Mathematics is everywhere around us. It is a very precise science that relies on formulas and concepts. I'm having a hard time coming up with an exact definition, but it includes measurements, numbers, and symbols. Like other sciences, it is used to explain natural laws.
I learn math the best when a teacher explains the concept and why it is that way. I like to know why we use certain formulas because it helps me to better understand what we're doing. Even though proofs can be long, they are also very helpful when one topic is building on another. I also learn by example. I like to be shown how to do something before I really know how to do it because otherwise I might end up practicing doing it incorrectly. I like to be shown the complete process while someone can explain why they are doing each step. It is not beneficial when someone just does the problem without any explanation.
My students will learn mathematics through a step-by-step explanation given of what the concept is followed by several examples of how to apply the concept. I've found that practicing the concepts is beneficial to remembering and fully understanding the ideas taught. My students will also learn through the opportunity to explain the concepts to each other. That way they will know what part they understand and what part they are still having trouble with.
One of the most important things is having ample time to ask questions. Like we do here, my high school had a math lab where students could go to get help. This provided a way for students to get individualized assistance with questions they had and ideas they were confused with. This can happen if homework time is made available during the class, as well. Students will also learn better if they are interested in the topic. Finding ways, such as news articles or example problems, to connect mathematical concepts to real life promotes students' learning in mathematics.
Some current practices that are detrimental to students' learning of mathematics is when only the teacher is speaking and explaining the concepts with a wall between them and the students. The classroom needs to be an interactive environment and open to questions from the students. Often teachers will just try to get the class through some material until they reach their favorite part of the curriculum without explaining the importance of what had been taught so far. Teachers need to try to keep everything relevant, as much as possible.
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Like you, I like to see examples of how to use procedures. Often times, the examples help me better understand the steps and purpose of the procedure. I also appreciate proofs, because often times I gain insight into why a procedure works or a particular fact is true. Sometimes the reasoning in the proof is easier for me to remember than the actual procedure, and so when I need to use the procedure again, I recreate it using the proof rather than trying to memorize and recall the procedure. Do you ever do that?
ReplyDeleteI was interested in the way you used the term "concept." At times, it seemed you were using the term to mean "procedure." Do you agree? Is there a difference between procedures and concepts?
I agree with your way to teach your students. Step by step explanation and practice is a perfect way to teach! I love your idea of making sure everyone has time to ask questions. That was a big problem in my math classes because of the little time. My high school didn't have a math lab but I think it would be beneficial to every student if there was one. I also like how you think students should be in an interactive environment. I agree that students learn better when they feel they can ask questions.
ReplyDeleteI really like the line "Like other sciences, it is used to explain natural laws". I totally agree with you on your explanation of mathematics. You also had some good ideas in your section on how you will teach. Having students produce their own explanations is probably very helpful in their learning process.
ReplyDeleteAlthough having a math lab and adequate time to explain and help each student, it might be helpful for you to also think of some alternate methods of helping students understand without such luxuries.
Overall, I think you have some great ideas.