Closing the Gap

This Tweet is the inspiration for this post. This quote by Phil Daro, and tweeted by my tweep Mark Chubb,  really speaks to my current feelings about how to help struggling math students.

My district is using MAP testing and learning how to use the data best. I think many teachers and administrators are happy to have some specific data on students. However, I don't think teachers found the data particularly surprising... students that struggle tended to have a lower score and students that excel tended to have a higher score.

The difference in the data from MAP testing compared to other testing we have done, is that the results come back with individual "plans" for students on what they "can do" and what they are "ready to learn next." This seems exciting to some and, for some reason, makes me pause. I, too, would love a prescription for what to do with students that struggle. Some teachers suggest that we have students watch Khan Academy videos or do targeted practice in IXL Math. For me, again, this plan sounds okay but not great. Why?

I'm going to go back to the quote above from Phil Daro. "A standard defines a finish line, not the path." While some may argue that math is scaffold and you have to learn one skill before you can learn another, I argue an opposite opinion. You can certainly understand integers without being able to proficiently add/subtract fractions. You could do algebra without knowing how many degrees in a quadrilateral. Not that any skill or procedure is not important, but I certainly don't have to wait for a student to master all "previous grade level skills" before they can begin to make sense of something "on grade level." In fact, learning something new might help a student make sense of something that was previously confusing.

For example, I am beginning a unit on ratios. Many of my students struggle with number sense and fractions. I could do a mini-unit on fractions with the thinking that if they can't simplify a fraction (or even write a fraction) how can they make sense of a ratio? Well, I'm not doing that. I'm embedding work with fraction strips as we discuss ratios (thanks to the CMP3 curriculum). Students are making sense of fractions and ratios at the same time. Are fractions something that students should have already mastered? yes. Would the unit be easier if they already could simplify fractions? yes. But is it worth it to do a fraction unit, out of context, and "wait" for students to master fractions? no! Learning the material in the context of ratios helps students understand fractions in a new way and many students are (for many, the first time) "getting" fractions!

So, if we put a struggling student in a lower group, intervention, or some other form of remediation that takes away from their opportunity to be learning "on grade level" material, perhaps we are just widening the gap as they continue to be "retaught" lower level skills and never get to experience content that students "on grade level" are thinking about. [[Let me be clear, that interventions are important, as long as they don't take away from a students' opportunity to have access to the high quality, appropriate, standards.]]

As the quote mentions, we need to start with student's prior knowledge, but assuming they can't do a sixth grade standard because they tested at a "third grade level" holds a student back from reaching their potential.


  1. I really like the idea of combining the ratios with fractions to help students see fractions from a different angle. It's nice that CPM has them combined for you! Throughout the unit you could support students through number talks that develop fractional thinking. Small group instruction could be differentiated based on some of the data you received from MAP. In my inclusive classroom I set the first 15 minutes for number talks/estimation tasks, then 15-20 for procedural fluency/math intervention - This allows me to work on a targeted standard/strategy/misconceptions... while the rest of the class is working to become more fluent on a standard they already grasp. Then the last 45-60 minutes is the math lesson. If your kiddos still didn't get fractions after all of that, then you might want to think about your next steps of course.
    I get what you're saying about ability grouping our students. It's one thing to give targeted math intervention in flexible groupings, but it's a whole other thing to track students. Have you read Principles to Actions? It's one of my very favorites. (When did I become such a math nerd?)
    "Tracking consigns some students to mathematical content that offers little significant mathematical substance. While some students are expected to engage in a variety of mathematics topics through multiple teaching and learning strategies, students in low tracks are often confronted with a narrow and fragmented mathematics curriculum, delivered with a limited set of teaching and learning strategies. Too often, because of the unproductive beliefs described below, the capacities of so-called low-track students are underestimated, leading to these students receiving fewer opportunities to learn challenging mathematics. Low-track students encounter a vicious cycle of low expectations: Because little is expected of them, they exert little effort, their halfhearted efforts reinforce low expectations, and the result is low achievement." It says a lot more than that and I already typed too much already, but basically once kids are in, they are in for life partly due to the poor mathematics curriculum and instruction, and partly due to their now worsened disposition toward math. Okay... I'm getting off the soap box now. You'll have to let me know how it goes. It would be interesting to see the data.

    1. Thanks for taking the time to comment! I'm really hoping that we move towards having a block math period (88 mins) next year because currently we just have 45 minutes a day. Not enough time!

      The other change I'm pushing for is getting rid of tracking for exactly the reasons you mentioned. Here's some more thoughts on that:


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