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How to Promote Productive Struggle In Math and Raise Math Rigor

Math LearningHow to Promote Productive Struggle In Math and Raise Math Rigor

October 6, 2021

The definition of “productive struggle” is effortful learning that empowers students to attempt solving new math problems using logic and prior knowledge before being explicitly taught a procedure.

According to the National Council of Mathematics Teachers’ Principles to Actions, productive struggle is an essential part of math learning: “Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.”

Struggling is neurologically essential for students, and teaching students that struggling is part of learning math can build creativity and authentic engagement.

Correcting Misconceptions About Productive Struggle

There are a few common misconceptions surrounding productive struggle and the best way to implement the practice in your classroom.

The most important misconception to clear up is that productive struggle is all about giving students overly challenging tasks that inevitably lead to persistent or unavoidable frustration.

This balancing act can become tricky for teachers in large classrooms with a wide range of educational needs and abilities.

For the greatest success, students’ efforts should be directed towards activities that require careful consideration and application of prior knowledge, rather than unsolvable, new, or overly advanced materials.

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The Importance of Embracing Productive Struggle in Math Classrooms 

Why is productive struggle important? The benefits of productive struggle in math are numerous.

  • Builds conceptual understanding: When students engage with rich, real-world tasks, they have to rely on their own reasoning and background knowledge rather than mimicking a teacher-led procedure. This messy process of sense-making builds conceptual understanding, which is an essential aspect of rigor in math learning.
  • Creates a student-centered environment: Productive struggle flips the usual script of teachers demonstrating a skill and students practicing it; instead, students actually begin with independent or peer work. This approach can be more engaging, and leading with the student-led portion of a lesson ensures it does not get cut if class time runs out.
  • Improves teacher feedback: While students engage in solving a new kind of problem, teachers can circulate and gather data on misconceptions and deliver just-in-time support. When the class eventually comes together as a whole group, teachers can then ground their instruction in a more precise idea of students’ understanding.

How Can Teachers Create a Culture of Productive Struggle? 

Research points to a few best practices for encouraging students to embrace productive struggle:

  1. Probing questions and insisting on sense-making: Teachers can support productive struggle by asking questions that encourage students to reflect on their learning. According to mathematics education researcher Hiroko Warshauer, “teacher responses such as ‘Tell me what you mean’ and ‘Talk about it some more’ or the insistence on sense-making with ‘Why is that?’ provide opportunities for students to elaborate on what they understand and to clarify the source of their struggles.”
  2. Peer collaboration: When a student is stuck, instead of swooping in with the answer, teachers can encourage them to check-in with a peer. Allowing students to collaborate and realize they are all struggling together relieves the discomfort of a “wrong answer” and instead normalizes trial and error as well as celebrates growth mindset.
  3. Reading the room: Creating a culture of productive math struggle requires monitoring and responding to students’ needs. For example, the class needs to move at an appropriate tempo that doesn’t rush the problem-solving process or necessitate shortcuts. Giving students enough time communicates that the process is more important than finding the answer. However, it is good to have scaffolded questions and support at the ready if most of the class is veering into frustration and unproductive struggle.

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Teaching Habits that Don't Encourage Productive Struggle in Math Students

Introducing productive math struggle can be a unique and alienating experience for teachers unfamiliar with the increasingly popular learning strategy.

Here are five teaching habits to avoid when encouraging productive struggle in the classroom.

1. Hand-holding

As an educator, it can be tempting to hover around struggling students so you can make yourself available as soon as they run up against a challenge.

However, rushing to aid students too soon can cut productive math struggle opportunities short and stunt the development of educational agency and confidence.

Instead of giving in to the temptation to be a Helicopter Teacher, work on developing teaching strategies that:

  • Cultivate independent problem-solving
  • Support strong critical reasoning
  • Teach students that encountering confusion and frustration are a natural aspect of growth and learning

Of course, teachers should be prepared to gently guide stuck students back on track when necessary to ensure progress doesn’t stall for too long.

2. Using Binary Feedback

Over-reliance on binary “right or wrong” feedback and math standards in the classroom can discourage students from exploring multiple approaches to math problems after getting stuck.

Instead of placing correctness on a pedestal, provide informative feedback that addresses learning gaps and acknowledges student successes.

By creating a safe space for students to brainstorm and work through potential solutions, teachers can instill higher levels of confidence in the classroom.

Over time, de-emphasizing correctness can create a learning environment that places genuine effort and enthusiastic engagement over right or wrong answers.

3. Sticking to Formulas and Equations

While it’s important for students to learn formulas, equations, and processes for practical applications, spending too much class time on rote memorization and similar teaching strategies can stunt the development of deeper conceptual understanding.

Instead of spending class time reviewing formulas and equations, ask your students to analyze real-world scenarios and identify formulas or equations that could solve the problem and save the day.

4. Valuing Smarts Over Hard Work 

Surprisingly, students who successfully solve challenging math lessons and are praised for their intelligence develop worse learning habits than peers encouraged for their hard work.

Emphasizing hard work over intelligence is a crucial aspect of cultivating a growth mindset amongst students.

Growth mindsets encourage students to expect some level of struggle when approaching new or complex mathematical concepts and celebrate a strong effort as enthusiastically as a correct answer.

While answering correctly is important, developing a positive and healthy relationship with learning (and the frustrations that so often come along with it) is crucial to long-term student success.

5. Emphasizing Time to Learn Over Mastery

One of the hardest adjustments for many teachers to make when implementing productive struggle is simpler than you might expect. So, what is it?

Making time for productive struggle.

Modern public school testing requirements have led to curriculums that overly value a strict learning schedule. This time-sensitive learning approach can make struggling students feel rushed and in danger of being left behind.

When this occurs, students may abandon topics or skills they haven’t yet mastered in an attempt to keep up with the pace being set by their teacher.

Slowing down and providing students with enough time to productively struggle with math lessons, develop new learning skills, and attain mastery over concepts, procedures, and skill sets enhance student confidence and strengthen neural pathways that support long-term knowledge and skill retention.

How Does Productive Struggle Help Promote Math Rigor?

The effortful learning required during productive struggling builds positive learning habits that translate into greater educational perseverance and learning outcomes that meet math standards.

Productive struggle develops math rigor by encouraging and reinforcing alternative problem-solving strategies and creative and diverse approaches to math.

Working through challenging math problems encourages a deeper level of learning while simultaneously preparing students to take on more complex and challenging mathematical concepts in the future.

How Does Yup Help Students Embrace Productive Math Struggle? 

Yup’s user-friendly on-demand tutoring platform is an ideal tool for stimulating vital productive struggle examples that ultimately leads to greater student success in math.

  • Yup’s Teaching Framework is designed to support and honor the importance of productive math struggle. When a student is stuck on a problem and logs into Yup, they receive guidance from a tutor, but the tutor never tells the student the answer, keeping the focus on the learning process instead.
  • Tutors provide students with feedback as they work so they can correct their own thinking, and they encourage students by praising perseverance and thinking over answer-getting.
  • The mathematical proficiency of Yup tutors is such that they are adept at seeing and valuing creative problem-solving processes (as opposed to believing that there is only one approach), allowing students to experiment with and evaluate different strategies.

Enhance Students’ Math Skills and Rigorous Understanding Through Productive Struggle With Yup

If you are interested in the ways Yup can be used inside and outside the classroom to facilitate productive math struggle, book a demo today.

You can also learn more about our revolutionary learning platform on our blog or teacher and administrator pages.

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