Have you ever had the experience where you are so sure of an erroneous understanding that you practically persist and argue to hold on to it in light of counterarguments?

Diversity of Expression

Often, in the classroom, I observe students that are so fixed in one way of thinking or doing things that they push away and stayed close-minded to well-intentioned activities and exercises that challenge their current way of doing things. Let’s take the following example from my own classroom:

I asked a group of students to determine the exponential pattern behind earning 2% annual interest rate on an investment of $13,000. We created a chart that mapped the money accrued to date for Year 0, Year 1, Year 2, etc. We discovered that we could just multiply $13,000 by 1.02 as many times as need (ie, number of years). Students began to protest that this was not a good way of solving the problem. They argues, why not do the following –

Year 0: 13,000

Year 1: 13,000 + .02 x 13,000

Year 2: Year 1 amount + .02* Year 1 amount = (13,000 + .02 x 13,000) + .02(13,000 + .02 x 13,000)

Year 3: Year 2 amount + .02* Year 2 amount = [(13,000 + .02 x 13,000) + .02(13,000 + .02 x 13,000)]+.02[(13,000 + .02 x 13,000) + .02(13,000 + .02 x 13,000)]

And so on and so forth…

I asked students to practice our newly discovered approach y = 13,000(1.02)^x (^ represents the raising of a base to an exponent). At the same time, I respected their arguments and gave space for them to make a decision on which method was more efficient and captured the pattern in a simple way. So, I allowed my students to work on the material during class on their own. Some students still persisted – the more tedious previously learned method (which is very important to understand in earlier math so it definitely should not be skipped) was “THE right way” and they were fixed on using it. However, something interesting happened…

The next day, I put together an activity to show the significance of exponential functions in solving similar problems – perhaps they would buy into using y = 13,000(1.02)^x over the longer method they supported. So I began modeling the longer method, and students started protesting again! No! Why can’t we just use the new way – it’s so much easier!! We like it!

This is not the first time I have seen this sort of hesitant behavior among students. Of course, there are many reasons for it. I am choosing to elaborate on one aspect: academic humility. Students (and all of us) so often think of MY or OUR method of doing things as “THE way”. Flavors of this feelings show up in subtle ways and sometimes bar our ability to open up to others and their ideas – because perhaps, they could be better and we could embrace them.

So, I stopped to talk to the students about why there was such a sudden change of opinion since the previous day. We spent time reflecting on the initial hesitation. And then, in this honest conversation, I dropped my message:

Learning well is not just sticking to what I (me only) feel is the best way in the moment…learning well is practicing the understanding that I may not know what is the most conceptual, practical, or effective way of thinking or doing things. And I am going to open up to new possibilities from my classmates and teachers.

This was, perhaps, a lesson that was more important than the lesson on exponents I had set up. Developing the idea that “I do not always know and there is much more to try and be curious about” (of course in limits) would change the way students approached material in class. It allows students to take a deep breath and let out a sigh of relief. There are a number of reasons why a humble attitude would leave us less anxious:

1. We no longer feel that we (as individuals) are the sole resource for ourselves.
2. We reach out to one another and develop a sense of community.
3. We are not so worried about being wrong.
4. We accept the possibility of others’ ideas being better than our own.
5. We begin to open up to others’ ideas and any sense of hierarchy in the group diminishes.

Thus humility allows us to be less anxious, uptight, and closed-minded. It is academic humility and humbleness regardless of grades, accomplishments, or accolades that keep us grounded – free from fearing failure and linked to true learning and growth.

Action for this post:

When you are in class or with a group of people next time and there is an argument or debate, stop to listen to others and, when necessary, question your own stance. Weigh the evidence against your feelings of what is right or wrong.