The
article argues that reform in math curriculum and instruction should be based
on providing opportunities to problematize the subject. The principles of the
proposed approach are different from many historic and current views of problem
solving. In contrast of frustrating students
with overly difficult tasks, the article
use “problematic” in a sense to
problematize what they study and “ allowing students to wonder why the things
are, to inquiry, to search for solutions and resolve incongruities.” A specific
example is presented from a 2nd grade classroom where students were
asked to find the difference between 62 and 37 and they were able to solve a
seemingly routine math question by using alternative methods. The article concludes
that the achievement is due to the choice of problematizing task over conventional
teaching. The article argues that widely endorsed application-based approaches cannot
fully resolve the misconception caused by a distinction between knowledge acquisition
and application. The article draws on John Dewey’s notion of reflective inquiry
to establish an alternative view of problem solving approach which advocates practices
of problematizing the subject. The article further examines how the approach
fits both views of mathematics understanding, functional and structural as well.
STOP:
The notion
of classroom culture is very clever. Given the current trend of advocating problem
solving over computation in the classroom, many obstacles need to be well considered
in order to provide the promised outcomes. In general, problem solving activities
seem to offer fertile ground for interaction between students and instructors
in classrooms, but there is not much proof showing that it will teach core
concepts effectively and efficiently across a variety of settings. As a
teacher, I always find myself needing to make compromises: giving students a challenge
produces chaos, but telling students exactly what to do at every step produces
boredom and little learning.
Question:
According to
the article, real-life problems provide a legitimate context for problematizing
mathematics. Will word problems provide a similar environment for engagement?
Thanks for your response - I found your question interesting, having not read the article. In fact, I often (perhaps mistakenly) think of 'real life problems' and 'word problems' as having almost the same meaning in a math class. I suppose the difference is that word problems are a created situation, generally with numbers that work out nicely and evenly to apply specific concepts, while real life problems are generally messy and don't have even and exact answers. The real life prooblems tend to frustrate students as they are never quite sure if they have the 'right' answer (much like real life!)... So, to answer your question - I think the engagement is different - students solve word problems because they are asked to. Some students are engaged and some are not. A real life problem, by definition would almost certainly have to be something a student wanted to solve for their life - so they would likely be engaged in it!
ReplyDeleteThanks for sharing, Ting. I believe having a real-life context for problems, or even a real-life problem itself may increase student interest and possibly engagement, if the students deem it relevant or sufficiently challenging to capture their interest.
ReplyDeleteThe article does seem to point out that whether they are mathematical/theoretical problems such as the example given for subtraction in the second-grade classroom, or real life / contextual problems, they both have the capacity for the problematising of mathematics. As we saw in the example, even though it was a typical and routine math task, the students were engaged in finding alternative solutions, and analysing how their answers were similar or different to one another. Such collective analysis may even help students identify or draw general principles on how problems could be solved, possibly increasing student understanding. Hence, word problems may also be able to provide a similar environment for engagement, though perhaps teachers may need to take a bit more time to think through how this can be done, since the context matters to student interest and engagement, and word problems may lack that appeal factor at first glance. Nonetheless, as the authors emphasise, it is perhaps more of the classroom culture and conditions (as you've mentioned in your 'stop'), which have a more significant influence on student engagement, rather than the type of problem.