First off, I’m sorry if I have a lot of excess in my writing. Writing is not my forte.
I’ve never really thought about what math is, and after thinking about it a while I’m still not sure. I would say that it is the study of numbers, but numbers may very well be just something that has been made up and simply a tool created in the field of mathematics. While most sciences would be the study of one specific thing, math is primarily a basses for other forms of study. Many different sciences use math in them. So it is hard to say that math is the study of change or the study of space (area). I guess to me math is a tool itself created or discovered in order to form a foundation for the study of many different things (physics, astronomy, etc).
I think that I personally learn mathematics best when I first learn the concept and the ideas behind it, then I learn the jargon terms and then I actually learn the arithmetic. If I learn it in this order I will more readily remember it and in many cases I will be able to re-teach myself the arithmetic if I first have a solid understanding of the concept. After learning all three parts of any given subject I also need to practice doing the arithmetic over and over again. This is how I feel I have best learned mathematics.
I suppose this is a fairly good structure for most students learning mathematics; however, I understand that everyone is different and that as a teacher I may need to find ways that will better suit my classes. I will also try to help my students figure it out for themselves. I have found that if I have to struggle a little and think about things on my own I will learn the material on a deeper level (if that makes any sense).
I haven’t seen how it is taught in schools since I graduated, but I remember a few things that they did that I thought were helpful. One of my teachers was good at making what seemed to be contradictions in math. This would catch the attention of the students and they would be interested to learn the new material that would explain the “contradiction” he gave at the beginning of class. Another way to catch the student’s interest was to tie it to real life uses. This gives meaning to what you are doing. Rather than “plug-and-chug” you are actually learning how to do something meaningful. Other than that all I can remember is like I said before, repetition and pushing students to struggle through learning the material themselves rather than just explaining everything to them. One thing that I didn’t see much of when I was in school, but there seems to be more of is the use of technology in the classroom (“smart” boards, computer programs, etc). If used correctly technology can help keep students interested and it can make it easier to do hard arithmetic in a way that allows students to learn the concepts which can give them a solid foundation for learning the arithmetic later.
I think that one of the worst things that was done in classes for me was some teachers did not try to build on what you had previously learned. If I learn something well in math and then have another class that builds on that previous knowledge it made it a lot easier for me to learn based on my solid foundation from the previous class. I had a lot of classes that felt like they were not at all correlated to any other math class I had ever had.
Subscribe to:
Post Comments (Atom)
The author of this post and I agree that the best way we learn mathematics is to learn concepts first then to practice them again and again. I agree witht he author of this post on this point because I have tried it in my own life. I am taught a concept and and practice the arithmatic again and again thus I find myself engraving the concept in my mind.
ReplyDeleteI respectfully disagree with the author of this post on the point that math is a foundation for most other sciences. I belive that other sciences can still be studied with out having a basic foundation of mathematics.
Perhaps we can consider the law of gravity in the feild of physics as an example. The effects of gravity can still be observed and studied without any former foundation of mathematics. The same is true about newtons law of motion. Although I do believe that having a foundation of mathematics does help imensley to understand these different fields of mathematics although without it these fields can still be studied
I agree with the author's definition of math... Math is really hard to define. I agree that math is the basic foundation for a lot of other areas of study. Without a basic knowledge of math, it would be difficult to progress in many other fields, especially sciences. There are many types of real life applications that math helps in solving. Math really is a tool that we use very often in life.
ReplyDeleteHowever, I feel that in my classes in high school, and even before, we did build on previous concepts. Without the knowledge from a prior class, I would not have been able to understand what to do in the class I was currently in. I also feel that everything that I had been learning in school all came together while I was in calculus especially. I think that even though it may not seem like it, all math does build upon itself.
I really like what you had to say. I also found it interesting and somewhat difficult to describe what math truly is. Yet, I believe it is different for every person.
ReplyDeleteI also liked how you talked about building on math learned in other classes. I think this is very important and helps students connect what they already know to new topics they will encounter.
Yet I do disagree with your idea of technology. Yes technology helps students figure out difficult problems and may even keep their interest. But as someone else said in their blog, I do feel that there is too much effort put into teaching students how to use calculators and the new programs created for making math "easier." I feel it takes away from the students learning on their own and understanding (fully) the concept at hand. It also may make them dependent on calculators to do the work for them.
I really appreciated the thought you put into what mathematics is. And I also really liked your conclusion. I don't think there is any pinned down definition on what mathematics is, but I do agree that math is a tool to help us understand things.
ReplyDeleteI agree that if people understand the reasoning and concepts behind math, then they can work through problems and reach valuable conclusions. Whereas, if they just have memorized algorithms but don't know why they work, they don't know where to apply them once they get out of a given section.
I agree that when you have a solid understanding of the concepts, it is much easier to go back and review the arithmetic. And while this is an exellent way to teach mathematics to students, I agree with your point that each student learns differently. It is important to get to know the ways in which your students learn easiest in order to help them grasp the material.
ReplyDeleteAlthough technology can be very useful and even helpful for examples and aid in learning, I believe it may be detrimental to students if they become too reliant on it. I think that students need to have the chance to work on the problems themselves in order to fully understand them. I do think that technology can be a very good thing in the classroom, there just needs to be some sort of limit to its use.