Productive struggle in the elementary mathematics
We associate the word “struggle” with something that is challenging or difficult. The instinct of a teacher is to make mathematical tasks and concepts easily achievable, but that instinct sometimes favors surface-level mastery over more in-depth and rigorous problem-solving ability. While we hate to see our students struggle, the level of struggle achieved by students can be beneficial when it is productive.
Knowing what you are teaching and how you plan to teach and assess each academic standard along the way is key to promoting productive struggle in your classroom. This, in turn, will empower students and boost their growth and achievement, creating a generation of learners who are geared to persevere and problem solve.
Below are some strategies I use in my classroom to promote productive struggle.
Growth Mindset Environment
Building a fearless classroom culture is the cornerstone of productive struggle. The message that learning comes from struggle is rooted in how we approach this in the classroom. We discuss what persistence means and that giving up on a task won’t equate to growth. Feedback from teachers and peers isn’t meant to always find fault, but to provide analysis and growth opportunities for all involved.
In my classroom, we establish a learning goal and look at what each step looks like en route to mastery. We discuss at length the challenges that can pop up along the way. One critical thing I avoid is offering immediate feedback based on whether a solution is correct or incorrect. Instead, I have the class or group offer an “agree or disagree” approach. If a student disagrees, he or she must explain why and offer a different perspective and strategy. This creates a low-risk environment for all students to see things from various viewpoints.
Using math games in the classroom is a great way to implement a growth mindset environment. Students have background knowledge in struggling with games, and this is a great entry point for all learners when you are building your environment. Using popular video, computer, and board games to present the benefits of productive struggle is a fun and easy strategy to remind students that they already have experience with productive struggle in their own lives.
Rigorous, Purposeful Tasks
Any meaningful assignment you place in front of your students is considered to be a math task. The question at hand is: “Does this task align with and address all parts of my standard?” Rigorous math tasks should allow all students entry, while at the same time offering multiple solution paths. When selecting a task, analyzing your standards beforehand and understanding misconceptions and “trip up points” along the way is key to the effectiveness of the task. These tasks should take time to work through, allowing students to think deeply about each part to advance their learning.
After analyzing standards and then selecting a task, I use heterogeneous ability groups in my class to work through different parts of the task. Students are encouraged to show their work in various ways through the use of math manipulatives, diagrams and models, and equations. This allows us to have rich mathematical discourse when different strategies and solution paths are displayed for the class as part of our task analysis. Small group instruction and partner group activities are also critical to the success of tasks. Students are able to struggle collectively while I offer guidance and strategy options as they work.
Planning for and Responding to Struggle
Planning for struggle will become second nature as you dive deeper into your instruction. I approach each lesson with questions in mind that are directly related to potential pitfalls for each task and activity. Our district uses the Ready Math curriculum, which provides teachers with a list of questions that promote mathematical discourse and which can be applied to any math task. Some of the questions I incorporate most into planning for productive struggle are:
- Would another method work as well or better?
- Is there another way to explain your strategy?
- How does your strategy compare to another student’s method?
- How would you explain what you know right now?
- Can you connect what you already know about this skill to what you’ve learned today?
Having questions in mind for specific points in a lesson where you want students to struggle is as important as the task itself. Whatever questions you choose to ask, it is important that they are purposeful, intentional, and impactful. Building time into your instruction is also important for productive struggle. Providing ample time for students to work through a task is critical, and using purposeful questions to guide them through a task can help.
The online component of our math curriculum – i-Ready – provides me with valuable data about the standards and skills my students are struggling with. This data, in conjunction with knowing my math standards, gives me advance knowledge on where misconceptions may arise for an individual student. I am able to adjust for this student’s struggle through my planning for whole group and small group instruction since I have the data readily available.
Data collection through this online component and through our common formative assessments gives me an opportunity to find patterns in student learning, which leads to knowing where struggle will present itself for each standard. Collecting data also allows you to better group your students for small group instruction. Whereas my student small groups are heterogeneous ability groups, my teacher-led groups are homogeneous ability groups and give me the flexibility to differentiate struggle based on the group of students I meet with.
Students who are performing one or more grade levels below are offered more scaffolded instruction to a rigorous, on grade level task with a specific and purposeful entry point and various strategies presented for use. I might ask them to explain their thinking using a more concrete approach through manipulatives in order to achieve a certain level of mastery along the way to overall mastery. This is based off of the goal we set at the beginning of the lesson that is specific to each group I meet with.
Students performing on grade level or above are presented with the same rigorous task, but my questioning provides productive struggle on a deeper level. I might ask them to provide me with a pictorial or abstract explanation, and advance from there deeper into the standard where they are productively struggling towards another level of mastery based on our goal.
Kyle Cantrell is a 5th grade teacher at John Pittard Elementary School in Murfreesboro, Tenn.
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