Goal-Free Problems

Asking a student to find the solution to a problem creates high cognitive load that she may end up making a lot of mistakes. This is especially true when the problem requires many sub problems to be solved, and students tend to make many more errors in these sub goal stages than at the final goal stage. This effect is called the stage effect.

An alternative to help students learn problem solving is to ask them to find the value of as many unknowns as possible, rather than finding a value for a specific goal. As an example, given a programming assignment, students are asked what are the unknowns rather than asking them to create a final program. This can be open ended and the students may go off on a tangent if not properly guided. Of course, no one would hire these students if all they can do is to come up with unknowns(!), but this strategy can be used as a scaffolding device to help students connect what they already know and what we want them to know. New knowledge can be built up as the unknowns are identified, and how these unknowns are related to what has already been learned.

Reference:

Ayres, P. (1993). Why Goal-Free Problems Can Facilitate Learning. Contemporary Educational Psychology. 18, pp 376 - 381.

Student Self-Explanation

Student self-explanation of material they just read has been shown to be effective in producing robust learning gains in a number of disciplines. However, past research results have not been clear whether performance gain is due to student simply paying attention to explanation generated by the instructors, or explanation generated by the students themselves. One research has shown that explanation is more effective when the students generate it rather than simply paying attention to instructor generated explanations (Brown and Kane, 1988), while in another case, the reverse is true (Lovett, 1992). Most recently, Hausmann and Vanlehn (2007) show that generating self-explanation while students attempted solving problems and studying examples is more effective in normal as well as robust learning (which means knowledge is retained over a significant period of time and demonstrated in far transfer of problem solving) than students who comprehended and paraphrased explanations generated by the instructors.

Self-explanation, coupled with learning by examples, can be very effective in student learning. Learning by examples has a lower cognitive load than learning by doing or solving problems, based on cognitive load theory. Thus comparing students who learn by doing a number of questions with those who learn by working through a number of examples, the cognitive load in the latter is much lower, and this affords the students the capacity to come up with general solution principles through self-explanation to improve their effectiveness in learning.

A related theme is that students who self-monitor their learning and comprehension in addition to self-explain the material they learned are better problem solvers than those who don't. By self-monitoring, this means that the students keep track of what they know and what they don't know, what are the parameters and data provided by the problems they are trying to solve, what needs to be solved, how the problems relate to the examples they have worked through having specific goals such as looking for solution methods rather than equations, formulas, similar contexts, etc.

References:

Brown, A.L. and Kane, M.J. (1988). Preschool Children Can Learn to Transfer: Learning to Learn and Learning from example. Cognitive Psychology. 20(4), pp 493 - 523.

Hausmann, R.G.M. and Vanlehn, K. (2007). Explaining Self-Explaining: A Contrast Between Content and Generation. In R. Luckin, K.R. Koedinger, and J. Greer (Eds). Proceedings of Artificial Intelligence in Education (2007). Amsterdam, The Netherlands: IOS Press.

Lovett, M.C. (1992). Learning by Problem Solving versus by Examples: The Benefits of Generating and Receiving Information. Proceedings of the Fourteenth Annual Conference of the Cognitive Science Society, Hillsdale, NJ: Erlbaum, pp 956 - 961.

Cognitive Load Theory (CLT)

Cognitive Load Theory is all about efficiency where efficiency is defined in terms of learner performance and learner mental effort. CLT suggests that we have only a limited amount of cognitive capacity for solving problems in our short term working memory (as opposed to long term memory for information storage). The higher the learner performance and the lower the learner mental effort (which occurs in the short term working memory), the better! According to CLT, there are three main types of cognitive load when one tries to learn something: intrinsic load (due to the complexity of the content to be learned), germane load (due to the instructional activities), and extraneous load (due to wasted mental resources on irrelevant material). Thus, in a first year computer programming course, learning to program in Java imposes the intrinsic load, providing worked examples on a variety of programming tasks contribute to the germane load, and requiring students to work within a complex integrated development environment (IDE) impose extraneous load on the students. Efficient instruction maximize germane load and minimize extraneous load.

Cognitive load depends on the interaction of three components: the learning goal and its associated content, learner's prior knowledge, and the instructional environment.

Reference:

Clark, R.C., Nguyen, and F., Sweller, J. (2006). Efficiency in Learning. San Francisco: Pfeiffer.

Worked Examples

An important discovery of Cognitive Load Theory (CLT) (Sweller, 1988) is that studying partially worked examples provide better learning results for novices in computing than working through problems from scratch or studying completely worked examples. Gray et al. (2007) suggested the use of fading worked example as an effective strategy for lowering cognitive load in the novice phase of skill acquisition in programming education.

The idea of a fading worked example (FWE) is a sequence of partially worked examples in which each problem in the sequence contains one fewer worked step than its predecessor so that, in the end, the learner is given a problem to solve with no worked steps provided. Thus in systems programming, instructors may start with a fully worked example (Clark et al., 2006) from a problem statement, to analysis, design, coding and testing. Then the next example may involve all steps except coding. The next example may remove design, etc, until the students are required to solve a problem given just a problem statement.

The key to creating FWE is decomposition of each learning goal into smaller steps. As an example of using FWE for learning programming, each aspect of a programming language is identified. This includes variable, expression, assignment, iteration, subroutine call, etc. Next the use of each of these aspects in a program is related to the dimensions of problem solving, namely design, implementation and semantics.

How does studying worked examples compared to actual practice? Actively solving practice problems imposes much more mental work than reviewing worked examples. However, skipping study of worked examples may impose too much cognitive load on the learners when they try to jump into practice assignments right away. (See Guzdial blog entry.) Studies have shown that students who learned by doing took twice as much time to learn as students who learned from worked examples (Mayer, 2008, chapter 9). Students also benefit more with worked examples if they generate explanations as they study the worked examples (meta-cognitive skill development).

A compromise between worked examples and actual practice is a completion example where some of the steps are demonstrated in a worked example and the other steps are completed by the learner as in a practice problem.

It should be noted that as learners gain expertise, worked examples actually become detrimental and they are better off working all the problems. The worked examples can become redundant. This is where FWE will be most useful.

Reference:

Clark, R.C., Nguyen, and F., Sweller, J. (2006). Efficiency in Learning. San Francisco: Pfeiffer. (Chapter 8).

Gray, S., Clair, C., James, R., Mead, J. (2007). Suggestions for Graduated Exposure to Programming Concepts Using Fading Worked Examples. International Computing Education Research Workshop, Proceedings of the third international workshop on Computing education research. pp 99-110.

Mayer, R. E. (2008). Learning and Instruction (2nd ed). Upper Saddle River, NJ: Merrill Prentice-Hall.

Sweller, J. (1988). Cognitive Load During Problem Solving: Effects on Learning. Cognitive Science. 12(2).