*Proceedings of the Canadian Engineering Education Association*.

Miller-Young, J.E. (2013). Calculations and expectations: How engineering students describe three-dimensional forces.

*The Canadian Journal for the Scholarship of Teaching and Learning 4*(1), Article 4, 1-11.

I have grouped these two papers together since they are almost the same. The first is a 2010 conference paper and the second is a 2013 journal paper which includes all the 2010 work as well as a bit more data. The study was interested in digging into the details of how students visualise three dimensional statics problems when what they are presented with is a 2-d diagram. The data collected was students’ think-aloud processes of answering two questions, one without context and the other in a real-world context. The 2013 paper also included data on a quiz question which was part of a standard course assignment. All three problems required that the students see the page as the given vertical coordinate plane (

*xy*in the three problems) and the third axis (

*z*) extending out of the page in the positive direction. Points with a negative

*z*-coordinate, in other words, are behind the plane of the page.

The students seemed to find the problems relatively difficult. The author found three main themes in student errors. (1) The students struggled to visualise points behind the plane of the page or vector which extended behind the plane of the page. The two-dimensional drawing on the flat page had to be visualised as a three-dimensional collection of vectors and the students found that particularly tricky for vectors extending backwards relative to their gaze. (2) The students did not always use the provided context to help them visualise the problems. One of the problems involved a pylon with guy ropes attaching to the ground, which was idealised as the flat

*xz*-plane. All the ends of the guy ropes in this problem were on the

*xz*-plane and had a

*y*-coordinate of zero, yet some students struggled to see that. (3) The students reached too quickly for equations to try and answer questions even when there was not enough information to answer the question that way. The tendency to calculate something using a formula is ubiquitous across all maths and physics teaching and is no surprise. This final data point serves only to add to the depressing mountain of similar results.

*Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understandings and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.*