To me, mathematics is a process and tool by which we are able to form relationships between quantities of different forms (such as measurements) and decipher the meaning of numbers including equations and geometry. Mathematics also helps to teach one how to think in processes.
I personally learn mathematics best through step by step explanation and example from someone who is knowledgeable about the subject, such as a teacher. It is really important that I am shown the process of solving a problem, not just given the equation for solving it. I also think that going through several examples is helpful in the learning process, and of course, doing several problems by myself helps me learn as well.
I believe that everyone learns mathematics best through slightly different processes. I think that a variety of examples with explanations and hands on experience is the best way for students to learn. Not all students may understand a concept right away, but when given several types of examples of how to apply a concept, it is likely then that different examples will help different students understand. I think it is then beneficial for students to try different problems that apply that concept with the availability of someone nearby to help if needed. It is also important for teachers to get constant feedback from the class to if they are explaining concepts in a way that they understand and clarifying as needed. It could also be quite helpful to the students learning if a student is occasionally asked to re-explain or discuss a concept to/with other students that was just taught. An environment needs to be present for the students that is comfortable where they feel they can at any time express whether they do or do not understand what is being taught.
In most all of my high school math classes I had teachers who clearly explained concepts and gave ample examples to help students understand what was being taught. They then would give us time in class to begin working homework problems and during this time classmates and the teacher would be available to help with any problem you might have trouble with. These practices in math classrooms are very beneficial to students and will really help them learn the material that is being taught.
I do not believe it to be beneficial at all when a teacher stands at the front of the classroom and simply gives a lecture on the material while writing on the board. In this situation they give a lecture of the material and explain the material in the way that THEY think students will understand, not in a way that the students actually will understand. In this type of scenario they rarely ask if students understand, and even if they do ask, in this type of a situation, students rarely feel comfortable stating that they do not understand.
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Jenepher,
ReplyDeleteI absolutely loved what you said about how students all learn differently, so therefore, when a teacher is presenting new information, it is vital for him/her to present the new concept in different ways so that each student will connect with one of those ways and learn successfully and efficiently. I think that is brilliant and is something all teachers should know. The way that they learn is not necessarily the way the majority of their students will learn.
Something that you could have included in your opinions to make them stronger would have been to give specific examples of the different ways one concept can be taught and how those ways will connect with different students. That is the main thing we as teachers will need to learn.
Thank you for your post!
I completely agree that teachers should use examples in order to help students know how to do the math problems they are doing. This helps the students to learn how the problems should be solved, and it gives them a pattern to follow. Also, allowing time in class for the students to attempt the assignment is another great way to help with the students learning, and gives them the opportunity to ask questions about the assignment.
ReplyDeleteHowever, I think you might also mention that there are other methods to use in teaching to help the students not only know how to do the problems, but understand the concepts that you as the teacher are trying to teach them. For example, hands-on activities that are used to illustrate and teach a concept can be very helpful for students who struggle to grasp and understand concepts (such as using dice and flipping coins when teaching probability). Like you said, not all students learn the same way, which means that a variety of teaching methods increases the possibility of helping all students understand.
I agree that lecture is not the best way to teach students. You made some great points there.I also agree that examples are a major way of learning math. By doing practice and repetition we understand how to solve problems. But I also think that teachers not only to need to show the problem but why the problem works and what it means to do the process. I think many students get bogged down by methods that they don't understand why they are doing it. Anyways, I loved what you wrote and your thoughts. I especially liked your experience with starting HW in class. That has always helped me too.
ReplyDeleteI liked your idea of having students explain concepts that were just taught. In explaining a concept, you really have to understand it.
ReplyDeleteI agree that we need a good environment in our classroom? As teachers, how can we build the correct environment?
I agree with you when you say that too many teachers just get up in front of a class and lecture, expecting students to follow along and learn just from words alone. Not everyone learns like that and at best, only a few students would walk out feeling like they gleaned anything from class.
ReplyDeleteOne thing I thought about while reading your post was how a teacher could incorporate student suggestions into their class. When I think back to high school and even more prevalently in college, my teachers have been pretty set in their ways and it didn't seem they would deviate ever.