Richard Strausz posted Jul 9, 2013 8:40 PM: > > I recommend that beginning math teachers find some > teacher blogs to follow and participate with. > > Here is an algebra-related post to check out with > links to a number of others: > > http://blog.mrmeyer.com/?p=17391 > I must confess that - as I'm NOT a teacher of beginning math (algebra, etc) - I have not regularly been following Dan Meyer's blog (to which you've often provided links). However, I did carefully read through the one you have referred to above - and I've also quite carefully studied Robert Hansen's (RH's) criticism of the blog entry [RH post dt. Jul 10, 2013 12:25 PM is available at http://mathforum.org/kb/message.jspa?messageID=9164075 ].
1. RH's criticism is not without merit. This blog post of Dan Meyer's does indeed generally strip the algebra from the problem and reduce it to "an exercise involving guessing and arithmetic" (in RH's words). [It does a little more than that, in my opinion - but that's another matter].
2. At the same time, I do know that a great many students at that level really do struggle (and very often fail) to 'get their heads around' the 'idea of algebra'. Those students do need help to do that - i.e., 'get their heads around algebra'. It is not impossible for the average student to do this - witness the many who have indeed done so.
3. It is the responsibility of the teachers at that level to give the students that specific needed help. 'Great' teachers and even just 'good' teachers do learn how to meet this responsibility, by intuition and instinct, as it were.
4. It is the responsibility of the 'teacher training' the teachers have been through to have equipped them to deal with the difficulties encountered by those students of 'beginning algebra' (and, indeed, with 'learning difficulties' generally). If the schools of education providing the teacher training have failed to equip prospective teachers with such skills, then they have failed their remit.
This does NOT mean that you should "BLOW UP THE SCHOOLS OF EDUCATION" (as has been recommended elsewhere at this Forum - and perhaps even here: I've not studied all the posts at this thread). It simply means that the schools of education should carefully take a re-look at how they are accomplishing their 'Mission', i.e. "training teachers".
5. Dan Meyer's blog post COULD BE useful as it provides a link to the arithmetic platform the students may be familiar with. However, it does require some further consideration on the question of just how to go from there into the algebra involved - specifically on the issue of helping 'students get their heads around algebra'. It is not impossible (or even extraordinarily difficult) to do this - for the great majority of students, at least.
Dan Meyer's blog post would have been truly useful (to teachers and to students) if it had made an attempt to do just that - provide the needed link to the 'algebraic way' of solving that problem (and other such problems):
- -- actually demonstrate one or more practical ways to enable students 'get their heads around algebra';
- -- help teachers effectively analyze and understand student problems in understanding 'the idea of algebra' - and to help teachers synthesize practical means to tackle such difficulties (and many others) that will always be encountered by students.
6. There are simple ways of 'looking at systems' that can help quite significantly in such situations. The attachments to my post heading the thread "Democracy: how to achieve it?" describe the simple and effective 'systems approach' to do all of the above - http://mathforum.org/kb/thread.jspa?threadID=2419536 .
7. It surely is necessary that the 'schools of education' adequately equip future teachers with such useful tools.