- What is mathematics? Mathematics is a language in which to calculate patterns and change, broken down into different categories such as algebra, geometry, and calculus, each represented by their unique symbols. Symbols on a page is no more mathematics than sheet music is music - it takes a learned mathematician to take those symbols off the page and apply them to create real mathematics, as it takes a learned musician to take notes off a page to create music.
- How do I learn mathematics best? I learn mathematics best by a) having a great teacher that can put across the ideas adequately, and b) studying notes and homework to solidify those ideas. If I do not review, much is lost from my learning.
- How will my students learn mathematics best? My students will learn mathematics best by me going through the material carefully and clearly, asking questions and giving quizzes frequently to make sure they understand the material. That way I know what they still need to work on, and when we can move on.
- What are some of the current practices in school mathematics classrooms that promote students' learning of mathematics? I think one of the main methods today is testing. The curriculum today is so focused on standardized testing and "getting the grade" that much of the curriculum is aimed towards passing those big tests. In order to pass the big tests, teachers give regular tests in class, which promote students to study and achieve.
- What are some of the current practices in school mathematics classrooms that are detrimental to students' learning of mathematics? A practice that is detrimental to students' learning today is when teachers ONLY focus on testing. What I mean by this is that some teachers give homework with the aim of giving students practice to prepare for the test, then they do not collect it with the aim to grade it. This generally leads to students slacking off up until right before the test, where there it no time left to adequately learn all the material. Small quizzes and graded homework is important for the learning of the students.
Wednesday, January 6, 2010
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I rather like your explanation on how math on a sheet of paper is like sheet music. Sometimes a sheet of someone else's math homework can mean literally nothing to me, whereas another homework could be ridiculously cool to me.
ReplyDeleteI have mixed feelings on the whole grading homework thing. I'm not sure if grading all homework for accuracy really is the best way to prepare students for a test.
I agree with your point about focusing on testing. Often times teachers because so focused on helping their students pass the test that they forget about the real purpose of teaching. In my high school, we had to pass state-wide standardized tests in different subjects in order to graduate. As a result, teachers often worried if they should continue with their current curriculum or change focus of the class to more of the test material. I feel that a change of focus simply for a class is detrimental to the students' learning and the excelling in later math classes.
ReplyDeleteI wonder if testing is truly a good way to promote learning. I often feel that students cram in studying the night before and simply forget a majority of the information after the test is done with. If my thought is true, then tests are not truly promoting learning, but rather, they promote memorization. As a result, I believe that students' participation in class and their effort on homework or class projects is a better reflection of learning.
I definitely agree with you on the whole need for a good teacher to help you learn math. I was SO lucky to have great teachers all throughout junior high and high school, and I really feel that's why I have such a great love for math now. One thing that I'm not sure about is the effectiveness of testing. I know that I've crammed multiple times for a test the next day, and as soon as the test was over, so was my knowledge on the subject. While I do think that tests are good checks on knowledge, I think that you're idea of having multiple quizzes is a better idea. Quizzes aren't as stressful to students as tests are, and, if you pattern them carefully, they can be used as a means to keep students remembering all that they've learned.
ReplyDeleteI agree with your idea that frequent assessment is valuable, particularly if that assessment is used to inform instruction. I think that testing can be one type of assessment that can be informative, but I also use questioning in class and students' responses to homework problems to help me decide what I still need to do to help my students understand. I particularly like these informal kinds of assessments because I can do them more often than tests and they don't take up as much of my time, like creating and grading a test does.
ReplyDeleteYour opinion that it is valuable to have a teacher who can put across ideas well also resonated with me. I would encourage you to think about how teachers do this. What's the difference between the actions of a teacher who puts the ideas across well and the actions of a teacher who doesn't? The more specific you can be about this, the more able you'll be to put ideas across well when you start teaching.