"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

Wednesday, October 29, 2014

Worked Examples

Some educators do express an aversion to spoon-feeding because the process somehow implies that a student is provided with so much help that there is no room left for thinking. Perhaps, there is indeed no more need to think, but educators must remind themselves that learning is different from thinking. Thinking requires expertise or experience. Learning, on the other hand, oftentimes starts from scratch. Providing steps to students is necessary. This guidance acts as a scaffold to support learning. Inquiry in the hands of a novice can be easily unsuccessful if the learner is not provided with anything. What is important is to figure out the amount and type of support that is needed. One may appreciate this with IKEA manuals. Assembling a child's chair like the one below does not need multiple pages:


But assembling the following cabinet from more than a hundred pieces obviously requires looking at a multi-page manual:
Learning chemistry is no different from being able to assemble furniture from IKEA. One simply has to browse a General Chemistry textbook to see that there are likewise worked examples (similar to a step by step manual):


What goes into a worked example depends on the difficulty level as well as the current standing of the learner. The example above assumes for example that a student already knows how to rearrange an equation:

There are students who need more guidance while there are those who need less. Getting the correct amount of guidance necessary is important. Providing too much simply overloads the student. There is a limit to what can be placed in our working memory. If the mind gets too preoccupied with items that should have already been learned then the mind cannot tackle any new material. This is "over spoon-feeding". On the other hand, not giving enough guidance is likewise taxing on one's mind. This is what students would normally regard as "impossible". To illustrate this in a scientific study, educational researchers have looked closely at how students in secondary schools in Australia tackle specific lessons in geometry:
The paper scheduled to be published in the American Educational Research Journal finds that a "step guidance" approach works best for geometry instruction while "problem solving" is the worse. The difference between "step guidance" and "theorem and step guidance" is demonstrated in the following example:


Above figures copied from
  • Sahar Bokosmaty
  • John Sweller
  • and Slava Kalyuga
Learning Geometry Problem Solving by Studying Worked ExamplesEffects of Learner Guidance and ExpertiseAmerican Educational Research Journal0002831214549450first published on October 3, 2014 as doi:10.3102/0002831214549450

"Theorem and step guidance" can be regarded as one hundred percent spoon-feeding while "step guidance" leaves some parts that students should already know but still shows what the student must do step by step. In this particular example, the results show that there is obviously a huge difference in learning outcomes (measured by both similar and transfer tests) between students with and without guidance. There is only a small difference between "theorem and step" and "step" guidance. However, with a much more advanced topic such as the one illustrated below, the difference provides a very useful insight:

Above figures copied from 
  • Sahar Bokosmaty
  • John Sweller
  • and Slava Kalyuga
Learning Geometry Problem Solving by Studying Worked ExamplesEffects of Learner Guidance and ExpertiseAmerican Educational Research Journal0002831214549450first published on October 3, 2014 as doi:10.3102/0002831214549450
With the lesson above applied to students three years apart in schooling, the "theorem and step" guidance ends up working best with 7th grade students while the "step" guidance approach provides the best learning outcomes with 10th grade students. On the other hand, problem solving without guidance works poorly in both sets of students.

One can easily extrapolate these studies to the learning of young children. Young children need a lot of support and guidance. The guidance must come from either textbooks or teachers. Teachers, however, are the only ones who are in the right place and time to gauge where a student stands and can therefore tailor the worked example according to the student's needs. But obviously, without either a textbook or a teacher to provide guidance, we really cannot expect too much from the student....



No comments:

Post a Comment