1. What is mathematics?
Mathematics is a subject in school, in which students learn about numbers and problem solving.
2. How do I learn mathematics best? Explain why you believe this.
I learn mathematics best by reading the book, paying attention especially to the sample problems. I study every step, and then I test myself by doing the practice problems. If I get stuck, I go back to the beginning of the chapter and re-read how to do that part before applying it again to the practice homework problems. This is how I learn mathematics best. I know it is the best way because it has produce successful results all through my mathematics past as well as it allows me to not be personally dependent on anyone else to learn mathematics.
3. How will my students learn mathematics best? Explain why you think this is true.
Even though I learn on my own from the book, I believe my students will learn mathematics the best from what I like to call "dramatic learning." Many students in today's society believe they are not good at math, and I do not think reading from a book will help them to improve. They will need someone who can explain the concepts clearly and in a fun, exciting (dramatic!) way. By developing hands-on methods (excluding having them write problems on the whiteboard!), I believe most students will learn mathematics the best because of the visual and more applicable ways of looking at mathematics.
4. What are some of the current practices in school mathematics classrooms that promote students' learning of mathematics? Justify your reasoning.
To be honest I do not know a lot of the current practices of mathematics in the classroom, but I know what my math classes did. Nightly homework promotes learning because the students need to try problems on their own in order to really learn mathematics; they cannot simply watch the teacher do a problem during lecture and then be able to reproduce a similar problem on the test without practicing other like problems. So I think daily practice problems are very helping in learning mathematics.
5. What are some of the current practices in school mathematics classrooms that are detrimental to students' learning of mathematics? Justify your reasoning.
I think one current practice that I noticed in my middle school and high school years in math classes that was detrimental to the learning of mathematics was too much daily homework. There is no need to do 20 problems that are all alike. 3 to 4 problems will suffice. I feel lots of students became overwhelmed at all the homework every night, and therefore decided that they hated math and gave up on trying. I think practice problems are good but within reason. Too much practice will cause students to not try at all and will hinder their learning of mathematics.
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Hey I like how you explained your way of learning. I wanted to explain it like that but for some reason there was too much in my head and it didnt come out like I wanted it. Anyway, I agree with reading and paying attention especially to the sample problems. I would do that and then pay close attention in lecture and take good notes and then jump into the homework after lecture.
ReplyDeleteHowever I don't fully agree with the current practice that is detrimental. I think that the more repetition is better for learning. the more one works out a concept the more understanding comes.
I ike this authors ideas of current detrimental practices to students of mathematics. I agree with this idea because in my opinion performing the same kinds of problems and many of them aver and over again seems very monotonous and teteous and quite frankly a waste of time. I think the practice should be doing a different variety of problems in one area that give the student a broad range of problems they may encounter on exams and tests as opposed to many of the same type of problems.
ReplyDeleteI do not fully agree with this author on the point that going back in the book and reading sample problems and applying the method used on the sample problems is the best wayto leanr, It may work for this author but I find for myslef sample problems are not broad enough and cover the simpler way to do problems when the problems in the book are much more complicated than the sample problems, and therefore do not help you much when the practice problems become tougher.
I agree with so many of your thoughts. Nightly homework definitely solidifies the concept because, like you said, the students can't just copy what the teacher is doing. It lets them know what they understand and what they are still confused about. Too much repetitive homework also seems unnecessary because it will become tedious and some students won't do it.
ReplyDeleteI am impressed that you were able to learn through solely reading the book. I was never able to do that, but rather required at least some sort of explanation. I think many of my peers did, as well. This would work for students, too, but I also agree that the more fun and exciting something is, the more students will want to pay attention and learn it.
Annalee,
ReplyDeleteI like what you said in your closing paragraph about how unnecessary homework overwhelms and can frustrate students. Math is such a frightening subject to so many students that the last thing we as educators should do is magnify those fears.
My two oldest children learned mathematics just the way you did. They never listened to the teacher, and would often have the assignment done by the end of the teacher's lesson. Some people can be very successful in mathematics classes by using this method. I always wondered, though, about the instruction that they were receiving in class. Did they choose to learn this way because the instruction was bad? Could they have learned better if the instruction was different? I don't know.
ReplyDeleteI'm glad you're thinking about motivating your students. My children definitely learn more in the classes in which they feel motivated. I sometimes think that the best motivator is instruction that helps them make sense of the mathematics and be successful at the problems. I think people like to learn when they feel that they can learn.