Using examples skillfully and appropriately to illustrate complex ideas and procedures is integral to great teaching, no matter what discipline we’re talking about. In math, examples help to demystify the steps that mathematicians take to solve problems. In foreign language class, examples help to bring permanence to sentence constructions that are slippery and transient if only presented orally. During novel study, English teachers can help students to grasp the complex interactions between events, places, and characters by weaving in lots of carefully constructed examples. While all teachers use examples to some extent, I suspect that many teachers have never been trained on research-based principles of example-based learning. The fact that teachers continue to be asked to learn the craft of teaching through trial and error is one of the greatest tragedies of education.

In my last post, I shared Milou van Harsel and colleagues’ principles of example-based learning. As a framework for how to introduce a topic and slowly increase challenge, it works very well. In this post, I wanted to delve a bit deeper into each of their principles and give some, erm… examples, of what the principles might look like in everyday teaching practice.

Example-based-learning-principle

Most learning situations consist of problems to solve (Merrill, 2002). In science, a “problem” could be learning how to control variables during an experiment, in orchestra how to master a piece of music in advance of the concert, and in writing how to craft an introductory paragraph. Without someone available to give examples, or “E” for short, students have no choice but to learn through unguided problem solving, or “P”. We could represent a four-task problem solving sequence without any example-based guidance as “PPPP”. As I’ve written many times before, the evidence suggests that “PPPP” is not an efficient or effective way to learn (Sweller, 2021). van Harsel and colleagues’ previous work indicates it’s unlikely to be very motivating as well (pg. 2, 2021).

The Example-based-learning principle states that replacing a substantial number of problems with examples helps novices to learn more, with less time and effort, than attempting problems without any support from examples. Instead of withholding examples from students (i.e., PPPP), it would be more effective to replace problem solving with examples, such as by frontloading examples (i.e. EEEP) or alternating examples with problems (i.e., EPEP). As students grow in expertise, teachers should slowly fade out examples so that students end the instructional sequence with extensive practice of the material.

Example-study-first-principle

What works better, giving students a problem to solve first before allowing them to see an example, or giving students an example first before asking them to solve a problem? This is a question that continues to befuddle researchers. In the productive failure literature (Kapur, 2016), solving a problem first is thought to help students see the gaps in their own knowledge, which “prepares” them for example study. In cognitive load theory research (Ashman et al., 2020), studying an example first is thought to direct learners’ limited working memory resources to schema acquisition rather than guess-and-check problem solving. Once the schema is acquired through example-first study, this knowledge can be brought to bear to solve the subsequent problem.

As far as I’m aware, whether problem solving first (i.e., P,E) or example first (i.e., E,P) works better is still not set in stone, although there may be a slight advantage for E,P (van Harsel et al., 2020). Ashman and colleagues (2020) found that P,E might work better if the material is relatively simple (i.e., fewer interacting elements to deal with in working memory for the learner’s level of expertise) and that E,P will likely work better for teaching more complex material. The Example-study-first-principle compels teachers to consider starting their instruction with a well-crafted example, especially if the material is new and often challenging for students.

Lowest-level-first-principle

Imagine that you are teaching a sequence of lessons with, say, three levels: Level 1, Level 2, and Level 3. Maybe you are teaching the subtraction algorithm, and Level 1 is subtraction of two digit numbers without regrouping, Level 2 is subtraction of three digit numbers without regrouping, and Level 3 is subtraction of two digit numbers with regrouping. Would it ever make sense to start the sequence of lessons with Level 3 and then jump back to Level 1?

Of course not. The Lowest-level-first-principle is intuitive and straightforward: teachers should design lesson sequences that begin with the task at the lowest level of complexity.

Simple-to-complex-principle

What follows from the previous principle is that we should gradually increase the level of task complexity as students’ skill increases. When increasing the complexity of tasks, teachers should be tuning in to the rate that their students are successfully completing the tasks before increasing the complexity further. Rosenshine (2012) suggested that the best teachers achieve an 80 percent success rate in their classes, which shows that students are learning while also being challenged. Gradually introducing new difficulties, such as changing how the material looks on the surface or varying the conditions of practice, may help to keep the challenge – and cognitive load imposed by the task – within the limits of students’ current capabilities (Bjork & Bjork, 2009).

Start-each-level-with-example-principle

The final principle of example-based learning, the Start-each-level-with-example-principle, rounds out the list by suggesting that learners receive examples at the start of each new level. Essentially this last principle, alongside the others, provides support for an I do, We do, You do sequence of learning material, which is the hallmark of proactive, explicit teaching. In my recent presentation on cognitive load theory, I depicted this sequence, which is supported by research into the guidance fading effect (Paas & van Merriënboer, 2020), with the following slide:

In summary

Van Harsel et al.’s principles of example-based learning are a helpful guide for how to sequence and interleave examples into instruction. Teaching with examples helps to demystify the material and embed it in students’ long-term memories, which enables them to become expert problem solvers. Trying to get students to solve problems on their own with minimal instructional support may be trendy, but it’s a recipe for cognitive overload and deficient learning. On a final note, these example-based learning principles make it clear that teachers need to be highly aware and adaptive to the changes in expertise of their learners. Ongoing short-cycle formative assessment is key to ascertaining when in a sequence of instruction one, two, or more examples is needed, and when students can be set free to practice with the material through independent problem solving.

– Zach Groshell @mrzachg

References

Ashman, G., Kalyuga, S., & Sweller, J. (2020). Problem-solving or explicit instruction: Which should go first when element interactivity is high? Educational Psychology Review, 32(1), 229–247. https://doi.org/10.1007/s10648-019-09500-5

Bjork, E. L., & Bjork, R. A. (2009). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. In M. A. Gernsbacher & J. R. Pomerantz (Eds.), Psychology and the real world: essays illustrating fundamental contributions to society (pp. 55–64). Worth Publishers. https://doi.org/10.12968/sece.2018.14.7

Kapur, M. (2016). Examining Productive Failure, Productive Success, Unproductive Failure, and Unproductive Success in Learning. Educational Psychologist, 51(2), 289–299. https://doi.org/10.1080/00461520.2016.1155457


Merrill, M. D. (2002). First principles of instruction. Educational Technology, Research and Development, 50(3), 43.

Paas, F., & van Merriënboer, J. J. G. (2020). Cognitive-load theory: Methods to manage working memory load in the learning of complex tasks. Current Directions in Psychological Science, 29(4), 394–398. https://doi.org/10.1177/0963721420922183

Sweller, J. (2021). Why Inquiry-based Approaches Harm Students’ Learning. Analysis Paper (Centre for Independent Studies), 24(August), 15. https://www.cis.org.au/publications/analysis-papers/why-inquiry-based-approaches-harm-students-learning/

van Harsel, M., Hoogerheide, V., Verkoeijen, P., & van Gog, T. (2020). Examples, practice problems, or both? Effects on motivation and learning in shorter and longer sequences. Applied Cognitive Psychology, 34(4), 793–812. https://doi.org/10.1002/acp.3649

van Harsel, M., Hoogerheide, V., Verkoeijen, P., & van Gog, T. (2021). Instructing students on effective sequences of examples and problems: Does self‐regulated learning improve from knowing what works and why? Journal of Computer Assisted Learning, June, 1–21. https://doi.org/10.1111/jcal.12589

4 thoughts on “Demystifying Learning through Examples

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