What Is Personalized Education, and Why Does It Matter?

Suppose I’m teaching a student to solve this problem:

A rectangular garden is 3 meters longer than it is wide. Its area is 40 square meters. What are its length and width?

I know we can call the width $x$ and write the equation

Following the student

But before we start, I ask: “Do you know how to write an equation for this?”

They say no, so I ask: “If the width is 5 meters, how long is the garden?”

If they can’t answer, we first talk through what “3 meters longer than it is wide” means. If they say “8 meters,” I ask: “Then what’s the area of the garden?”

They say “40 square meters.” Now I know they understand the relationship between the length and width, and they can calculate the area. Next, I can ask: “If we don’t know the width yet and call it $x$, how would we write the length?”

These questions help me find where they’re stuck. One student needs help understanding the problem. Another needs to review how to calculate area. Another needs to learn how $x$ can stand for a number we don’t know yet. Each student needs a different next step.

Following the script

What happens when I teach without making these adjustments? I know we can solve the problem with an equation. I find out the student doesn’t know how, so I go straight into teaching it: call the width $x$, the length is $x + 3$, so $x(x + 3) = 40$. Then expand it and solve the equation.

I’m already explaining how to solve the equation, while they’re still wondering: “Why can the width be $x$? Why do we multiply these two things?” I assume they understand and keep going, but they’ve been lost from the start. It gets harder and harder, until they think: “There’s so much I don’t know. I’ll never be able to solve this.” Then they get tired and don’t want to keep learning.

What the student experiences

When I check where they’re stuck and adjust the next step, they have time to understand before we move on.

For the student, that can mean:

1. Having room to understand. Cognitive load research shows how the effort of searching for a solution can use up the mental capacity needed for learning. Helping a student with the step they're stuck on can give them room to understand it. Sweller, 1988
2. Feeling “I can do this.” In an experiment with children who struggled with mathematics, working toward small, near-term goals improved both their mathematical skills and their belief in their own ability. Bandura & Schunk, 1981
3. Wanting to keep learning. Those same children also developed more interest in arithmetic. Completing manageable steps gave them progress they could see. Bandura & Schunk, 1981
4. Learning more with help at each step. A 2011 research review found that tutoring systems giving step-by-step feedback produced substantially larger learning gains than systems responding only to final answers. VanLehn, 2011
5. Feeling better about the help they receive. In a classroom study of 768 students aged 12–15, students appreciated teacher support more when it was adjusted to their understanding. Van de Pol et al., 2015
6. Taking on more of the work themselves. A review of scaffolding research describes a process in which help follows the student's needs, decreases as they become more capable, and gradually leaves responsibility with the student. Van de Pol et al., 2010