Measuring the mathematical problem solving and procedural skills of students in an Irish higher education institution – A pilot study

Abstract

In 2010 the Irish second level mathematics curriculum underwent a period of significant change when a new mathematics curriculum was introduced. Some preliminary research has been carried out into the impact, if any, that this mathematics curriculum is having on students mathematics performance which have suggested that students' procedural skills are declining year on year however their problem solving skills may have improved (Treacy and Faulkner 2015). Additional research in this area also highlighted that students willingness to engage in problem solving activities may have improved (Prendergast et al 2017). However preliminary analysis on the impact of the reformed mathematics curriculum, if any, on students' performance in higher education noted that further research was needed in this area to definitively establish what is happening. This research therefore aims to explicitly determine whether the procedural and problem solving skills of beginning undergraduates are changing over time as a result of the reformed mathematics curriculum introduced in second level education. A paper based diagnostic test designed and developed is used in an attempt to determine this. This paper will detail the piloting of this diagnostic test with a group of higher education students in the Irish context.

Profiling mathematical procedural and problem-solving skills of undergraduate students following a new mathematics curriculum

“…Treacy and Faulkner (2015) carried out one of the first pieces of research to investigate whether there were any changes in students' mathematical performances after the introduction of PM. Their research examined students' basic mathematical skills on entry to undergraduate education and built on the work of Gill et al (2010) and Faulkner et al (2014Faulkner et al ( , 2020, all of which reported steady declines in students' basic mathematical skills over time. Although Treacy and Faulkner (2015) also found that the decline in students' basic mathematical skills on entry to higher education had continued after the introduction of PM, they outlined an indication that students' problem solving skills had improved over this period of change.…”

“…However, this is not a recently reported issue. The challenges that many students face when trying to apply the mathematics they have engaged with in a formal education setting to a work place setting, or indeed for the benefit of further study of formal mathematics, is something which has been reported in the literature for a long time (Faulkner et al, 2020;Hutton, 1998;Treilibs, 1979).…”

“…In addition to these two studies, the pilot study for the research that will be reported in this paper used a new diagnostic test developed by the authors (the methodology of which will be outlined later in the paper) to further examine whether students problem solving skills had improved following the introduction of PM. The study, which compared students problem solving and procedural skills in mathematics, found that students procedural skills were statistically significantly better than their problem solving skills (Faulkner et al, 2020). This study had a relatively small sample size (n = 87) and examined students from engineering and access education only.…”

Exploring Grade 8 Students’ Errors When Learning About the Surface Area of Prisms

“…For example, students' lack of knowledge in a particular concept is what happens in most South African schools where rote learning is promoted just for students to pass the tests and examination without conceptual understanding (Mahlaba, 2020). Rote learning generally leads to students experiencing difficulty to apply simple mathematical concepts to applied scenarios (Faulkner, Breen, Prendergast, & Carr, 2020).…”

“…Both groups, could not use the correct mathematical methods. Research revealed that such errors are due to either students' misunderstanding of mathematics questions or/and difficulty in application of simple mathematical concepts to a new scenario (Faulkner et al, 2020;Fitriani, Turmudi, & Prabawanto, 2018). Such errors can be interpreted as transformation errors.…”