One of my favorite anecdotes regarding fractions is the failure of the “third pounder”. The fast-food chain A&W, a competitor of McDonald’s, created the burger to compete with the famous “quarter pounder”, and sold it for the same price. The initiative failed, and the consensus was that people believed they were being overcharged - after all, four is bigger than three.

I have no doubt that most people would have completed exercises in their primary school that demonstrated why a quarter was, in fact, less than a third. I’m sure they listened patiently as their teacher explained this fact to them - perhaps multiple times. And yet, here we are.

What does this story tell me as a mathematics educator? 

It tells me we’re teaching math the wrong way. 

The Cost of Teaching Math with a Top-Down Strategy

Education is fundamentally a top-down system in nearly every nation in the world. A government body defines learning objectives and benchmark standards for each grade level, and it’s up to teachers to help their students meet them. 

It is precisely this one-size-fits-all approach that leaves students feeling left behind, alienated, and disconnected from education. In no subject is this more acutely apparent than in mathematics. As a result, high schoolers exit the education system not knowing that ⅓ is more than ¼!

We could be doing much better than this. But, how?

Student-Led Learning is the Future of Education

Motivation is a key factor in learning success. When students are interested and excited about what they’re learning, they are more likely to achieve curriculum standards. So, why don’t we build student motivation by putting them in the driver’s seat?

This is precisely what student-led learning is.

Student-led learning reverts the top-down approach and puts students in charge of their own education as much as possible. 

What’s more, student-centred learning has been proven to achieve superior educational outcomes, particularly in STEM subjects like math. 

Here are some key components of student-led learning that we try to include in Matific:

Choice: Research shows that when students get the chance to choose, they develop intrinsic motivation and self-efficacy, no matter what grade they’re in. We offer students plenty of choices in Matific by allowing them to choose which problems to work on and navigate between different types of activities. 

Active Learning: Rather than offering students worksheets to complete passively, student-led learning encourages students to explore topics on a deeper level. We incorporate this into our math activities by featuring manipulatives, offering lab experiences that have multiple correct answers, and more.

The Teacher is a Resource: Rather than dictating everything students do, teachers become guides and facilitators. This happens very easily with Matific. Students can advance at their own pace while teachers observe their progress. Then, when students may require extra in-person support or feedback, teachers can step in and offer help. Or, teachers might suggest additional projects to challenge and further develop skills in high-achieving students. 

As students learn, the teacher is always there to guide them. However, it is in a collaborative way. Both students and teachers are free to suggest activities, exercises, and projects that will propel the students’ learning forward. Many times, students and teachers can work together to discover the best ways to learn that match students’ interests and teachers’ learning goals.

Real-World Relevance: To be engaged, students want to know WHY what they’re learning is important. In other words, what will all of these math skills help them with in the real world? Research has proven that relating content to real-world problems can boost engagement.

This is why we incorporate real-world scenarios into Matific wherever possible. Through story-telling and word problems, we ground math skills in real life.

A Framework for Student-Led Learning in a Top-Down System

We know that teachers operate in a top-down education system. They have curriculum standards to meet and administrators to answer to. Yet, we believe we can have it both ways! It’s possible to meet curriculum expectations while also adopting a student-led framework.

The approach we have settled on is to provide teachers and students with everything they need to succeed in the system in which they operate, yet we take the additional step to centre the experience on the students learning mathematics every chance we get. We’re proud to be one of the only platforms that take these concerns to heart. Here are some considerations we use when developing Matific content. These considerations are also relevant to classroom teachers, administrators, and anyone involved in education. So, feel free to make use of them!

• Motivation: What does the student want? Is the motivation internal, or external?
• Goal-oriented behavior: What kinds of things does a student do in response to that motivation?
• Attentive engagement: What makes a student truly connect with the subject matter?
• Perseverance: How does a student keep their goals in mind in the face of adversity or struggle?
• Achievement: What does success look like, and how do we celebrate it with them?

Everything we do affects this progression in some way. At its heart, Matific prides itself on facilitating authentic learning of mathematics for every student. 

This means we: 

• Build intrinsic motivation to discover new mathematical ideas.
• Help students form their own goals for their mathematical learning.
• Provide ways for students to engage with mathematics - not just the “wrapper”.
• Help students internalise the value of what they’re doing and concentrate when it matters most.
• Help students feel the satisfaction of using a mastered skill and yearn for more.

With these steps, we offer a way to work within the top-down system that doesn’t bore and alienate students.

With a student-led approach, children can develop a deeper, life-long understanding of math topics that will serve them far into the future. It’s possible for students to exit the education system with a firm grasp of fractions! If we change our approach and listen to our students, we can change the face of education for the better.