1. Be there: I really enjoy all of my students in class (yes, every one). These past 11 years have really impacted me on the importance of being in class. I know I plan for every student all the time, and it makes it better if everyone is there, it’s not about me. Students can’t expect to understand content if they miss too many class periods. Missing students also impacts the learning of the rest of the class. Students drive my classes, and having multiple ideas and approaches are critical to class. I need them there.
It reminds me of an anthropology class I took in college. I did not show up for class after the first day. I got the syllabus and went home. I only showed up for test days. I ended up getting a B for the class, but to this day I can’t not tell you much about the class. I filled my short-term memory for the test, but that’s it- it’s short term. I regret that and sometimes consider retaking the class or at least buying the text again and actually studying the material
2. TRY: I start every year out with this word on my board. I want students to try. I tell them some things will be easy, and some hard. The most important thing is to try something, anything in fact. The only way to learn is to engage your mind.
This is my #1 check-in with students, if they ask for help but have not tried then one of two things happen. The first is that they report out on the problem to me (which many students do not like to do), the second is that they agree that they will reread the problem and determine what they need to do. If they get stuck after they have attempted some work, they can ask for help again. This normally takes students a month to understand and attempt, after that they can explain the problem and what they have attempted before asking for help on the next step.
3. Talk in Class: I expect students to talk. I expect them to talk a lot. In order to have rich discussions that will engage their minds, I need to have students communicate mathematics to each other as well as me. The format of the talking is varied: partner work, small group, large group, presentations and individual check-ins. This is the one area I push my students the most.
When I tell them I expect them to talk in class, I get a very wild reaction. Then, when they understand what I mean- the reaction normally shifts 180*. I do tell them I understand that they will get off task at times, and when I first introduce this type of behavior in my class I tell them that they need to live by the 90% rule. 90% Mathematics, 10% other. I know conversations will drift, they are only 13, but in the initial weeks I just ask “Are you keeping with the 90 rule?” and they know exactly what I mean and expect. After the first month the types of conversations they have is truly awesome. I wish I would take my own advice and start to tape them, I barely keep up with all the great ideas.
4. Show your work (to help ME understand): I have always said: “Math is Messy!” I HATE erasers, and regularly stop my students from using them. I want to see work shown, and it’s not just to make homework longer or to torture them. Drawing diagrams, taking notes, underlining, sketches, anything and everything is useful.
I was having a conversation with one of my students about a problem (I have conversations, not help sessions or answer confirmations) when I noticed she started to erase her work. I took the pencil out of her hand (one of the good times teachers take the pencil away) and asked her what she was doing. She seem surprised but said she had some wrong thinking down and wanted to start over. I took her paper away, wrote only the problem and asked her what her incorrect thinking was. She was unable to remember what she had done or what she needed to correct. I told her that is why I don’t want to see her erase work. It is the “notes” of solving math, it gives her the outline of what she has done and what she needs to do. I asked her to show me where she thought she went wrong. I then asked her to start her new work beside that point but to leave it. As she started working, she realized that her initial work was right, she just solved the problem in a different way. Having both solution paths side by side allowed her to compare her methods where she would not have been able to before.
5. Understand you work: “Rules vs Understanding” is my class motto. I want students to make deep connections to the mathematics they do so they can replicate and refine it. I want things to make sense so they can tackle problem solving outside of the classroom in everyday situations. I want students to have such confidence in their knowledge that they can argue with me about problems, that they will take the marker out of my hand, march up to the board and teach- helping the class find a solution.
I had another conversation about a problem with a student and they found an answer, then reflected on that answer and determined it was correct (and could defend that stance). When I asked them who did the problem, they said that they started it, but needed my help to finish. I asked them what part of the problem I did, the answer was none. I asked what answers I gave them, the answer was none again. I asked them who solved the problem, the answer was that they did it themselves. The pride in their eyes and tone of voice tell you how powerful that is to students- they start to believe that they can be independent learners.
6. Get a correct answer: Do not get me wrong, having a correct answer IS important in mathematics, it is just not the end-all-be-all of their evaluation and grade. The process is important, but so is the answer. I am trying to prepare my students to become responsible adults after school, and if they can’t produce the correct answer then I have failed in that. How long with they last at a job where they give incorrect change? How can they be successful small business owners if they do not evaluate sales trends? How can I expect them to work in research labs if they are not accurate, knowing that the slightest error will nullify their research?
There have been many pushes to just focus on the process and not worry about the outcome. Let me tell you the secret of that. If you are REALLY focusing on the process, communicating with students and giving them proper intervention- the correct answers take care of themselves. Don’t make either part more important, but stress they are equally important. Reflecting on your work and deciding if you answer is correct only strengthens their understanding.