As I’ve been working with teams of teachers on Project-Based Learning (PBL) and teams of math teachers on digging into the Math Modules, I’ve seen a connection between the 8 Standards for Mathematical Practice (MP) and the 8 Essential Element of PBL. Time and time again, as I’ve heard from math teachers that PBL is just too hard to implement in their classrooms, I’ve pulled out the Standards for Mathematical Practices and showed them the connections you see in the table below. And, teachers digging into the modules can see how these Standards for Mathematical Practice are woven into each lesson through a variety of methods of instructional practice that require students to use the level of thinking and behaviors that the practices embody.
These MP standards are the Math Habits of Mind that we want our K-12 students to be exhibiting as they learn the Common Core Learnin Standards for Math. For example, how many times at parent conferences and open house nights have you had conversations with parents about their child not understanding math or giving up too quickly when they run into a math roadblock? MP1: Making sense of problems and persevering in solving them is one of the math habits of mind. Students need to learn to expect math to make sense and to look at math problems through the lens of inquiry – to try and try again. With PBL we have the same conversations with teachers about perseverance because PBL is a student-led inquiry process. Our students today are not used to inquiry learning; they’ve been led by the “Sage on the Stage” and spoon-fed answers to questions when they’ve struggled the least little bit. I know, I’ve seen it in my Chemistry classroom, countless times! “Come on Mrs. Keim, just give us the answer so we can move on!” Moving from being that “Sage on the Stage” to “Guide on the Side” can be overwhelming and, yes, a bit frightening! Relinquishing total control over the classroom to invite student-led inquiry is foreign to most of us – it’s not how we were taught to be educators.
Math teachers can really get to know the Standards for MP to give them the fuel they need to light the fire of student-led inquiry in their math students. Illustrative Math is an excellent resource for understanding the math practices and it has videos that show they practices in action in math classrooms. Another great set of resources for teachers are the KATM Common Core Math Flipbooks from the Kansas Association of Teachers of Math (KATM). These K-12 Flipbooks are intended to help teachers understand what each MP standard means in terms of what students must know and be able to do. One of my favorite parts of the flipbooks is the question stems for each MP. As you switch over to a more student-led inquiry classroom you will find yourself needing to “ramp up” your questioning to lead your students along that path of questioning and making sense of math at a deep conceptual level.
For math teachers starting or continuing on the journey of PBL, here’s an example of how the MP standards are tied to the essential elements of PBL. The first essential element in the PBL process is a focus on significant content and authentic issues. This element is tied directly to MP1: Make sense of problems and persevere in solving them, and MP2: Reason abstractly and quantitatively, and, finally, MP4: Model with mathematics. The use of real-world problems and applications can help students understand that math is supposed to make sense; it’s not just a set of algorithms and mnemonics to memorize. Letting students struggle through finding an answer, especially if they are working with a group of their peers to reason out the answer using mathematical modeling, can lead to that “Aha!” light bulb moment of understanding that then leads to the deeper conceptual understanding of that concept. Students who can talk to other students about the “Why” of their math answers using reasoning and modeling, instead of just the answer itself, are building that deep conceptual knowledge that they can then refer back to as they problem-solve a different set of questions. Isn’t that what we all want for our students?