Friday, October 31, 2014

How it Must Feel

Imagine yourself as a student who has always had a hard time with math. Honestly, you are not even sure why there are sometimes multiple variables in the same formula. When the teacher starts a new topic, you may need to see it 4 different ways and have it be repeated a lot of times in order to become somewhat proficient at the skills involved, even though the general idea is sometimes (not always) accessible to you. When other people discuss mathematics in groups, the speed at which they are discussing the ideas often flies right over your head, but you feel embarrassed to ask them to explain every part to you, because other people all seem to understand it fine. So, you do ask some questions during class, enough to make some progress on the work, and then you wait until you can find the teacher to ask for more help. You can only find the teacher to meet outside of class about once a week, and by then you already have more questions accumulated than can be answered in one session, so that although you think the concept is probably important, you just want to know the bottom line of how to get through the various problems you are going to see on the quizzes. So, the quiz comes and goes and you feel defeated by your score, even though you are working hard everyday in class and your teacher can also see that, too. You go home with the quiz and you don't want to even look at it for now, even though you know that you probably should start thinking about the re-quiz and that the teacher will probably start something new either tomorrow or the next day, and that the cycle will likely repeat itself.

What do you do?

In every class I teach, there are some kids whom I meet outside of class on a weekly basis. For many of them, that is enough. For some, that isn't. I love the idea of heterogeneous grouping, because I believe in all the things that other math educators believe, which is that it promotes safer learning environments, teaches diverse students to work together, promotes growth mindset, etc. But, at the end of the day, I don't know what to do in a practical sense to help these kids who experience those cycles of disappointment in every unit. I try to vary up what I do to help them build the conceptual understanding of underlying topics (ie. Math Talk, problem-based learning, visual representations), but realistically I have to balance too much going-back-to-basics against the majority of the class's need to develop other, more sophisticated, skills and concepts. Open-ended problems sound awesome in theory, but in reality we still need coherent conceptual and skills development the majority of the time. 

So, what do you do besides trying to be empathetic?

I don't have an answer right now. In the past, I have had great success in homogeneous grouping at helping the slower-paced classes build confidence and feel successful with a smaller set of topics, but I find that goal very challenging/elusive when those lower-confidence students are situated in an environment that is perhaps just faster-paced than they can handle. I am fortunate that most of my students give me 100%. I have no doubt about that. But, how can I grade them all on an absolute scale based on what they know, if they are all starting off at very different places along the spectrum of prior algebra experience? And, more so than grading, how can I serve them all? 

Those are open questions in my mind. Would love if you could chime in to enlighten me in your thoughts about this. 


  1. I think about this issue a lot too. In my experience, I find heterogenous grouping to be the best way to serve the kids who struggle, but a huge part of my success with it I think has to do with the effort I put into developing a rich classroom culture around problem solving. Right now, I am finding the value in cooperative learning and heterogeneous grouping to be in students learning problem solving strategies from each other, which breaks down the kids' preconceived ideas about who the "smart ones" are in the class. If the classroom culture is too much about computation and skills and procedures, then the student interactions revolve around who gets it and who doesn't. If the culture is about how many ways can you solve the problem and comparing your strategies to other people's strategies, then everyone is learning from each other instead of one kid who "gets it" explaining it to the kids that "don't get it."

    I create that kind of classroom culture by starting a unit in a really open ended way with highly accessible but complex math tasks that elicit the big ideas of the unit. I see what strategies emerge and let students spend lots of time learning from each others' ideas and talking about their strategies and why they work. About a week into the unit I begin naming their strategies explicitly and asking them to practice using each others' strategies. If I need to show them one, I do a little mini-lesson to give them a tool and then we go back to problem solving. In the last week or two I begin funneling their learning toward a specific set of skills or learning targets and have them reflect on what they have been learning. This approach of starting with the kids' own ideas and shaping the learning around them seems to serve all of my kids really well, especially the ones who struggle.

  2. Getting to this post very late, but this topic has also been a lot on my mind. Something that we're trying this year in terms of grading is that half the grade comes from content and the other half comes from mathematical practices (our own version, not the Common Core). This gives students whose strengths are not speed and procedural fluency a chance to shine in other ways and a way to feel like there is hope for them and that math has parts that are approachable and other parts that are challenging for everyone. We also do a lot of individual choice in designing unit projects so that students can choose ones of an appropriate level of challenge and try to bring in cross-disciplinary strands so that those who have strengths in other fields can showcase them and increase their access to the material. This also helps students be area specialists who others can go to for help with incorporating art or programming or writing, etc into their projects. But it is a continuing struggle, especially as we plan to move into more heterogenous groupings for next year and I hope to see this discussion continuing.