Standard for Mathematical Practice 1: Make sense of problems and persevere in solving them
Somewhere on the path to training my students to make sense and persevere during problem solving, I realized the importance of living to that standard myself in terms of expectations and presentations. This standard isn’t about doing the word problems. To teach SMPs to the full intent of the CCSS, tremendous shifts need to happen, and I’m not there yet…but I’m working on it. To get some forward momentum, here are some questions I have started to ask myself.
- Will my students remember more of how to make sense of this problem or more of what to do? In the past, when I explained a concept and then showed my students what to do, I noticed my students were tuning out until I started step-by-step examples. When I began using explorations and assessing on concept, expectations and performance began to change. My direct instruction became shorter, and my students learned to persevere in reading non-fiction. Hey, isn’t that what’s in the ELA standards? While in times past students may have refused to read and think through, wanting me to give them the answers, that has changed. I believe I have the ELA teachers to thank for being able to tap into those non-fiction reading skills in math, thinking their way through explorations. And they are so proud of themselves! Even with extended periods of direct instruction now, I pause frequently, allow students to anticipate, connect, think ahead, talk with their neighbor and try to figure out what I am about to say. I assess their progress during lessons and allow those who are already onto it to work ahead. Invariably now, much more of my class time is spent on students’ reasoning than my explaining.
- If I teach this method, what math sense will students avoid? Nixthetricks.com has been an invaluable resource for me to figure out the difference between a trick that students use to avoid reasoning and a mnemonic used to visualize or recall a DOK 0.5. I am seeing the difference it makes when students have a deep understanding of a small set of extensible tools as opposed to a large set of “always do’s.” I question myself whenever I use words like, always, just, put, move, ignore, cancel…” and push myself to find and develop strategies for students to connect prior reasoning to current. I’m collecting ideas here if you care to contribute.
- Is there a way to help all students see? Sometimes students are not able to make sense of concepts regardless of their perseverance because they can’t visualize a key feature. Years ago I figured out that many of my college students had a history of failing trigonometry. The fundamental problem was that they couldn’t see the opposite side from an angle. With a little experimentation, I noted that 100% could see the opposite side if they pinched the angle with their fingers. Since that time, I have determined to figure out what each student is thinking or seeing that prevents them from making sense of a concept. Sometimes I can see it in their work, but sometimes I can only figure it out when I ask them to explain. Finding opportunities for those discussions is much easier when I talk less and have them figure things out with their seatmates more.
- Are rote procedures so important that they should command the major emphasis in this situation? Algebra 2 has traditionally been laden with memorized procedures and missed opportunities for meaningful open modeling problems. One of the arguments for teaching procedures such as synthetic division, automatic fraction clearing, and memorizing formulas to factor perfect cubes has been for efficiency or because they might need it in college. When students start tuning out and asking, “Why do we have to do this?” my question to my colleagues has become , “Should we take another look at our curriculum?” Losing students to boredom or irrelevance is a problem. That problem is for teachers who should be making sense of the situation and persevering to solve it.
Of the 30 different kinds of jobs I have had in my life, teaching is by far the most demanding; but it also the most gratifying and, in that sense, a privilege. if we are going to be good at what we do, we need to shift and change with the needs of our students. That takes a combination of understanding their needs and persisting in meeting them with the time that we have. I say the time that we have because the truth of it is, our jobs are never really done.