Greeno and Hall describe the use of representations in the classroom. When they speak of representations, they are describing a three-part system involving the item being represented, the representation itself and the person giving meaning to a representation. According to this definition, there can be no representation divorced from an interpretation. They also describe the flexible nature of representations and the necessity of providing opportunities for students to create their own representations. They point to the importance of teaching both the creation and interpretation of canonical representations as well as novel ones.
Wu and Puntambekar’s article describes the use of multiple forms of representation in the science classroom. They provide a detailed description of the four different types of representations and their affordances in the classroom. They divided representations into verbal-textual, symbolic-mathematical, visual-graphic and actional-operational. They also provided a description of the necessary scaffolds needed for students to be able to use multiple models.
I really liked Greeno and Hall’s emphasis on representations as a means to an end instead of an end in themselves. Even learning the commonly accepted representations can be done in context, which will give both the representational form and the content more meaning than addressing each individually (in addition to being a more efficient way to cover content).
I also thought the Greeno and Halls’ idea that we should have students present on their work halfway through a project was excellent. Part of what makes big projects (like those we will encounter when using modeling, argumentation and representation) so difficult is that students work for a long time with little feedback. Some students will procrastinate, and some will put a lot of effort into an idea that will not solve the problem. Having students present halfway through their work will help them accomplish these big tasks that we are going to be asking of them.
Wu and Puntambekar off-handedly mention that dynamic models may make students passive learners. I wish that they had delved into this idea more. Is there a point at which using multiple models as described in this article over-scaffolds students and removes opportunities for them to use and develop problem-solving and thinking skills?
I think that the concept of model progression could be very helpful. I know that I have been shown representations in classes and felt entirely overwhelmed, but then gone back to those same representations when it came time to study for the test and found them really useful. Scaffolding students up to the advanced representation with simpler ones can help them see the benefits of certain representations as well as help them to actually use the representations to aid learning.
Ginsburg and Russ and Sherin both describe the clinical interview. Interviews are a means to understand what students think. As teachers, this is an incredibly important piece that we often have to guess at while planning. We try to determine what students’ prior knowledge probably is, but rarely have it laid out before us. Pre-tests can be helpful in this, but clinical interviews certainly provide more information about how students think about the topic to be covered.
As noted in the reading, planning for a clinical interview is incredibly difficult. You have to guess what direction students will go in their answers to your open-ended questions to be able to have any kind of plan beyond your opening question. They describe the importance of establishing trust with the student being interviewed that they aren’t being evaluated. I think it will be harder to convince students once we’re the ones in charge of their grades. Students also need to trust us that we are genuinely interested in their thought process, not just in seeing how much or little they know. I think it will be especially difficult to determine how to “seed” or give hints as the interview progresses appropriately. Because as teachers our end goal involves using how students think to bring us to how they learn, seeding in an interview could be incredibly useful if it teaches us about how to help the whole class learn the content. But the balance between hints and teaching seems like it will be incredibly tricky to strike. Other parts of the interview will also be difficult such as determining whether giving students time to think is helping them form ideas or making them uncomfortable
The whole interview process and all of the benefits described in the readings reminds me of the benefits of argumentation and explanation in the classroom. Interviewing seems to me to be a sort of microcosm of the wide category of explanation. And while the readings heavily emphasized that we should not be evaluating interviews, Ginsburg consistently contrasted interviews to standardized testing, highlighting the superiority of interviews. I think that explanation and argumentation in the classroom as described by Reiser et al provides a way to assess that includes student thinking and Vygotsky’s ZPD, taking advantage of all of the benefits that Ginsburg points out of going beyond the standardized test.