Source:
"Problem Posing in Mathematics Education." Problem posing: reflections and applications. By Stephen I. Brown and Marion I. Walter. Hillsdale, NJ: Lawrence Erlbaum, 1993. N. pag. Print.
Problem posing in mathematics education counters the traditional way of teaching math where an authority poses a problem and students simply solve it. The benefits of problem posing are that it can interest and motivate students; it can dissipate fear and anxiety caused by imposed curriculum; it can cause students to take more responsibility for their learning; educators can discover that various students have different talents as they pose problems. Problem posing activities should be incorporated into all sections of math rather than isolated; this article poses five themes that should be incorporated into formal and informal mathematical experiences “if mathematics is to be viewed as an act of liberation.”
Sensitivity 1: An irresistible problem solving drive
Students immediately jump to solving a problem even when a problem is not posed; this is problematic because students new mathematics think that the subject is just about solving problems. Instead, students should be aware of the entity they are examining (whether it be a situation, concept, object or problem etc.) and be aware of their reaction to it because doing this allows itself to meaningful enquiry.
Sensitivity 2: Problems and their educational potential
When presented with a problem, there are other meaningful pursuits than simply solving it. For instance, neutralizing a problem is when students create situations and pose problems themselves. When students understand the variations of the problems they pose, they can understand the solutions. They can also ask questions of themselves (ex. how can we group the problems our class generated?).
Sensitivity 3: Interconnectedness of problem posing and problem solving
When we solve problems, we restructure them in order to understand them. Also, we often do not appreciate what we solved unless we have pose a new question. When we ask questions about solutions, we understand our solutions and see connections in unexpected places.
Sensitivity 4: Coming up with problems
There are two ways to come up with problems. One is to accept the given and to ask how it might have been developed and so forth. The second is to challenge the given. Brown and Walter coined the ‘What-If-Not’ strategy. This method involves five steps. The driving force that makes it effective is that this strategy separates varying the attribute of a problem (step 3) and posing a question in a new form (step 4). When these steps of problem posing are separated the variations give rise to ‘possible worlds never imagined’ and problem posing becomes an act of creativity.
Sensitivity 5: Social Context of Learning
Problem Posing counters the notion that mathematics is a solitary activity. Instead it is more true to the way that mathematical ideas actually evolve; having students participate in this way makes them also aware of mathematics as a field.
Stop:
“If learning mathematics is to be viewed as an act of liberation”
I used a few quotes in my summary because there are key quotes that are written quite beautifully in this chapter. This introductory phrase caused me to pause and really ask, what is the purpose of mathematical problem posing? As I read the article the first time I wondered if the authors assumed that as one understands mathematical concepts they are intellectually liberated in some way. I found, rather, that phrases such as liberation and radical reminded me of critical theory and that problem posing can be linked to this; this appealed to me. Walter and Brown assert that problem posing offers a chance for students to question content, each other and the way we interact; it causes students to question the status quo and what is imposed on them. Not only does it deepen understanding of mathematical concepts it allows for creativity in math and opens up ‘worlds unimagined.’ This phrase reminded me of Maxine Greene, she talks about the liberal arts in this way saying they open up possibilities to the ‘not yet imagined.’ Ultimately, I think providing students a space to see new possibilities in any discipline avails them the opportunity to see new possibilities for themselves.
The authors conclude that the benefit of problem posing is that it causes students to question content and question how we interact and educate each other. To solve problems in pedagogy is better than searching for the perfect problem-solving curriculum.
Do you (for)see problems in problem posing pedagogy? What problems need to be solved or addressed when considering problem posing as a way of teaching?
Based on my experiences, students usually are not interested in posing a problem or question, they did not see any value to take time and create a new question. From their point of view mathematics is all solving the problems which takes time and energy, so what should they takes more time to pose a problem in which they had to solve it after that..!! So, I think the best results will be gained if teachers firstly explain the benefits and reasons behind problem posing. If students fully understand the aim of this task thy will participate with precision and passion. Student’s willingness to pose a problem is a key to gain the best results, otherwise, just copying another problem and changing the names and numbers cannot be helpful.
ReplyDeleteThe best way to be benefited from the problem posing is different from student to student. Based on the weak points of students (in mat), teacher can ask them to pose a particular question. Teachers exactly know the weakness of her/his students so she/he can use his/her knowledge and awareness to focus on particular parts and subjects. When students ask to pose a problem in a particular subject they need to deeply think of that part and analyze the variety aspects of that subject. I think posing a problem is a reverse way of solving it, so students need to think of its solution when they are posing it.
I think that the greatest advantage of problem posing is that it is relational, there is relation to other students to instructor and to the mathematical theory being explored. If we think of math as scratches we make on surfaces to communicate ideas, then opening this connecting world to student creativity allows for further expression and understanding. Problem posing can create multiple vantage points, views, and springboards for articulating mathematical relations and concepts. I also believe in opening up any mathematical exercise or application for a inquiry into the question itself develops an understanding and appreciation of the field of mathematics. This can support curiosity and sense of attachment to mathematics.
ReplyDeleteI appreciate that students will possess a variety of learning styles eg. visual-spatial, verbal-linguistic, introvert, social and may find preferences for certain modes of representation. Problem solving could be a challenge and a benefit for sharing diverse interpretations.
The problems that I see have to do with practicalities of typical public school set-ups in which teachers may be spread thin among students with diverse social-emotional situations. However, this is a practical consideration and does not discount the overall practice.
I agree, Amanda. The relational component is so important. What I like about problem-posing is that both teacher and students act as mathematicians so it creates a community of thinkers.
ReplyDeleteIn my view problem posing is a suggested steps of which teachers are at liberty to train their students to follow when tackling mathematics. At liberty because different problems require different approaches and its of no use if can reach the answer to go through other steps.
ReplyDeletePosing is a technique to be introduced to the students and can be used in daily life approach where one require analytical thinking before engaging into any situation. In most cases this method is very good where the examiner awards marks in each steps used not simply interested to final answer.
The problems which may discourage students to use posing method is, if its placed as a rule that the steps has to be followed , let students come up with their own steps and encourage discovery.