3 Act Math: Structure and Making Connections

3 Act Math

Preface:

I just wrapped up a fairly successful school year. My students definitely learned a lot more this year than last, but I still feel like there is a ton of room for improvement. Specifically, I need to do a better job making connections between PBL tasks and the concepts taught.

I’ve been working hard to create 3 Act Math tasks this year. However, I’d like to focus on the details of implementing the tasks. My hope is that this post will provide some things that have and haven’t worked for me and also get feedback and suggestions from the countless other teachers doing a much better job than me! I’d really like to hear what has and hasn’t worked for you.

Before:

One of the biggest challenges I discovered is how to properly add structure to 3 Act Math. The goal of the tasks is to promote inquiry and openness, and I want to stay true to this focus. However, I’ve found that a lot of my students need a little extra structure in order to make it through the activities. My question is, “how do we add structure without compromising the openness and flexibility of the tasks?”

The main attempt I’ve made to add structure is by changing the setup of the handout I provide for each lesson. Here is an example of the original handout I used at the beginning of the year.

original handout

 

My goal with the handout was to allow for as much workspace as possible and to promote the openness of the task. Then, I attempted to make the activity more concrete on the second page by providing space to make connections to the Algebra concept being taught. I found that this setup was sufficient for my students who were already “math confident,” and they would hit the ground running with the task.

However, I noticed that my students who were less confident in math often hit roadblocks and ended up not fully attempting the task. I think my presentation was too open, and this was difficult for the students to process. A lot of it was probably due to the fact that most of them had never encountered PBL before and didn’t know how to approach an open-ended task.

After:

Later in the year, I thankfully saw a tweet from Michael Fenton that included a handout he adopted from Andrew Stadel. I tweaked it slightly and ended up with this.

New Handout

The new handout added enough structure to the task for my less confident students to hang with it for a bit longer, and I feel like it brought more students into play. But, is it too much structure? What do you think?

Next Year:

What does this have to do with making connections? First, adding structure will hopefully keep more kids in the game with the activities. This will create a greater opportunity to make connections. Second, the format that Michael and Andrew provided allows the students to organize many of the great thoughts and conversations that occur during the lessons. I believe this is crucial for connecting the task with the concept.

But I still know that more needs to be done in order to make connections, and this is where I would really like your input. How have you had success in your classroom with connecting concepts to PBL activities? What are your suggestions?

One item I’m going to add next year to each task is a final report handout.

Final Report

I think this will help get students’ thoughts on paper and also allow me to see what misconceptions they may have. Also, it opens up the door for students to analyze other students’ methods of problem solving, and this will hopefully lead to more concept connecting.

I’m really interested in hearing what you have to say. Ultimately, the students benefit when we collaborate so feel free to drop a comment.

 

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9 thoughts on “3 Act Math: Structure and Making Connections

  1. This is a great reflection Dane. I’ve gone through a similar process myself. Check out what I use here:
    http://robertkaplinsky.com/wp-content/uploads/2014/05/Problem-Solving-Framework-v7.1.pdf. It is modified from something Geoff Krall showed me and some ideas from Dan and Andrew. The top row is notable because anyone can do it… just write down the problem and take a guess. The next row is a bit more challenging in terms of critical thinking. What do you know and need to know. Then I have them skip the title and conclusion. It is only on the front so it scans better. They flip it over to do the work and return to the title and conclusion at the end. The sheet is also flexible enough to work regardless of whether there is an Act 3 or not.

    Great job and keep it going.

    1. Thanks Robert! Wow, I really like that handout. The flexibility you mentioned will transition well for other activities. I’ll definitely file that one away for next year. Thanks for the feedback!

  2. Hey Dane,

    Keep up the great work.
    You said, “I still know that more needs to be done in order to make connections,”
    I can totally relate! I find it challenging at times to connect the conceptual understanding of a 3-Act lesson with procedural fluency. Theoretically, I like using a 3-Act to launch a concept, but sometimes it can be extremely challenging for students because their lacking prerequisite skills, usually related to procedural fluency. I’m interested in front loading more 3-Act lessons with more procedural work.

    Robert has a solid handout. We (Dan, Robert, and I) used a different handout for a recent NCSM project. Email me for it and let’s continue this conversation via email.

    1. Thanks for the reply Andrew! I definitely encounter the same things you’re mentioning. I’ll send you an email. Looking forward to continuing the conversation.

  3. Dane, great reflection! Thanks for sharing. 🙂

    A few thoughts in response:

    “Specifically, I need to do a better job making connections between PBL tasks and the concepts taught.”

    I’m definitely in the same boat here.

    I love this collection: http://wmh3acts.weebly.com/3-act-math.html

    I’ve been thinking about collecting my own 3 Act catalog (weak as it may currently be) in one spot online. Seeing yours is inspiring.

    “My question is, ‘how do we add structure without compromising the openness and flexibility of the tasks?'”

    I enjoyed reading your thoughts on this. I’ve been toying with the idea lately that, in the long run, my students might be better served if I give them fewer handouts. For example, I’m a huge fan of Fawn Nguyen’s Visual Patterns. I took her handout (which you can find at visualpatterns.org) and tweaked it, ending up with this: https://www.dropbox.com/s/cjp5fnokeykuyrx/Visual%20Patterns%20Handout.pdf

    But lately I’ve been wondering if it might be better to say, “Alright kiddos, take out a blank sheet of paper (totally blank, not lined) and fold it in half. Fold it in half again. Now unfold.” And then to guide them to use the four corners to represent the situation visually (sketch of the “next step”), numerically (in a table), algebraically, and in some other way (possibly graphically, or pushing further with algebraically by having them solve backwards).

    It feels like a “teach a man to fish” issue, and I haven’t yet thought through how this might play out in a 3 Act scenario, but I’m definitely curious. In fact, I feel a blog post coming on…

    However my thoughts end up on the issue of adding the right amount and kind of structure, I’ve enjoyed reading your experience/journey.

    “One item I’m going to add next year to each task is a final report handout.”

    Gold. Definitely stealing this. I think post-task reflection could be one of the most powerful components in a well-executed 3 Act task.

    Thanks again for sharing!

    1. Thanks for the comments and positive feedback Michael! I really appreciate it!

      I really liked your idea to just give a blank sheet of paper and lead the students to come up with the structure we’re looking for. I agree that this might be better for them in the long run. Ultimately, we want them to learn to “reason and wonder” (love that), and teaching them to fish might be the best way to do this. After reading your reply, I’m thinking it might be beneficial to start the year with a structured handout and eventually wean the kids off and arrive at the blank paper approach.

      Great feedback as usual! I’m looking forward to seeing your future posts and potential 3 Act Catalog. Keep up the great work.

  4. Has anyone had any experience having students create their own 3 act math story? Did you create a rubric for it? I am looking to have students create one for each trimester. I am wondering what experiences other have had. Thanks.

    1. Unfortunately, I have not had students create their own 3 act stories yet. That is a great idea though. Let me know if you end up getting more information or do it yourself. I think a good rubric could be helpful for sure.

      Thanks for the comment.

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