What do I remember about my actual learning experiences with math at this time? Well I mostly only recall the use of manipulative's. I guess that's the kinesthetic learner in me. I recall counting apples. I also recall using those rod like creations that represent the tens and the little squares that represent the ones. I recall being able to piece these together, or at least I -think- I do. I can't really remember much of what we did with them. Used them for counting I suppose.
The thing I remember most vividly though, were these 3-D wooden shapes that fit neatly in the palm of your hand. Cylinders, cones, spheres... I recall building things with them, or rolling them around. That wasn't the mathematics objective I'm sure, but maybe these are some of the things we did as we waited for our turn during Christmas concerts (we all waited in our classrooms on such special nights and brought board games from home to play with our classmates. But I'm sure we could have gotten quite tired of them and came up with our own imaginary play with anything and everything we could get our hands on, just as any kid would). Yet, I do also recall learning from them. The idea of learning what a cone was, by relating it to what a drawn triangle was, or a sphere from a circle. Such learning brought to life with the tangible form of these 3-D shapes that i could hold in my hand and personally examine from all angles, was wonderful. This would be much easier than seeing these shapes and their angles represented by dashed lines on a paper, or at least I would assume. This makes sense to me anyways.
My son recently came home with homework involving such 3-dimensional shapes on paper. He had to cut them out and glue them on another paper, and then proceed to cut our their corresponding names spelled out on another sheet of paper, and then glue these names underneath the shapes. Thinking back now, I think I would much prefer the manipulatives. No. I know I would. A 3-D shape isn't the same when it is on paper. It's supposed to be 3-Dimensional after all.
I recall when, in Grade 3 or so, my teacher scolded me for not doing homework or something else, and then proceeded to embarrass me by digging through my book-bag (although he had no reason to do so, as I was not playing with anything that was in there during class. I was actually going to my cousins house after school to play barbies). I watched in horror as he began to drag out every barbie doll and pony that I had stuffed in there, counting them out loud as he went. When he got to ...say 23, I automatically knew that he had missed my favorite purple 'my little pony', so, I reached into the bag and pulled out one more, meekly announcing a "24". Hey, there's some math! I knew how to count! Anyways ... these are the things I recall the most, not how the teacher assessed our learning, or the role of the teacher. Maybe it isn't simply that I can't remember but that I really didn't like mathematics back then, because I love language arts. I always did, and I recall writing stores in class most of all, and I would be able to tell you that one form of assessment there was the taking in of our work and handing it back with a mark. As I ponder what I just wrote, I wonder if I'm even being truthful. I could be recounting my high-school years, which started in a school that held grades 7 through 12. Well, I am doing my best here...
The only assessment I can think of that I can positively say was in elementary, was in kindergarten. We had these books. I recall doing math in these books, coloring shapes and such. Coloring by numbers. coloring this, and coloring that. Drawing lines to matching pictures....and then coloring them. I'm assuming that the teacher looked at these to see where we were at with the various activities... or maybe she would simply check to see if we colored within the lines.
As for what mathematics looked like. Well in Kindergarten, the room had many different areas. Different centres I suppose. Maybe one of them was for math or manipulatives? Maybe not. I'm guessing there was a sandbox though! That's all I can dredge up from memory. I used to have a VHS of my kindergarten graduation. We were in the classroom before it began. Something tells me I recall these centres from watching that video, and not from my actual memory of that exact time and experience in my life.... and now I am left to wonder just where that VHS tape could be. That's how great my memory is. Not that the tape would do much good. I haven't anything to play such dated material on anyways.
I do recall enjoying those manipulatives and those kindergarten coloring books. These things brought a sort of 'fun' element to learning. One that I guess wasn't as evident in the other areas of learning about mathematics, such as the times tables and telling time.
Math in high-school. I can recall much more of those days. Most of it was negative. I had one teacher who was my Uncle and whom seemed to be trying to make the statement to the whole class. No, to the whole school, that just because he had children and nieces/nephews in his classrooms, that he wouldn't treat them any better. Well he sure didn't. To hit his point home, I swear he treated us worse. Well, me at least. I wasn't in the classrooms of any of his other family members, so I couldn't tell you about their experiences. Another homework not done incident (I swear these must have been the only two times in which I didn't have my homework done. I was so organized that many could have called me obsessive over it at one point in time, not to mention being a fairly goody two shoes when it came to homework and studying!). Anyways, he made me sit outside the classroom. Needless to say, no learning got done for me that day, only a resentment for my teacher, and maybe for math too. Then there was Mr....Brown? He was temporary. Thank God! I recall raising my hand on many different occasions even though I knew it was futile. He would never ask me my question or attempt at describing the problem to me in any other way than the way he wanted to explain it. Even when I would ask it outright. He would ignore me completely.
In my last year of high-school, I had the option of taking an advanced math course that was only offered through distance education. With the support from my classmates, I decided to give this a try and it was going well. But then, a few months into the year, I moved to a new community, and thus, a new school, and I lost this close-knit support and went back to academic mathematics. In this school, I gained astounding grades (seriously, I got 100% on EVERY exam. A HUGE change from my regular 70's and 80's). I wasn't naive and I didn't feel that I'd earned them - the teaching at this school was just so different. It was like they had given up on their students or their teaching, or both, and just started handing students answers and grades. They let students off with so much, and just brushed many problems under the carpet, neatly hidden out of sight.
Through these experiences, I managed to build an uneasiness with mathematics, and created a sort of love/hate relationship with it.
So when I came to University, 11 years after my graduation from high-school, I saw the option to either take ONE math course, or TWO math courses. Being out of practice so long, and with my background, I felt it only natural to choose to do the ONE math course! The notion of a math placement test was lost on me. I never even heard of it until after my calculus course was done and over with. So Math 1000, or calculus, is what I took one summer intersession, along with a psychology course. And I can tell you, it was hard work! My prof, on the first day, while writing out a calculus equation on the board, proceeded to work out within it, a problem using the foil method on the board. He announced that if we did not know how to do what he was doing, then we'd best go back to 1090. I knew WHAT he was doing, but had no recollection as to HOW he was doing it. Who would have thought that Math 1000 was more complicated than Math 1090? As a newcomer to MUN, not I.
But, with the help of and many visits to the teachers aide, one of her very helpful textbooks (God love her!), and good ol' YouTube, I stayed up many nights until midnight and taught myself algebra, so that I could learn calculus. I came out with 80 in both my psychology and calculus courses, and was quite proud of this. Once I got the hang of how to do the math, and what was actually going on, with a teacher and a teachers aide who could explain it to me in a way that made sense, I grew a great fondness for math, one of which I'd never felt before.
I had debated a minor in math after this, but with more courses completed in psychology, I went with psychology and the calculus course remains the one and only University course that I have completed to date.
Today, I teach math to my children, mainly through the use of manipulatives. (I also bought them wooden blocks for building things, though I am yet to buy them wooden cones, cylinders and spheres). That's about as major a use of mathematics for me that I can think of at the moment.
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