I am going to restrict my comments to data literacy. Not because I have nothing to say about the other ones but because I've been thinking about quantitative literacy for a long time. Data (quantitative) literacy is a vital skill. Since the economic collapse in 2008, I've been wondering about whom many people got themselves into trouble purchase houses or cars or whatever that they couldn't really afford but were lulled into thinking that they could. I know it's not really a mortgage broker's job to dissuade a potential homeowner from getting an inappropriate loan but maybe they should consult more. How many Wall Street stockbrokers and other financial retailers didn't really understand the mathematics behind the derivatives they were selling? Quantitative literacy is important because data is becoming more prevalent in society. (You can't even be a 1st grade teacher without being confronted with data on your students almost daily.) Because of the vaulted status that mathematics holds in our society and because so many people have anxiety linked to numbers, knowledgable people can use data and mathematics intimidate the less literate (or numerate, if you prefer). To become responsible citizens, people must learn that just because there is a number attached to a statement that does not automatically imply that the statement should be believed. The mathematics classroom seems like a natural place to expose students to data analysis. Some people might argue that practical applications of data should be the only thing we teach in school. I think that is misguided. We can't limit math class to data analysis. It would be like only teaching kids how to fill out job applications in English class. Sure, job applications have reading and writing but its just one kind. Mathematics has existed since the beginning of humanity because it can be used to answer questions about the world and it can be used to explore questions with no physical manifestation.
Puntambekar and Hubscher present an informative argument about how the term "scaffolding", now so prominent in classrooms, had taken on a very different meaning than originally intended. Scaffolding was designed to be one-on-one, tutor and student. As the idea of scaffolds were applied to the classroom, the notions behind what constitutes a scaffold have been generalized. Puntambekar and Hubscher argue that maybe we've overgeneralized too much. I couldn't help but wonder if the term scaffold was really appropriate. Regardless, they present a few suggestions for how to implement scaffolds in classrooms to keep with the spirit, if not the letter, of the original idea of a scaffold. I found it refreshing that the researchers took into account that classrooms are (often) diverse and complex learning environments. I anticipated their suggestion that scaffolding tools be removed from environment over time as students need them less. That seemed perfectly reasonable to me.
I hadn't encountered Zygotsky's work until I started graduate school. I knew about Thorndike and Skinner and behaviorism, and Piaget and constructivism, but not Zygotsky and Brunner, and cognitive psychology. I wonder if other teacher preparation programs introduce the concept of Zone of Proximal Development. From the Puntambekar and Hubscher article, I got the sense that some teachers don't really understand ZPD. Without some basic understanding of ZPD, teachers would naturally struggle with how to structure supports for students and the importance of removing them when students no longer need them. I see this subtle tension whenever we use manipulatives in math classrooms. Some teachers and parents will argue against using base-10 blocks to model addition and subtraction because students need to know how to add and subtract without them. But that's not the right argument. Some students will need to use the models because the abstraction of adding and subtracting is beyond their *current* cognitive development. The base-10 blocks are one way for an adult to provide guidance to a student. Maybe addition and subtraction without a model are outside of the student's current ability but by providing the base-10 blocks, those concepts move into the child's ZPD. Maybe. I feel like I might have to read Mind in Society again over the summer.
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