Are Your Math Students Getting the Wrong Answers? Good!

Are Your Math Students Getting the Wrong Answers?
Good!
Kiddom’s HQIM Builds a Growth Mindset

Are you a teacher who spends hours each week searching for instructional materials to supplement a curriculum you don’t feel measures up? If so, at least you’re in good company. A recent national survey shows that our school teachers are spending almost twelve hours a week finding instructional materials and/or making them on their own. That’s not fair to our educators or to our students. This data underlines the national need to secure, and utilize high-quality instructional materials. No educator has an unused half-day every week to spend looking for additional curriculum materials, especially when they could be utilizing their energy and time to focus on what’s most important; teaching!.

The good news is that a high-quality math curriculum like Illustrative Mathematics and Open Up Resources provides teachers with the support they need. By utilizing preloaded misconceptions in the curriculum, teachers can strategically plan their lessons while also receiving support in planning how they will teach by identifying potential pitfalls. This approach enables educators to anticipate common misunderstandings and tailor their instruction to address these areas directly, leading to more effective learning outcomes… No longer do they need to spend time and energy imagining what their students might get wrong and why, or looking for that material online without the assurance that the information they receive is accurate, aligned to state standards, and on grade level.

Instead, teachers who leverage Kiddom’s high-quality instructional math curricula have the strategic advantage of copious student misconceptions-strategically placed where teachers need them to move their students forward in their procedural fluency. Addressing these misconceptions often requires targeted instruction, hands-on activities, real-world applications, and opportunities for students to explore and discuss their reasoning all of which are also included in the curriculum. By identifying, utilizing, and redirecting misconceptions, educators can help students develop a more robust and accurate understanding of mathematical concepts.

So, what is the mind shift that is required to utilize student misconceptions effectively?

On the flight back from a recent California school district master teaching session, scrolling through LinkedIn, I saw this picture (see below): I was immediately struck by how it applied to the mindset shift required by mathematics teachers to effectively use student misconceptions to nudge students toward mastery.

At Kiddom, we’ve seen the most effective math teachers shift their mindset from seeking to avoid or eliminate student misconceptions before they happen, to rooting misconceptions out earnestly, to pave a smoother road toward mastery afterward.

(Milani, 2023)

The image shows bricks blocking someone’s path, labeled as “failures as obstacles,” contrasting with another image of a bridge made from those bricks, labeled as “failures as lessons.” It symbolizes the shift in education from avoiding student misconceptions to using them to progress.

Just like this meme, viewing student mistakes as an obstacle makes them a hindrance. Rather, viewing student misconceptions as the very solution to the problem is a paradigm shift; like our little friend diligently seeing failure as a lesson, student misconceptions can be the material you use to build the road students take to arrive at mastery. This shift in mindset is subtle, powerful (and backed by research).

Rather than viewing student misconceptions as a sign of poor instruction on the part of the previous teacher, we must acknowledge student misconceptions as expected and useful materials for teaching and learning, and use them as such. In fact, student mistakes share the same DNA as student success (effort, calculation, and courage). This is no accident; we should all strive to be the teacher-alchemist, who can transform student misconceptions into student mastery, shows up prepared for instructional routines, identifies which specific misconceptions to look for, and knows how to respond and utilize them, thanks to the intellectual preparation she performed through their HQIM. But student mastery isn’t the only positive outcome of providing a valuable space for all student efforts in the classroom.

Valuing Student Misconceptions Builds Positive Math Mindsets

For students in a fixed mindset, mistakes may only confirm what they fear: that they are incapable of mastering a skill. Fixed mindsets solidify the belief among students that their inherent qualities for success are static and incapable of growth or development.

“You’re either a math person or not,” they say. YIKES!

Fixed mindsets unfortunately use mistakes to reinforce that presumption. “Fixed mindsets fuel negative attitudes toward mathematics and can contribute to math anxiety.” Believe it or not: the way a math teacher utilizes student misconceptions emphasizes the kind of mindset their students will adopt. Teachers who do not value the utility of making mistakes will encourage students to think the same way.

Your belief in a student’s potential to grow is key in encouraging them to see their own capabilities for development. It’s all about nurturing their confidence and helping them realize they can achieve more than they might think!

In a growth mindset, teachers expect students to make mistakes and to pivot upon them, recognizing mistakes as indications of areas where they can improve, if given time and the opportunity to reflect and try again. As we know from Kapur and Dweck, making mistakes helps our brains to formulate more sophisticated relationships between concepts. In a growth mindset, things may start with natural talent, but dedication and self-belief soon follow when the work gets difficult (not passive acceptance that only smart people can do it). Students with growth mindsets don’t believe ”they can’t”, they believe that they can if they are allowed to try. Students with growth mindsets cultivate a love of learning and resilient work ethic that will take them farther in life. When students with growth mindsets encounter failure and misconceptions, they dig in deeper and focus. In classrooms where misconceptions are embraced as opportunities for effort and focus, a culture of positive math mindsets flourishes. When every effort is valued, authentic engagement soars, paving the way for a cascade of benefits for students.

Making Space for Mistakes Builds More Equitable Student Communities

Finally, by valuing student misconceptions, we promote inclusivity, prevent cumulative disadvantage, and level the classroom playing field. We know some students often feel like they are bad at math, especially when math is difficult for them. When students encounter misconceptions in classrooms where mistakes are not appreciated as essential learning opportunities, they may unfortunately start to withdraw from making genuine efforts. Research shows that students of marginalized populations display more of a tendency to be silenced by their mistakes and suffer from cumulative disadvantage. After multiple mistakes, they end up clamming up and stopping the process of inquiry, which ends up reducing the engagement of the learning experience for everyone. Said another way, when some students feel disenfranchised and hedge their efforts, the entire classroom suffers.

However, when we build classrooms full of growth mindsets…

• We acknowledge the value of the voices of different students.
• We encourage different learning styles to be demonstrated, normalized, and accommodated.
• We make a more equitable learning experience for all involved.

When you team up with Kiddom for your high quality math curriculum, your classroom isn’t just powered by our dynamic teaching and learning environment, but by the best researched, most equitable, and most effective pedagogy on the market (supported by first-class professional learning), that helps you to meet the needs of all students.

How do you ensure all your students’ efforts are valued in your classrooms?