This paper presents the author’s personal reflection on
work in mathematics education in low-income, mostly Latino communities in
Tucson. Over more than a decade, the author had been involved in the development
of apprenticeship-style approaches to the teaching and learning of mathematics.
It is claimed that “the research was driven by an equity agenda that
capitalizes on building on the students’ and their families’ knowledge and
experiences as resources for schooling” and was driven by the implications for
the mathematical education of these children if their experiences and
backgrounds were used as resources for learning in the classroom.
One of the key characteristics of the work was the involvement
of the community; parents, students and teachers all collaborated to develop
curricula. I see the benefits of offering teachers opportunities to learn
first-hand about the experiences of the community and reconnect with their
students’ families; however, this approach raises more questions about the role
of teacher in this approach especially when Leslie (one of the teacher who worked
with the author) wrote in reflecting on the impact of household visits: “it provides a real look at the whole child”.
I agree that the approach helps the family to know teachers better while
allowing teachers to learn ways to respect other cultures and therefore to
think about the classroom in the community, but I am concerned with what elements
are included in part of this “real” look of the child, and what options are
available for the teacher to adjust classroom instruction accordingly.
The proposed approach requires parents (and other
adults who are important in the life of their students) to provide resources
towards the development of the mathematics learning modules. For example, in
the construction module (asking students how to build an extra room in the
yard), the teacher allowed parents to answer students’ questions. It was
successful in this context, but would it work in a math-intensive situation?
Even though the author intended for math to play a role in the construction
module, would the students to view the activity as a math activity or just an
activity which happened to use math in it? I am lacking confidence that both
sample modules can be validated to be mathematical activities in terms of reasoning,
abstracting, and generalizing math concepts. The author argues that there are
many challenges to be overcome in the pedagogical transformation of household
knowledge into mathematical knowledge for the classroom. The author further
states that these challenges are related in part to teachers’, students’ and researchers
beliefs about what counts as mathematics. Indeed, the activities introduced in
the paper were more social than mathematical.
My question is: will apprenticeship in mathematics help
a majority of students gain mathematics competence outlined in new curricula?
As an educator, I see the value in being intentional about making these connections between mathematical concepts and students' prior knowledge in their real life. I believe that the connection to the experience, when used well, can be an experience that students internalize more deeply, because there is a heart connection and not just a head connection, when they can see value in the application of concepts.
ReplyDeleteTo be honest, I don't think there is a need to emphasize that this is a Mathematics activity. After all, one of the key purposes of education is to better prepare kids for real life, of which problems are rarely only based on the skills from one subject alone. Nonetheless, I do agree that the role of the teacher is integral in such activities, as are the inherent beliefs of the supporting families and community. The teacher can point out the links between mathematical knowledge and their application in real life problems more explicitly, to emphasize the value of what students learn, if only to help enhance motivation when students see meaning of their learning beyond just tests/exams. Undeniably, the extent of the value from such activities also critically depends on the belief of the community - if positioned as a project that perhaps is done once or twice a year, that provides students that opportunity to practise the range of knowledge and competencies learnt, and the community backs it up fully, the learning, both academic and character-wise, will be invaluable!
The big ideas of the new curriculum such as 'Numeracy helps us to see patterns, communicate ideas, and solve problems.' and 'Geometry and measurement empower us to make meaning of the world.' have obvious links to the tasks you describe and can help the students articulate these important connections. However, an often mis-interpretation is that this will be sufficient. The goal is to make connections between tasks such as these with school-based learning. I hope no-one would suggest that doing a task such as designing an outdoor garden should be the end of a students' math education - they still need to learn concepts such as area and proportion, but hopefully a hands on task can help them gain competence by putting it into context.
ReplyDelete"designing an outdoor garden should be the end of a students' math education", I like it. The problem of the superficial math activities is that we only scratch the surface of the math concepts and pretend we have learned enough.
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