March 29, 2020
I always struggled trying to learn math and science. It wasn’t natural for me. Some students “got it.” They understood math. But I never did. I “got by.” Friends helped me with assignments, or I copied off my neighbors. I never really took the time to learn and invest in my mathematics abilities. This was because I had a fixed mindset when it came to math. I thought—well I always do poorly at math—I must be bad at math. In a weird, sort-of-rational way, I believed that I was permanently bad at math. I didn’t have any successes to prove otherwise!
Many other students and families feel this same way. These families are frustrated because they know their student is bright and smart. She is just having a hard time learning math. I believe this is more about the way that math and science are currently being taught in schools than it is about the learner. Math is being taught as a lecture. Teachers have a strict agenda of what they want to teach. They give their lecture, pass out a worksheet, and then expect the students to learn the ideas. This is outdated and simply doesn’t work.
This style of teaching doesn’t hold its ground when compared to the new research being published on math and science education. The research today shows that students learn math and science when they hear themselves verbalize their own mathematical and scientific thinking. This is a huge finding. Up until now, teachers have been relying mainly on lecture-based teaching. They lecture during class, maybe assign some worksheets to keep the students busy, and they send them home with work to complete.
I grew up taking math courses centered around lecture. They were all about one person presenting the ideas. The problem with lecture-based mathematics and STEM courses is that students often think they understand what is going on, but in reality they are missing a few small distinctions on how to complete the problem or activity. These small misunderstandings compound on each other until eventually the student is so far behind that they need massive assistance in order to catch up. But these small misunderstandings don’t have to compound! We can stop them in their tracks!
If students were allowed the opportunity to simply discuss the concepts every day, then they would learn them much quicker. This is because when we discuss ideas we are better able to see the small holes in our own understanding. This allows learners to ask questions and fill in the gaps. Specifically, in active learning class rooms students spend the majority of the class discussing concepts, ideas, and working together on practice problems. This is the ideal way to learn math and science. But these courses require professors who invest a significant amount of time and energy into planning their courses and their course structure.
In college, I was fortunate enough to study under such a teacher. She not only knew mathematics, but also had a Ph.D. in mathematics education. She knew how to teach math. The entire course was centered around small groups. This is where everything started. We sat at a small table of 3-4 people and we discussed ideas *before* she taught us what the core concepts were. Most of the time we were able to figure things out in our small group!
Learning like this was difficult. It was challenging to learn this way because we weren’t simply spoon-fed the answer. We had to find it ourselves. We had to discover it. I took algebra 1/2, and algebra 3/4 this way. I also took pre-calculus and even two discovery-based calc I and calc II courses.
In my calculus classes, we spent weeks at our table discussing the concept of “rate-of-change.” We looked at graphs and got a good feel for what rate of change was. We learned that when you look at a graph, you can determine at what rate it is changing at any certain moment. Imagine zooming in on one small square of a graph. How fast is the line changing in that moment? That is what a derivative is. We learned that before ever hearing the word “derivative.” By the time she wrote the equation for a derivative on the board, we had already learned what it was. It was as if we built the meaning with our own hands. We felt as if we owned that word. We knew it inside and out.
Most people walk away from calculus course not learning anything. I’ve asked many people what they learned. (Try asking people yourself)! People generally say that calculus was useless and that they didn’t learn anything. “I can’t remember anything from that class,” they say. And that is a total shame! Because the concepts of calculus are so incredible. These concepts are fundamental to our lives. I think about rate of change all the time. You can apply it to the stock market, to human psychology, to climate change. What I find really fascinating, is that you can even apply rate of change concepts to your own learning. Think about it: every course moves at a certain rate. And each chapter moves at a different rate. It is also important to be able to think about your own rate of learning in each moment. How fast are you improving? Is your rate of change fast enough to learn all the material? If you aren’t learning at a fast enough rate, then you simply won’t do well in the course. If you realize you aren’t currently learning things at a fast enough rate, then you have to come up with a new plan or strategy. It’s all about having the right approach and mindset when it comes to learning.
One method we use with our clients—to increase their rate of learning—is to use active tutoring strategies. This means that we engage with out students. No longer are these students simply passively learning new knowledge. We believe that passive education is demoralizing. It reduces students’ confidence. It erodes their belief in themselves and their own ability to learn. Because essentially the message of lecture based STEM education is that: we are the intelligent people with all of the answers, and all you can do is sit down in front of us and diligently take notes and learn. Active learning flips this around and empowers students.
Why is active learning so powerful?
Active learning is inherently engaging. It gets students involved in the process of their own education. They cease to be passive observers of knowledge and become actively engaged in their own learning. This is empowering. It teaches them that they have control over what and how they learn. Active learning teaches kids to have a GROWTH MINDSET. It helps to shatter the fixed mindset which is inherently limiting. The whole idea of active learning is built around the growth mindset–that if you apply yourself, you can grow, you can improve, you can become better. And you do this by rolling up your sleeves and getting to work…. NOT sitting back and watching.
Importantly, active learning has been shown to do two main things: 1) it increases students’ overall academic achievement and 2) it improves students’ attitude towards math and science. It does all of this while also reducing misunderstandings about science and improving students’ understanding of big ideas and concepts.
Active learning works so well because it shifts learning from a one-size-fits-all approach to one that is inherently personalized and tailored to each student.
At Tutor Portland, we use an active approach to tutoring. Instead of simply giving answers or showing students how to solve problems, we ask them questions. We engage our students in critical thinking and in-depth discussions about concepts and topics. We ask questions and try to get students to connect the ideas they are currently learning to ones they learned last term or last chapter.
This is often the first time they have *ever* thought critically about the ideas they are learning in school. It’s a dramatic difference once students become engaged with the material. It changes from something abstract to something up-close and personal.
We follow a few “active tutoring” rules very closely:
- The tutor is simply a guide, a facilitator — the tutor is not a teacher.
- We give students time to think.
- We create a comfortable and relaxed learning environment.
- We ask open-ended questions.
- Curiosity is a quality which we embody, and which we attempt to bring forth within our students.
- Teach ethical behavior and thinking.
- Focus the session on the student. Not on the tutor or the parent or anyone else.
These are guidelines which help us create a positive and active tutoring environment.
Updated March 2020.