PhD Life · Uncategorized

PhD Friday Week 1 Synthesis

For the past few months, I’ve been in a rut regarding my research topic. On one hand, I feel like I am just scratching the surface of an immensely large body of literature on analogy and comparison for learning in laboratory and classroom settings, which makes is both overwhelming and motivating. But on the other hand, I also feel like pursuing my current line of research is too theoretical and not preparing me for the kind of career I want to impact learning beyond the classroom by designing educational technology.

After reading the papers I summarize below, I feel like I’ve finally had a breakthrough that can combine both my theoretical and applied interests. In addition to helping me think of some new research ideas, I think the learning principles discussed are relevant to teachers and learners outside of academia. I look forward to discussing any ideas that the following article summaries make you think about!

Gamification of Cognitive Training 

Two different protocols of working memory training using an N-back task led to mostly similar improvements and performance on transfer tasks. As expected, participants reported being more engaged and expending more effort in the gamified condition of the N-back task which was designed to have more motivational elements than the non-gamified condition. Participants in the gamified condition showed greater improvements in working memory after four training sessions than did participants in the non-gamified condition.

My Two Cents: This paper harkens back to an early stage of my research career when I was completing an honors thesis on the psychological construct of executive function, which includes working memory, inhibitory control, and switching ability (which is kind of a combination of the other two). Although I focus less on these psychological constructs now, the principles for what makes a good game are relevant citations for me to follow up on when I design my own educational software.

Variation Theory

The authors outlined some tenets of variation theory that inform the selection of examples for instructional purposes. Variation theory recommends a progression of examples that first enable contrast, then generalization and then fusion. What this means is that students need to see non-examples as well as examples to illustrate the important point that a teacher wants them to learn. For example, it is hard to know what defines a triangle until a triangle is contrasted with a square or a circle. Then after seeing several examples of triangles being contrasted with other things, you learn each of the properties that makes a triangle special. Combining all of these triangle properties helps you understand the concept of a triangle. In the rest of the paper, the authors detail what is made possible to be learned (different from what is actually taught and what from students learn from a lesson) through a teachers’ selection of examples and tasks in two different lessons on solving equations.


My Two Cents: This is where my breakthrough started to materialize even though the paper was still very much focused on in-classroom learning. Variation theory is basically what all of my ideas about why comparisons are important boils down to and I have yet to see it explicitly implemented in educational technology.

On top of giving a very applied explanation of how variation theory might be used to plan a lesson, this article happened to be in a special issue that includes other articles I was excited about: applying principles of cognitive psychology to teaching. Even though the other articles in the special issue barely mentioned variation theory, they all seemed to fundamentally depend on these ideas.

Example-based learning, self-explanation and comparison

Example-based learning is the idea of providing students with a set of examples that helps them develop the common procedural or conceptual thread between them. Different from traditional math instruction in which a teacher demonstrates solving several math problems in the same way, example-based instruction would be more akin to a student looking over the worked out examples and the explanations for each step in a textbook. In his article on example-based learning, Renkl made the case that this technique is most effective when students engage in self-explanation while they are studying the worked examples, especially when students are new to the material.

Self-explanation was a separate technique further outlined in another article by Rittle-Johnson, Loehr & Durkin (2017). In contrast to a common practice in several math classrooms in which the teacher has the main responsibility for explaining the reason for a problem-solving step or the principle that two problems have in common, self-explanation is when students do this work themselves. The greater mental effort expended by the student when self-explaining helps improve retention over hearing someone else explain. However, students need to be trained in how to do high-quality self-explanations. Unfortunately, not much detail was provided on how to do this besides

These two techniques were combined in a chapter on comparisons more broadly. Durkin, Star & Rittle-Johnson (2017) acknowledge that there are several types of comparisons that are beneficial for learning depending on what is being compared and what question is asked. Comparing an incorrect solution with a correct solution (an example of example-based learning) is beneficial but is more beneficial for students with higher prior knowledge who are better able to distinguish the important differences and figure out the reasons why one is correct (self-explanation). For students who are less experienced with material to be taught, it is more helpful to compare the same solution method for multiple problems in order for them to gain confidence with one method before introducing them to alternative methods for solving similar problems.

My Two Cents: I see each of these techniques relying on variation theory. In order to have effective example-based learning, examples that highlight different and similar features need to be carefully selected. Prompting students to make comparisons helps draw attention to these differences and similarities as well as encourages them to explain their reasoning for why these differences and similarities exist.

Which principle is most relevant to your teaching and learning experiences?


Durkin, K., Star, J. R., & Rittle-Johnson, B. (2017). Using comparison of multiple strategies in the mathematics classroom: Lessons learned and next steps. ZDM, 1-13.

Kullberg, A., Kempe, U. R., & Marton, F. (2017). What is made possible to learn when using the variation theory of learning in teaching mathematics?. ZDM, 1-11.

Mohammed, S., Flores, L., Deveau, J., Hoffing, R. C., Phung, C., Parlett, C. M., … & Zordan, V. (2017). The benefits and challenges of implementing motivational features to boost cognitive training outcome. Journal of Cognitive Enhancement, 1-17.

Renkl, A. (2017). Learning from worked-examples in mathematics: students relate procedures to principles. ZDM, 1-14.

Rittle-Johnson, B., Loehr, A. M., & Durkin, K. (2017). Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles. ZDM, 1-13.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s