Speaking of a one-size-fits-all approach to learning, I have recently been told about in another discussion group a blog on Challenge by Choice: http://challengebychoice.wordpress.com/. Students choose their own levels of challenge for assignments and exams. The levels are green, blue, and black--with black being the most challenging. There is a lot of information on this blog post, and I have not had the time to read it all and think about it. This idea makes sense because different students come into a course with different levels of ability and preparation. If all exams and assignments are the same, then not all students are being appropriately challenged. Some students will find the work too easy, and others will find it too difficult.
Placing the decisions in the hands of students helps encourage students to take charge of their learning. And students might not trust the teacher's judgment as well as their own judgment anyway. And students are free to move from one level to another throughout the course. Thus, if the students choose a level lower than they are capable of reaching, they can discover that for themselves and move to a higher level later. I believe we can encourage such independent thinking and learning even further by encouraging students to seek and invent their own problems that they are interested in solving or to learn whatever mathematics they are interested in learning. Of course, the students will need some guidance in making these decisions. We also will need to identify what mathematics is essential for them to learn so that the students don't miss learning that mathematics. That is, the course does not need to move all the way to the other extreme into a total free-for-all, totally unstructured course either. I mention that only because my experiences with discussions in education have shown me that some who oppose reformist views of math education seem to believe that all reformists want to push math education all the way to an extreme as far away from traditional math education as possible.
I strongly agree that teachers are often forced to teach in ways that still assume a one-size-fits-all approach to math education (and education in general). Many online courses at many online schools assume this because we are required to use their tests and their assignments and their syllabi. So all students do the same assignments and same exams, regardless of their major, their interests, their needs, their abilities and previous preparation in mathematics, etc. When I think about this, such problems give me yet another reason to oppose common course structures. I tried to do away with common course structures at another school but no luck. I wasn't surprised, especially since a well-respected mathematics professor there had tried the same thing for years with complete failure. If they weren't going to listen to him, then it is no surprise that they wouldn't listen to a lowly graduate student (I was a graduate student at the time when I was at this school--the University of Kentucky). But I had decided to try anyway, and I wish I had thought of this reason at the time as one to add to my letter.
I believe that there are several reasons we see such problems persist: administrators and parents do not like drastic and unfamiliar changes to traditional teaching of mathematics ("What the heck is this stuff you are trying to do? I didn't learn math this way!"), many want quick and easy ways to evaluate teachers and courses--such evaluations are much easier when all courses are run in similar ways with similar assignments and exams for everyone, many are not aware of what the real problems are, many want to cater to students' wishes rather than determining what is best for students, many others do not want such changes made until they know how the problems should be fixed--that is, they are afraid of trying something new when it has not been tested in advance, and others I have not mentioned.
I like Dan Meyer's idea that we tell students too much. If we tell them too much, then we basically do the thinking for them rather than teaching them how to do the thinking for themselves.
And I like his presentation on "impatient problem solving." That is, textbooks often give problems that are quick and easy to solve. Even if a textbook manages to give a more involved problem, the textbook breaks it down into multiple parts. Part a--find this. Part b--find that. Part c--do this. And so on. Rather than having the students try to figure out what needs to be done to solve the problem, the textbook lays it all out in front of them. But many real-world problems are not like this at all! We need to figure out for ourselves what we need to do to get the solution we seek. I take it from your comments that you might have seen the same video or a version of the same video I am referring to. For the benefit of others, I will include the link to this video: http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html.
Another serious error is not teaching students how to think and reason mathematically. Skills in mathematical reasoning and in problem formulation and problem solving will go much further than any specific math content they learn. Furthermore, any specific math content they need to learn will be easier for them to learn than otherwise. Without any genuine problem solving skills and mathematical reasoning skills, any math content they learn they cannot use anyway and will become totally useless to them. Finally, students end up missing the point of what mathematics is ultimately about.
On 7/30/2010 at 12:14 am, Amy wrote:
> I agree that teachers should encourage critical > thinking skills and how to solve problems without > just memorizing facts and formulas but rather learn > to interpret and solve problems with their own > reasoning and like you said "learning to think". > > I love your comment 'We should shed the notion > of the "one-size-fits-all" approach to teaching > because students > are not clones of each other: What works well for one > student > may not work well for another student. Maybe some of > those turned off > by traditional curricula might like math better > because they have more > options that now appeal to them or simply because the > traditional curricula was taught to them in these bad > ways." > > I recently watched a video clip of a math teacher > name Dan Meyer. He made some very eye opening > comments about the way we teach math these days. It > is not a "one-size-fits-all" curricula. Why would it > be? We clearly know that students learn differently > yet we are still forced to teach in ways that doesn't > recognize this. In his video, Dan suggests that as > teachers we should be less helpful to our students. > Stop giving them all of the information and encourage > them to plug it into a formula to come up with an > answer but instead include them in the formulation of > the problem. We should give them the "bare > essentials" and let them go from there. Allow the > students to make mistakes and learn from them, to > come up with their own formulas and reasoning. > > Students may start to see math in a different way > when we as teachers stop doing the "textbook" way of > teaching math and start bringing it to life! As Dan > put it in his presentation, math makes sense of our > world, it is the vocabulary for our intuition"