When I think of some of my favorite math bloggers/writers I can sense their frustration with how math is currently taught. Some refer to the "dumbing down of the curriculum", others say that rote memorization and skills are emphasized over understanding. In the incredible Lockhart's Lament, the loss of rhetoric, proof, and play with mathematics in schools is mourned for.
Image courtesy of XKCD.com (to read it is to love it)
Helping students discover fundamental concepts in math is a wonderful experience for all involved, yet as Lockhart himself admits, this can take a long time. Sometimes I cannot wait, I have things I want the student to use the math and the understanding can come afterwards. You see for me, math is both a beautiful thing but also a tool to be used. One can use an Arduino to create amazing things without understanding all of the design, science, and math behind it (in fact that was a part of its design), one can participate in the building of an FRC robot while learning along the way (it was similarly designed this way).
In the same way, the Pythagorean theorem can be tremendously valuable long before its understanding of how or why. While some would rail against this use before understanding, I find that it encourages motivation, play, and also progress. Often Math/Science teachers tell me that they never have the time to get to programming math because they are so busy trying to have them understand it before they can apply it. In my mind you will never get there in the unfortunately short amount of time we have students each day/year.
In my opinion, to try and teach understanding before application will often time go over student's heads and not stick in their minds in the long term. I would love to see what classrooms could accomplish if they were to start using math right away to build, create, derive, etc. Understanding would come but it would come from the student's aha moments and play.
In the same way, the Pythagorean theorem can be tremendously valuable long before its understanding of how or why. While some would rail against this use before understanding, I find that it encourages motivation, play, and also progress. Often Math/Science teachers tell me that they never have the time to get to programming math because they are so busy trying to have them understand it before they can apply it. In my mind you will never get there in the unfortunately short amount of time we have students each day/year.
In my opinion, to try and teach understanding before application will often time go over student's heads and not stick in their minds in the long term. I would love to see what classrooms could accomplish if they were to start using math right away to build, create, derive, etc. Understanding would come but it would come from the student's aha moments and play.
A car mechanic learns by playing and experimentation because often the manuals and experience fail to explain a problem, but a mechanic who has no basic understanding of the car, is just tinkering in their garage and is likely to break something. More so in the medical field where it would be grossly unethical to operate without understanding. On the job training is in my opinion the best there is but it is worthless if there is no foundation of skills.
Project based learning requires that we dive in and learn as we go but we must also have a skill set to build upon. At the beginning of the year, I am limited by what projects I can do with students because of their limited math, technology, and critical thinking skills. But as these grow throughout the year, I find them more and more able to do and create. By throwing them into the deep end and saying figure this out, they gain a mastery more quickly than a stepwise process would.
The pure math/applied math debate rages on even within the upper echelons of the math community as does the one over the superiority of theoretical and experimental science. What has been proven time and time again is that some gravitate towards a side but the community is stronger because of both. I can't imagine a class where my students constructed everything from first principles and derived and discovered all math/physics as that would seem to me to be too slow a pace and not my style of learning. Yet, a year spent only applying equations mindlessly would similarly leave the students at a disadvantage.
I don't struggle with the balance, I seek quality. As Allison mentioned in her post, I get frustrated by those who rabble rouse and say that teachers are doing it all wrong but don't provide any steps to improve. If your class is so amazing then share in detail. Don't just post on your blog, "My students are engaged and discuss math like Euler and Gauss reincarnate." Post the lesson, the dialog, a video, something! I know we cannot replicate another's teaching exactly because that depends on the context, relationship, style, etc. But, at least give us something to work with and inspire instead of just tearing others down.
I agree more than anyone else, that things need to change for the better. What I am unwilling to do is cut down the efforts of hard working passionate people (like the Khan academy) because their work is in its infancy or is being misused. I am also similarly frustrated with those who call for reform but provide no resources or ideas. If a teacher is online and reading blogs, that is a good thing and they should come away equipped and supported not guilt ridden. If there is something that needs correcting or calling out, then by all means do it, but it should always be coupled with resources or ideas on how they can improve.
Finally, lets all remember what has been said about opinions. No matter who you are or how popular your blog, always remember that there is more than one way to teach "right". If your background is in pure math, then teach that with passion and your students will love it; if it is in the application of it (e.g. engineering) then likewise do that. Students love passion and while we should seek balance, if you are bored or confused, your students will be likewise. But let's please stop name calling and using superlatives. If someone's math or teaching looks weird and different to yours, learn from them but stop saying it "isn't math" or that they are "destroying critical thinking" at least unless you are willing to provide evidence or support to other teachers to help them see your side.
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The pure math/applied math debate rages on even within the upper echelons of the math community as does the one over the superiority of theoretical and experimental science. What has been proven time and time again is that some gravitate towards a side but the community is stronger because of both. I can't imagine a class where my students constructed everything from first principles and derived and discovered all math/physics as that would seem to me to be too slow a pace and not my style of learning. Yet, a year spent only applying equations mindlessly would similarly leave the students at a disadvantage.
I don't struggle with the balance, I seek quality. As Allison mentioned in her post, I get frustrated by those who rabble rouse and say that teachers are doing it all wrong but don't provide any steps to improve. If your class is so amazing then share in detail. Don't just post on your blog, "My students are engaged and discuss math like Euler and Gauss reincarnate." Post the lesson, the dialog, a video, something! I know we cannot replicate another's teaching exactly because that depends on the context, relationship, style, etc. But, at least give us something to work with and inspire instead of just tearing others down.
I agree more than anyone else, that things need to change for the better. What I am unwilling to do is cut down the efforts of hard working passionate people (like the Khan academy) because their work is in its infancy or is being misused. I am also similarly frustrated with those who call for reform but provide no resources or ideas. If a teacher is online and reading blogs, that is a good thing and they should come away equipped and supported not guilt ridden. If there is something that needs correcting or calling out, then by all means do it, but it should always be coupled with resources or ideas on how they can improve.
Finally, lets all remember what has been said about opinions. No matter who you are or how popular your blog, always remember that there is more than one way to teach "right". If your background is in pure math, then teach that with passion and your students will love it; if it is in the application of it (e.g. engineering) then likewise do that. Students love passion and while we should seek balance, if you are bored or confused, your students will be likewise. But let's please stop name calling and using superlatives. If someone's math or teaching looks weird and different to yours, learn from them but stop saying it "isn't math" or that they are "destroying critical thinking" at least unless you are willing to provide evidence or support to other teachers to help them see your side.
Subscribe to BrokenAirplane and keep up with all of the latest education and technology resources!
