Prior to taking this course, I had already been familiar with the fixed
and growth mindset from teacher's college, but I never thought about how I was
taught had impacted my mindset in math until we had
discussions in class. As a student, I usually got good marks in math and I was
always proud to see all the check marks on my test papers. Therefore, math
became black or white for me; you can be either right or wrong and there are no
other possibilities. This fixed mindset in math soon led me to do whatever I
could to get to the right answer even when I did not understand how or why
certain concepts worked that way. Whenever I got stuck, I just went straight to
the formulas or asked my teacher and friends to show me how to solve a question
and memorized the method, because after practicing the same type of questions
many times, I was able to answer them correctly. I knew this strategy was not
good, but I kept with it because it worked for me and it got me through all my
math classes until grade 11 / 12 math. That's when I hit a wall and realized my
formulas and memorizing do not always work. In fact, I found myself getting
extremely frustrated that I wasn't getting good marks anymore. What was worse
was that I had to face the fact that I actually had no understanding of
fundamental concepts in math; for example, why I had to invert and multiply
when dividing fractions. It was very difficult for me to accept that I had no
understanding in basic math because I used to firmly believe that I did thanks
to my high marks in elementary school. I wanted to give up and entirely quit
math but I decided to give it one more try. I went back to grade 2-8 math and
with my brother's help, I properly learned the basics all over again. By
"properly", I mean I understood why
the concepts worked and how they were
related to each other.
Because of my experience, now I tell my students to always ask
themselves how and why in math. It's better to struggle now than later as it
becomes that much more difficult to re-learn and fix all the misconceptions in
math. In Jo Boaler's video, she mentions how when you make mistakes in math,
your brain grows, but there is no growth when you just get the "right
answer". This shows that it is not just okay but essential to make
mistakes in math. I think that math anxiety starts quite early in school - as
young as grade 1 - when students come to believe that they are not a math person
after getting the wrong answers over and over again. However, if we teach them
this mindset of "mistakes are absolutely necessary for brain growth",
they would develop a whole different attitude toward math.
One thing that I've been pondering about is whether or not giving marks
in math or any other subjects is really beneficial to students. It seems that
assigning grades can easily lead to a fixed mindset, especially when students
study just to get good marks on tests and forget everything afterwards, which
is not reflective of true learning. However, I think that giving specific marks
is needed at some point because there will be students who won't try their best
if there are no goals...
Hi Hannah, in response to your question about whether it is beneficial to give marks, I would say the answer to that is "no", because it fosters extrinsic rather than intrinsic motivation. I have done a lot of self-directed learning lately outside the education field, including taking courses (online and in-person) which I paid to attend. None of these courses assigned marks. I didn't even receive a certificate of completion or credits towards a degree, however, the education was there. That's in an ideal world. In the real world, marks are "currency" to determine who gets into university program, so until that changes, and colleges/universities find a different method to accept students into their programs, grades will be here to stay. The courses I was referring to early, had no barriers to admission other than the cost (i.e. I didn't have to submit a transcript of my marks). Technically, a similar situation applies to teacher's college, and you can "buy" your education by going to an American school if you don't get into the Ontario. But now, I hear that even Ontario faculties of ed are having a hard time filling all their spots.
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