Teaching for a Math Mindset: A Not Yet Successful Study

So I was lucky enough to have the opportunity to teach in the Head Start summer program at my international school here in China. The program is intended to help students going into high school to gain exposure to full English immersion classes in Math, Science, Socials, and Language Arts. I taught four blocks a day for 70 minutes each. Each class had anywhere between 12 – 16 students. Ten days straight; on the one hand, no break (kinda brutal), and on the other, open curriculum (YES! Free reign).

I had lofty plans. I’d been refreshing myself on Jo Boaler’s work about mathematical mindsets (see my previous ramblings here). I was going to do a little study.  Please note that I do not have any experience whatsoever doing educational research. While I have a general understanding of the scientific method, I was mostly doing this out of pure curiosity and a desire to become a better teacher.

Like all good mathematicians and in the name of good science, it was perhaps inevitable that first time was not the charm, and rather than have a very successful, replicable study, I instead gained some knowledge about how I might proceed in the future. Nice.

Content that I had planned to cover in 10 days would have taken closer to 18. The students had an incredible range of English speaking ability, with drastically varied dynamics between groups of students. The schedule did not operate on a cycle, so I saw the same group of students at the same time each day, which definitely influenced their learning experience. For instance, Group C who were absolute angels and ready to learn each day in my first period class were exhausted by the time they got to third period, which led to more behavioural problems in the classroom.

STUDENT DYNAMICS
Group A: A challenging group. I saw them the period right before lunch each day and there was a group of four students who were unable to sit still and wandered the class during inappropriate times, such as in the middle of me giving instructions. I lost my cool on this group; shame on me because I wasn’t able to regulate my emotions and respond calmly to the situation. Just to clarify, a “losing my cool” moment for me doesn’t mean shouting or yelling, which is neither helpful nor productive. I simply raised my voice to get the students attention. But, in that moment,  I had lost my cool because I let the students dictate my response rather than carefully assess the situation and respond calmly and accordingly.

Group B: Did absolutely anything in their power to NOT pay attention. Would whine anytime I introduced a new activity. Would put their heads down and sleep in class. I saw this group after lunch each day, they were my last and perhaps most challenging class because of the incredible amount of sleepers and students who wanted to do absolutely nothing. There were definitely some gems in this class that would have benefitted from being in a group with other, more responsive students. Lots of patience and flexible teaching strategies required.

Group C: The first group I saw each day and by far the best group. Students had a decent command of English and I rarely had to repeat myself. They would listen and follow instructions the first time. Students would always do as they were asked. The challenge with this group was pushing them to work slightly beyond their zone of proximal development.

Group D: A diverse group with students who always wanted to be two steps ahead, students who needed a lot of personal assistance, students who got distracted easily, and students who were happy with just coasting along.

HOW I COLLECTED DATA
I used Boaler’s Mathematical Mindset Teaching Guide as a self assessment tool for how I was and was not strengthening growth mindset culture in my math classroom. I wanted to focus on changing students’ inclinations towards math learning, challenging those who believe math is a subject that defies creativity and passion, and pushing those who already saw themselves as “math” students to expand their definition of what math is. With the help of my math mentor, I settled on collecting data through a mindset survey.

Students took a before and after survey. I added two prompts on the after survey that required students to provide written answers to the following:
– What I think math is…
– How math class makes me feel… 

A source of error here is that for students with low English level, they may not have fully understood the meaning of the statements they were agreeing or disagreeing with. Another possible source of error (though unavoidable) are those students who “did” the survey by randomly clicking boxes just to appease their dear teacher.

HOW I TAUGHT
I chose content from YouCubed’s Week of Inspirational Math. I chose these tasks because they were all low-floor, high-ceiling tasks and were designed to build good mathematical habits of mind. For example, on day 1, we did an activity called “Four 4’s” which encouraged students to think creatively and work collaboratively to come up with as many expressions as they can that equal the numbers 1 – 20 using only four 4’s and any mathematical operation of their choice (see picture below).

Other activities we did:

  • Escape Room Challenge: A mixture of math puzzles, grade 9/10 content from trigonometry, polynomials, and simplifying expressions. Designed by me and was meant to last one period, ended up taking two.
  • Number Visuals: Students examined visual representations of numbers 1 – 36 and were asked to identify and describe patterns (prime v composite numbers, factorization…etc.).
  • Paper Folding: An activity from YouCubed that challenges students to slow down and justify their answers. (Meaning that, anybody who claimed they were “finished” after five minutes clearly did not understand the activity…)
  • Movie: Students complete an agree/disagree questionnaire and watched The Man Who Knew Infinity about an Indian mathematician named S. Ramanujan making waves in England. Great movie starring Dev Patel. We did a discussion circle afterwards that touched base on prompts from the questionnaire that students were interested in exploring. (E.g. “Math is creative”)
  • Pascal’s Triangle: Find and describe patterns hidden in Pascal’s triangle.

In terms of assessment, I wanted to stay as far away from tests or quizzes as possible. Instead, I focused on providing students with specific, written feedback on their journal entries, group quizzes, and one final presentation at the end. I wasn’t concerned so much with what they knew, but rather the process through which they were learning and engaging with the material.

The Four 4s Activity

Students working on the escape room activity.

Looking for patterns in the Visual Numbers activity

That time a puppy wandered into my classroom. Oops.

RESULTS

Before

After

Select responses to “What I think math is”
Interesting”
“The most important things we need to learn”
-“Have unlimited creativity”
“Magic”
“Subject between creative and and teamwork”
“is very interesting. make my brain growing”
“beautiful”
“fantastic”
“Math makes me hate and love”

Select responses to “How math class makes me feel”
“Better”
“Moer interesting than chinese class”
“It may not very interesting, but OK”
“happy that I learned a lot”
“I feel very good, I meet very good teacher also know the very good friend in the math class”
“exciting”
“I feel happy when I fiand the ancer”
“free”
​”Good! make me more confedent”

WHAT I LEARNED
​A majority of students already had tendencies towards a growth mindset in mathematics, perhaps as a result of the general high regard Chinese people hold for mathematics as a subject. For the most part, students liked math and saw themselves as capable of achieving if they worked hard enough. Of the 59 students I taught, a small number of students (three or four) were of the opinion that they were “just not math people” and were extremely hesitant in trying.

In the end, I can’t really say definitively which factors of my teaching influenced (or failed to influence) a stronger growth mindset towards maths. What I do know is that the switch to low-floor, high-ceiling tasks was extremely freeing — for me and for the students. It allowed us to take a concept or idea as far as we wanted to go. There was no script or prescribed problem set that the students had to work through in increasing levels of difficulty, but rather a greater depth of thinking, and the time and space for that thinking to happen. Despite (or maybe thanks to?) the lack of testing (there were none), students still engaged with the tasks and content at high levels, drawing conclusions they might never have done with a pre-made worksheet of the skills they were supposed to practice.

By building a stronger focus on increased depth of knowledge, it then follows that a necessary norm to advocate would be that math isn’t about speed. When people refer to themselves as not “math people”, that’s usually what they refer to, the fact that they aren’t fast at mental arithmetic. But math is so much more than that.

In all, while it is hard to say from the students’ perspective whether or not they appreciated a stronger switch to teaching with mathematical mindsets in mind, I know that for me it resonates as a noble endeavour. Yes, it is much easier to write a test and spend 70 minutes of your life making sure no one cheats. But take that same test, rip it up, and replace it with a diagram, an equation, a single question, a blank sheet… and possibilities begin to emerge. Some groups may reach a higher level of understanding and some may not, but then again, we teach students, not subjects.

Mindset

Picture a circle on the center of a blank page. Along the circumference of the circle are six spokes, evenly spaced. If you were to write down one word for each of the spokes that defined who you are, what would you write? 

For me, these words are: female, older sister, Chinese, Canadian, teacher, learner… These are important parts of my identity, they fundamentally shape who I am and how others view me, however, if I am not careful, they can also label me and lock me in. We all have assumptions about ourselves that can hinder us from reaching our true potential. To be more specific, I recently had a conversation with a good friend of mine who told me about an article she read that said the reason why many females are overqualified for their jobs are because women tend not to apply for a position if they feel they do not fulfill all the requirements, whereas males will if they feel they fit most of the criteria. I wondered how many opportunities I missed because I told myself I wasn’t good enough to try. 

I recently interviewed for a position that required teaching AP physics. With my measly, almost-two years of full time teaching, and zero experience with physics (or AP for that matter), I definitely did not think I had all the requirements for the job. But I thought about what my friend told me, and I said- to no one in particular- “Heck, what do I have to lose?” Lo and behold… I was stunned when I landed an interview… and even more amazed when they called me back for a second one. 

If such a small shift in my thinking could have led to such a significant outcome, no doubt this can apply to all areas of life and learning as well. I am currently reading Mindset by Professor Carol Dweck. I wonder a lot about how I can help my students uncover the hidden assumptions they have about themselves in order to develop a growth mindset. We talked about what it means to have a fixed versus growth mindset at the beginning of the year and what that looked like for different people. We explored the nature of science and how important it is to acknowledge failure in science. We discussed our ideas about how success is like an iceberg; magnificent and grand on the outside, when in fact much of it is submerged and hidden below the surface. I try to make it real for my students and have them connect it to their own lives, but most of all I’m trying to build a classroom culture that enables them to feel safe taking risks, making mistakes, and to fearlessly embrace new challenges. I struggle with this every day. Sometimes I feel like I am making good headway, and other times I feel like I’m picking my students up by the feet and trudging  them through the mud, shouting, “Come with me! There is a light at the end of the tunnel!!! Just keep moving!” 

And with that last bit of imagery, I shall kindly remind myself that learning is a process, and that we each move on our own time. 

When I think about Carol Dweck’s research on mindset I am reminded of my grandfather, who, throughout all the years I have known him, has shown me in his own way that it is NEVER too late to learn a new skill or to grow your mind. When I was eight or nine, I remember grandpa practicing to get his truck driver’s license. He had only been in Canada for a few years at that point, had never driven a truck before, did not have access to one, and was unable to take lessons, but that did not stop him. He took us out to Canadian Tire and bought a toy truck with remote controls. I remember watching him maneuver it around the carpet in his bedroom, studying it from different angles, gathering information about the spacing, and so on. He practiced like this diligently for days before his driving exam. Even I tired of watching the little truck move around in endless loops, turns, and parking maneuvers, but grandpa always aimed for perfection. This was the type of man my grandfather was.

I used to hate going to Chinese school on the weekends, but grandpa insisted that I persevere because he was afraid that I would lose my heritage and that my future children would forget their ancestry. This thought frightens me also. I never used to think learning Chinese was very important. I just knew how going to Chinese school made me feel – stupid and inadequate. It was like being sent to a correctional facility for not being born to the right circumstances. To hide my feelings of inadequacy I worked even harder to get good grades. I memorized difficult words, I practiced spelling them out over and over, and people told me how smart I was. 

It wasn’t until one day my grandpa said something to me that I finally was able to breathe. I didn’t even know it then, but I was suffocating. I had been trapped by the need to prove how good I was, that I too could read and write, two things that seemed to come so effortlessly to others. I used to cry myself to sleep because it seemed that no matter how hard I tried or how much I worked at it, I would never be fluent in Chinese like my family. So, when grandpa said those words to me I knew the facade was up. I didn’t have to pretend anymore. He said, “Even if you are not very smart or talented at something, with effort and practice we can make up for the things we lack. This is me, your grandfather.” And then he said, “You and I, we are both hard workers, no?” I will never know what prompted grandpa to say those words to me, but I just know that when he did, at that very moment, I felt true clarity and a huge sense of relief. It didn’t matter that I wasn’t great at something, what mattered was that I tried.