I am starting a 6 part series in this blog on the topic of Thinking and Mathematics. Through discussions, I would like to work on understanding how thinking and mathematics are linked in school. Also, it will be interesting to try to figure out how the system of teaching and learning mathematics is evolving or stagnating.
I see the 6 parts as this: (suggestions are welcome)
Part One: Mathematics in Education
Part Two: Why Do So Many Students Dislike Math?
Part Three: Is Math Dead?
Part Four: The Path of Least Resistance
Part Five: Is Change Necessary?
Part Six: Thinking Groups
I would like to start the discussion by asking this question:
What kind of thinking is required of mathematics students?
Posting the comments received on my facebook page:
ReplyDeleteI don't have any of the required Profiles to be able to post a comment on your blog so I'll answer briefly here. What seems to be missing is Conceptual Thinking - the How and Why aspects, rather than the nuts and bolts equations. Kids can learn equations, but unless they understand how to creatively apply them to their given situation, those equations are meaningless strings of vague symbols. I'm 50 and I still have no idea why it's important to know how to map an equation to an x-y grid. Teach kids to ask Why and then give them the tools to derive the answer. Teach them to Think, not Compute.
Facebook Quote: Lisa Floyd
ReplyDeleteThis is very true Paul. It reminds me of all the "why do I need to know this?" questions. I am not sure I ever received an answer!
Facebook Quote: Paul Baker
ReplyDeleteThe answer was always "because it's going to be on the test." Hardly useful, for substantive education, for the real world. However, there is a certain value to that concept in the real world.
Facebook Quote: Lisa Floyd
ReplyDeleteWell yes I received that answer, but I wanted to know more than that! Maybe I secretly wanted to know how soon I could forget it!
Facebook Quote: Paul Baker
ReplyDeleteThat's the whole point. The lesson is not perceived as being at all useful because the student isn't taught why it's useful. If something's not useful to you, you don't want to allocate resources towards it. You end up with a circle of frustration. The only winner is the test score which raises the school's profile but does little for the students.
Facebook Quote: Mark Johnson
ReplyDeleteThe reason why the student learns it is simple. The student learns it because somebody who knows more understands that it is important. (That's the theory anyway. Sometimes the implementation is lacking.) I admit that it doesn't work for adults (and it doesn't work for me!), but challenging the relevance of every lesson is a very poor way of getting an education. Paul, I agree that some students never need to map an equation to an x-y grid (even though I consider it a basic tool). On the other hand, many people see little need for fine arts to be taught in school. I think it's all part of a basic education.
Thanks for the wonderful discourse! I have long thought that the problem for most students is the memorization and the mimicking of algorithms that creates that problem of "why do I need to know this?". No one needs memorization outside of context and that is what is happening when the context is solely higher test scores.
ReplyDelete