math Recess” over the course of the next couple of months and to further dive into the 5 ways I can share math with my students.