One of my favorite sites for promoting mathematical discourse and allowing students to see patterns and connections in mathematics is Fawn Nguyen’s ww.visualpatterns.org.
I first learned of this website from a Twitter chat that I regularly participate in and couldn’t wait to try it out with my students. I decided to try it out in our small groups and simply ask students the following questions:
- What do you notice?
- What do you wonder?
- What do you think will come next in the pattern? Can you draw it?
- Explain your thinking.
It didn’t take long for the room to be full of chatter around the task. The website quickly became a favorite and students would ask me throughout the day if we would be using it in small group.
In my opinion, the greatest challenge in teaching today is student motivation…and if you can find that magical tool that combines deep conversation, connections to mathematical concepts AND your students are excited about participating…you run with it for as far and long as you can!
One thing that I have noticed about students over the years is when they understand, when they TRULY understand a mathematical concept, they are eager to share their learning with others if given the chance to do so in a creative way.
The interesting part is that many times my students who are reluctant to share at first aren’t students who struggle with a math concept, they are students who understand the concept, but don’t want to be singled out by a teacher who always calls on them. They have come from classrooms that value answers and they have already lost their excitement for learning.
However, if we stop making mathematics about answers and start making it about problems that can have creative solutions, those students are just as excited to share as others because they get to show what they really care about…who they are and what they have to offer the group; Not a one word answer to someone else’s problem.
One of the many great things about Fawn’s website is that the tasks are low floor, high ceiling. Every student in the classroom can enter the task and begin talking about the mathematics they see. Look at this example. Each student in my classroom could count the number of objects, tell me what shapes they were, notice that there were more each time, etc. and the students who needed a challenge could easily set to work figuring out what the 7th image would look like while the rest of the students continued their conversations. It really is beautiful to see. Everyone working on the same task and every conversation a little different.
During this particular task I heard:
“No the fourth shape would have four on the bottom row because each time they added a row to the bottom with one more”
“They just added one more to each row.”
“There is 1 triangle in the first one and 3 in the second one…”
And students couldn’t wait to get up and explain their thinking to their peers. They even established ways to label their thinking to make it more clear to each other.
The amazing thing about these tasks is that they are giving students the opportunity to see patterns and relationships between numbers in a visual way so that they can create connections between concepts.
Math classrooms should be creative spaces for students to explore, connect, argue and explain. Places where students can be engaged in problems that are exciting and stimulating. When I find a resource that can support that goal, it’s a win!