"Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labor in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honor it, add to it, and one day faithfully hand it to your children. Thus do we mortals achieve immortality in the permanent things which we create in common." - Albert Einstein

Monday, February 9, 2015

Should I Explain Or Should I Listen?

There are two methods through which one may teach. Showing examples is one (Worked Examples) and another is allowing for students to provide their solution on their own (Generation). Both can lead to better performance. How two entirely different approaches to teaching can both lead to enhancing learning can be explained by examining the material to be learned and the background of the student. How much guidance a student needs depends on two things, the complexity (or novelty) of the material and the expertise of the learner. This dependence comes mainly from the cognitive architecture of the human brain.

The material to be learned can either demand resources from either long term memory or the working memory. Long term memory deals with materials that have been learned while the working memory serves as a scratch pad for the specific task in hand. How much is present in one's long term memory defines expertise. One of education's objectives is to increase what is stored in the long term memory. If a problem at hand requires a solution already stored in long term memory, the solution can be easily retrieved and used in the working memory without significant cognitive load. On the other hand, with a problem never encountered before, one is required to generate a solution from scratch. It should be obvious that this puts a heavier burden on one's brain. It is actually good that the human brain has a maximum working memory capacity. Otherwise, it may simply come up with a large number of permutations and combinations of all the solutions it has in its long term memory. It is the inherent limitations of the working memory that need to be considered in choosing between Worked Example and Generation.

What is required from the working memory depends on what the learner already knows and the complexity and novelty of the material to be learned. This has been recently demonstrated by Chen and coworkers. Their work is published in the Journal of Educational Psychology:

The Worked Example Effect, the Generation Effect, and Element Interactivity.
Chen, Ouhao; Kalyuga, Slava; Sweller, John
Journal of Educational Psychology, Jan 19 , 2015, No Pagination Specified.

Abstract The worked example effect indicates that examples providing full guidance on how to solve a problem result in better test performance than a problem-solving condition with no guidance. The generation effect occurs when learners generating responses demonstrate better test performance than learners in a presentation condition that provides an answer. This contradiction may be resolved by the suggestion that the worked example effect occurs for complex, high-element interactivity materials that impose a heavy working memory load whereas the generation effect is applicable for low-element interactivity materials. Two experiments tested this hypothesis in the area of geometry instruction using students with different levels of prior knowledge in geometry. The results of Experiment 1 indicated a worked example effect obtained for materials high in element interactivity and a generation effect for materials low in element interactivity. As levels of expertise increased in Experiment 2, thus reducing effective complexity, this interaction was replaced by a generation effect for all materials. These results suggest that when students need to learn low-element interactivity material, learning will be enhanced if they generate rather than study responses but if students need to learn high-element interactivity material, study may be preferable to generating responses. (PsycINFO Database Record (c) 2015 APA, all rights reserved) 
As mentioned in the above abstract, the study looks at two groups of students from China. One group is composed of Year 4 (about 10 years old) students who are just being introduced to calculations of areas and perimeters of polygons while a second group comes from Year 7 (about 13 years old) students. The older students have already taken a geometry class during which the topics involved in this experiment have already been covered. Year 4 students therefore represent students with much lower expertise than the Year 7 students. Both years of students are randomly divided into two classes. One group receives high guidance (Worked Examples) while a second group receives low guidance (Generation). Both groups tackle two types of geometry problems. One is simple while another is complex. At the end of the sessions, assessments are administered to gauge how much students have learned in both types of geometry problems (simple versus complex). The results are summarized in the following figures:

Year 4 students (low experience)
Graph based on data from the Journal of Educational Psychology
Year 7 students (high experience)

Graph based on data from the Journal of Educational Psychology
Almost every class taught in a school contains simple and complex topics. It appears that when dealing with beginners, it is important to provide direct and explicit instructions (Worked Examples) on challenging materials. On the other hand, for reviewing topics that have already been covered, it is beneficial to allow learners to develop the answers on their own (Generation).

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