A quick post!
The school year is officially underway, with one week in the books. Because we are on a block schedule, this means I’ve seen each of my classes twice.
This year, I’m teaching 1 section of Geometry, 1 section of Precalculus, and picked up 2 sections of Algebra 2 Honors. I’m super excited about my schedule, the mix of old and new, and the opportunity to teach an honors class at MA.
I kicked off my Algebra 2 Honors class with an awesome “Think of 2 Numbers” puzzle that came from the teacher who previously taught the course. He generously shared his entire (amazing) curriculum with me, and I’m so looking forward to digging into the cool problems and explorations he has refined over his 10 years with the course. Here’s the puzzle:
After playing with this puzzle long enough for the class to make a conjecture about how to figure out the 2 numbers (and putting a student on the spot to figure out MY two numbers), we did brief introductions, then moved into our next activity.
I decided to use this NRICH “Algebra Match” activity that has students silently, in groups of four, trade away cards with mathematical expressions until each group member has a matching set of 4 cards. The rules?
- No one can talk or give non-verbal signals to other members of the team.
- Each member of the team starts with four cards in front of them.
- The cards in front of each person should be visible to everyone.
- Team members can only give cards; they cannot take cards from someone else.
- Each team member must have at least two cards in front of them at all times.
Here is one of my classes busy at work on the activity.
After each group successfully matched the cards, I asked them to take a moment to reflect on the experience by responding to a few prompts. We discussed the first few together, and then I went home and read the answers to the last two (more personal) questions, collecting some of my favorite responses to share back to the class on the second day. Here are the questions I posed, and some of the responses I got:
What are some of the benefits of group work in math class? What are some of the challenges?
D Block responses
(p.s. not on the board, but on a student’s paper. “Group work is challenging when people are stubborn. It’s even more challenging when stubborn people are incorrect.” lololol)
E Block responses
(p.s. not on the board, but nearly half of the students in this class wrote that a challenge with group work is “being on the same page” or “getting everyone on the same page.”)
What do YOU need to be successful during group work? From your peers? From me?
D Block responses
- “I need space to work things out before writing down my ideas to be successful in a group. My peers would need to be willing to be wrong, but also willing to correct me if I’M wrong.”
- “I need to stay focused and finish my stuff.”
- “Nothing. I’m very easy-going and working in groups has always been easy for me.”
- “I need for everyone to be engaged and trying to do the work.”
- “Time to fully discuss with group mates. Hear out everyone’s ideas – not shut someone down.”
- “Time to fully work through and discuss the problem.”
- “A friendly atmosphere and teammates not significantly above or below my level. Clear directions and help if all group members agree we’re stuck.”
- “I need to communicate with my group mates and make sure I’m on the same page as them. I need my peers to be open to going over things and explaining problems if I need help.”
- “Be prepared and focused, fully committed.”
- “I need to make sure that I both listen and share ideas.”
- “Patience and focus from all the partners. Also, not rushing if even only one person is behind.”
E Block responses
- “People who fully listen to other ideas but also participate”
- “I need a diverse group of learners. I need some support because I usually take on a larger workload and get stressed or overwhelmed.
- “Good communication and time management skills (for myself). Willingness to share and collaborate (from peers).”
- “I really like being in groups that are quiet until everyone is finished and then they discuss.”
- “Time to understand the concept and not just follow along.”
- “Enough time.”
- “The time to think through problems first.”
- “I need to be able to distribute ideas and have them heard.”
- “To be successful, I need peers that work at about the same speed as me.”
- “I need supportive peers who are understanding, patient, and positive. From you I need mostly the same things, support being paramount.”
- “I need my peers to have a positive attitude, and be willing to share their ideas as well as listen to mine.”
- “The most important thing to me in group work is that everyone is kind and respectful to everyone and their opinions and ideas.”
- “Just no need for me to feel embarrassed if I am one of the few in the group that doesn’t get it.”
- “Lots of communication. Arguments are okay if they’re managed. Time to work on our own (in groups.)”
- “Group members who are open to opinions and not stubborn. Everyone should have a turn to talk.”
What individual goals do you have for yourself as a mathematician during group work this year?
D Block responses
- “I want to let others participate (in the past, I wasn’t very willing to let others do much for fear they would mess it up) during group work this year.”
- “Stay on track and always keep focused on finding the answer”
- “Collaborating effectively and sharing ideas to help each other along.”
- “I want to try to help other people.”
- “Having more confidence in group work and share my ideas. Don’t be afraid of taking risks and making mistakes.”
- “I want to collaborate better as well as develop my skills with algebra.”
- “Know when to step down. Fully understand everyone’s thinking, not only my own.”
- “I hope to actually understand the material instead of only memorizing answers.”
- “Be helpful and humble and learn to see things in different ways.”
- “Try to become more of a leader and take charge while solving problems instead of following what other people figure out.”
- “I hope that I can keep up to the pace of my peers and help them out too.”
E Block responses
- “To say more. Last year I was frequently hesitant to speak up and sometimes missed my time to shine!”
- “Share ideas I’m unsure about/take risks.”
- “Sometimes in group work I can get too bossy or take on too much leadership, or (depending on the class) I can also be scared to say anything, so I really want to find a happy medium for sharing my ideas.”
- “I would like to become better at solving problems faster.”
- “Be an active participant/leader.”
- “I hope to grow confident as a mathematician and perform the best I can. I hope to be able to help my peers and not just be someone who waits to be told something or have something explained to me.”
- “I want to feel more confident in my answers, and also feel more at ease with asking for help from my peers.”
- “More confident in sharing my ideas (if I’m not sure they’re right.)”
- “Step up when I need to and step back to get other people involved.”
- “I want to put as much effort and work into team work as I can, and have a positive attitude.”
To be honest, I wasn’t sure how this activity or the debrief afterwards was going to go, so I was pleasantly surprised to see that the task was sufficiently challenging (mostly because of the “no talking” requirement, although it did give me a sense of which students might be a little rustier with their algebra or need to rely on scratch paper vs. working in their heads) AND that they really dug into the discussion afterwards in a way that I think helped establish some class norms for group work that will pay off throughout the year.
At the end of class, we returned to the “Think of 2 Numbers” trick, where (again, stealing Jamie’s idea) the students had to prove algebraically why the trick worked for homework.
That was all just Day 1! Day 2 was even cooler! I’ve already written quite a bit and want to get back to enjoying my Saturday (it’s a beautiful day in the Bay Area!), but here’s the problem we tackled to start class on Day 2 and OH BOY did the students take it even farther than I had expected.
This is going to a fantastic group, and a fantastic year. I’m in love.