Intro to Math: Circles and Squares

School is back in session! One of the students I tutor apparently has no homework tonight, otherwise I don’t know when I would have had time to put this into writing – things got busy in a hurry.

I’m doing the whole #teach180 thing so if you’re desperate to see more frequent updates from the classroom you can follow me on Instagram, @multiplefactorsi. I’ll be posting every day, held accountable by a reminder on my phone. I hate tiny little red numbers on that screen, so you know I’ll be following the rules.

Anyway! The first week of math class I always do “intro to math.” We started with some talk about what topics in math we were going to do over the year, and then we spent some time on an arts integration project inspired by these tasks for small children. This would have been awesome if we had more time, or maybe they would have gotten old – who can say? A couple students finished them beautifully at home, and others have kept their unfinished projects in case of momentary boredom. I’ll attach that whole assignment.

img_0565

img_0572

PDF of the assignment: day-1-arts

The second day was all about seeing things from multiple perspectives and integrating multiple viewpoints into collaborative work. We started with a number talk, something I loved when I first saw it but just never used. I took the one from YouCubed’s “Week of Inspirational Math,” week 2 day 1. I had been very nervous that our conversation would be nothing like the thought-provoking and joyful example video, but this went amazingly. Here’s our board:

img_0574

Inspired by Sarah at Math = Love, who was in turn inspired by other bloggers, we then launched Broken Circles. That was great! I love hearing students talk about math, but I also loved the no talking rule. It’s also an inspired touch that one circle completes itself. In one group, the person with the “A” pieces sat there, self-satisfied while the rest of the group struggled, and it was kind of glorious. It’s almost like the point of this task was to show that working together and paying attention is crucial.

Between that and our next collaborative task, we went over our group norms. I translated them into Spanish for an extra touch, and perhaps that will inspire me to do more group work in Spanish class? Time will tell.

img_0577

The end of Wednesday we started the Pentomino task – I blogged about Pentominoes last time I did it, SO long ago! This year I didn’t leave as much time and consequently they didn’t come up with quite as many combinations, but I do still think it was a useful exercise in visualization and pattern recognition. I’m kind of in love with my independent reflection for that task, attached. Why indeed can you not build a 6×6 square?

Independent Reflection PDF: pentomino-ir

Things are shaping up, but I already know I won’t have nearly enough time to blog as I’d like : 0

Factoring Amazing Race

Sometimes I have a strong temptation to use my blog solely for successes and never mention anything that isn’t great within my classroom. But I recently had a realization so simple that I don’t know how my teaching could possibly have been effective before it! Realization: students won’t work together effectively until they are together on a team.

kids amazing racing

We had this excellent all-school camping trip last week, but as a consequence class did not take place for an entire week. I was concerned that they would have forgotten everything, so for my Math 2 class I created an Amazing Race game to review and practice binomial factoring. All along I had been encouraging them to work together and ask each other questions, but everyone was either lost and totally un-focused, or focused on doing their own work, not motivated to help others.

amazing race cards

I had them in 3 groups for the Amazing Race. I put three students who were on the verge of full understanding with an extremely competent but extremely quiet student. My thinking was that the quiet student could shine and the on-the-verge students would quietly listen in order to gain full understanding. This group was fairly effective although never fully cohesive – I mainly saw them interacting one-one-one rather than as a full group. I put four on-the-verge but potentially less-motivated students together so that they would all have to participate fully in order to understand. This went well – some of the best conversations came out of this group. Then I put a brilliant and patient student with a very silly but very smart student and two students on the struggle bus. I think that at least one of the strugglers is doing really well after that, but the other one is still struggling. I’m feeling sad about this but I’ll catch up with her on Make Up Work Day.

Intro to Math Week Year 3: Arts Integration Edition

Just finished my last academic day of the first academic week of the school year. As it has been for the last couple of years, this week is “intro to math week,” and this year I focused specifically on arts integration, keeping the mathematical standards of practice front and center.

On day 1 we spent some time on the syllabus, focusing on class procedures and previewing the upcoming units. Thanks to keeping this blog I have plenty of pictures of previous classes doing the work they’ll be doing, so it’s not just a line about functions or data or whatnot on a sheet of paper. Then I had them each take a Math Attitude Survey. Somewhat unsurprisingly, most of the new ones had some pretty negative associations with math. Kids also weirdly LOVE sharing bad experiences in math classrooms, so it’s a nice first day icebreaker. I took everyone’s three words and put them into a word cloud:

math word cloud 2015

I’ve always been too scared to re-administer the survey at the end of the year, but I think I should do it, or at least have them give me three words again.

The next day was all about arts integration. I had them re-examine the mathematical practices and compare them to the National Core Arts Standards, since I had personally noticed so many great links. Some of them were a little unsure at first, or had trouble understanding what individual standards meant, but they didn’t shy away from asking each other or me for clarification, and the resulting conversations were pretty cool.

art and math

Then we watched this TED talk by Daina Taimina, or at least most of it – it’s super long [for my kids’ attention spans & non-university math levels] and the important parts are at the beginning and end. I love this talk so much though. It inspires me to see her construct her own understanding, especially given her initial troubles with the subject, I enjoy seeing stereotypes smashed, and is the perfect example of arts integration. The art form makes the mathematics more concrete and comprehensible, and the mathematics provides structure and context for some interesting-looking pieces.

Typically I have some major emphasis on group norms, but I didn’t want to insert something else random into this week, so instead today we just had an extended journal reflection and then dove right into our first topics. I’ll teach them the group norms as we start doing our first group tasks. I realized earlier that I’ve never actually blogged the group norms, so I’m working on a separate post about that.

So far things are going well BUT hey it’s only the first week.

Intro to Math Week

The first week of regular classes was an “Intro to Math” for all 4 groups.

Day 1: Syllabus (boring) & growth mindset (inspiring!)

Day 2: Establish group norms & introduction to Pentominoes

Day 3: Pentominoes Task

For their first collaborative challenge, each group had to come up with as many different ways to form a 5×5 square using Pentominoes.

Image

Between the 4 classes, the students came up with 193 distinct ways to form the squares! I’m very impressed with their teamwork and problem-solving skills so far.

To wrap up their work in groups & introduce an element of individual accountability, I gave them an independent reflection that is a little bit more abstract. We didn’t finish that in class last week so we’ll go back to it on Monday.

As classes get into full swing I’m very quickly realizing that:

1. I do NOT have enough time to cover everything! At our school, every Tuesday is a field studies day, plus students all either do service learning or an internship on Fridays. Classes are already only 50 minutes long, but on Thursdays they’re 30 minutes because of the school meeting & P.E. (I’m teaching yoga!). The schedule is awesome and the students get lots of valuable experiences they wouldn’t ordinarily be able to have, but it’s a huge challenge for an integrated curriculum.
2. Teaching 4 totally new classes is going to be really difficult. Most of the material I have taught before, but in a different order, or a different way, and certainly to different groups of students. I alternate between being REALLY EXCITED about trying new stuff and REALLY OVERWHELMED at how much work I have to do on a constant basis.

I hope everyone else has started off the school year well!