In this article, Brown and Walter describe
five sensitivities that should be embedded to mathematics experiences when
teachers introduce problem posing, focusing on pedagogical perspective.
1: An irresistible solving drive:
According to the authors, in some cases,
students try to find out answers or solutions that are given without much
thought. But it is important for students to think and understand what a
problem is, what alternative mathematical entities are, what mathematical view
is as problem-solving when they pose their own problems.
2: Problems and their educational potential
The authors question what we can do for a given
problem other than coming up with the solutions. They believe students can
create the new problems into the situation, and this variation/creativity
enriches to understand original problem and enable to pose other possible
educational problems aside from problem-solving.
3: The interconnectedness of posing and
solving
The authors claim that there might be unexpected
logical connections in which problem-posing and problem-solving.
4: Coming up with problems
The authors categorize problem-posing into
two types: accepting and challenging. For challenging the given, they suggest
“What if not?” strategy to be heuristics problems as following: (p.23)
- Make a selection
- Notice the attributes of the object
- Vary the attributes
- Ask a question about the new form
- Analyse the questions
5: The social context of learning
The authors address importance of social
context of learning in problem posing environments which are relationship of the
individual and the group. They show the readers several ways to create problems
for group interaction such as the case of using editorial boards.
Response:
I agree with the authors’ idea of the
sensitivities to problem posing in mathematics. As per my teaching experience for immigrant
students in Japan, they tend to answer the mathematics problems by utilizing
their assumption from parts of the sentence (some words), pictures and figures within
the question because they have little Japanese language proficiency to
understand the given problems. However, although not always, they surprisingly correctly
answered those problems. This fact supports the idea in the first sensitivity.
Therefore, problems in textbooks and drills in mathematics have common features
across different countries, and I suppose some students who are familiar with
it might be able to answer the questions in different languages.
However, I have never seen the cases that
the above immigrant students challenge problem posing. In addition to their limitation
of language, there are no contents intend to problem posing in mathematics textbooks
and drills and are a lot of the repeated problems instead. I suppose there
might be no developments about problem posing in terms of textbooks and drills,
thus the mathematics class used those problems might have no chance of
heuristic learning for the students including non-immigrant students.
Questions:
Do you think the mathematics textbooks and
drills are containing enough contents for the problem posing process? If so,
has it been changed over the past years?
Problem solving as a focus has been talked for years. Unfortunately, over the years, school mathematics has become more and more disconnected from the mathematics that mathematicians use and the mathematics of life (Boaler, 2016). Students spend thousands of hours in classrooms learning sets of procedures and rules that they will never use. I argue that our textbook contains too much "statics" contents which do not encourage development of habitual mathematical mind. One obvious feature of this type of instruction is that a large portion of the process of learning mathematics is scattered into isolated “facts” which often leave students clueless about the significance of the process. Our challenge then, is to create an environment for creative and flexible use of current textbooks and material.
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ReplyDeleteI think that many teachers do focus on the problem solving process in the classroom (with the teacher as expert) and do not think much about applications. Many teachers still think that as long as your answer is correct, you have reached the content goals for the lesson and they have succeeded in imparting the information to their students. Where are the opportunities for application? Synthesis?
Currently, it seems that many math texts are not designed for the problem posing process. Drills in themselves lend themselves to placing the teacher in the knowing position, questioning the students.
What I see in my math classroom is students who are good at problem solving in their textbook, but can’t use those skills in real life! When I give them real life situations, such as design a game, make a budget, etc. they struggle to use their mathematics skills.
Interesting discussion!
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