Okay, so this is one that has been bugging me. As the Common Core starts to get underway, I have seen a lot of activities (mostly at the grade school level but some High School as Well) that claim to be addressing the Mathematical Practice of Mathematical Modeling.
Most of these look something like folding some paper, playing with m&m’s, or some other food based manipulative and/or drawing pictures so students can see the math. These activities are great for students to be able to see and feel the math they are working with. However, this is not addressing the Mathematical Modeling standard of the Mathematical Practices.
Modeling WITH math VS modeling THE math.
The Standard states that students will model WITH mathematics, not model THE mathematics. Here is the text from the common core.
“CCSS.MATH.PRACTICE.MP4 Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another.”
Notice that there is nothing in there about making models of the math but rather using math as a tool to “solve problems in everyday life.” I absolutely love this part of the Common Core, because solving everyday types of problems is the way math was created, and what it was created for in the first place!
Please don’t fall into the trap of modeling THE math but seek problems and activities that require students to model WITH math by finding engaging real world problems that require students to “unlearn what they have learned” and apply math to solve the problems.
The Practices Will Assess Below Grade Level
I recently went to a professional development at my district put on by a fabulous presenter. He actually has a doctorate in Geometry and worked on a consulting team for Smart Balanced (one of the two companies that are making the Common Core Assessments). He said something very important. He said that the standards for Mathematical Practice will actually be assessed below grade level. He said the reason for this was because it was too difficult to know if a student wasn’t able to model mathematically, or reason quantitatively, or whatever if the content behind that question was at grade level. What if the student just didn’t know the content but was good at reasoning? It Makes sense to assess the MP’s below grade level then.
I will say it one more time in case you didn’t catch that. The MP’s will be assessed with content that is BELOW GRADE LEVEL! That means that if you want to give your students a mathematical modeling situation you don’t have to tie it to a Content Standard. Want to review percents? Want to review Fractions or Proportions? Why not make a mathematical modeling problem!!! If you are a geometry teacher you don’t have to stress about fitting your proof by transformation into a real world problem! or if you teach Algebra you don’t have to make that problem about matrices or Logrhythmic functions!
Since I teach at risk youth, a lot of them desperately need review on these basic concepts. Not only because they missed the concepts in their educational passed for one reason or another, but more importantly because they desperately need them as most of them will be going into trade and professional schools as opposed to 4-year universities. These kinds of programs can place them in well paying careers but many of them need the students to be good problem solvers, and have a good grasp of the basics.
I know from reading the Common Core that it is written to addess this very issue, however if we as teachers miss the boat and don’t understand that they need opportunities to apply these concepts, not just learn them, then this issue won’t actually get solved, and students won’t get the opportunities they need to become good problems solvers.
The Problems with Problems
This is no easy task. The students that I am currently working with have been raised under the Old CA State Standards. Your state may not be the same but in CA they put so much emphasis on testing, and so many standards, that we didn’t have any time to teach problem solving. Therefore when my students see a word problem, they freak out, they try to get to the answer too quickly without any solid strategies for doing so. Because I was never expressly taught strategies either (maybe you were maybe not) I can just do it. I don’t really know how I do it exactly.
I have had to spend a lot of time and energy figuring out how to get students to learn these strategies and get “unstuck” with more difficult problems on their own. I have had some success but like most I am still working on it. This is mainly a topic for another article, but If we aren’t even trying to give them opportunities to model with mathematics they won’t even get the chance to try, and we won’t be truly helping them be good problem solvers.
So if you want to address the MP of Modeling, put the construction paper and the macaroni back in closet and start seeking, interesting real world problems for you and your students to grapple with together. you’ll probably have more fun…
Where to find some good problems
Again there is not a lot out there yet as far as good High School level problems for this, but that is changing.
The first step is to watch this video from Dan Meyer. He was a Keynote Speaker (along with Levar Burton -Go Geordi! okay so i’m a nerd…) at the 2014 CUE conference and it literally was lifechanging. It’s a bit long but it’s totally worth it. I was sitting near the back on the right :-).
He also has a video on TED talking about real world problems. Here as a link to his website where you can look at and post perplexing problems.
It’s kind of a weird website to look at but try clicking on search and typing in a concept like “percents” or “volume”.
Here is another one I found. Someone posted these problems based on the Philadelphia math standards. The site says it’s more for middle school based but some of these problems are surprisingly challenging. I have used several of these as is and altered to my students needs. Also, remember that we are looking to go below grade level anyway.
I will also start posting my own problems on LetsPracticeGeometry.com but because my current focus is to write worksheets for the Geometry Content Standards that may be a while… I may start posting my own versions of some of these with question prompts. For now I didn’t want to hold back these incredible resources.