Self-regulation in Vector Calculus

Project introduction and background information

Since the 2019-2020 academic year, the course Vector Calculus for AT, EE and TN has been assessed according to open book, technology-mediated principles. Students have access to course notes and can use graphing software and online calculators. The emphasis has shifted from the memory and computation requirements of a traditional vector calculus course towards higher order thinking skills and greater alignment with the real-world technical workplace.

To set good assessment items, design principles were formulated, with decision making as the underpinning principle. A well designed vector calculus problem can be solved in multiple ways. By seeking to identify characteristics of curves and vector fields and by employing the three great theorems of vector calculus, students can choose between solution strategies of greater and lesser complexity.  

Despite aligning the teaching and resources of the course with the principle of decision making , teachers have observed that the students show poor self-regulatory behaviour. If a problem has an obvious solution strategy, the majority or significant minority of the students tend to choose that strategy instead of considering whether other, simpler, solution strategies exist.

Objective and expected outcomes

It has been shown that writing about one’s problem solving process significantly aids the “understand the problem” stage of problem solving. The metacognitive demand of the writing process to “think about one’s thinking”, encourages deeper engagement than might otherwise occur. In problems with multiple possible solution strategies, this deeper engagement would ideally encourage information acquisition, making connections and making goal-oriented decisions.

In this project, all students taking the course were invited to a pre-exam extra support session, dubbed a Master Class. The students would received an intensive class on decision making. Whereas the four standard lectures in the course cover specific topics (for example line integrals, or Stokes’ Theorem) the Master Class was focussed on decision-making, drawing on all syllabus topics, making use of decision trees and illustrating how characteristics of specific curves, surfaces and fields can offer opportunities for problem solving. Thereafter the students solved two vector calculus problems, under experiment-control conditions related to the step of "making a plan".

Personalised formative feedback was provided to every student. Data has been collected on problem solving behaviour and analysis will continue throughout 2024.

Results and learnings

After collecting the data, we needed to code it. For this we created rubrics for coding the students' written plans as well as their problem solving progress. Coding the data took far longer than expected. Only after the data were coded could we proceed with analysis.

We have some results, which we summarise as: writing a plan seems to make the students more confident about their problem solving, with less shifting between strategies during problem solving. However, writing a plan had no significant effect on their problem solving proficiency nor on their ability to recognise an inappropriate strategy as such. Also, writing a plan appeared to lower the likelihood of completing the second, harder problem.

We are busy writing up these findings for a conference in November. The paper will be submitted in early July, hopefully, and will be published in November. In the meantime, we shall continue analysing the data, because there may be more to be found. In particular we shall be looking at students' problem solving in the exam. 

I regard the project as still ongoing, at least for a few months, so will include more detail at a later time.