Reading my classmates posts this week both validated my thoughts and made me think how I could incorporate Jasper methodologies into my practice. Now that BC Math 10 teachers have had their Provincial Exam shackles removed, there is theoretically time to weave “real world” problem solving into the course. In addition, the new curriculum is noticeably less rigorous– it appears as though for every new learning outcome that has been added, we have “lost” about three. (Is this a good thing? Well, that is a completely different blog post to be written…)
Reflections that I have included on classmates posts include:
On Vibhu Vashisht’s post: “To respond to your question, I think that I would like to do a Jasper-esque problem at the end of my course (Foundations/Pre-Calculus 10), once the concepts have been taught and rehearsed. I think that students would really sink their teeth into a “real life” problem that involved concepts from the course and with a group dynamic, everyone at every skill level could participate. The new Math 10 curriculum has a probability component in it now, so devising a problem that incorporates a game would be very cool. Perhaps after trying it out once, I would consider having more through out my course, but I am not prepared to jump in with two feet, at this point.”
On Catherine Servko’s post: “My ultimate point is that when adopting new strategies, I believe it is advisable to not let the pendulum sway to an extreme. So keep some rote learning on the basic skills— ones that are critical to continue in academic mathematics in high school and post-secondary. But then, adopt new strategies that also allow students to receive the socio-cultural, anchored learning affordances. Best of both worlds!”
On Mary Sikkes’ post: “Sometimes, it is hard to NOT overthink things. I think that you should just give the Jasper approach a shot, on a relatively small scale, and then reflect on what went well and what could be adapted for next time. It is kind of like bringing in a new form of technology to your practice— it will likely not be perfect, but it gets the ball rolling, at least!”
In response to Anne’s reply on my post: “The one time, as a student in grade school, that I dreaded math, was when I clearly did not have the basic skills down pat. I was at the end of my Grade 3 and I was at my third school in that grade. I was so behind the other kids with my times table knowledge. I would feel so dumb because we would sit in groups of three with a student flashing cards and testing us. Public humiliation felt horrible! However, once I caught up in that area, I started liking math again, and really appreciated the fact that with extra effort, I could do as well as anyone. When in Grade 5, Mrs. Wong gave us a challenge to complete all of the questions in the supplemental math text, I took her up on the challenge and was the first student done (and got the first pick off of the prize table!) You could imagine that my basic, fundamental skills were automated and accurate after having completed hundreds of extra questions. I truly believe that Mrs. Wong’s competition is one of two main reasons that I went on in math in university. It allowed me to confidently attack the more difficult problems in every math class in Grade School and set me up to enjoy learning new mathematics. I appreciate that not everyone will respond to rote learning competitions, as I did. But at the end of the day, it really worked for me.”
This week, Catherine Sverko, mentioned the “grey nature” of teaching. Becoming a “Shades of Grey Educator”, is a time-consuming and at times, overwhelming metamorphosis. Considering each student as a whole individual, can be messy, because in order to do so, the personal qualities of the individual can not be ignored. Not every educator is prepared to “go grey”, either. A counselor who is on a temporary contact mentioned to my colleague that she is really enjoying her time at our school because when she approaches teachers to make accommodations for her clients, the teachers actually make them happen without difficulty. Apparently, this is not always the case at other schools.
As individuals, we do not all learn at the same rate, and have the same preferred methodologies. I would speculate that perhaps more than any other subject, students bring an incredible amount of psychological baggage with them into the mathematics classroom. To think that one approach to mathematical learning is going to reach out to every student that enters your room, is optimistic at best.
My ultimate issue with adopting the Jasper methodology as one’s main pedagogical approach in mathematics is that it does not seem to give students enough repetition, to truly learn a particular process. Also, if groups are being utilized, the weaker math students risk being dragged along (happily) by the stronger math students. Can we simply sugar coat a core literacy such as mathematics, in the spirit of having students “like math” more? I do not think this is a wise approach. To quote a colleague of mine, “In high school, we do not want to sacrifice the top 20 for the bottom 80.” I think that classrooms that remove the rote components of mathematics are doing just that, in the name of making math “real”, and “fun”.
I am not saying that the math classroom should purely be rote learning. I am actually quite eager to employ a Jasper style approach as an activity that brings my course to its conclusion. I think that it would serve as an engaging way to review and concurrently have students work together in teams to address a realistic situation mathematically.
As a non-purest, rote-learning advocate, I surely must ask myself, how much rote is enough? That I do not know, although with some research, I may be able to have a definitive answer. In the meantime, I have come across The Bulletproof Musician’s blog, who espouses that if it takes about 40 repetitions to learn something, then we should aim to 100% “overlearn” (i.e. do 40 additional repetitions) for mastery.
I would estimate that in my own mathematics learning, 100% “overlearning” is about right for me. I am not the sharpest knife in the drawer, however, I am certainly not the dullest, either. For some of us, perhaps 0% “overlearning” is required, and for others, 200%. If the ultimate goal is to have our students master the concepts, I believe our classroom approach should attempt to accommodate these differences; although who is to say there is only one way to accomplish this? We do not learn any skills be merely watching others— if this were true, we would all play basketball like Steve Nash. Learning skills required repetition. Repetition requires perseverance and will. Should our students not possess both of these qualities, at what point is it OK to say that maybe a career involving academic math is not someone’s destiny? Moreover, should we continue to lower the rigor of our mathematics classes so that the “bottom 80” enjoys math class more?
What do you think?