Kacie Travis is a high school math teacher, blogger, and teacher-author from Fayetteville, AR. She is here today to talk about some valuable elements of the Common Core Standards of Mathematical Practices.
The Common Core State Standards (CCSS) have become a controversial and highly debated movement in education. The standards have been praised, bashed, banned, and everything in between. Regardless of your feelings about the standards, their implementation, or the testing that accompanies them, the creators got one thing right: The eight Standards of Mathematical Practices.
The Standards (SMPs) are not grade specific and are not a list of skills, but rather are how students should approach the learning of mathematics as they become proficient with the skills. They are desired habits of mind. They are also not new. These practices about how to learn mathematics have been around and researched for many years before the concept of common state standards. They’ve just been renamed and made popular by the adoption of the CCSS.
Why should these standards be exempt from the wrath of the Common Core (CC) protesters? Here are a few reasons to give them a serious chance.
CC Math is often critiqued for too much conceptual understanding and a lack of practice and procedural fluency. (A different debate.) The SMPs demand the balance between the two sides, where deeper conceptual understanding and fluency harmonize. Note the wording of the subject of each sentence in the SMP descriptions. It refers to “mathematically proficient students.” These are the goals for what we desire students to be able to do. They cannot get there without fluency and that requires practice.
While each one requires some knowledge of algorithms and procedures, I think #7 and #8 particularly draw attention to the acknowledgement and practice of the patterns that lead to algorithms.
Teaching students to think about their learning and their thinking process is crucial to a deeper understanding of what they are learning. Across all subjects. But, in math, there seems to be a hole in the learning process that can only be filled by students understanding their learning process.
Explicitly teaching students the SMPs and referring to them throughout your lessons is what it takes to get them to fully understand. Spend time the standards. Demonstrate the connectedness of the SMPs to how they are learning in class. Post them. Point to them. Talk about them. The SMPs that need the most explicit teaching are #1 and #3.
Make sense and persevere. Students don’t naturally want to persevere. It is uncomfortable to struggle, but the productive struggle is the where the most efficient learning takes place. It takes lots of modeling, lots of practice, and lots of positive encouragement. Students need to feel safe even when they get an answer wrong and they need to feel secure in knowing the most learning will take place in the struggle, not in getting the correct answer every time.
Construct and critique. Students also need to learn effective ways to communicate mathematically. They need to be able to precisely (#6) explain what they are thinking and discern whether or not their thinking aligns with other students’. This also requires modeling and practice. Students at any level should be able to have a developmentally appropriate conversation in which they are critiquing the reasoning of others.
Once you can get students immersed in the SMPs and they understand not just what they are learning, and not just why they are learning, but how they are learning, they begin to take ownership. It takes a lot of work for students to arrive at proficiency with the SMPs, but with year after year, with the students being held to the same eight standards of practice, the math will come more naturally.
Please don’t mistake me. I am not saying it will become easier. (That may happen for some students, but this is not what we should be striving for, because that’s hard to control.) But they will become more fluent with every facet of the language that is Mathematics. And just like a Rube Goldberg machine, confidence will fall into place, setting off a chain reaction that leads to sincere engagement.
The learning will be more relevant to students, which makes them interested in learning. Wow. Students interested in learning math all from eight simple practices? Yeah, I believe in them. You should too.
Kacie Travis is a high school math teacher, blogger, and teacher-author from Fayetteville, AR. She is married and has 4-year-old twin boys, Ben and Jack. You can get to know her more at her blog, Managing and Motivating Math Minds or check out her resources at her store, Kacie Travis.