Today I came across this 2005 dissertation written by Elizabeth Kaczmarczyk: “The acquisition of intellectual expertise: A computational and empirical theory.” The reason this came up in my search because the study was performed using Calculus content.
Here’s the abstract:
In order to develop intellectual expertise, a novice learner has to acquire cognitive abilities seen in experts: They need to be able to categorize problems before solving them, and be meta-cognitive about their learning, so that they can select the best problem-solving strategies. The process by which learners acquire these abilities is not well understood. The goal of this dissertation is to understand how instructional delivery methods can help learners acquire the cognitive abilities necessary to become experts. The study was motivated by initial structured interviews with mathematics faculty, which led to the formulation of three hypotheses: (1) Traditional sequential delivery methods inhibit learning and retention; (2) Integrated delivery methods increase learning and retention; (3) Incrementally increasing the complexity of the material will lead to the best performance. An artificial neural network was then used to test these hypotheses computationally. The network confirmed the hypotheses, demonstrating that an Incremental delivery leads to better learning than Drill and Test learning or Fully Integrated learning. These computational conclusions led to the prediction that an Incremental Learning delivery method will encourage meta-cognitive abilities necessary to achieve expertise. This prediction was tested experimentally on human subjects. Qualitative and quantitative data from the human study verified that (1) Incremental learners develop the most effective study and test taking strategies; (2) Incremental learners have the best conceptual development; and (3) Incremental learners have the most positive reactions to learning. I hope that these results will benefit society, because by changing the way we educate students, more learners can pursue advanced study, and use their expert, creative insights to address society’s most challenging problems.
The abstract mentions the subject of meta-cognitive abilities (a topic I am very interested in). Certainly, there are a lot of reasons to follow the link to the full-text article and take a look at this one.