Hopefully you’ve already read the first two posts (Post1 Post2) about the Rights of the Learner because now we’re unpacking each one. Think back to a moment when you were sitting in a math classroom and you thought to yourself “WHAT THE WHAT IS GOING ON???” The professor/instructor/tutor is saying or writing something on the board and hasn’t taken a breath in like 20 minutes. You’re impressed that they’ve gone this long without breathing, but you’re about ready to pass out because you’ve been holding your own breath waiting for the “light bulb” to come on and for you to finally understand the mathematics that is being communicated. And then it happens… they turn to look at you for a confirmation that you’ve been following what is happening. All you can do is this:
Then you hear a sigh or eye roll because you can’t answer their question or shake your head in agreement that you know what’s going on.
If this has ever been you (which you should nearly everyone at one point in your life), then you’re not alone. Actually, being confused is a GOOD thing. Being confused can mean a lot of things for you as a math learner (maybe you were confused with the instructions/the task at the beginning or you understand the mathematics, but not in the way that it is being presented, to name a few). But what it SHOULD NEVER MEAN is that you are NOT smart in math or do not have the potential to learn and communicate what you know about math. Yet unfortunately, in our mathematics classes, feeling confused or struggling with the mathematics is something that our students avoid (and unintentionally, some of our teaching practices encourage too). Students don’t want to feel stupid or not smart in front of their peers. So students avoid this by being quiet or using coping skills like repeating what the teacher has said to “just make it through the lesson.”
Our kids don’t need to just “make it through the lesson” if they utilize their first right of the learner! If students know they have the right to be CONFUSED, then they have the right to say “I don’t understand it… yet” until they achieve some resolution (which is hopefully learning the mathematics at hand). Students who utilize their first rights of the learner engage in “productive struggle,” which Hiebert and Grouws (2007) use to refer to the “effort to make sense of mathematics, to figure something out that is not immediately apparent” (p. 387). Productive struggle doesn’t mean that kids flounder and helplessly suffer in silence in a classroom. Instead it means, that teachers create opportunities for students to use what they know about mathematics while they explore and grapple with what they have left to learn.
Case in Point: Randy Philipp and others at San Diego State University conducted multiple interviews with children who were solving math problems in their Integrating Mathematics and Pedagogy project (IMAP). In one famous video, Gretchen is asked to solve 70-23. She writes the problem vertically as:
And tries to apply the standard algorithm (typically you would regroup the tens digit so that you can subtract 3 from 10). But when Gretchen solves the problem she says her answer is 53 because 0 minus 3 is 3 and 7 minus 2 is 5. The interviewer asks Gretchen if there is another way that she could do it (notice that she doesn’t tell Gretchen that she is wrong). Gretchen retrieves base ten blocks (a unit of ten and smaller individual ones). By using the blocks, Gretchen says that the answer is 47, but she doesn’t get it because the answer “has to be 53.” The interviewer sensing Gretchen’s frustration doesn’t step in to give her the right answer, but asks her again if there’s another way, maybe a hundreds chart (a 10×10 grid that children use to count, operate on numbers, find patterns) that can help. Gretchen again finds the answer of 47, but remains unconvinced. She thinks the answer has to be 53 (and she again states that 0-3=3 and 7-2=5). Near the end of the video, Gretchen looks at her answer of 53 and two methods that resulted in 47, looks at the camera and exclaims “BUT I DON’T GET IT.” She doesn’t understand why she got 47 using two methods when the answer, at first glance, is 53.
This is a PERFECT example of Gretchen using her right to be confused and not letting this confusion mean that she won’t ever learn that 70-23=47. Instead, Gretchen is engaging in productive struggle about her knowledge of base ten. She’s confident in using the traditional algorithm, albeit one that begs more questions as to how she is thinking about 0-3, and needs more experience in thinking about why 0-3 is not necessarily 3 in this case.
The first right of the learner is the right to say “But I don’t get it” like Gretchen ….and to be ok with that. Too often, we have children sitting in our classrooms who are terrified of saying that they don’t understand, that they are confused, that the task/lesson didn’t have an appropriate entry point for them (ok, kids won’t say that, but that was my teacher voice coming through). Instead of helping kids to AVOID being confused, embrace it. Tell kids “I am SO HAPPY that you said that. This tells me that I might need to take a look at where you’re at with your thinking about this task or idea.”
Everyday with my elementary pre-service teachers, I make room for them to practice their right to be confused. I actually give them divergent formative assessments that help them to question what they know (when 2/4 is a perfect answer for 1/2 + 1/2) so that they learn how to probe their own thinking. When my new teachers see that being confused or productively struggling is actually a good first step to learning, they start to see how their students need to know that they have the right to be confused. And if I find that some of my students NEVER say that they are confused… this means two things: they are still afraid to tell me or the task isn’t challenging them enough. Either way, it’s my responsibility to do more as a teacher.
So the next time you feel like just know… it’s your right to be confused. Embrace it. Know that you’re developing more synapses and neural connections to the knowledge that you have now with the knowledge you’re about ready to put into your beautiful brain!
Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on student learning. Charlotte, NC: Information Age Publishers.
Philipp, R. A., Clement, L., Thanheiser, E., Schappelle, B., & Sowder, J. T. (2003). Integrating mathematics and pedagogy: An investigation of the effects of elementary pre-service teachers’ belief sand learning of mathematics. Paper presented at the National Council of Teachers of Mathematics: Research Pre-Session, San Antonio, TX.