The type of education(project) I feel being described in this article resonates in me as project-based learning or problem based learning wherein students are allowed to construct their own meaning of an open ended problem and figure out a way to solve a problem with available resources and guidance. They rely on their prior knowledge base to assess what new knowledge they would need to tackle the problem at hand.
The focus of this article is however slightly different from the problem/project based learning as we know it since it explores the vision of math as a social construction. If the emphasis is on fostering meaning making based on personal social experiences, how would a teacher ensure that the student does not end up having any misconceptions and has a clear understanding of the fundamental concepts, rules and laws in mathematics? I feel this danger because math unlike other subjects has several laws, formulas and follows a certain logical pedagogy with respect what knowledge is taught when.
I like the five step curricular process but the difficulty in building lessons around this idea would be alienating students that lack the logical reasoning and have difficulty associating conventional mathematical notion with physical experiences. Translating everyday language into something that has mathematical value might be a difficult task for some students and might discourage them from exploring maths in the future.
The article mentions the issue with the project with respect to sustainability and facilitation in order to accommodate change. I feel that it might be very difficult to sustain a fully project based class as it would require a lot of resources as well as facilitators would have to have a sound understanding of various social constructions of various mathematical concepts to facilitate a class wherein they would be exposed to new ideas and would have direct the students to appropriate resources to develop their understanding.
As outlined in the article there might also be issue with the emphasis being on group activities whereby students might stray away from the “actual work” and engage in personal talk not pertaining to the task at hand. I also feel that certain students might be unable to express their ideas as there would be no right answer and they would feel opposed by competing ideas. Also, certain students might not be able to relate to other’s ideas and therefore might want to work in separate groups which would then lead to segregation of the class based on common ideas and beliefs.
These problems are prevalent in ideas that encourage students’ individual understanding while keeping the class together and creating a safe environment for everyone to contribute. Usually certain ideas are more popular than other and when students are young they tend to join the bandwagon either to retain friends or remain popular. I can also see how this might not successful with new immigrants and students with specific learning needs.
Hi, Lipi, While I definitely wouldn't say that problem-based or project-based learning, or the Algebra Project method, are perfect, I wonder about all the concerns you raised. I think that many of these concerns apply to many different styles of teaching. Do you think this type of pedagogy is especially problematic? Which of the concerns you raised do you think apply only to this type of pedagogy, and which apply to other traditional or reform styles of teaching?
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ReplyDeleteTime-off task and Group problem-solving
ReplyDeleteLike you Lipi, I often look at students working in groups during the semester, and note all the time off task. However when I look at unit and year-end assessment- it is these group sessions that seem to result in the most enduring learning. I have just made many notes in my course notes from last semester – to remind myself of what worked well and for group tasks that I could use next time (always easier to see when you’ve taught the class before).
Changing Everyday Language into Math Language
ReplyDelete"Translating everyday language into something that has mathematical value might be a difficult task for some students and might discourage them from exploring maths in the future."
I agree with you that this is a concern, Lipi. I encounter this problem every time I ask students to explain how they solved a math problem. They know how to do it on paper, but as soon as I ask them to explain it or to answer a communication question involving explaining detailed steps, they can't seem to get the words out! I think it's an important exercise for all students that we try to make the "Discourse of mathematics" as "transparent" (Davis p.82) as possible by encouraging explicit exercises (as painful as they may be for the students) to turn their everyday language into language with mathematical significance.
"As outlined in the article there might also be issue with the emphasis being on group activities whereby students might stray away from the “actual work” and engage in personal talk not pertaining to the task at hand. I also feel that certain students might be unable to express their ideas as there would be no right answer and they would feel opposed by competing ideas."
ReplyDeleteHi Lipi;
I completely agree with you that this is a challenge. However, I believe we can make it work. I've seen group work and mathematical discourse work brilliantly in junior/intermediate classrooms so there is not doubt in my mind that they can work in secondary classrooms.
In 2007, the Literacy Numeracy Secretariat published a monograph entitled 'Student Interaction in the Math Classroom: Stealing Ideas or Building Understanding". The monograph was based on research by Dr. Catherine Bruce, Trent University.
I've uploaded the file on google docs so anyone can access it:
https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B_YrpITfs0DhNDIzMDRkNDYtZjU4MC00MjBhLTk2ZmUtZDI0ZjhjZWU2ODc4&hl=en&authkey=CPDH9_QM
In the monograph, Bruce builds a case for student interaction in the math classroom. She reminds us that "left to their own devices, students will not necessarily engage in high-quality math-talk. The teacher plays an important role". She offers Five Strategies for Encouraging High Quality Student Interaction and Guidelines of Whole-Class Math-Talk.
Her summary encompasses several ideas we've discussed already:
" In order to move beyond this competitive and isolating approach which has had limited success, students must be encouraged to work, think, and talk together while engaging in powerful mathematics tasks. Clearly, the teacher plays a pivotal role in shaping the learning environment. By providing students with a framework for interaction, students can be guided effectively towards working as a learning community in which sharing math power extends understanding and leads to higher levels of achievement."
I agree with Vivien that it will be painful at first but our students do learn to articulate their ideas.