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Unpacking Productive Struggle (Part 2)

Updated: Feb 17

In part 1 of our series on productive struggle, we talked about why we should value productive struggle and how productive struggle differs from unproductive struggle. We made a case for productive struggle by acknowledging that offering opportunities for students to struggle is aligned with what neuroscience has to teach us about how students learn best. Most importantly, we discussed that instead of helping students avoid struggle, we need to help them navigate struggle.


This week we will get practical. What do we as teachers actually do in the moment when students are struggling in our class? As with all complex questions, there is no one-size-fits-all approach. First, we have to identify the source of the struggle. Then, we can apply a strategy that will help students navigate that struggle. It is easy to assume that when students struggle it is always because of one thing: gaps in learning, or lack of motivation, or lack of skills. But this is not true! By becoming more granular about the actual struggle students are facing, we can offer guidance that does not stifle their thinking but also doesn’t leave students making no progress over long periods of our limited class time.


Here are multiple sources of struggle that students may face:
  • Difficulty understanding the task and what is being asked

  • Not able to get started on a problem, despite having a general understanding of what the problem is about

  • Difficulty with calculations

  • Difficulty accessing prior knowledge

  • Not enough time

  • Not finding traction in a problem, strategies are exhausted

  • Difficulty navigating the social component of group work

  • Not able to justify an answer

  • Not able to verbally express their thinking

  • Not able to represent their thinking on paper


These struggles could turn into sources of frustration for students, leading to off-task behavior or students shutting down, unwilling to keep trying. Or, they could turn into an opportunity for learning, both in the academic sense of prompting the discovery of new ideas, as well as the broader sense of being able to identify and access resources that allow for persistence in any challenging task, in the math class or otherwise.


With this in mind, I now offer a variety of strategies you can try based on the source of the struggle. I will use the context of a standard EFFL lesson to make this more concrete, but the strategies can be generalized to all sorts of struggle tasks.


For a downloadable version of this table, click below.



Struggle Source

Strategy

Difficulty understanding the task and what is being asked

  • Read the intro box at the top of the Activity as a whole class. Make sure students understand the context before launching them into group work.

  • Ask: “What is this problem about?”

  • Consider: “What would this look like without any numbers?”

Not able to get started on a problem, despite having a general understanding of what the problem is about

  • Give them a few minutes. Don’t intervene too early. Think time is necessary for generating ideas.

  • Offer a simple 3-column graphic organizer divided into “What do you know?” “What do you want to know?” and “What’s one thing you could try?”*

Difficulty with calculations

  • Offer a tool (such as a calculator) if the calculations themselves are not the main point of the lesson.

  • Ask: “What would this look like with easier numbers?”

Difficulty accessing prior knowledge

  • Distinguish between social knowledge and logical-mathematical knowledge when deciding what information to provide.

  • Plan a warm-up around a certain skill if you think it might be a barrier to the lesson.

  • Point to a resource (notes from previous lessons, a peer, an anchor chart, Google, etc.).

Not enough time

  • If students are still actively working through ideas and trying out strategies, give extra time. This is where learning is happening!

Not finding traction in a problem, strategies are exhausted

  • Use a sequence of focusing (not funneling) questions to help generate new ideas.

  • Allow groups to send a “spy” to check in on other groups (Peter Liljedahl calls this “mobilizing the knowledge” and explains how this fosters student autonomy.)

Difficulty navigating the social component of group work

  • Use the read-discuss-write protocol to offer structure to the group work.

  • Chunk the lesson, assigning students to work on a few questions at a time in their groups (rather than the whole front page), then debriefing those questions as a whole class, and then launching them to work on the next few questions.

Not able to justify an answer

  • Ask: “How do you know?”

  • Have students attempt to first convince themselves, then convince a friend,  then convince a skeptic (a framework from Cathy Humphreys).

  • Ask for convincing evidence and reasons that would “hold up in court.”

Not able to verbally express their thinking**

  • Elicit student thinking with questioning techniques. 

  • Expect student responses to not be tidy, clean, and clear.

  • Ask other students to restate, revoice, or summarize another student’s idea. This helps bring clarity and assigns competence to the student whose idea is being shared.

Not able to represent their thinking on paper**

  • Allow students to make informal sketches, pictures, and diagrams that make sense to them before insisting on a specific model or representation.

  • Wait to introduce and discuss specific models until the whole class debrief. This is an opportunity for YOU to extend and build on students’ thinking. Direct instruction of a helpful model that can be used for reasoning (like an area model or a double number line) is totally appropriate.

*The idea of this 3-column graphic organizer was presented in "Productive Math Struggle" by John SanGiovanni, Susie Katt, and Kevin Dykema.


**Pam Harris of Math-Is-FigureOutAble often reminds us that students can do more than they can say, and they can say more than they can represent. This is helpful to keep in mind because we have to recognize that verbally expressing one’s thinking and representing that thinking on paper is challenging and requires practice! This kind of struggle is almost always productive though, because it is directly related to developing students’ mathematical communication skills.


Keep the goal in mind

For many of these struggles, the strategy you choose to help students is dependent on the main idea of the lesson. If the main goal of the lesson is to help students understand slope as the rate of change, then offering the slope formula when students get stuck and teaching them how to identify and plug in x1, y1 and x2, y2 is not helpful! It is robbing them of the opportunity to make sense of the idea that we are partitioning a total change in our output variable into singular increments to find a unit rate. 


However, if the goal of the lesson is to understand that functions with an increasing rate of change are concave up and have increasing average rates of change, then pointing students to a resource for finding the average rate of change on a single interval (“We did AROC all the way back in unit 1, does anybody still have their notes from then?” or “Can anybody remind me how we calculate the average rate of change over an interval?”) is completely appropriate. At this point, calculating the average rate of change is background knowledge, and students will miss the main point of the lesson if they are too distracted by being unable to figure out how to do the calculations that will reveal the pattern of the function.


Besides just identifying the main instructional goal of the lesson, you should also be very clear about the purpose of your interaction with groups during the Activity portion of the lesson. This will impact how you go about helping students navigate struggle. In the book “Productive Math Struggle” by John SanGiovanni, Susie Katt, and Kevin Dykema, the authors make a helpful clarification. Your role as the teacher is to help resuscitate thinking, not rescue answers. Remember, the goal is not to get them an answer to this one particular problem. It is to advance their thinking around a topic and equip them with tools and strategies they can use now and in the future when they encounter struggle. 


Knowing when to step in


If group members are talking, trying out ideas, or still generating new strategies, do not step in! If they are struggling but progressing, LEAVE THEM ALONE.


To identify when you should maybe step in, look for groups that are completely quiet or talking about things unrelated to the lesson (these could be avoidance strategies). Neither of these are signs that you absolutely must intervene! But they are indicators worth paying attention to and investigating further. Move towards these groups, look at their papers subtly, and keep listening.


When a group is completely quiet, I go over and check on them but without interacting with them quite yet. If they’re each trying a strategy, or filling out a table, or doing calculations then I leave them alone. If it is quiet but no work is getting done, I ask a very neutral question: “Which one are you working on?” If they can’t answer this, I tap into my strategies for helping students navigate the social component of group work. If they can answer it, I ask: “What are you thinking so far?” I then use focusing questions to help students progress toward the main idea of the lesson, without taking over the thinking or forcing them into my own strategy.


What to do if the whole class is struggling

If you notice the majority of groups struggling for the same reason, try the "catch and release" strategy. This means you pause all the groups to make a clarification, provide a hint, or offer a question that might prompt them further. Better yet, you would have a student share an idea that you think would be helpful to others. Do this sparingly though, because constant interruptions to group work can be annoying, disempowering, and can disrupt students’ flow of thinking.


Is it ever okay to just tell students the information they need to get them out of the struggle?


Yes. There are some things that are considered “social knowledge” that are based on convention and cannot be deduced or reasoned through. For example, if we’re talking about a 16-inch pizza, we mean that the diameter of the pizza is 16 inches. This is a naming convention. Having students wrestle through whether the 16 inches refers to the circumference, radius, or diameter is not worthwhile and the differing opinions won’t lead to constructive mathematical debate. It will also detract from the main idea of the lesson. 

However, many “social knowledge” items can be garnered from the group, rather than told by you explicitly (e.g. “So when they’re saying 16-inch pizza, what do they mean? Who knows how pizza places refer to sizes?”). Another piece of social knowledge would be the vocabulary attached to a specific concept. Students won’t just come up with the fact that a triangle with two congruent sides is called isosceles. However, in the EFFL model we wait to attach the formal language until the debrief rather than pre-teaching it. This is considered “just-in-time” instruction: giving information when it’s needed, and not at the beginning by default, before students are able to store it in a way that is attached to meaning.


When the missing piece of information is logical-mathematical, we want students to reason about it. This is knowledge formed by the construction of relationships within one’s own mind. For example, students may need to identify an angle that is coterminal with 5π/6 in order to progress in an activity. If this is a source of struggle, we ask focusing questions or suggest a tool students could use to figure it out.


Conclusion

Part of the professional work of teaching is being able to pinpoint the source of struggle for a particular task for a particular group of students. It is critical to acknowledge that struggle comes in all shapes and sizes. When we lump all struggle into one category, we end up offering a one-size-fits-all type of “help” that takes over too much of the thinking in some scenarios or leaves students without any actionable next steps in other scenarios, leading to frustration and a potential impasse. Having a set of strategies at our fingertips to help students navigate struggle can help us make real-time decisions that support our classroom goals.




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1 Comment


Brent Ferguson
Brent Ferguson
Feb 28

Yes. Brilliant follow-up. Thanks, Dr. Calc, our community's medic-in-residence. I'm struck by the vast number of teachers that use your EFFL lessons and worksheets to engage students in good tasks, and also to make their lives easier by having ready-to-use materials handed to them on a silver platter. But there seem to be relatively FEW who are reading this blog, engaging the ideas within it earnestly, and growing their philosophy and practice as teachers as a result of pivots to their daily work. You deserve a much broader audience with this writing, IMHO. How can that develop?

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