Entry #1

What is mathematics?

In general mathematics seems like a group of rules and axioms that are then used and applied in certain ways to solve problems. Mathematics might also be described as a field that studies proportions, measurement, combinations, transformations, properties of numbers and sets using numbers and symbols.

How do I learn mathematics best?

I learn mathematics best when I have already had some exposure to the material beforehand, such as skimming the section prior to class. Whether I give much thought to it or not, at least my mind is somewhat familiar with some concepts so I don't feel completely confused during lecture. I also find it very effective when I am quizzed on material throughout the course in shorter intervals. I feel like this helps me to retain information better and it gets me started on the memorization process. I also feel like I learn best when the teacher goes at a slow enough pace and leaves time for us periodically to think about the material and respond to questions he/she will propose. This helps me to continue thinking during a lecture rather than just mindlessly letting information be copied into my notes.

I also like it when I am given enough time to work out homework problems as well as having many available sources for help such as a TA, office hours, question/answer time in class etc. Often times I think this helps me in more of a mental way. If I know I have enough time and can get help when I am stuck, I am more likely to really give my homework a fair chance and have confidence as I go through and solve problems.

Another technique that I have found very useful is when either the teacher or myself takes the time to connect, relate, classify, integrate etc. the new material to past material. This helps me to find the common ground between certain concepts so that key differences stick out, allowing me to have a better grasp on the material taught.

How will my students learn mathematics best?

I feel like my students will learn mathematics best when they feel like I care about their learning and will help them help themselves succeed. I feel as though often times students are intimidated by the knowledge of their teachers and don't have the confidence to ask questions. So I believe that trying to create a more positive environment would be beneficial.

I also believe that periodic quizzing would help students to more easily retain information. Also, more interactive approaches such as mini group problems or allowing students to write problems up on the board and explain it to their classmates. I think this builds confidence and helps the students to understand the information better. Taking time to review material and connect past ideas is also a strategy that I believe would help students grasp concepts.

What are some of the current practices in school mathematics classrooms that promote students' learning of mathematics?

Allowing students to ask questions on the homework before it is turned in promotes students' learning because they get to have teacher feedback and learn the correct way to do the problems. Also, when teachers allow students to work together, students are learning from others and also solidifying the concepts in their own minds. I believe that periodic quizzing also helps students remember information easier and helps them start preparing for tests. I also think it is beneficial when teachers change things up a bit and throw in worksheets or group projects so that math doesn't become as tedious to the students.

What are some of the current practices in school mathematics classrooms that are detrimental to students' learning of mathematics?

Although I said working in groups can promote students' learning, sometimes I believe it can be detrimental because certain students rely on others' knowledge to get by, without understanding the material for themselves. Also, I believe it can be detrimental to a student's learning when they are always meticulously graded on homework. I feel as though homework is still a part of the learning process, and if it is graded so strictly, some students can start to lose confidence in their ability to understand the concepts. Another area that I feel to be detrimental is when too much homework is assigned, as the subject may become more of a burden and the zeal for learning can be lost. I also think it is important for teachers to explain why things are so. Sometimes this step gets lost in teaching students and their understanding becomes more memorization than anything else.