To me, mathematics is not just manipulating numbers or using a correct formula to plug a whole bunch of things into. Mathematics includes understanding, exploring, and discovering. It includes looking outside of the box, and creating new ideas that can be tested.
How do I learn Mathematics best?
I learn mathematics best when the teacher has a very structured way of teaching the basic material, then gives examples, and then allows the students to make discoveries about what they have just been taught on their own. Then, as students try to do an assignment, the teacher allows for questions to be asked, and then helps the student when they get stuck.
How will my students learn mathematics best?
Students have many different ways that they learn. I would try very hard to use many different methods to teach students. These would include visual learning, such as writing on the board, hands-on activities that illustrate the principle I am teaching, examples that we would work through in class together, and then time for the students to try it on their own. This would hopefully work by using different styles of teaching to reach the different styles that people learn math the best.
What are some of the current practices in school mathematics classrooms that promote students learning of mathematics?
Many mathematics classrooms these days are doing exactly what I suggested I would do with my students, which is to use a variety of teaching methods to try and reach the different ways that the students would learn. I thoroughly enjoyed my Statistics class where we did many hands on activities that illustrated and demonstrated the principles we were trying to learn. The result was shown at the end of the year when we took the AP Statistics test, and all who took it either got a 4 or a 5 because we understood the concepts so well. As teachers continue to be creative in the way that they teach the material, more students will grasp the concepts that sometimes seem difficult in mathematics.
What are some of the current practices in school mathematics classrooms that do not promote students learning of mathematics?
This, I believe, occurs when teachers fall in to one of two categories. The first are the teachers who simply get up in front of the class, talk for the whole class period, and then give an assignment to the class as the class is leaving. The second are the teachers who do not have a solidified structure. Teachers need to be flexible, but if there is no structure to the class at all, the teacher can lose track of what he or she needs to teach the students, and can also teach things out of order of the best way to teach them. These two practices in school mathematics classrooms make it very difficult for students to learn math, because it does not allow the student to discover or learn for themselves, and doesn't allow them to try the concepts on their own.