I’m a 3rd year high school math teacher working with 14–16 year old kiddos in San Francisco. (Are 14 year olds even kiddos anymore?) I’ve decided to spend my summer learning about design, something I’ve always had a yearning to learn but never had the time to. Now that time has presented itself, I have no more excuses!
After reading the first twenty pages or so of Don Norman’s “Design of Everyday Things”, I realized that a lot of core concepts mentioned so far in the book can be applied to teaching, and that learning design can actually make me a better teacher. The quotations I’ve included are all from Don Norman’s book, and I’ve included excerpts of my related teaching experience.
Quantitative and qualitative approaches are crucial to teaching high-school math
“Engineers are trained to think logically. As a result, they come to believe that all people must think this way, and they design their machines accordingly. When people have trouble, the engineers are upset, but often for the wrong reason. “What are these people doing?” they will wonder. “Why are they doing that?” The problem with the designs of most engineers is that they are too logical.”
This reminds me greatly of my teaching experience. Many times I would explain a concept or problem thoroughly and technically, only to find blank stares after 10 minutes of explaining. What could possibly be confusing? In what way can I change my explanation so that it makes sense to my freshmen? How can I explain a concept in way that makes sense without the numbers? This may seem counter-intuitive in a math class, but I find that non-number examples are actually really helpful because it provides students a way to understand qualitatively, not just quantitatively, both types of reasoning are crucial for understanding math.
Everyone learns differently and a purely quantitative approach is sometimes ineffective when dealing with high schoolers. A more effective approach involves coupling quantitative approaches with qualitative ones, such as story-telling, and connecting to math through analogies and metaphors to real-life.
An example of a quantitative + qualitative approach is when explaining operations involving positive and negative numbers. I like to relate positive and negative numbers back to money. A positive number represents money you have and a negative number represents money you owe. This example helps students conceptualize why a negative plus another negative number creates a larger negative number. If you owe $3 and you owe another $7, you owe a total of $10. By starting off with this question instead of “what is -3 + (-7)”, students have the opportunity to think about the problem in relation to their own lives first, then apply that knowledge to answering purely quantitative problems such as “-3 + (-7)”. I know a handful of students who can answer the qualitative question seamlessly, but doubt themselves when they answer the same question quantitatively. Little do they know how much they do know, and that they do actually know the answer when rephrased. This is not to say that a purely quantitative approach doesn’t work for some people, some do indeed learn better and have no problem solving the quantitative problem. But a quantitative + qualitative approach opens doors for more students to enter as well as creates a more well-rounded understanding of math.
Learning math is like learning how to ride a bike
“Engineers, moreover, make the mistake of thinking that logical explanation is sufficient: “If only people would read the instructions,” they say, “everything would be all right.” ”
If you’ve ever built furniture from IKEA or first learned how to drive a car, you might have experienced that the instructions might not be clear all the time. If I read a 100-page manual on creating the perfect Picasso painting, I still cannot recreate the painting, regardless of how talented I may be.
Learning math is like learning how to ride a bike. I can read all the instructions on the manual, yet am still lacking “information” or shall I say experience to ride a bike?
Surprise surprise, when making my first stride, I fall hard. What was missing from the explanation? Is knowing the information to ride a bike the same as knowing how to ride a bike?
In teaching, we must use many different variations of explanations to fit the needs of our students. Explaining a concept in just one way (and in our way of understanding) will not reach the rest of the room because that may not be the same way the rest of our students are thinking. Students can read a manual all they want, but they will eventually need dive in on their own, and make mistakes along the way.
Students are humans, not machines
“We have to accept human behavior the way it is, not the way we would wish it to be.”
This hits very close to home. Students enter the classroom with a range of complex emotions and moods, a couple of them being: hungry not having had breakfast that day, self-doubt from past failures in math classrooms or in general, frustration and anger based on a rumor about them circulating the school, sad after a recent break-up, and many, many more.
All of these complexities contribute to how that student acts that day, whether they have their heads down, are able or unable to concentrate, or feel the urgency to text their friends about something. It’s impossible to remove these emotions and moods from our students, but we as educators can provide nurturing environments and norms to support our students who are experiencing these states. In Human Centered Design, an approach that “puts human need, capabilities, and behaviors first, then designs to accommodate those needs”, I truly believe that this is in the core of teaching, especially when behaviors and capabilities do not align. We cannot teach to humans like they are machines, just like how designers cannot assume that every user is going to interpret a device’s/ application’s mechanisms the same way.
If you’ve ever made a mistake, raise your hand. Don Norman states that “we must design our machines on the assumption that people will make errors”.
In the traditional classroom, making mistakes in front of class is a mark of shame or disgrace. But why is this the case if we all make mistakes ourselves?
Even while teaching, I would make mistakes from time to time, and sometimes would be called out for it by a student. This was something I was extremely anxious about during my first year of teaching, what if a student asks a question that I do not know the answer to? My mentor provided a helpful perspective that sticks with me throughout my teaching career: Once you get to a level of comfort with your own teaching, you will be delighted when you receive a question that you don’t know the answer to. Lo and behold, she was right. Fast forward to present day teaching, I embrace my mistakes and treat it as a teaching opportunity to show students that it’s okay to make them and we all do, however careful we can be. Because we are humans, not machines.