How can we prepare our students for a successful school year? I work with students mostly one-on-one, and with the school year under way, I’ve been thinking about this issue a great deal. Whether your perspective is classroom teacher, coach, tutor, or parent, there are valuable preliminaries that can help enhance the learning environment. I try to set the stage with a few important messages I want my students to hear.
First and foremost, I tell students to “Bring Your A Game” to their math learning. This means that they can’t just let the math class happen TO them, but instead they have to actively ENGAGE with the material in class and for homework. Take down the teacher’s notes and examples, and if something seems confusing, mark it to ask about later. Put in full effort to make sure you’ve done the work (even if the teacher doesn’t check it*). Work slowly and mindfully through the problems, and watch out for “avoidable errors” (my preferred term for “silly mistakes”). Know what things tend to trip you up: for example, double- check negative signs and units on answers. Don’t wait for the test; when you get a quiz back, figure out what went wrong so you can get it right next time.
Students tend to think that each new course brings all new math, but I remind them that they can rely on the fact that all of the math they have ever learned is still true! “Use what you know” about the + and – signs of the four quadrants to help with the unit circle in trig, and for calculus, build the difference quotient definition of the derivative on the formula for slope. This also helps when you don’t know where to start on a word problem or a geometry proof. And making connections between mathematical concepts deepens understanding.
Just as an athlete might train by doing different types of workouts (rather than more repetitions of the same exercise), math students can learn something better by trying to “find more than one way” to a solution. I try to highlight alternative methods of solving by posing questions:
- What would happen if you didn’t distribute first to solve this equation? –15 = 3(x – 8)
- Is this student’s reasoning correct?
- Find the error in this work.
- Can you solve this (geometry problem) another way?**
I constantly tell my students to “show your mathematical thinking.” One obvious reason for this is so you can get partial credit for wrong answers, if the teacher grades that way. But the main purpose is that showing your steps makes it more likely that your work will BE correct. You can reflect on your thinking process through a problem, which helps improve retention and understanding, and enables you to explain it to others when needed (and study for a test later). If you have poor handwriting, make it readable (enough). If you are using a calculator or doing some arithmetic in your head, sketch a graph or jot down what you are computing so your process is clear. A friend’s daughter summed it up this way: “I feel it is important to show my work. My teacher and I can see what I’m thinking. It’s hard to see it if it’s only in my head.”
Another key to success is to “know your resources.” Does your teacher have a website? Is there an online textbook? Who is in your class you can study with? Don’t forget to search Google, YouTube, and Khan Academy if you are stuck on something and can’t proceed. I remind students that getting help from a tutor isn’t the only way to get assistance. Go to your teacher for extra help because they can see your effort and they can focus you in on the key concepts.
A final message is to “persevere even when it gets hard.” This is more than just SMP #1 talking, this is about being confident that you can do it and being willing to grow your mathematical skills. One teacher at my son’s Open House night spent time coaching us parents that the class was going to be challenging (and explained why), and gave strategies students could use to facilitate their understanding. She said “if you aren’t getting at least a few things wrong, then you aren’t learning something new.” I try to reinforce a growth mindset in my students and a belief that they can achieve the goals they have set for themselves.
I think it’s going to be a very good year…
NOTES & RESOURCES::
* Students often don’t put in effort if there isn’t a grade attached. As a teacher, if you want to promote habits of doing homework, showing mathematical thinking, checking results, extending to more than one solution etc., try to consider this in your grading scheme. See Wilson, Linda. “What Gets Graded Is What Gets Valued.” Mathematics Teacher 87, no. 6 (September1994): 412–14.
** This summer I worked for awhile on the Art Of Problem Solving Geometry course with an online group. I was impressed by the focus on finding more than one solution: “Doing a problem two different ways is an excellent way to check your answer” and “When you can’t find an answer right away, try finding whatever you can—you might find something that leads to the answer! Better yet, you might find something even more interesting than the answer.”
These messages about approaches to learning are one version of Classroom Norms. Read more here about one teacher’s use of Jo Boaler’s suggested list. And here is a consideration of how to change the norms that students may have become accustomed to, in order to increase student engagement.