Diving into a connected series of lessons this week, I am trying my first rep at creating students who are authors of their learning in mathematics. The lesson series is the culminating process of three areas of mathematics innovation I have learned from Brian Stockus’ (@bstockus) Numberless Word Problems, Chris Shore’s (@MathProjects) Clothesline Math, Annie Fetter’s (@MFAnnie) #NoticeWonder, and mathematical literacy. Similar to app smashing, putting these pieces together made sense to me, so last school year, I created this series of lessons around 3.OA.4, a problem our girls were having a hard time with at the time this series was created. Through this process, our girls formalized their thinking, and became masters of their understanding here.

As with most learning experiences, I wanted to start the girls with a #NoticeWonder experience, but I needed a problem to build this around. The right problem makes a big difference in getting exhausted students with negative mathematics experiences to begin the journey anew. The Frameworks for California Mathematics for third grade provided an excellent pseudo context to build the problem around, when I found this example, I knew I was on to something.

Two things that made this problem stand out:

1. The problem has a feminine hero, powerful for learners to identify themselves in the role of the main hero.

2. The problem has monkeys, who does not love monkeys, so interest factor immediately built in.

Although I had the problem in hand, the problem was too manufactured, it lead straight to the problem, and students could access, or they cannot. About this time, I had discovered Brian Stockus’ Numberless Word Problems, I loved, loved, loved this approach to inviting students into the learning, and this seemed like a natural fit. Stripping the problem down to build up to an open ended prompt, the natural fit for this process was a #NoticeWonder approach. I went one step further, using a strategy similar to my use of the Fraser model, called a Diamond Paper that Dr. Boaler introduced to our learning cohort of improvement specialists. The one sided paper is now two sided, with the problem solution on one and the #NoticeWonder problem on the back.

For each passage, students write a #NoticeWonder statement, then share with their partner, then share out whole class. This slow process grows in complexity each time. And with a couple of reps under my belt now, I am not surprised that students will proudly proclaim the answer to the Frameworks problem usually around the third time we #NoticeWonder, which provides immediate satisfaction, but isn’t the center stage of learning.

The 4 statements I created for this problem are:

Once students are through this process, they create a question from their #NoticeWonder statements. The range of questions if usually interesting, but this is their first rep at doing this process. Next, the students share their created questions with their partners, and then their group. I then have them flip their sheet over, and they must synthesize their questions together, or create a new question that the whole group is going to answer. After a few moments, the group shares out their questions, I project them and write them down by group, and this is their second and third reps. Finally, we, as a class, synthesize these questions down into one more question, we all write down in our diamond on the flipped side.

Once students have their question, the students go about solving our problem. Having usually done this in pieces, this week I got a chance to attempt this part and it took a whole two hours for students to get through these pieces, including the solutions. I will note that the students were with me the entire time, and we did do a couple of brain breaks (a stretching routine and a couple of GoNoodle sing and stretches). The great thing was one student stopped me and said, “This is so great, I wish we could do it everyday.” I asked her what about the process she liked and she said it was the writing…I know, these students liked to write about the mathematics. Another good note, the teacher said after she returned from taking the students to the bus that several of the students told her that their brains hurt, and they knew that that meant they were learning – we are a growth mindset district and that’s the power of harnessing the work that Dr. Jo Boaler and others are doing.

The next day is our short day, the second lesson is a kinestetic activity for students, and to test if the learning from the previous day actually stuck. A bonus from the previous day, I lucked out that one of the students started solving the class problem with a number line and that made for a natural opener. So I started with a picture of this students work and I ask the students to #NoticeWonder again (I loved when the student recognized his work was being highlighted). Moving into modeling what the students are going to do, the teacher, a student, and myself all worked together to model it. We had less that 30 minutes to launch this problem, with almost five minutes before the students left for the day, the students were launched on their task. It was an amazing flurry of using jump ropes and paper tents to sequence the numbers. There were three blank tents that students were asked to write the number they identify from the pattern. This uncovered some great misconceptions, as most students nailed the pattern, but made mistakes on writing the blank numbers. One group wrote had 0, 4, 8, 12, 16, 18, 24 and another group sequenced 0, 4, 5, 10, 12, 16, 24, do you see the misconceptions? Both mistakes are easily understandable in the context of the day, and both groups told me the pattern was counting by 4s.

Now the moment I was dying to know, I asked each group, “How might the pattern they sequenced be related to the problem we did yesterday?”

EVERY STUDENT could tell me that the number sequence represented the number of bananas and the number of cards represented the number of monkeys. Apparently the process and the sense making from the problem really, really stuck. And one student summed up this experience for everyone, “This is the funnest math thing yet!” I couldn’t help but think, “Wait until tomorrow my friends.”

The next day launched the newest addition to this family of lessons, I want the students to write an ebook about their own problem related to this problem sequence. We will start with a traditional paper style book, but I’d like to push this beyond to the point that students are creating a powerful learning experience for other students. The students were introduced to the book “written” by our girls when they were in third grade last year. I handed a copy of the book to each student and we read through it whole class. Many students noticed that the bulk of the book was the scaffolding sequence of sentences we #NoticeWonder about on the first day. As time was again limited on this process, I wanted to make sure we got exposure to the book idea and build the students excitement to diving into the writing process in another class meeting.

I am excited to dive into having students formally dive into writing their two books and how I might sequence out those pieces in detail. I do want students to write one book that is around the same content, and I’d like them to write another that is open to their hearts desire. I am not sure how to sequence all these pieces out yet, that is some careful thinking and sequencing I will need to do today to get ready for next week. Once students products are available, I will gladly share them here, and I’ll look forward to your responses.