Mathematics is the study of numbers and how they can be applied to everyday situations. It is a type of problem solving and even a way of thinking. I learn mathematics best by writing it down, figuring the problem out after I have been taught the correct process to complete the problem. Repetition is also critical for me, the more times i see a certain type of problem, the more i understand how to solve it and why it works. I think my students will learn mathematics best by numerous different methods. All students are different and different techniques work better for each individual student. I believe that teaching by whiteboard encouraging students to follow the steps by writing the problem on their own paper is effective for some. I also think visual aids can help many students. Simple things like hanging posters in the room with equations on them or showing how to do a problem using a picture. Applying the mathematical idea to real life situations helps lots of people too, because they feel it is a productive use of their time to be learning that particular material.
In schools today the beneficial methods of mathematics teaching in place are 10 minute quizzes at the start of class, the encouraging of group work both in and out of the classroom, and having students do certain problems on the board in front of the class. 10 minute quizzes at the start of class were very helpful to all students in my high school math classes in subjects such as the unit circle and derivatives and integrals. The students had to memorize these equations for the quizzes so when the equations were needed other than the quiz it was always fresh on the students mind. Group work in the class can sometimes be a waste of time but when monitored and forced to be productive by an assignment it is very helpful for students to talk with others to better understand the subject. Similarly, it is very helpful when a student does a problem on the board and walks the class through the steps he/she used to arrive at his/her solution. This allows students to hear different explanations of how to solve problems which might be more clear to them.
Some ineffective practices in school classrooms are teaching directly from the textbook and poor distribution of students in classes. Teaching directly from the textbook is boring and loses the attention of students. Use the textbook as an aid to a lesson that does not require students to have the textbook in front of them at all times. A big problem in most high schools is that there are not enough teachers to beneficially teach all the students. The result is that really smart kids end up in classes with those slower to learn. There is nothing wrong with the students that take longer to understand a subject, but their comments can be distracting to students who have already grasped the concept and end up second guessing themselves.
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I agree with your comment about group work and having students work through problems on the board. These tactics were used in my high school math classes and I found them to be very helpful. I especially found that when I explained problems to the class, it helped my understanding of the concept increase in addition to increasing my confidence level in mathematics. Furthermore, I found explaining problems and getting help from my peers was a more comfortable situation and I actually learned more from working with them.
ReplyDeleteI wonder how useful posters are in the classroom. I was never exposed to math posters in my upper level math classes, such as algebra and calculus. I am not sure how useful seeing an example of how to solve for x on a poster will truly help the student, especially because then you run into problems during tests about having to cover them up (so students do not cheat).
I think that a certain amount of practice and memorization can be very helpful to students. Sometimes when students are trying to solve a difficult problem and they do not have particular facts or procedures at their fingertips, they find it very difficult to solve the problem. On the other hand, I remember memorizing a lot less than other students in my class because for me, it was easier to recreate the mathematics than try to memorize it. Did you have a similar experience?
ReplyDeleteIt is common practice in many classrooms to have some type of short mathematical activity at the beginning of class. It sounds like your teachers often gave quizzes. Some teachers assign a POD, or problem of the day. Do you think that having students do a POD would be helpful, too, or should they just do quizzes? Are there other types of short activities that might be beneficial at the beginning of class? Is it sometimes better not to have a short activity at the beginning, but to go directly into the day's activities?
I really liked your thoughts about the 10 minute quizzes. I think it really helps students do better on the test, because they had to prepare for the quizzes. As you said, it also helps the lessons because students are more familiar with the material.
ReplyDeleteI respectfully disagree about your statement about group work in class being a waste of time. I feel it is one of the best ways students learn how to solve problems. It also does wonders for students’ social skills and learning how to deal with people that disagree with them.
PS I think your blog title is awesome.