Mathematics is the study of patterns that occur in the world and the relationships of objects in our world. Mathematics is also the foundation of how we study science.
How do I learn mathematics best?
I learn mathematics best by having a brief lecture and working through examples in class. I think that I learn best this way because it gives me an opportunity to be introduced to the topic and then requires me to demonstrate what I have just learned. I believe that being required to demonstrate what I was recently taught helps to solidify what I need to know.
How will my students learn mathematics best?
I think that my students will learn math best by having an environment in which they participate heavily in the lecture. What I mean by this is working through the lecture and allowing them to help figure out what to do next. Even if the path that they ask to take is wrong, I think that the direction should be pursued in order to demonstrate why it was wrong. We learn best from our mistakes and if all my students see is me lecturing perfectly what they are to do, I don't think that they will learn as well what they are supposed to do.
What are some of the current practices in school mathematics classrooms that promote students' learning of mathematics?
In many of the mathematics classes I took in High School I was expected to demonstrate homework problems on the white board. That was part of our mathematics department's policy. This allowed me, and every student to not only gain confidence in our work but it also gave us an opportunity to teach each other instead of just having lectures. I think that that is a very effective part of a mathematics classroom.
What are some of the current practices in school mathematics classrooms that are detrimental to students' learning of mathematics?
This is probably something that many people will disagree with. I feel like mathematics in the schools currently places too much of an emphasis on the need to use a calculator. Granted I understand the value and importance of understand how to use a calculator, I feel that teaching those skills has trumped the necessity of teaching students basic arithmetic. A calculator is definitely useful when multiplying a 5 digit number by a 3 digit number but it does not save time to need a calculator to multiply 6 by 8.
I really like your definition of Mathematics; very well put. I understand that you think class participation is essential in learning. Not only do I agree with that, but I also think it can be a lot of fun. But might I suggest that you use a different word than lecture. To lecture is to instuct a class, a practice in which students do not necessarily participate. I think what you are talking about is something like a guided collaboration. (I wish I had better words for it.) This would be something where the teacher leads the learning and seeks for student participation. This would then encourage much participation like you had talked about.
ReplyDeleteI like the idea of students participating in the lecture. That way they can maintain a certain focus and interest on the material. I hadn't really thought about having them choose the wrong way to do something and correcting them, but I agree that it is a good tool for ingraining them with the correct way to do it. I also completely agree that giving students the opportunity to teach each other is very beneficial to their learning. That is why I have found study groups so helpful in my math career. Perhaps there is a different way to have them teach each other without being in front of the whole class. That does teach them to be prepared, but more timid students, such as myself, might be intimidated by being in front of the class and get flustered.
ReplyDeleteI actually agreed with you on the calculator situation. I mean i loved my calculator in High School. I still learned alot but I haven't hardly used my calculator in college and I feel my growth in my abilities and knowledge of mathematics has increased at least twice as fast. Writing problems on the white board in a classroom always seemed like a waste of time for me. Why let only a few students work at the board? Okay give everyone a turn...well then you've wasted your whole class period taking turns. And it always made me anxious and afraid to attend class. Maybe a more affective "white board" method would be to have a mini white board under everyone's desk so everyone can work on a problem at the same time and then hold up their white board when they finish for others to see. Maybe it could be a game for more motivation?
ReplyDeleteI agree that one of the good ways to learn is through examples. That is also how I learn best. It is good to be able to make use of the material you just learned and put it to the test to see if you actually understand the underlying concept. I think examples are a great way to demonstrate the concept before sending students on their own to work the homework problems.
ReplyDeleteI wonder if having the students participate so much in the lecture part of class would be helpful. To me, it would probably get a little confusing. What I mean is, maybe hearing the incorrect ideas of other people would get the students confused, and they wouldn't remember which way is correct. Although mistakes are a part of the learning process, the students may get mixed up with all the different paths that are attempted. I know that I would probably confuse which method or concept was actually the correct one. Participation is a great idea. However, I wonder if it maybe it might be better just to have the students participate in the examples.
I liked your idea of math as a science. Math is definitely a tool to solve problems and understand the world.
ReplyDeleteI really liked your ideas on how your students will learn math best. I think it's a good idea to get student input and work through mistakes in class and understand why that doesn't work. If you don't work though student intuitions in class, then when they're at home and get a "brilliant idea" and get lost they don't know where to turn. Also, it builds sound mathematical reasoning.