Math is the study of numbers and how to manipulate them for use in the world. It really is what makes the world we live in work. Without math we'd have no computers, cell phones, cars, amusement parks, movie theaters, plumbing, the list is endless. That's what math is.
- How do I learn mathematics best?
I best learn by example. If I can see how something works it makes doing that thing SO much easier for me. I'm a big fan of the 'plug and chug' method where you're given a set way to solve something and you take that way and 'plug' the various parts in and 'chug' away at solving the problem. I really struggle trying to figure out wordy theorems and definitions. I like knowing what the definitions and theorems are, but then I need to see how they apply to what we're talking about. Learning by example is what works for me.
- How will my students learn mathematics best?
I believe that my students will best learn the same way I learn, by example. It makes sense for this to be true because of the fact that you teach best what you're best equipped to teach, and I'm best equipped to teach by example. As evidenced by these posts, I'm not the most adept person when it comes to words so using examples will best assist me in teaching my students important concepts. I've had quite a bit of tutoring experience and the people that I help have always understood the best when we actually work through a problem instead of them trying to figure it out by me talking about it.
- What are some of the current practices in school mathematics classrooms that promote students' learning of mathematics?
One thing is the obvious fact that it's being taught. You can't learn what you're not taught. :) One practice that I think is very beneficial is group studying. When you are learning a subject with your peers I believe that you can explore more aspects of the subject because you are learning through more than one perspective. I also feel that the tried and true method of daily homework assignments is another great way for students to learn. Math is something that needs to be focused on a little bit each day as opposed to big chunks of learning only once or twice a week.
- What are some of the current practices in school mathematics classrooms that are detrimental to students' learning of mathematics?
One of the things that I find most detrimental is the whole 'draw a picture' approach to math.
Students in elementary school are being asked to visually represent everything that they do in math, and it's not necessary. I realize that everyone learns differently and that visual representation is one of the best ways to learn; however, I feel that the majority of students would learn math better if they learn it the way it has been taught for years; i.e. 2+2=4. I especially feel that the 'draw a picture' approach is detrimental because of the fact that when students reach higher level classes, such as Algebra 2 and Calculus
, there are some things that just can't be represented visually.
I too learn through examples, but I also find that I need a bit of explanation as examples are presented. While examples are a great way to show someone how a problem is done, that does not necessarily mean they learn how to do it for themselves. We also need to make sure to give them plenty of opportunity to think on their own. I would suggest that when you help someone through an example to make sure that you aren't doing all the thinking for them. Let them do as much as they can for themselves.
ReplyDeleteAs for your comments about "drawing a picture", I would have to disagree. Visual representations are a great way to learn! It allows for a student to relate it to something tangible. "Drawing a picture" is a great way to organize the information given. Yes, 2+2=4. I can memorize that without actually knowing what it means, and I would never know how to apply it. But if you "draw a picture" or have a visual representation, like I have two balls now and if I receive two more, how many will I have? Well, I "draw the picture", or hold up my figures and count, and conclude that I now have 4 balls. You don't truly understand numbers without some kind of visual application. Numbers represent how many objects there are. They are always connected to a visual object. Thus, "drawing pictures" is a great way to learn. I don't think that we can truly learn math without being able to "draw the pictures" that go along with it. Even Alg. 2 and Calculus can be represented by pictures. When you take the derivative of an equation you get the velocity, and when you take the second derivative, you get the acceleration. Saying that, is just words. When you graph it, i.e. "draw a picture", you see how they relate to eachother, and when you understand how they relate, math can come easier to the learner. "Drawing a picture" has so many applications in mathematics.
I believe that you are correct in teaching by example. When examples are used, students can see how a problem can be solved. When teachers teach concepts and then go through examples with the students, it seems to help the students learn how to solve problems a lot better then just lecturing.
ReplyDeleteHowever, I think that mathematics requires more then just knowing how to solve problems. Mathematics includes understanding the concepts behind the problems. Examples to problems can only take you so far. This is why I think visual representations of the math you are learning are actually VERY helpful, because they help you to understand the concepts, rather then just having a knowledge on how to do certain problems. Once you understand the principles behind the math, that is when you can solve any problem, even those that may seem outside of the box.
So you seem to like math the same way I do. The only problem I have found with this is that as I have gotten into higher math you can't always just plug and chug and expect to be able to do well in your class. Somehow you need to put it across to your students that it is also important to learn the logic behind what you are doing. So this comment is sort of a disagree and agreement because I learn the same way as you and the reason I love math is because of the plugging and chugging, but at some point you need to understand the theories that explain your recipe.
ReplyDeleteDuring a calculus lesson I was teaching a couple of years ago, I was breezing through a series of algebraic manipulations when one of my students raised his hand and commented that I did algebra really quickly. Without thinking, I replied that I liked to feel the wind rush through my hair as I sped through a problem. So I'm very sympathetic to your liking of plug and chug mathematics. There's probably a little bit of that in all of us math teachers, or we would have chosen a different profession. Unfortunately, being good at plug and chug mathematics becomes less of an asset as you progress in mathematics. It is also true that it is less valuable in the workplace now than it used to be. Being able to reason and think about mathematical ideas and processes is probably more valuable these days.
ReplyDeleteI also appreciate your opinion about math without pictures. I agree that being able to do math without pictures is a valuable skill. In fact, that's what makes algebra so powerful--we don't have to think about what all the symbols mean when we perform operations. It makes the solution method much simpler. At the same time, however, pictures help me make sense of mathematical ideas, which is important to me. When I get stuck on a problem or solution, I can often get unstuck when I think about what things mean and draw pictures or diagrams.