Paul Hernandez-Martinez | Swinburne University of Technology, Hawthorn (original) (raw)

Papers by Paul Hernandez-Martinez

Frontiers in Education, 2024

People are more motivated to put effort into learning when they know they will be able to put the... more People are more motivated to put effort into learning when they know they will be able to put the learnt content to use. These relevance perceptions play a motivating role in the learning of mathematics, a subject renowned for its abstraction, hard examinations, and usefulness in many fields in society (research, industries, etc.). In this article, we describe a study on upper secondary students in an advanced mathematics course and their perception of the relevance of mathematics in future professions, in particular regarding two concepts in their curriculum (logarithms, trigonometry). We defined relevance as a connection between an object (relevance of what?), a subject (relevant for whom?), an asserter (relevant according to whom?), and a purpose (relevant to what end?).
The aim of the study was to know (1) what relevance perceptions students held regarding the advanced abstract mathematical concepts, and (2) how students can develop these considering that students do not yet know exactly what future is ahead of them. We interviewed pairs of students (n = 14, 17–19 years old) in two parts. The first part of the interview revealed that students learned mathematics within a traditional school culture that emphasized practice-and-drill of pure mathematics and that did not in any way inform students about the use of mathematics in research and workplaces. After exposing students to authentic applications of logarithms and trigonometry, the second part of the interview showed the power of imagination when it connected students to future professions for which mathematics was relevant. Instrumental in effectively prompting students’ imagination were visualizations showing applications of the mathematical concepts within workplace contexts. Drawing on Leont’ev’s version of Activity Theory, we theorize students’ assertions of the relevance of mathematics through the dialectics of self and collective (relating one’s own goals and more general motives), the dialectics of use-value and exchange-value (needing mathematics for later life or for examinations), and the dialectics of mathematization and de-mathematization (while mathematics is used in many workplaces, it is hidden in instruments).

In this paper we analyse the activity of a group of engineering undergraduate students while work... more In this paper we analyse the activity of a group of engineering undergraduate students while working on a mathematical modelling task. Using Cultural-Historical Activity Theory as analytical framework, we focus our attention on their social interactions to understand how these mediate the collective sense making of the group and determine in great part the outcome of the activity. We conclude that a key factor to students’ mathematical learning in collaborative tasks is the quality of peer interactions which stems from students’ competences, such as communicative and inter-personal skills.

•Taking a socio-cultural perspective of affect in education, we use observations of two groups of... more •Taking a socio-cultural perspective of affect in education, we use observations of two groups of undergraduate engineering students to explore the role of emotions on the students’ mathematical thinking and learning while working collaboratively on a mathematical modelling coursework assignment outside the classroom. Our analysis revealed complex interrelations between patterns of emotions and aspects of mathematical learning. We conclude that ‘negative’ feelings might sometimes lead to positive consequences on the activity of individuals and conversely, that ‘positive’ feelings do not necessarily lead to positive outcomes. Hence, pedagogical practices should aim to foster a range of emotions that can open possibilities for students’ success. Research into the role of emotions (and affect in general) in mathematical thinking and learning has gained considerable interest in the past few decades. However, most of this literature has studied emotions from a psychological perspective, often seeing emotions as separate from an individual’s cognition. More recently, there has been a shift in perspective, with an associated effort to explain affective issues from a socio-cultural view (Roth, 2007). In this paper we take the latter perspective. Our aim is to study the role of emotions in the mathematical (social) activity of undergraduate engineering students working in small groups. Here, we analyse two separate groups of four students each, working on a group mathematical modelling coursework assignment (Figure 1) as part of a second year 12-week compulsory engineering mathematics course at an English researchintensive university. The course was designed according to ideas on mathematics collaborative learning, mathematical modelling and the development of employability skills (e.g. effective communication, presentation skills, et cetera). Our analysis focused on the students’ emotions expressed within these collaborative situations, and the role that these affective factors had in the students’ mathematical activity. Hence, our research questions were: (1) How and why emotions emerge within students’ group work while working on a mathematical modelling assignment? and (2) What is the role of emotions on these students’ mathematical thinking and learning? THE WIND CHILL FACTOR If you ever have waited in a bus stop or taken a walk during a cold winter day then you know that it feels colder when the wind blows. This cooling sensation is caused by the combined effect of temperature and wind, and is known as the wind chill. Your group’s task is to come up with a mathematical formula (a model) to calculate the wind chill. You have to use the modelling cycle seen in lectures to explain your understanding of the problem and the assumptions that you made in order to arrive at your model. Once you have your model, you have to argue how you would test it and how you would refine it.

Education and Information Technologies

University students’ expectations of digital technologies in their studies are greatly influenced... more University students’ expectations of digital technologies in their studies are greatly influenced by their previous exposure both within the secondary school classroom and in their private lives. These expectations often play a powerful role in their approaches and learning strategies in their first-year university classes. In this work, we investigated students’ expectations and utilisation of digital technologies in their transition from high school to tertiary studies. A survey encompassing the Expectancy-Disconfirmation Paradigm was conducted amongst second year students across the university. The results showed students expected to use advanced IT technologies and equipment at university. The high expectations were similar regardless of demographic parameters, such as gender, school type or field of studies. The findings also indicated that most students perceived little disconnection between the technology they used in high school and that of university. The majority of studen...

Mathematical modelling (MM) is a powerful tool used by scientists and engineers to solve importan... more Mathematical modelling (MM) is a powerful tool used by scientists and engineers to solve important problems for humankind. MM opens many possibilities for inquiry and has been included in the PLATINUM project as one of the Intellectual Outputs, IO5 (see Chapter 5 for the complete list). We consider MM an important part of the teaching and learning process. We believe that helping to develop students’ modelling competencies we equip them with a valuable understanding of practical and theoretical concepts, prepare them for a life-long learning, and form them as critical citizens. This chapter is organised as follows. In Section 8.2, we share our views on why we teach MM, noting that our teaching practices are adapted differently to suit local educational contexts (types of students, programs of study, institutional traditions, constraints, etc.). We proceed with the discussion of what are the most important to us characteristics of Inquiry-Based Mathmatics Education (IBME) as a teaching approach. To explain authors’ understanding of how the MM relates to IBME, the concept of ‘active knowledge’ is introduced in Section 8.3. The key idea of this concept is that in response to the use of IBME in the classroom students’ engagement with MM activates previously acquired knowledge and facilitates its efficient use. In Section 8.4, partners present examples of the use of MM within IBME practices and comment on how students activate their mathematical knowledge. Each example shows multifac�eted connections between MM and IBME. We reflect on the lessons learned from our contributions to the Intellectual Output IO5 in Section 8.5

The paper reports on the views and use of mathematical modelling (MM) in university mathematics c... more The paper reports on the views and use of mathematical modelling (MM) in university mathematics courses in Norway from the perspective of lecturers. Our analysis includes a characterisation of MM v ...

The aim of this paper is to describe and validate the development of two measures constructed to ... more The aim of this paper is to describe and validate the development of two measures constructed to measure AS students disposition (i) to enter HE and (ii) to further study mathematically-demanding subjects, which we regard as potentially significant variables in monitoring or even explaining students progress in to different studies in HE. The items for the scale were constructed on the basis of interview data, and drew on a model of disposition as sociallyas well as selfattributed. Drawing on Rasch analyses of pilot and ‘main’ data sets, we find that the two scales each produce healthy one-dimensional fits on what we take to be a ‘strength of commitment to enter HE’ and ‘disposition to study mathematically-demanding subjects further’ respectively. However, as a measurement scale for this sample in this context the former scale suffers from a ceiling effect: our sample are overwhelmingly committed to entering HE (at the early stages of AS level mathematics course anyway). To ‘correct’ for this, we added some harder items to the analysis at a later data point, and found (i) an item that improved separability of the instrument for the higher scorers, and (ii) a massively misfitting, hard item that is worthy of future research.

Journal on Mathematics Education

This paper aims to describe the development process of the Observation Protocol for Teaching Acti... more This paper aims to describe the development process of the Observation Protocol for Teaching Activities in Mathematics (POAEM) and to report the findings from the qualitative and statistical analyses used to provide evidence of validity and reliability of the information collected with the first version of the POAEM. As part of this development process, 20 teachers from Mexican primary schools were videotaped twice while teaching mathematics. The study assessed the reliability of the POAEM rubrics. Results showed that the dimensional structure of the instrument can be grouped in one factor. A generalizability study provided information on the different sources of error in the measurement, showing that the dimensions accounted for 78% of the variance. This study provides an exemplar of the design and validation of an instrument that can help other researchers develop their own instruments and data collection to generate evidence of validity and reliability in different sociocultural ...

Educational Studies in Mathematics

Collaboration between Mathematicians and Mathematics Educators is crucial in advancing knowledge ... more Collaboration between Mathematicians and Mathematics Educators is crucial in advancing knowledge on the teaching and learning of Mathematics, particularly in advanced Mathematics pedagogy. However, there is a need for the type of collaborations where Mathematicians and Mathematics Educators can find common ground, and the synergy of their expertise results in new, hybrid meanings and understandings that can benefit practice. This paper aims to help researchers from these communities come together by presenting a novel methodology for collaborative inquiry and qualitative data analysis—dialogical inquiry—based on Mikhail Bakhtin’s theory of dialogism. In this framework, “truth” is conceived as never finalised but always coevolving through dialogue that involves participants with different “voices” and “languages”. We describe the three principles that underpin dialogical inquiry: motivation, power balance and a process for solving disagreements. These three principles interact togeth...

Eurasia Journal of Mathematics, Science and Technology Education

The Delphi method (DM) was initially conceived as a forecasting technique whose results are based... more The Delphi method (DM) was initially conceived as a forecasting technique whose results are based on the consensus of a panel of experts. It has been used in many fields, assisting researchers, policymakers, and others in setting directions and future agendas. This study presents an application of the DM, with a broader interpretation of the notion of “expert” as a qualitative tool to explore gender issues in science, technology, engineering, and mathematics (STEM) education. Its aim is to analyze the use of the DM as a technique to achieve agreement among a group of early-career researchers from the UK and Mexico, who are not considered “experts” in the traditional sense. The other aim was to explore the advantages and disadvantages of using the DM in this context. We used three stages to collect information and reach a consensus. The first two were online activities, and the last consisted of a five-day face-to-face workshop. In the first stage, participants sent research question...

Education Sciences

During the COVID-19 pandemic, technology has been used to a lesser or greater extent to facilitat... more During the COVID-19 pandemic, technology has been used to a lesser or greater extent to facilitate learning and has become an instrumental part of ensuring continuity of education. Students had no choice but to engage in online learning during periods of lockdowns. The quick transition to online learning had the potential to significantly affect the student learning experience and, as a result, their attitudes to studying at university. In this study, we examined self-reported students’ attitudes on their transition from face-to-face to online learning. Second-year students from Swinburne University of Technology in Melbourne, Australia, were invited to complete the questionnaire. Students reported a range of attitudes and experiences from very positive and enjoying discovering the new study mode to the very negative where motivation to study was lost and they were considering deferring or quitting their studies. Approximately half of the students discovered the benefits of both onl...

Understanding Emotions in Mathematical Thinking and Learning, 2017

Abstract This chapter seeks to explore the role of emotions in students’ dispositions toward math... more Abstract This chapter seeks to explore the role of emotions in students’ dispositions toward mathematics throughout their secondary school education. Drawing on data from a recent mixed methods longitudinal study in England, we first illustrate how the concept of emotions relates to that of mathematics dispositions from a measurement perspective and then provide evidence of a clear decline in these dispositions. Further qualitative evidence shows the intrinsic role of emotions in this decline: many students expressed negative emotions toward pedagogic practices that are common in secondary mathematics education. In contrast, positive emotions were expressed in relation to pedagogies that encourage diversity of practices, often linked to a social, “relaxed” atmosphere; but these practices were scarce. The challenge is then for institutions and teachers to develop environments that allow students a variety of experiences with mathematics that facilitates socializing and connecting of mathematics to their interests, aspirations, and ways of being.

This is the survey used in the research for the associated paper "Study Habits and Attainmen... more This is the survey used in the research for the associated paper "Study Habits and Attainment in Undergraduate Mathematics: A Social Network Analysis".

Research in Mathematics Education in Australasia 2016–2019, 2020

Reviewed in this chapter is the growing depth and variety of research being undertaken in the ter... more Reviewed in this chapter is the growing depth and variety of research being undertaken in the tertiary mathematics field. In particular, the scope of the research and issues being examined have been highlighted in sections:

This chapter analyses two second-year undergraduate engineering students’ narratives of engagemen... more This chapter analyses two second-year undergraduate engineering students’ narratives of engagement with a mathematics course aimed at developing mathematical modelling competences. Both of these students have come to university with enough science capital to expect they will be successful in their mathematics courses and are confident in their mathematical knowledge and skills, but their narratives revealed the different value that they attribute to mathematics, which is reflected in their engagement with the mathematical modelling aspects of the course. Bourdieu’s Theory of Practice is used to understand the complexities of social practices in the field of higher education and to explain the different positions that these two students take regarding mathematical modelling.