Mathematics is how numbers apply to every day life whether that's in the grocery store or in a NASA laboratory. It proves why certain things are the way that they are.
I learn math best if I understand why and if I can see all the different reasons why. Math has never been an easy thing for me and I usually have to see different ways to approach a problem before it really starts to make sense. I think that my students will learn best this way as well. By asking why, reasoning skills are developed that will help them to make connections for themselves. If students are just told how to do something, they'll choke when something out of the ordinary shows up because it didn't follow the pattern that they were shown how to do. It's also important for them to see all the different possibilities and angles that can be taken to find a solution. Each student will think different and one way might be great for one student while another doesn't understand. I think they'll learn best if they understand why and if they can see many possibilities to a solution.
Math assignments are great. You can't just learn math by listening to a teacher lecture, there has to be hands on experience that is varies within a topic so that they can see the application. I also have always thought that it was good that I had to memorize my times tables back in second grade.
I think that teachers that don't know how to teach are detrimental to students learning math. Teachers that don't care, aren't excited, don't show the application in every day life, and only show one way how to do something and can't explain why.
Teachers who don't care is one of my biggest pet peeves. It can be so frustrating when you have a teacher that cares more about telling you what they know, instead of finding out what you don't know. You are definitely correct about teachers not knowing how to teach being a HUGE detriment to students learning math. One thing that you want to be careful about though is focusing too much on the 'why' of math. While learning the 'why' is very important to math, I've had a few bad experiences with this in the past. For example, one of my teachers here at BYU would spend 30-40 minutes of the 50 minute class period discussing 'why' a certain method of solving DID NOT work. While it's important to understand why you can't do something, you need to make sure that you also give time to teach the correct method and also how to apply the method.
ReplyDeleteI agree to an extent with providing an explanation for why a particular principle works. A teacher must be able to convey to his or her students why something works and not just how it works. I had one teacher in high school that was absolutely brilliant but he could not explain why something was a certain way to students below his learning capability. Math came easy to him; he did not understand how math could not come easy to someone else. However, if all the class time is spent answering the why question, some students could get lost or confused. It is important to also go over specific examples so that students who need to see how to apply the principle will be able to do so.
ReplyDeleteI agree that understanding the reasoning behind the computations and procedures is very important. I personally like to know why, not just how. But I also think that mathematical knowledge is not very useful when I don't know why, because then I often don't know when to use it or how to adapt it to new situations.
ReplyDeleteI guess I disagree with the two comments above, because I've experienced way too much mathematics where I was never helped to understand the reasoning, and I've also seen in my own teaching how students are severely limited by only knowing how to do procedures and perform computations, and not understanding the underlying concepts, why the procedures work, and when to use them. Some students become so disillusioned because they never learn any of the reasoning. They end up developing the belief that mathematics never makes sense, or that they do not have the innate ability to do math. No wonder so many students hate math!
I was also interested in your comment about hands on mathematics. What did you have in mind here? Were you thinking of having them complete homework problems, or something else?