The Greeno and Hall article is about the importance of scientific and mathematic representations. Using representations/forms as tools helps students understand what could be an abstract problem. Greeno and Hall say that nonstandard forms are better for understanding while standard forms are better for representation. They lament about teachers not having enough time to teach what a lot of technical representations are for and why they are useful and effective. They also emphasize that students need to be able to know how to use multiple forms of representations in order to communicate their ideas with others as well as to achieve a deeper understanding of a topic. Understanding the meaning of representations is vital, in that the representation has to be for something and not just of something.
The Russ and Sherin article discusses the importance of a teacher gauging where his/her students’ knowledge levels are on a given subject before attempting to teach it. This is important because teaching that builds on students’ existing ideas is more likely to produce robust and meaningful learning. In order to gauge this level, teachers should perform an interview of sorts either individually with students or in a small group of students. The three key steps to this interview process are to contextualize the concept, probe student responses, and seed new ways of thinking.
In Ginsburg’s Chapter 4, he claims that the “clinical interview” is not something so easily done; one needs to practice in order to interview most effectively. He gives these guidelines as a starting point: preparing for the interview, recording the interview, establishing and monitoring motivation, assessing thinking, establishing competence, and determining learning potential. This is not a linear process to him, a lot of these steps are occurring at all times when you interact with a student in class, not just in the interview process. Ginsburg goes into great detail for all of these steps in the clinical interview, and to summarize, one definitely needs to prepare, prepare, prepare, and prepare before one’s interview takes place.
Overall theme with these essays is that teachers need to always be asking why or how a student is thinking about an answer or got to an answer to any problem or concept. We need to really think about how a student got to their answer before we dismiss it as wrong or inaccurate because the student’s thinking process is it’s own special thing. While I enjoyed the briefness of Russ and Sherin’s article, the thoroughness of Ginsburg’s article will help me more as a novice teacher because Ginsburg has literally thought of everything I will need to consider or think about before I begin that process. Working interviews into classroom time is a potential issue, but gauging the students’ knowledge is so essential that it should be worked into any teacher’s lesson plan.
Although I definitely see the merit in Greeno and Hall’s article, I thought most of it was very repetitive. I feel like a teacher would need to explain how a form or representation works in order to get students to be able to read said form. Also that it would be inherent that in order to represent change over time best, a pie chart would be a poor choice. A data table could work to show change over time, but a student would notice that if those points were plotted on a graph, one could “see” that change a lot easier. But perhaps that is not easy for some students to understand who are less scientifically or mathematically inclined. I think I just realized why I might be considered a “visual learner.”