In this chapter, William James asserts that every new behavior learned by a student results in an expression or reaction. He described this as “no impression without correlative expression” (p. 17). In addition, James also discusses the ineffectiveness of verbal reproduction used as an instructional technique. He talks about the benefits of manual training and stresses the importance of feedback. I believe this to be the pre-historic occurrence of ‘formative assessment.’
On the whole, I consider James’ pedagogical ideas presented in chapter five, well before his time. He stated, “When we turn to modern pedagogics, we see how enormously the field of reactive conduct has been extended by the introduction of all those methods of concrete object teaching which are the glory of our contemporary schools (p.17). This idea correlates with a current strategy used by some teachers called Concrete-Representational-Abstract (CRA) instruction. CRA is an intervention for mathematics that consists of three stages of instruction.
· Concrete. Students study concept through modeling. Concrete materials include hand-held blocks, chips, figures, etc. Virtual manipulatives and other forms of technology-based tactile exercises can also be used.
· Representational. Students represent the concepts and problem solving procedures using organizers, diagrams, and drawings.
· Abstract. The concept and procedures are presented using numbers, notation, and mathematical symbols.
I use this approach with my Math Strategies students, and I have had great results. The concrete activity helps the student understand the reason behind the procedures they are completing. I spent a semester researching ‘worked examples’. (Extensive research has been done on the effective use and design of worked examples. I say this only because, during that particular semester, I learned the hard way the importance of narrowing your topic). The brief version, that is pertinent to my discussion, is that worked examples contain two parts: The schema (reasoning) and the procedures (calculations). If students understand the reasoning behind the steps they are doing, they are more likely to transfer this reasoning to a new set of problems. I believe this to be the goal of mathematic instruction, and highly respect William James’ ideas for that reason.
James fully supported student feedback. “It would only seem natural to say that, since after acting we normally get some return impression of result” (p.19). I agree with James and know that students need feedback in order to know what to correct if their answer was wrong. More importantly, especially the context in which I teach, they need to know when they are right. This serves as motivation to keep going. The premise of teaching with concrete materials is for students to learn the ‘how’ and ‘why’ of the problem sets. In other words, the pedagogical goal is for students to develop an understanding of the concept. Assessing whether a student understands a problem is easy when they are asked to use mathematical symbols. For example, if x = 5, then they either have a “5” written down or they do not. I find grading the concrete activities rather challenging. How do you accurately assess if that goal has been obtained rather than just writing it off as a ‘participation grade’ ?
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| William did not attend my daughter Isabell's first choir performance. He waited politely in the car. |
Excellent thinking here.
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