# Inventive Learning

These projects have the goal of supporting the development of early knowledge.

# A Time for Telling: Online Statistics

There is tremendous excitement about the promise of on-line learning courses, often times centered on video-recorded lectures and automatically graded problem sets or essays. The major appeal is the dissemination of high-quality knowledge that is available and affordable to all. Yet, hidden in this vision is an unpleasant reality; current online courses are very efficiently disseminating one of the worst models of instruction - sitting and listening to a lecture, and then solving a set of procedural problems. Flipped instruction, which sends the videos to watch at home (oh joy), and then uses class time for solving problems is a weak solution. Ideally, on-line learning could break from the legacy pedagogies of the past to create more effective learning.

The on-line statistics course is a demonstration project that shows there is a new model of pedagogy that can complement and massively enhance the value of lectures, readings, and problem sets. The basic proposal is that if students first try to induce (invent) their own statistical methods from very well-organized data, it will prepare them for future learning from the lecture and beyond. In this model, students engage in problem solving, before they hear the relevant lecture, and not just after.

For instance, in the figure, students receive four data sets. Each one represents a different baseball pitching machine. Each black circle indicates where a pitch landed when the machine was aimed at the X in the center. Students need to come up with a "reliability index" for each pitching machine. This activity helps students understand the key issues in measuring variability, and it prepares them to understand the standard deviation formula more deeply.

In prior research, we have demonstrated that there are ways to create a 'time for telling,' and we have shown that 'telling too soon' is counter-productive. Here, we cash out this research by making a break the mold model of on-line instruction for one of the most problematic topics in social sciences, namely statistics. If successful, the course will serve as a model for a new way of creating on-line (and brick and mortar) instruction that can far exceed the learning outcomes of the current approach of "tell and practice."

# Relevant publications:

- Schwartz, D. L., Chase, C. C., Oppezzo, M. A., & Chin, D. B. (2011). Practicing versus inventing with contrasting cases: The effects of telling first on learning and transfer. Journal of Educational Psychology, 103(4), 759-775.
- Himmelberger, K., & Schwartz, D. L. (2007). It's a homerun! Using mathematical discourse to support the learning of statistics. Mathematics Teacher, 101(4), 250-256.
- Schwartz, D. L. & Bransford, J. D. (1998). A time for telling. Cognition & Instruction, 16, 475-522.