1. What is mathematics?
Mathematics is finding a concrete process to solve a problem. It is not very debatable that is what makes it so perfect.
2. How do I learn mathematics best? Explain why you believe this.
I learn mathematics best when a teacher can explain a process and then give examples on how to solve related problems. Since most mathematics is a process with little opinion involved, it is necessary to learn a lot by example. Once I can to a few examples it is easy to do almost any similar problems.
3. How will my students learn mathematics best? Explain why you think this is true.
I would like my students to be able to learn mathematics best through asking questions when they don't understand. I would like them to also learn by working on guided problems in class and then being able to test their own abilities as they go home and try to do similar problems on their own. I think that if they can follow and participate through suggestion or question they will be better able to complete homework problems which will help the ideas stay strong in their mind. It is an invigorating feeling to be able to do a homework problem all by yourself so that is what I would like to see my students enjoying.
4. What are some of the current practices in school mathematics classrooms that promote students' learning of mathematics? Justify your reasoning.
When students are encouraged to give their suggestions on how to solve a problem, it strongly promotes their learning and confidence. When they give a correct solution, or even if they give a mostly correct process to find a solution it helps to reassure their studies and knowledge. Another current practice is splitting students up into small groups or partners to work on harder problems. It helps the students to bounce ideas off of each other and using their notes and textbook they are able to find solutions without very much help needed from the teacher. A valuable tool for students is their text and it is so important for them to realize this is more than just a spot to find homework.
5. What are some of the current practices in school mathematics classrooms that are detrimental to students' learning of mathematics? Justify your reasoning.
A major detriment to students' learning is when teachers assign homework that they don't intend to collect. This puts the students in a situation where most of the time they don't actually do the assignment. I find homework to be one of the most important ways to learn math. When students don't diligently try the homework on their own, it puts them at a disadvantage for the exams.