A virtual learning environment for pregraduate mathematical students

Peer-reviewed

Interactive Calculus in a Virtual Learning Environment

The teaching of higher level mathematics for technical students in a virtual learningenvironment poses some difficulties, but also opportunities, now specific to that virtuality.On the other hand, resources and ways to do now manly available in VLEs might soon extend to all kinds of environments.In this short presentation we will discuss anexperience carried at Universitat Oberta deCatalunya (UOC) involving (an on line university), first, the translation of LaTeX written existent materials to a web based format(specifically, a combination of XHTML andMathML), and then the integration of a symbolic calculator software (WIRIS) running as a Java applet embedded in the materials, intending to achieve an evolution from memorising concepts and repetitive algorithms to understanding and experiment concepts and the use of those algorithms.

El aprendizaje reflexivo en la formación inicial del profesorado: un modelo para aprender a enseñar matemáticas = Reflective learning in the early formation of teachers: a model to learn to teach maths

In this study we analize the application of the reflective learning during initial formation mathematics teachers. This model is based on the sociocultural theories of the human learning and assumes that the interaction and the contrast make possible the coconstruction and the active reconstruction of knowledge.In order to make the study, it was left from a sample of 29 teaching students. The qualitative analysis allowed to identify factors that facilitate the incorporation of the reflective learning in university teaching, as well as the degree of effectiveness of this model to learn to teach mathematics

Learning Preferences with Kernel-Based Methods

Learning of preference relations has recently received significant attention in machine learning community. It is closely related to the classification and regression analysis and can be reduced to these tasks. However, preference learning involves prediction of ordering of the data points rather than prediction of a single numerical value as in case of regression or a class label as in case of classification. Therefore, studying preference relations within a separate framework facilitates not only better theoretical understanding of the problem, but also motivates development of the efficient algorithms for the task. Preference learning has many applications in domains such as information retrieval, bioinformatics, natural language processing, etc. For example, algorithms that learn to rank are frequently used in search engines for ordering documents retrieved by the query. Preference learning methods have been also applied to collaborative filtering problems for predicting individual customer choices from the vast amount of user generated feedback. In this thesis we propose several algorithms for learning preference relations. These algorithms stem from well founded and robust class of regularized least-squares methods and have many attractive computational properties. In order to improve the performance of our methods, we introduce several non-linear kernel functions. Thus, contribution of this thesis is twofold: kernel functions for structured data that are used to take advantage of various non-vectorial data representations and the preference learning algorithms that are suitable for different tasks, namely efficient learning of preference relations, learning with large amount of training data, and semi-supervised preference learning. Proposed kernel-based algorithms and kernels are applied to the parse ranking task in natural language processing, document ranking in information retrieval, and remote homology detection in bioinformatics domain. Training of kernel-based ranking algorithms can be infeasible when the size of the training set is large. This problem is addressed by proposing a preference learning algorithm whose computation complexity scales linearly with the number of training data points. We also introduce sparse approximation of the algorithm that can be efficiently trained with large amount of data. For situations when small amount of labeled data but a large amount of unlabeled data is available, we propose a co-regularized preference learning algorithm. To conclude, the methods presented in this thesis address not only the problem of the efficient training of the algorithms but also fast regularization parameter selection, multiple output prediction, and cross-validation. Furthermore, proposed algorithms lead to notably better performance in many preference learning tasks considered.

Cómo enseñar matemáticas en las primeras edades a partir de contextos de vida cotidiana = How to teach mathematics to young students based on everyday contexts

This paper stresses the importance of developing mathematical thought in young children based on everyday contexts, since these are meaningful learning situations with an interdisciplinary, globalised focus. The first part sets out the framework of reference that lays the theoretical foundations for these kinds of educational practices. The second part gives some teaching orientations for work based on everyday contexts. It concludes with the presentation of the activity 'We’re off to the cinema to learn mathematics!'

Matemáticas y juego = Mathematics and games

In this article we try to look at the learning of mathematics through games in the first years of schooling. The use of game resources in the class should not be carried out in a uniquely intuitive way but rather in a manner that contains some preliminary reflections such as, what do we understand by games? Why use games as a resource in the Mathematics classroom? And what does its use imply?

Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

Conceptions of mathematics teacher education : thoughts among teacher educators in Tanzania

This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.

Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

Learning information technology business in a changing industry landscape. Introducing Team Entrepreneurship in Renewing Bachelor Education in Renewing Bachelor Education in Information

Speed, uncertainty and complexity are increasing in the business world all the time. When knowledge and skills become quickly irrelevant, new challenges are set for information technology (IT) education. Meta-learning skills – learning how to learn rapidly - and innovation skills have become more essential than single technologies or other specific issues. The drastic changes in the information and communications technology (ICT) sector have caused a need to reconsider how IT Bachelor education in Universities of Applied Sciences should be organized and employed to cope with the change. The objective of the study was to evaluate how a new approach to IT Bachelor education, the ICT entrepreneurship study path (ICT-ESP) fits IT Bachelor education in a Finnish University of Applied Sciences. This kind of educational arrangement has not been employed elsewhere in the context of IT Bachelor education. The study presents the results of a four-year period during which IT Bachelor education was renewed in a Finnish University of Applied Sciences. The learning environment was organized into an ICT-ESP based on Nonaka’s knowledge theory and Kolb’s experiental learning. The IT students who studied in the ICT-ESP established a cooperative and learned ICT by running their cooperative at the University of Applied Sciences. The students (called team entrepreneurs) studied by reading theory in books and other sources of explicit information, doing projects for their customers, and reflecting in training sessions on what was learnt by doing and by studying the literature. Action research was used as the research strategy in this study. Empirical data was collected via theme-based interviews, direct observation, and participative observation. Grounded theory method was utilized in the data analysis and the theoretical sampling was used to guide the data collection. The context of the University of Applied Sciences provided a good basis for fostering team entrepreneurship. However, the results showed that the employment of the ICT-ESP did not fit into the IT Bachelor education well enough. The ICT-ESP was cognitively too tough for the team entrepreneurs because they had two different set of rules to follow in their studies. The conventional courses engaged lot of energy which should have been spent for professional development in the ICT-ESP. The amount of competencies needed in the ICT-ESP for professional development was greater than those needed for any other ways of studying. The team entrepreneurs needed to develop skills in ICT, leadership and self-leadership, team development and entrepreneurship skills. The entrepreneurship skills included skills on marketing and sales, brand development, productization, and business administration. Considering the three-year time the team entrepreneurs spent in the ICT-ESP, the challenges were remarkable. Changes to the organization of IT Bachelor education are also suggested in the study. At first, it should be admitted that the ICT-ESP produces IT Bachelors with a different set of competencies compared to the conventional way of educating IT Bachelors. Secondly, the number of courses on general topics in mathematics, physics, and languages for team entrepreneurs studying in the ICTESP should be reconsidered and the conventional course-based teaching of the topics should be reorganized to support the team coaching process of the team entrepreneurs with their practiceoriented projects. Third, the upcoming team entrepreneurs should be equipped with relevant information about the ICT-ESP and what it would require in practice to study as a team entrepreneur. Finally, the upcoming team entrepreneurs should be carefully selected before they start in the ICT-ESP to have a possibility to eliminate solo players and those who have a too romantic view of being a team entrepreneur. The results gained in the study provided answers to the original research questions and the objectives of the study were met. Even though the IT degree programme was terminated during the research process, the amount of qualitative data gathered made it possible to justify the interpretations done.

Learning about brain physiology and complexity from the study of the epilepsies

The brain is a complex system, which produces emergent properties such as those associated with activity-dependent plasticity in processes of learning and memory. Therefore, understanding the integrated structures and functions of the brain is well beyond the scope of either superficial or extremely reductionistic approaches. Although a combination of zoom-in and zoom-out strategies is desirable when the brain is studied, constructing the appropriate interfaces to connect all levels of analysis is one of the most difficult challenges of contemporary neuroscience. Is it possible to build appropriate models of brain function and dysfunctions with computational tools? Among the best-known brain dysfunctions, epilepsies are neurological syndromes that reach a variety of networks, from widespread anatomical brain circuits to local molecular environments. One logical question would be: are those complex brain networks always producing maladaptive emergent properties compatible with epileptogenic substrates? The present review will deal with this question and will try to answer it by illustrating several points from the literature and from our laboratory data, with examples at the behavioral, electrophysiological, cellular and molecular levels. We conclude that, because the brain is a complex system compatible with the production of emergent properties, including plasticity, its functions should be approached using an integrated view. Concepts such as brain networks, graphics theory, neuroinformatics, and e-neuroscience are discussed as new transdisciplinary approaches dealing with the continuous growth of information about brain physiology and its dysfunctions. The epilepsies are discussed as neurobiological models of complex systems displaying maladaptive plasticity.

Socially shared metacognitive regulation during collaborative learning processes in student dyads and small groups

Traditionally metacognition has been theorised, methodologically studied and empirically tested from the standpoint mainly of individuals and their learning contexts. In this dissertation the emergence of metacognition is analysed more broadly. The aim of the dissertation was to explore socially shared metacognitive regulation (SSMR) as part of collaborative learning processes taking place in student dyads and small learning groups. The specific aims were to extend the concept of individual metacognition to SSMR, to develop methods to capture and analyse SSMR and to validate the usefulness of the concept of SSMR in two different learning contexts; in face-to-face student dyads solving mathematical word problems and also in small groups taking part in inquiry-based science learning in an asynchronous computer-supported collaborative learning (CSCL) environment. This dissertation is comprised of four studies. In Study I, the main aim was to explore if and how metacognition emerges during problem solving in student dyads and then to develop a method for analysing the social level of awareness, monitoring, and regulatory processes emerging during the problem solving. Two dyads comprised of 10-year-old students who were high-achieving especially in mathematical word problem solving and reading comprehension were involved in the study. An in-depth case analysis was conducted. Data consisted of over 16 (30–45 minutes) videotaped and transcribed face-to-face sessions. The dyads solved altogether 151 mathematical word problems of different difficulty levels in a game-format learning environment. The interaction flowchart was used in the analysis to uncover socially shared metacognition. Interviews (also stimulated recall interviews) were conducted in order to obtain further information about socially shared metacognition. The findings showed the emergence of metacognition in a collaborative learning context in a way that cannot solely be explained by individual conception. The concept of socially-shared metacognition (SSMR) was proposed. The results highlighted the emergence of socially shared metacognition specifically in problems where dyads encountered challenges. Small verbal and nonverbal signals between students also triggered the emergence of socially shared metacognition. Additionally, one dyad implemented a system whereby they shared metacognitive regulation based on their strengths in learning. Overall, the findings suggested that in order to discover patterns of socially shared metacognition, it is important to investigate metacognition over time. However, it was concluded that more research on socially shared metacognition, from larger data sets, is needed. These findings formed the basis of the second study. In Study II, the specific aim was to investigate whether socially shared metacognition can be reliably identified from a large dataset of collaborative face-to-face mathematical word problem solving sessions by student dyads. We specifically examined different difficulty levels of tasks as well as the function and focus of socially shared metacognition. Furthermore, the presence of observable metacognitive experiences at the beginning of socially shared metacognition was explored. Four dyads participated in the study. Each dyad was comprised of high-achieving 10-year-old students, ranked in the top 11% of their fourth grade peers (n=393). Dyads were from the same data set as in Study I. The dyads worked face-to-face in a computer-supported, game-format learning environment. Problem-solving processes for 251 tasks at three difficulty levels taking place during 56 (30–45 minutes) lessons were video-taped and analysed. Baseline data for this study were 14 675 turns of transcribed verbal and nonverbal behaviours observed in four study dyads. The micro-level analysis illustrated how participants moved between different channels of communication (individual and interpersonal). The unit of analysis was a set of turns, referred to as an ‘episode’. The results indicated that socially shared metacognition and its function and focus, as well as the appearance of metacognitive experiences can be defined in a reliable way from a larger data set by independent coders. A comparison of the different difficulty levels of the problems suggested that in order to trigger socially shared metacognition in small groups, the problems should be more difficult, as opposed to moderately difficult or easy. Although socially shared metacognition was found in collaborative face-to-face problem solving among high-achieving student dyads, more research is needed in different contexts. This consideration created the basis of the research on socially shared metacognition in Studies III and IV. In Study III, the aim was to expand the research on SSMR from face-to-face mathematical problem solving in student dyads to inquiry-based science learning among small groups in an asynchronous computer-supported collaborative learning (CSCL) environment. The specific aims were to investigate SSMR’s evolvement and functions in a CSCL environment and to explore how SSMR emerges at different phases of the inquiry process. Finally, individual student participation in SSMR during the process was studied. An in-depth explanatory case study of one small group of four girls aged 12 years was carried out. The girls attended a class that has an entrance examination and conducts a language-enriched curriculum. The small group solved complex science problems in an asynchronous CSCL environment, participating in research-like processes of inquiry during 22 lessons (á 45–minute). Students’ network discussion were recorded in written notes (N=640) which were used as study data. A set of notes, referred to here as a ‘thread’, was used as the unit of analysis. The inter-coder agreement was regarded as substantial. The results indicated that SSMR emerges in a small group’s asynchronous CSCL inquiry process in the science domain. Hence, the results of Study III were in line with the previous Study I and Study II and revealed that metacognition cannot be reduced to the individual level alone. The findings also confirm that SSMR should be examined as a process, since SSMR can evolve during different phases and that different SSMR threads overlapped and intertwined. Although the classification of SSMR’s functions was applicable in the context of CSCL in a small group, the dominant function was different in the asynchronous CSCL inquiry in the small group in a science activity than in mathematical word problem solving among student dyads (Study II). Further, the use of different analytical methods provided complementary findings about students’ participation in SSMR. The findings suggest that it is not enough to code just a single written note or simply to examine who has the largest number of notes in the SSMR thread but also to examine the connections between the notes. As the findings of the present study are based on an in-depth analysis of a single small group, further cases were examined in Study IV, as well as looking at the SSMR’s focus, which was also studied in a face-to-face context. In Study IV, the general aim was to investigate the emergence of SSMR with a larger data set from an asynchronous CSCL inquiry process in small student groups carrying out science activities. The specific aims were to study the emergence of SSMR in the different phases of the process, students’ participation in SSMR, and the relation of SSMR’s focus to the quality of outcomes, which was not explored in previous studies. The participants were 12-year-old students from the same class as in Study III. Five small groups consisting of four students and one of five students (N=25) were involved in the study. The small groups solved ill-defined science problems in an asynchronous CSCL environment, participating in research-like processes of inquiry over a total period of 22 hours. Written notes (N=4088) detailed the network discussions of the small groups and these constituted the study data. With these notes, SSMR threads were explored. As in Study III, the thread was used as the unit of analysis. In total, 332 notes were classified as forming 41 SSMR threads. Inter-coder agreement was assessed by three coders in the different phases of the analysis and found to be reliable. Multiple methods of analysis were used. Results showed that SSMR emerged in all the asynchronous CSCL inquiry processes in the small groups. However, the findings did not reveal any significantly changing trend in the emergence of SSMR during the process. As a main trend, the number of notes included in SSMR threads differed significantly in different phases of the process and small groups differed from each other. Although student participation was seen as highly dispersed between the students, there were differences between students and small groups. Furthermore, the findings indicated that the amount of SSMR during the process or participation structure did not explain the differences in the quality of outcomes for the groups. Rather, when SSMRs were focused on understanding and procedural matters, it was associated with achieving high quality learning outcomes. In turn, when SSMRs were focused on incidental and procedural matters, it was associated with low level learning outcomes. Hence, the findings imply that the focus of any emerging SSMR is crucial to the quality of the learning outcomes. Moreover, the findings encourage the use of multiple research methods for studying SSMR. In total, the four studies convincingly indicate that a phenomenon of socially shared metacognitive regulation also exists. This means that it was possible to define the concept of SSMR theoretically, to investigate it methodologically and to validate it empirically in two different learning contexts across dyads and small groups. In-depth micro-level case analysis in Studies I and III showed the possibility to capture and analyse in detail SSMR during the collaborative process, while in Studies II and IV, the analysis validated the emergence of SSMR in larger data sets. Hence, validation was tested both between two environments and within the same environments with further cases. As a part of this dissertation, SSMR’s detailed functions and foci were revealed. Moreover, the findings showed the important role of observable metacognitive experiences as the starting point of SSMRs. It was apparent that problems dealt with by the groups should be rather difficult if SSMR is to be made clearly visible. Further, individual students’ participation was found to differ between students and groups. The multiple research methods employed revealed supplementary findings regarding SSMR. Finally, when SSMR was focused on understanding and procedural matters, this was seen to lead to higher quality learning outcomes. Socially shared metacognition regulation should therefore be taken into consideration in students’ collaborative learning at school similarly to how an individual’s metacognition is taken into account in individual learning.

Utilising student profiles in mathematics course arrangements

This thesis develops a method for identifying students struggling in their mathematical studies at an early stage. It helps in directing support to students needing and benefiting from it the most. Thus, frustration felt by weaker students may decrease and therefore, hopefully, also drop outs of potential engineering students. The research concentrates on a combination of personality and intelligence aspects. Personality aspects gave information on conation and motivation for learning. This part was studied from the perspective of motivation and self-regulation. Intelligence aspects gave information on declarative and procedural knowledge: what had been taught and what was actually mastered. Students answered surveys on motivation and self-regulation in 2010 and 2011. Based on their answers, background information, results in the proficiency test, and grades in the first mathematics course, profiles describing the students were formed. In the following years, the profiles were updated with new information obtained each year. The profiles used to identify struggling students combine personality (motivation, selfregulation, and self-efficacy) and intelligence (declarative and procedural knowledge) aspects at the beginning of their studies. Identifying students in need of extra support is a good start, but methods for providing support must be found. This thesis also studies how this support could be taken into account in course arrangements. The methods used include, for example, languaging and scaffolding, and continuous feedback. The analysis revealed that allocating resources based on the predicted progress does not increase costs or lower the results of better students. Instead, it will help weaker students obtain passing grades.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.