I’ve been using different math prompts for the past few years. I usually introduce the prompts and give students time to work in a group to find a solution. Students often work together, struggle, and eventually come to a solution. It’s expected for students to document their journey in solving the problem in the prompt. Last week I gave this prompt to one of my upper elementary classes:

When I first introduced the problem the students had a million questions. The questions were mostly related to what operations to use and hoping that I’d give away a few hints. I want the students to succeed, but I also want them to become more responsible for their own learning. I answered the questions related to the directions, but intentionally didn’t give away any information regarding what procedures/operations to use. The students were then divided into groups and given 20 minutes to find a solution and present the answers to the class. The next 10 minutes or so were challenging. Challenging may be an understatement. The students struggled, period. They had a tough time knowing where to start after finding how many dollars fit in a ream. The less I spoke the more the students seemed to flounder. Students began to look at each other and within to find a solution. After the initial 10 minutes, the groups began to click. Students started to find that their solutions were working. The students were beginning to make progress. The students were pumped and I tried to hide my own excitement for them as some groups were still struggling. Groups were gaining momentum and near the 20 minute mark most groups were finished or partially finished.

The students then presented their journey in problem solving and the process used to find the solution. Each group solved the problem (or came close to solving the problem) in a different way, but all the groups learned from each other during the presentations.

Following the presentations, the class had a discussion related to the math prompt. The groups reflected on how challenging it was to persevere through the struggle of not knowing how to solve a problem. I’m glad that the students were able to experience the struggle. Moreover, I’m glad that some of the students were able to use math problem solving strategies and look within and to each other to persist.

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Hey Matt,

Last year’s PD for us middle school teachers was solely about designing and implementing groupworthy tasks. The biggest take away in the design process was including resource cards, or hints, so that students have access to the problem without giving it all away. In essence begin with just the prompt. If they don’t know where to begin, give them resource cards that addresses what information is helpful to solve the problem such as:

1) “What do you know about the size of a one dollar bill? Would knowing how many dollar bills fit on a sheet of paper be helpful–how could you estimate that?”

2) “Would knowing how much paper weighs be helpful?–Is there anything in this room that could help you make that estimate?”

3) “What does one ton weigh?–where could you find that information?”

I wrote about a similar task that I used as a formative assessment and I experienced the same thing you did. Since it was formative I collected their individual work after 15 minutes and gave them written feedback to prompt further thought. In this case the feedback were my “resource cards”. The next day I returned their work and allowed them 15 minutes to continue working independently. Then I put them into groups to collectively come up with an improved solution.

It was a lot of work, but worth it.

I don’t know if this approach is something to consider. Just tossing it out there.

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Mary,

I like the idea of using resource cards and providing written feedback periodically. My team has been discussing the usefulness of formative math tasks this year. One of our goals is to create additional math tasks for grades 3 – 5. Thanks for the comment.

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Matt, I love the task, including the fact that students were forced to persevere and did so. As my school is moving to an investigations based math program, the biggest obstacle that we have had to overcome is students who are used to being walked through all math problems and don’t know how to struggle with an end in mind. I think the lesson of productive struggle- with an end in mind and no clear strategy, but maybe a few inklings- could easily be one of the most important things we can teach our students, over and above the math skills we impart. I like Mary’s idea, but would caution against giving too much away. Maybe asking guiding questions that open a train of thought instead of suggesting the path directly.

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Yes, my school is also moving in the same direction. It’s a transition as some students are used to finding the one right answer by following a procedure, but they don’t necessarily understanding the mathematics. This becomes evident as students participate in these types of math tasks. Making mistakes is part of the learning process and exposing students to challenging math tasks gives students opportunities to collaborate, struggle, and eventually find a solution. I appreciate the feedback.

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I cannot wait to try this in my classroom. Thanks for sharing Matt!

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It seems to me that you have provided too much information to the students—giving them exactly the information they need to solve the problem and no other information. It might be better to give them just the question, and have them ask for what other information they need. You’d have to have some scaffolding, to keep them from floundering too much, but I think that what you outlined may be a bit too guiding to a particular approach that gets them to do arithmetic, but not much mathematical thinking.

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That’s wonderful that you’re letting the students struggle so early in their math careers! That struggling is so important: don’t give up on it just because they (or you) get frustrated, and great job wrapping it up with them reflecting on how struggle can be good.

I remember an assignment I gave my seniors in Precalculus last year–something about sketching a graph that was reasonable and finding an appropriate equation. They struggled and struggled, and after the hour and a half class (yes, it took them the whole class and they still weren’t done!), I looked back and wondered where the time went, wondering if it was a waste of time. I think my seniors didn’t get enough of what you’re giving your students, so they weren’t ready for the kinds of problems I was throwing at them: they just wanted to sit and be told how to do problems. Keep up the great work!

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In general, I think that students at the elementary level have limited experience with math task problems. Understanding how to cope with a challenging problem (math or anything) and the struggle that ensues is important. Thanks for the comment.

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Often the most learning occurs in “the struggle”. Thanks for sharing!

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Love it! I’m going to reference this on my blog where I posted recently about perseverance.

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Great! Do you have a link?

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Here you go Matt

http://mrdardy.wordpress.com/2013/09/22/perseverance/

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How often do you do this type of problem? It seems to me that kids would either really get into it (or at least be comfy with the struggle), or start to dread it (sorta depending on the kinds of kids you had in class?) or both.

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I’m using these types of tasks once per month. Students at the elementary level aren’t often exposed to this type of problem solving activity, so it can be a challenge. Many of my fifth graders now look forward to the math task challenge. My younger students have the most trouble finding a starting point. Overall, I feel like it benefits the students and makes them accountable for thinking of not only the answer, but the procedures needed to find a solution. Thanks for commenting.

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Hey,

Great class. You say elementary but that design works at every grade level. I was just at ccss workshop and your lesson is the perfect layout for a high school modeling opportunity.

I am going to try to implement this idea my classes. More collaboration and reporting out.

Nice work.

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Yes, that’s the beauty of math tasks. They can be modified and used in a variety of grades. Thanks for stopping by and leaving a comment.

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