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Anonymous
Math Problem: Mary Helen + Problem-Based Learning = ?
The adolescent learner that I am describing, Mary Helen, is in 11th grade at a school that practices problem-based learning in all levels and areas of math instruction. Though she likes, and has always liked, math in general, Mary Helen does not care for PBL math at all; she previously attended schools that delivered math instruction more traditionally – lessons given by a teacher, followed by guided practice and subsequent independent practice. A quick learner and high achiever, MH excelled in this kind of environment, and her confidence at those schools always made her eager for more. Her teacher this year, new to the school and method, though a seasoned professional and dynamic teacher, mentions to the class that at this school, students seem to have low confidence with math. MH blames the instructional approach.
A typical class in PBL math commences with a “show what you know” problem, loosely based on the previous night’s homework. The “swyk” are collected and graded, though they do not affect a student’s grade, they count toward participation. This is followed by discussion of either the swyk or the previous night’s homework among table groups, which consist of 4-5 students. This takes most of the class time, and Mary H insists that the teacher does not engage, but turns any question back to the inquirer. As a result, “Joe,” the most confident student at the table, usually ends up explaining the trickier and more frustrating problems, which seems to frustrate MH even more. In traditional instruction, she tells me, when the teacher explained, the students were equal, even if not always on the same level. Joe can be brusque and condescending, she says, in a way a “real” teacher never would be. Though she does not say so, I wonder if MH’s aggravation is compounded by not to be the one explaining. As class comes to a close, a new problem set is distributed for homework.
Mary Helen likes the old style of math because she finds it easier to comprehend; she feels more supported with the teacher answering questions. But the question persists: complaints aside, is Mary Helen learning the math? She is, though not mostly in class with the table group. Rather, MH ends up visiting the math lab quite frequently. It is a large office staffed by the math teachers in the school, and students can drop in whenever. MH visits with an increased urgency before assessments. She likes the math lab because the teachers there readily provide instruction and explanation, according to traditional methods. MH is clearly more at ease with these linear, traditional practices – what Paolo Friere (1970) would call the “banking” method of instruction, where the knowledgeable instructor “deposits” knowledge to a willing recipient, along with whatever other ideological power dynamics the relationship presents.
The elements that MH details about the PBL classroom sound quite familiar to practices routinely deployed in an ELA classroom, where students discuss texts in large or small groups, interacting with and responding to each other, often without the teacher’s input. I ask MH about this. She concedes, but insists that it is not at all the same because in ELA, an argument is as strong as its support, but in Math, there’s a right answer.
The PBL approach constitutes what Etienne Wenger (2009) terms a “community of practice,” since it exhibits a “domain: all three characteristics: “a domain, a community, and a practice” (3). As a learning model, Wenger argues, the community of practice benefits all members more than the apprenticeship model, which proceeds via, “a complex set of social relationships through which learning takes place mostly with journeymen and more advanced apprentices” (4). The advantage of communities of practice, such as the problem-based learning math class, should be that the community of learners constructs knowledge or accesses learning as a group, thereby rendering the learning process more organic. Here, Wenger (2009) echoes Friere’s (1970) logic that knowledge should be learner-group constructed in the interest of a self-managed life, rather than as a way to participate in a corporate, top-down method. In such a community, each member is assumed to have agency and authority. In communities of practice, everyone works together because each is invested in the success of the group. Yet in these math classes, at the end of the unit, students are assessed individually, rather than in table groups. The community model breaks down, then, because each individual is assessed without reference to the work or constructed knowledge of the group.
It is easy to see the benefits of such a practice in which students construct knowledge and thereby understand that knowledge in a more organic way than Friere’s “banking” model. Teaching to a test, and indeed an existing structural dynamic, as Friere points out, strips the learner of self-efficacy on a number of levels (66). So why should it be that Mary Helen resists the more organic, empowering knowledge offered by Problem-Based Learning? It seems ironic that she considers the banking method more egalitarian, but when you think about it in the larger context of assigning grades, it makes complete sense. Because the instructor evaluates the exams and assigns the grades, the teacher-student power dynamic is secure; that part of instruction remains unchallenged in this model. It stands to reason, then, that MH would prefer knowledge to proceed along the same axis.
Indeed, the overall model of the school, and of post-secondary education in this country -- the years leading up to college application - are not collaborative; they are, by contrast, extremely competitive. PBL math fits uneasily into such a system. As long as the math lab is an option, though it’s time intensive, it is reliable and comfortable. Mary Helen navigates through the hybrid model of PBL with the quick fix of the math lab. She can be honest that she does not really care about the method of instruction; she cares about her individual outcome. It seems like the school/department has to commit one way or the other, rather than keeping a foot in both the banking model and the community of practice model. Selective college admissions are a zero-sum game in this country. Ranking matters and MH will follow the surest path to the higher rung on the ladder. She is a prisoner fallen in love with her chains, her head forever “forward.”
References:
Friere, P. (1970). Pedagogy of the oppressed. Seabury Press.
Wenger, E.C. (2009). Communities of practice: A brief introduction. University of Oregon Scholars Bank. https://scholarsbank.uoregon.edu/xmlui/bitstream/handle/1794/11736/A%20brief%20introduction%20to%20CoP.pdf
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Hi Elizabeth!
Thank you so much for this! It is really quite a comprehensive and balanced discussion of the well-intentioned PBL model and a young person who does not quite benefit from it. It would be easy to rant because of your obvious proximity to and care for Mary Helen. From this, I really appreciate your honest observation and, again, your balanced analysis.
Education is quite faddish. Your whole discussion speaks to what does a parent, teacher, or administrator do when a well-meaning educational initiative, like PBL, just doesn’t work. As the old saying goes, if it ain’t broke, don’t fix it. And from this, how do we advocate for the old that wasn’t so broke to begin with? In a world of polarization and deep investment in education, I wonder how we advocate for the tried and true when there is a strong push for the untried and untrue? Perhaps it is math lab. Perhaps it is tutoring. Perhaps it is student, parent, or student-parent advocacy to the teacher. Perhaps it is all of the above. Perhaps even none.
I wish I had a concrete answer. And I wish the stakes were not quite as high.
Given the strength of your observation and analysis as well as your obvious care for Mary Helen, I am sure you will make it through to the other side. Just do what you both think is best. Experiment and persevere. One day, one step, one moment at a time.
Thanks again for sharing!
Dino