This week’s article by Greeno and Hall continues to build on our established ideas of modeling, but this time in a different way. The purpose of their paper is to introduce and define representations so that the reader is able to see their relevance inside the classroom. They describe representations as mathematical expressions, graphs, tables, drawings, notes, diagrams and denote that these representations are an integral part of the classroom because through them students are able to demonstrate understanding and reasoning skills. They chose to break down representations into three parts:
First, representations are not ends in themselves, they should be used to explain and communicate ideas using the representation not just be able to interpret the representation and answer a simple question about it. The representations are the tools through which scientists continually communicate their work to their intended audience.
Second, these representations are useful and serve a purpose to communicate an idea. They are also used to emphasize or keep track of information discovered throughout the scientific process.
Third, representations require that people interpret it and give it meaning. There must be someone to look at the information and draw a logical conclusion based on the representations. The representation is then used to support the conclusion.
The next two articles, (Russ & Sherin and Ginsberg) discuss the importance of the student thinking interview. Both articles highlight the importance of student thinking because of it’s ability to reveal where students struggle in their understanding. The interview process should focus on the student and always ask them to explain their statement or how they came to believe that statement. A clinical interview should probe the student’s thoughts about a certain topic or idea. This strategy can be used to understand the student’s prior knowledge about a concept; the student’s inability to grasp a concept, or what final question or realization leads the student to understand the concept. Thus, clinical interviews provide the teacher with insight on how to design their lesson with this information in mind. The articles highlight the importance of the process of clinical interviews as follows: Gain the trust and confidence of the student so that they feel they can speak freely. Ask open-ended questions that allow the student to explore the question in many directions. Probe the student for more, ask them to explain what they mean or how they came to that conclusion. Ask the student to represent his idea with a drawing or diagram.
This process is very difficult to direct and is difficult for the student to experience because it forces the student to show that he/she has concrete understanding of the concept or it exposes the student’s gaps in reasoning or content knowledge.
As this is my second opportunity to conduct a student interview, I am interested to see if probing for student understanding becomes easier. All three articles seem to stress that students should use representations to display and explain their knowledge of a concept. Clinical interviews normally include a diagram so that students are able to depict what they are talking about and then explain parts of the diagram after the proctor probes them. Teachers must continue to press students for explanation and reasoning throughout the interview because we want to understand the student thinking process and how they arrived at a conclusion. Insight on the thought process is more valuable because you can see which concepts serve as roadblocks to student understanding or what pieces of information are difficult for students to conceptualize.