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Self-efficacy in non-routine problem solving in STEM education


Dr Tanya Evans, Dr Mike Thomas and Dr Sergiy Klymchuk have designed an intervention to examine whether employability prospects for STEM students studying mathematics could be improved.


Read their original paper: https://doi.org/10.1080/07294360.2020.1818061


Read more in Research Outreach


Image credit: Inked Pixels/Shutterstock





Hello and welcome to Research Pod. Thank you for listening and joining us today. In this episode we will be looking at the research of Dr Tanya Evans and Emeritus Professor Mike Thomas from the University of Auckland and Associate Professor Sergiy Klymchuk from Auckland University of Technology. The team examines the employability prospects of students in Science, Technology, Engineering and Mathematics, or STEM, education.


Have you ever heard of the ‘cat on a ladder’, ‘prisoners and hats’, or the ‘train collision’ problem? Puzzles such as these are used by many companies as part of their job interview process in order to evaluate candidates’ problem-solving skills. They consider that the ability to solve puzzles relates to the creative thinking required to solve innovative real-life problems.


Dr Tanya Evans, a lecturer in the Department of Mathematics at the University of Auckland, together with Dr Mike Thomas, Emeritus Professor of Mathematics Education, also from University of Auckland, and Dr Sergiy Klymchuk, Associate Professor of Mathematics at Auckland University of Technology, have developed an intervention that examines whether the employability prospects of STEM students studying mathematics could be improved.


The occupations most in demand in today’s labour market include data scientists, app developers and cloud computing specialists – jobs that didn’t exist ten, or even five years ago. The World Economic Forum predicts that technical breakthroughs, shifting the frontier between tasks performed by humans and those performed by machines and algorithms, will transform global labour markets. If recent graduates are to succeed in such a rapidly evolving employment market, they will have to demonstrate both intellectual flexibility and their ability to adapt to novel settings. Globally, over the past decade, focus on the identification of graduate attributes and employability skills has intensified, with employers highly valuing attributes including those referred to as the ‘C’ skills: Creativity, often associated with lateral thinking, Curiosity, and Critical thinking.


Some university educators consider producing well-rounded individuals with higher thinking skills to be of paramount importance and put less emphasis on students’ employability. While training students for employment is not the only aim in gaining a university education, the value of their qualification in terms of employability is a major concern for students. This has prompted the consideration of graduate attributes within a number of higher educational settings and highlighted the importance of transfer of learning, meaning the ability to apply previously acquired knowledge and skills in novel problem-solving situations.


The team refer to previous work done by researchers Pugh and Bergin, who, in a paper published in 2006, comment that “without transfer, the relevance of formal schooling is limited.” Their research explored the influences of motivation on cognitive processes related to transfer of learning and recommend that future research utilises the four motivational constructs: achievement goals, interest, self-efficacy, and intentional transfer. This synthesis of the motivational influences on transfer guided the research team towards the tool of their analysis, the motivational construct self-efficacy.


In the context of transfer, self-efficacy refers to confidence in the ability to do or learn a skill that can successfully transfer to another domain. Reviewing the literature, the researchers found that self-efficacy is positively associated with transfer of learning via mechanisms that include its influence on cognitive engagement and persistence.


In addition to self-efficacy specific to mathematics, the researchers conceptualised a novel construct, lateral thinking self-efficacy, which they defined as “a learner’s confidence in their ability to solve non-routine problems”. This relates to the creative thinking ability required to solving innovative real-life problems in the workplace. It is therefore pertinent in transfer of mathematical learning to novel domains.


This research employed a case study conducted at two universities in New Zealand. The research team collaborated with lecturers to design and implement an intervention in two second-year mathematic courses. They aimed to design an intervention that could be easily integrated into existing undergraduate mathematics education, therefore requiring only a small developmental investment.


The courses were delivered over a 12-week semester comprising three 50-minute lectures per week. In the middle of each lecture, the lecturer would ask students to attempt to solve an unfamiliar non-routine problem. These non-standard, unstructured questions were presented in an entertaining way and the students were free to work individually or in small groups. A brief discussion of the solutions would follow with the activity taking 2-5 minutes to complete.


At the end of the semester, a student survey was conducted in class in the form of a paper-based questionnaire made up of ten questions. Three questions were on demographics, with the others exploring the interplay between the students’ lateral thinking self-efficacy, performance, gender, prior achievement, together with their feelings, beliefs and attitudes towards non-routine problem solving. The students were also encouraged to provide open-ended answers together with any unsolicited comments that they wanted to add. In total, 137 students – 81 males, 53 females, 3 unidentified – from two second-year mathematics courses participated in the study, with a response rate of 97% of those present.


A sequential two-phase data analysis approach was used to reduce reliance on Likert-style instruments and move toward a greater use of narratives. The first phase involved the qualitative analysis of students’ responses to ascertain their views on various aspects of the intervention. The second phase involved the use of a quantitative technique to investigate frequency counts for each of the themes identified in phase one. From these, the relative frequency of differential responses to the phase one themes from students with high versus low lateral thinking self-efficacy was determined.


The results suggest that the attitude profiles of students with high and low lateral thinking self-efficacy differ significantly towards non-routine problem solving with respect to three dimensions that span their affective domain: vision, enhancement utility, and emotional disposition. The affective domain describes people’s attitudes to capture how they deal with things emotionally and includes their feelings, beliefs, motivations, and values.


The analysis revealed that significantly fewer students with high lateral thinking self-efficacy viewed non-routine problem solving as a challenge when compared with those with low lateral thinking self-efficacy. Significantly more students with high lateral thinking self-efficacy had positive emotional dispositions towards non-routine problem solving than those with low lateral thinking self-efficacy. Likewise, significantly more students with high lateral thinking self-efficacy had positive ratings on both the Enjoyment theme and the Engagement theme than those with low lateral thinking self-efficacy.


Interestingly, the students’ prior performance in mathematics did not appear to affect their confidence in solving non-routine problems. There was, however, a significant association between students’ confidence in solving non-routine problems and their performance in solving them.


The study uncovered a significant difference between genders when lateral thinking self-efficacy was observed. The proportion of males reporting confidence in solving nonroutine problems was significantly greater than the proportion of females, despite no significant association between gender and self-reported non-routine problem-solving performance. This important distinction raises key questions about equity with regard to employability attributes and prospects for females in particular. The especially unfortunate part of these inferences is how heavily they factor into crucial decisions such as the types of jobs females choose to apply for, in lieu of actual facts. Could an implication be that female STEM graduates are less likely to apply for jobs at technology companies such as Microsoft, Google and many others that use puzzles as part of their job interviews? This may explain the ‘leaky-pipeline’ phenomenon that is evident in the underrepresentation of women in STEM fields.


Previous research has demonstrated that students’ emotions can have a profound effect on both their academic engagement and performance. The impact of positive and negative moods on problem solving has also been observed. Experiments suggest that a positive mood promotes flexible, creative, and holistic ways of solving problems, with students relying on generalised, heuristic knowledge structures. Taking these considerations together with the findings of this study, the research team postulate that targeting an activation of positive emotions during the stages of non-routine problem solving could improve lateral thinking self-efficacy. They also suggest that ensuring that future graduates’ experience the enjoyment of understanding a solution, rather than feeling frustrated when a solution is not explained well, would moderate their epistemic emotions during similar interventions.


Further research into non-routine problem solving in STEM education, funded by the Teaching and Learning Research Initiative, New Zealand, is being conducted by a larger team led by Associate Professor Klymchuk.


That’s all for this episode – thanks for listening, and stay subscribed to Research Pod for more of the latest science. See you again soon.

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