Sunday, October 20, 2013

Oh those preconceptions...


 
One example of a preconception students may have the authors provide is that “properties are generally believed to belong to objects rather than to emerge from interactions” (Donovan & Bransford, 2005, pg. 399), another example of a preconception that students bring to the classroom is the idea that math is ridiculously difficult and that it has very few practical uses. This in turn causes some students to believe that math just happens in math class and never anywhere else. So much that when they are introduced to mathematical situations in “real life” they often result to either asking someone else, using a calculator/computer or just giving up on the issue entirely.

I was one of those students who held quite a few preconceptions about “doing” math and applying math knowledge to “real life” mathematical situations. I always enjoyed school and learning! It never really mattered much to me what I was learning, I just had a good time because it always seemed so fun. It was fun, and it was easy. My mom has been teaching for years and I was one of her first students. I knew many things that my peers did not simply because she’d taught them to me years before I was required to “know” them in school. In kindergarten I was so advanced mathematically that when everyone else in my class was pulling out their counting chips, I was on my way over to the “big school” to take math with the second graders. That was a big thing for me and I loved it!! By the time I got to middle school I really thought I was quite the math and science wiz because I (and a couple hundred other kids) were interviewed and selected to go to this brand new magnet school, and my magnet was Math, Science and Computer Applications. The way we were taught math and science made me even more interested in it, it also allowed me to see how practical and relevant math and science really were. There were tons of inquiry opportunities and chances to show our creative designs and processes. We used our hands and our imaginations to learn just about everything and it stuck!! Of course I can’t remember everything we did, or what all we learned for that matter, but what I do know is that by the time I got to high school I felt totally different about the maths and sciences. In high school, math and science consisted of books, books and more books. It became nothing more than definitions and expected outcomes. I quickly lost interest. Donovan & Bransford even say that “If students are not helped to experience this (inquiry) for themselves, science can seem dry and highly mechanical. Indeed, research on students' perceptions of science indicates that they see scientific work as dull and rarely rewarding, and scientists as bearded, balding, working alone in the laboratory, isolated and lonely” (pg.406).
 

 
 
My grades didn’t reflect it though. I guess because I had good study skills and work habits, I was able to “figure it on out” but my cognition did. I absolutely began to loathe math. I still loved science because at least we got to dissect some things, but math meant absolutely nothing to me whatsoever. It was taught in isolation and conceptually, that’s the way I began to look at it. I took all the maths there were to take by the time I finished 11th grade and I thought, finally the torture of this that is math is over, but my mom had other ideas…as usual, so she insisted I continue to take maths I didn’t even need, so I took Calculus and College Algebra. Big blah. I grew so tired of formulas and algorithms and “cookie cutter” ways to “solve” problems I didn’t know what to do with myself. There was no creativity allowed at all.
 
 
There wasn’t much allowed in science either, but at least, if we were dissecting something I could possibly remove or puncture another organ to see what might happen, without my teacher noticing, but that was pretty much the extent of it. My understanding of math was limited and incorrect, I absolutely hated it, and what’s more, I could find absolutely no use for what I was being taught outside of the class. Although I still earned A’s and B’s in advanced math classes, I somehow knew I still didn’t understand it. I knew that because if I was challenged with say for instance the simplest of mathematical understanding like multiplying or dividing some numbers mentally I’d have to grab a sheet of paper…disgraceful. The truth is math is practical and can be quite fun to learn.
 
Although the piece I'm referencing deals primarily with science instruction, I think subject pedagogy can be interchangeable, meaning that we can apply best practices in one subject to another. My preconceptions about math gained in high school changed my whole outlook on math. I thought math and eventually science had to be rigid and complex because that’s what I’d been taught through implications. When educators teach subjects like math and science in isolation and without imaginative flexibility students who used to be fascinated with doing that subject can lose interest.
 
 
Donvan & Bransford suggest teachers teach in ways that allow and even perpetuate their students to undergo changes in their thinking and noticing in order to ensure understanding (pg. 401). This is a more productive approach to teaching subject matters. Similarly, a more productive way of thinking about the preconceptions students bring is to accept that they have them and know how to encourage them to dispel them through self-exploration. According to this section of the reading, teachers should engage students preconceptions about a subject or subject matter, in order for to learn more about that subject or subject matter (Donovan & Bransford, 2005, pg. 399).  Teaching students maths and sciences, and other subjects for that matter, in a way that is relevant to them is most effective. This way of teaching students who come with preconceptions about certain subjects and subject matters allows them to shed those ideas in return for deeper understanding. How Students Learn promotes an overarching theme of inquiry based teaching, which I think is of utmost importance. This pedagogical approach encourages students to take control of their own learning, which in turn makes them own what they’ve learned. This is different from just learning something because your teacher says you have to.
 

The text suggests the way we were taught science was insufficient. It plainly says “simply telling students what scientists have discovered is not sufficient to support change in their existing preconceptions about important scientific phenomena” (Donovan & Bransford, 2005, pg. 398).  I decided I wouldn’t teach math or science the way I was taught a long time ago. I wanted to make sure math and science meant something to my students and that it wasn’t just taught in solidarity; I also wanted to make sure I taught my students in a way that their preconceptions about subject matters were supported or dispelled, but at least addressed. In short, I teach concepts so that they’re relevant and fun. I build my lessons around my student’s inquiry about subject matters. Of course I have indicators I am supposed to teach, and I teach them, but I teach them in ways that my students can understand and own them.
 
 
For example, starting lessons with an objective reading can be beneficial for students because it lets them know what the goal is for that particular subject for that day. It can be counter effective though if you’re using an inquiry based approach that would require students to come to a conclusion on what they’ve learned. I combine the two concepts by posting the objectives, but only addressing them after they’ve been done. Similarly, I never present my students with vocabulary words and their definitions when beginning a lesson. I will however ask them what they already know about a relevant vocabulary word and then have them share that knowledge with the person beside them. We “find answers” together and I encourage them to find multiple ways in which to do answer questions and complete challenges. I never give them the answer to anything, whether it’s “What’s today’s date?” or “Can you spell a word for me?” I make it the expectation in my classroom that they use their resources and brains to find answers to questions they have. I believe this approach to teaching inspires my students to think critically and problem solve, not just when doing classwork but all the time. It also makes them find answers on their own, which helps them internalize what they’ve learned and hopefully with that knowledge, they will see other ways in which to apply what they’ve learned. These examples I believe reflect what Donvan & Bransford and the other authors of this piece had in mind.
 
Written in response to this question.

Donovan, Suzanne M. & Bransford, John D. (2005). How Students Learn. Committee on How People Learn, A Targeted Report for Teachers

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