Saturday, August 15, 2015

How Do You Like Your Bacon (Math Modeling)?

During the past few weeks I've had the pleasure to work with and learn from teachers in various places in the country, facilitating district/school workshop trainings as they prepare for their school year. Part of our time together was working on problem-solving tasks and breaking down Mathematical Practice 4: Model with Mathematics. At some point, either before lunch or in the afternoon, I tossed up this Estimation 180 challenge and asked:
How long to cook the bacon, starting with a cold skillet?

I love this estimation challenge because it showcases many parts of the modeling process, especially the two following parts:
  • Identifying variables
  • Formulating a model
Here's why. Teachers instantly start asking questions like:
  • How do you like your bacon?
    • Crispy, charcoal, or like beef jerky?
  • What type of bacon is it?
    • Turkey bacon or real bacon?
  • Is it thick cut or the other stuff?
  • Is the bacon room temperature, cold, or frozen?
  • Is it cooked on a gas or electric stove?
  • How hot is the flame?
  • What is the percent decrease in size of one strip of bacon?
Teachers are identifying variables and asking for information that matters to them in order to formulate a model. I love it. I have also done this Estimation 180 challenge with students before and they have asked many of these same questions too. I love it.

I had a great conversation with Joe Schwartz and others at TMC15 about state tests lacking what the modeling process demands: asking questions. Why do the SBAC and PARCC tests not have students simply ask questions about scenarios? If we're asking students to identify variables and ask/search for information necessary to formulate a model and solve a problem, why don't tests place more of a focus on this? What if we presented students with scenarios a la the Math Forum and simply have students first submit mathematical questions that could be solved. What if we then followed it up with giving students a list of three to four questions they could solve and they pick one?

Another great conversation I had with Nathan Kraft and others at TMC15 was the idea that direct instruction can have a negative connotation in the MTBoS. A similar notion is that the instructional strategy "I do, we do, you do." also has a negative connotation. With problem-solving and mathematical modeling, direct instruction is not the focus. The focus is conceptual understanding. From my experience, I've learned that timing and placement of direct instruction is what matters. I've been catching up on reading NCTM's Principles to Actions and I highly recommend it to anyone; teachers, coaches, parents, administrators, students, and more. It's about 100 pages. Get on it! I think it paints a pretty clear picture why, how, and when conceptual understanding should take place in relationship to procedural fluency.

Principles to Actions really does a great job driving the point home that procedural fluency is important. However, procedural fluency won't stick nor have significant meaning if the students lack the conceptual understanding first. When I'm done with Principles to Actions and have had a chance to let it simmer in my brain, I plan to blog more about it. I also need to explore the Principles to Actions Professional Learning Toolkit.

Last, and certainly not least is literacy. I'm glad that one teacher at a recent workshop voiced her concern about teaching literacy in math and that the use of multimedia in a 3-Act task or an Estimation 180 challenge really doesn't strengthen literacy. I agree.

Trust me, I'm all about building literacy. However, the more I teach and work with teachers, the more I believe in the importance of making the conceptual understanding accessible first as a means to transitioning to procedural fluency and strengthening literacy by scaffolding. If I don't make the conceptual understanding accessible to my students, than I'm not scaffolding both the mathematical procedural fluency and literacy.

That said, I tried to imagine what Day 185's bacon estimation challenge might look like. I still love the visual and simple question and would still start with the current setup as the introduction to the task. Once students and teachers voice their questions, Act 2 information might be presented in text. Here's what I came up with (I know it could be better):
I have 20 minutes to prepare and eat breakfast before leaving for work. I need to cook 12 pieces of bacon for my family and the skillet only holds 6 pieces at a time. We like our bacon crispy, but not like charcoal. The gas stove will be at a medium to high heat. The first batch of bacon starts to sizzle one and a half minutes after I put the skillet on the lit stove. Five and a half minutes after the bacon starts to sizzle, it is about 65% cooked. Will I have enough time to cook all 12 pieces of bacon?
I'm not sure this blog post brings much closure. However, it has brought a greater focus for me as I prepare for the school year. I am more focused on
  • students asking questions
  • students building conceptual understanding first
  • teachers making conceptual understanding more accessible (as much as possible) 
  • teachers scaffolding their classroom activities and direct instruction to strengthen procedural fluency by building upon conceptual understanding
Does this sound reasonable?
How do you like your bacon?
Let me know. I'm on my way to finishing Principles to Actions.



  1. I like this! I also enjoyed Principles to Actions and needed a good reminder to review it. Direct instruction does have its place and I think the timing of it is everything. Does the placement differ based on the topic/subject? Does the placement differ based on the activity/task? Does the placement differ based on the students/class? I think that's why so many teachers either do too much of it or feel it's completely wrong to do; the timing is off and it doesn't do what they wanted it to accomplish.

    1. I think we can both benefit from Jamie's link to Phil Daro and students earning direct instruction.

  2. Love this blog post! I also enjoyed Principles to Actions! Probably a little too much. #mathnerd As far as direct instruction, I try to go by Daro's advice and have the students earn it. (Only happrnrd twice last year.) At that point they crave it and actually benefit from it.

    1. Thanks Jamie. Have a link to Phil Daro's advice? I also love his idea about avoiding the planning of individual lessons in isolation.

  3. Our homework at cpms math camp was reading principles to action. I wrote a reflection on my blog about it that highlighted points that stuck out to me. I read as far as the curriculum section and look forward to finishing. It's a gold mine.

    1. I tried searching your blog, but couldn't find a search feature. Can you add one?