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.
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.
Students working on the escape room activity.
That time a puppy wandered into my classroom. Oops.
“The most important things we need to learn”
-“Have unlimited creativity”
“Subject between creative and and teamwork”
“is very interesting. make my brain growing”
“Math makes me hate and love”
Select responses to “How math class makes me feel”
“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”
“I feel happy when I fiand the ancer”
”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.