Practical Thoughts on Differentiation in the Secondary Math Classroom

“There might be a student that doesn’t need modeling, but there is always one who does. So why wouldn’t I provide that first?”

I heard this recently on a favorite site. It sounded reasonable, and was spoken by a teacher acutely interested in her students’ success. She was talking about the “I do, we do, you do” strategy of gradual release, making sure that her students fully understood the expectations of the task she set before them. At times it may seem like the perfect fit, but far too often in secondary math classrooms we overuse this well intentioned, time tested lesson plan.

One powerful reason NOT to provide that first is that the modeling robs students that don’t need it of a chance to be creative, problem solve, and use strategic thinking – all higher depth of knowledge ways of processing their learning.  When we provide scaffolds for all it is easy to reduce everything to a dok level 1 – “Watch and do exactly as I do.” For more on depth of knowledge, see Robert Kaplinsky’s work here.

Differentiation is an important topic in education. At the high school level many people find it challenging to truly differentiate in a 55 minute period.  But here is a simple opportunity that actually creates time in your period – time that students can engage in those higher depth of knowledge types of thinking.

How can that work? Several models are possible, but all revolve around reducing or eliminating the whole class modeling and instead planning timely hints appropriate to various sticking points in the process.  Start with thinking about hints for your highest kids. What is the least you can say? What question could you ask to spark their thinking? The next set of hints could be more directed, potentially less open, and may encourage them toward a specific method. For the most helpful hints, basically just do your “I do” – either in writing or by giving then a link to a short video they watch on their phone. Label the hints 1A, 1B, 1C, 2A, 2B, 2C . ..etc. 1 represents the earliest sticking point – how to start.  A, B, and C represent the level of the hint. Students should be encouraged to take the least help possible. It is amazing how quickly your highest kids will adapt to that suggestion . . they are inspired by the challenge. But kids who need more help have it readily available.  

Double the effectiveness of this strategy by putting the students on vertical non-permanent surfaces. Definitely worthy of a blog post all it’s own, but simple enough to implement tomorrow. For a look at this strategy and the research behind it, check out Laura Wheeler’s blog here. A quick summary of the fuller body of work, “Building Thinking Classrooms” by Peter Liljedahl, can be found here.

Struggling with the mismatch between some hypothetical classroom ideal where every student is motivated just because they want to learn and grow, and the reality of grade-chasing, point-grubbing, homework-copying in your classroom?*  Long term, the research above can really make a difference, but to help in the meantime, some teachers use a pointing system for their hints.  All groups start with 10 points (or more if it is a pretty hard task with lots of sticking points).  C hints cost 1 point, B hints 2 points, A hints 3 points.  Points that aren’t used are extra credit on the assignment, and students can spend into debt – making their highest possible score 95/100 for example. Remind struggling students that 95, or 86, or whatever they work their way down to is so much better than the 50% for an incomplete assignment, or a 0 for not turning it in. And to begin to change that culture, be sure you celebrate successful completions equally – let students have joy in completing the challenge no matter how many scaffolds were used along the way.

Every day and lesson is different, and occasionally a bit of “I do, we do, you do” may be just the perfect amount of scaffolding/guided release for the specific task your students are working on.  Optimize those moments by listening to your students thinking along the way. But too often in a diverse regular classroom, we mis-serve both the top and bottom segments of our classes by doing all the higher level thinking for them. This model of differentiation is one way to support ALL learners in those classes.

*Ready to try something different with grading? Matt Vaudrey has a nice post about his experiments with a variation of Standards Based Grading  here.  And there are a thousand other great ideas out there. Look here for what came up when I googled: MTBOS on homework.

It truly is a wonderful time to be a math teacher.

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