What is mathematics?
Mathematics is the complete study of numbers. Also, it is the application of numbers to any and every situation possible. Math is a way of solving problems through quantifications, and classifying things symbolically and numerically. Math helps to understand everything around us, time, space, and everything in between.
How I learn mathematics best.
I learn math through two ways. First through understanding definitions. By understanding a definition to an equation or even a word, I have a greater idea of how something is to be understood or worked out. The second way is through example. By seeing similar problems, and how they are solved, I am able to understand the underlying concepts of similar types of problems.
How will my students learn math best?
My students will learn math best through example as well. This is true, because in each example, I will be sure that the definitions are understood. Also, by doing multiple examples, I can apply different situations to each problem, so that a great majority of the students that did not understand the first time, will see it in a different light and will be able to pick up on it.
What are some of the current practices in school mathematics classrooms that promote students' learning of mathematics?
I can think of a three main practices in math classrooms that are used to promote students' learning.
First, through independent study. In math classes I have been in, and in others that family members have been in, I have noticed a trend. Often times students are encouraged to read the material before hand or on their own in the classroom to see if sense can be made of concepts through that method.
The next practice I can think of is again, through example. In every class I have seen, teachers will spend a majority of the class doing example problems, to help clarify each of the different concepts.
The last way I can recall is through homework. Basically every math class involves homework. This gives students the opportunity to not only see practice problems, but to apply what they have learned and work on them by themselves.
What are some of the current practices in school mathematics classrooms that are detrimental to students' learning of mathematics?
One way that math is taught in classrooms that is detrimental to the students learning, is through pure lecture. If students are not given the opportunity to work out the problems with the teacher, a lot of them will not have the ability to work out a problem on their own.
Another way is by unclarity. An unprepared teacher can stand in front of a classroom and teach something completely off track, or much to advanced for the caliber of students he or she has in their classroom. By doing this, the wrong way, or the overly difficult way is implanted in a students mind, and they will refer back to this often times before thinking of the correct way to solve a problem.
I enjoyed reading your blog and agree with much of what you said. I think it is a wise choice to use examples as a main way of teaching mathematics because as you mentioned, with the use of several different types of examples teaching the same concept it is more likely that a greater number of students will understand and grasp the concept.
ReplyDeleteHowever, I think it could possibly be a mistake to assume that all of your students will learn in the same way that you do. We are all tempted to say this, including me, as we will teach to our students generally in the way that we learn because that is what will come naturally. But I think that it is very important that with each new class someone goes to teach that they need to get to know how the students learn and teach to that.
Thanks for the entry! It was enlightening!
I also think that examples are very helpful, particularly if most of the information of the lesson is delivered through lecture. I was interested to see how beneficial definitions are to you when learn mathematics. I think definitions play an increasingly important role in advanced mathematics, so this predilection for definitions will serve you well in your college math courses.
ReplyDeleteYou might be interested to know that some teachers during a lesson typically do not present a particular solution method and examples of how to use the solution method. Instead, they ask their students to solve the problem without first being given the solution method. What do you think of this approach? Would you ever approach a lesson this way?
I think that you bring up some great points in your blog about the way students learn math and also what practices should be used to help them learn. I also learn through examples. Without them I think math would almost be impossible to understand.
ReplyDeleteOne way that you might also reach your students is though helping them understand the principles behind each concept, in order for them to remain interested and get a better grasp on the concept.
I thought your discription of how you learn using definitions was really good, I totally agree.
ReplyDeleteDefinitions are so important, not knowing what symbols or words or directions mean makes solving problems so confusing.
I thought that your discription of math was very interesting to. It was well discribed but I think it could be summed up to simply problem solving.