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Designing learning environments to teach interactive Quantum Physics a

Sonia M. Gómez Puente & Henk J.M. Swagten a

a

Eindhoven University of Technology, Eindhoven, the Netherlands

Version of record first published: 14 Aug 2012

To cite this article: Sonia M. Gómez Puente & Henk J.M. Swagten (2012): Designing learning environments to teach interactive Quantum Physics, European Journal of Engineering Education, DOI:10.1080/03043797.2012.708722 To link to this article: http://dx.doi.org/10.1080/03043797.2012.708722

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European Journal of Engineering Education iFirst, 2012, 1–10

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Designing learning environments to teach interactive Quantum Physics Sonia M. Gómez Puente* and Henk J.M. Swagten Eindhoven University of Technology, Eindhoven, the Netherlands (Received 28 March 2012; final version received 26 June 2012) This study aims at describing and analysing systematically an interactive learning environment designed to teach Quantum Physics, a second-year physics course. The instructional design of Quantum Physics is a combination of interactive lectures (using audience response systems), tutorials and self-study in unit blocks, carried out with small groups. Individual formative feedback was introduced as a rapid assessment tool to provide an overview on progress and identify gaps by means of questioning students at three levels: conceptual; prior knowledge; homework exercises. The setup of Quantum Physics has been developed as a result of several loops of adjustments and improvements from a traditional-like type of teaching to an interactive classroom. Results of this particular instructional arrangement indicate significant gains in students’ achievements in comparison with the traditional structure of this course, after recent optimisation steps such as the implementation of an individual feedback system. Keywords: peer instruction; formative feedback; audience response systems; students’ engagement

1.

Introduction: theoretical framework

Empirical studies in physics education research have pointed out numerous misconceptions and other student difficulties in learning models, analogies, problem solving, knowledge of representations and deriving the relationships (Thompson et al. 2011). Literature on novice problem solvers in the context of physics indicates that students often tend to use trial and error rather than determining a solution approach (Savelsbergh et al. 2011). Furthermore, studies in this field disclose that, although experts solve problems by first digging into underlying concepts, students try to solve problems by looking for equations and worked examples instead of understanding the concepts (Ding et al. 2011). Research into the effectiveness of approaches in teaching physics has revealed that combining instruction, practice and providing feedback to students in problem solving are educational aspects that support the development of cognitive skills that are essential in physics (Ferguson-Hessler and de Jong 1993). Evidence of empirical studies shows that enriching situational knowledge may support students to create a proper problem solution strategy (Taconis et al. 2001, Savelsbergh et al. 2002, 2011). Contemporary experiences in physics classes have incorporated and experimented in recent years with activating learning strategies and the engagement of students in questioning. *Corresponding author. Email: [email protected]

ISSN 0304-3797 print/ISSN 1469-5898 online © 2012 SEFI http://dx.doi.org/10.1080/03043797.2012.708722 http://www.tandfonline.com

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The educational purpose of asking questions has been addressed as a mechanism to direct students’ attention, to stimulate specific cognitive processes, to communicate information to the instructor and students and to facilitate and articulate classroom discourse. Supporting the thinking process of students by conceptual questions enhances student’s underlying understanding of concepts needed to solve physics problems (Beatty et al. 2006). Approaches such as workshop Physics (Laws 1995), tutorial-based instruction (Redish et al 1997), Socratic dialog lab (Hake 1992), active learning problem sets (van Heuvelen 1991) and peer instruction (PI; Mazur 1997), and its combination with technology devices methods such as just-in-time-teaching (Novak et al. 1999), have been empirically investigated and have shed light in students’ gains, understanding and motivation. The primary and common element in all of these pedagogical methodologies is active engagement to support students’ learning. The PI method has become a common approach in introductory undergraduate physics courses in the last two decades as a response to traditionally taught classes in which little attention is paid to students’ understanding. PI varies the traditional lecture format by setting multiple-choice questions in a series of short presentations and challenging students’ conceptual understanding. PI challenges students to think deeply about conceptual material and to be engaged in peer conversations. In later years and with the development of technology devices methods such as the so-called clickers, audience response systems (ARS) have become a widespread instrument for interaction, especially with large groups. Students answer displayed questions electronically using a remote control device. The software displays the students’ answers and, although the response is anonymous to their peers, the teacher can easily associate answers to individual students for testing and feedback purposes. Classroom response devices add an extra learning moment as a feedback tool. Likewise, it also enhances information for the teacher to optimise lectures and adjust course materials, to assess students’ preparation and to manage interaction. The use of digital feedback methods promotes individual and group collaborative learning processes, improving students’ performance (Henriksen and Angell 2010). Reported data from the first 10 years of experimenting with PI (Crouch and Mazur 2001, Fagen et al. 2002, Ding et al. 2008, Lasry et al. 2008) have revealed that having students read before class and work on pre-class web-based assignments supports their understanding and prevents them from conceptual misconceptions. Results of experiments combining ARS methods with peer-to-peer activities reveal that these methods enable students to think like physicists by having them ‘talk like a physicist’ (Henriksen and Angell 2010). Embedding peer-talk methods into lecture classes enhances the process of reasoning, challenging each other with arguments, developing new insights as a result of a thinking process and practising physics in their discussions. Finally, studies in other disciplines on the combination of peer discussion on clicker questions and follow-up explanations by the teacher improve the average student performance substantially (Smith et al. 2011). Technology-based instructional methods aim not only at increasing student activity but also enhancing learning by providing frequent assessment and feedback in real time. The underlying rationale of formative assessment is that results serve to improve teaching and learning (Black 1998, Chen et al. 2010, Majerich et al. 2011). Formative feedback on individual learning identifies the gaps that students still need to cover. Although all these class talk models have proved to be empirically suitable to teach freshman years, it still remains a field for investigation whether this clicker pedagogy can be effective in a different learning environment to enhance students’ achievement. Building upon the abovementioned theoretical underpinnings and empirical evidence in first year courses, the instructional design of Quantum Physics (QP) offers a positive case of a ‘class-that-talks’ method with small groups suitable for an upper-level physics course (Milner-Bolotin et al. 2010). The particular instructional design of QP includes educational elements such as peer work, alternation of educational forms, such as lectures, with tutorials and self-study along with the use of electronic

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systems for individual formative feedback. The present authors’ interest lies in investigating empirically the impact of these didactical elements in second year courses. This paper is intended to present a case study that has been built upon researched-based practices of several loops of instructional adjustments. Initially, the interactive engagement comprised a block of clicker lectures and tutorials and self-study time, with small groups of students. Based on the success of this first loop, a student-centred follow-up system was included, consisting of weekly individual formative feedback focusing on conceptual, prior knowledge and homework questioning. Significant gains in students’ achievement can be appreciated when comparing these clicker classes with traditional courses. These adjustments and improvements are intended to inspire physics teachers to create a meaningful learning environment for second-year physics classes. In this introduction the results of previous positive experiences with the use of ARS in physics courses have been explained. Next, a snapshot of the instructional design of QP is presented as an adapted model of PI and question-driven teaching appropriate to teach second year university physics. The research method is then described and the results of this case study are outlined. Finally, in the conclusion, the successful educational aspects of this case are summarised.

2.

Instructional design

Teaching with the use of an ARS is not something completely new in physics courses at the Eindhoven University of Technology. The first attempt to motivate students with the use of clickers goes back to the 1970s. At that time, Poulis et al. (1998) taught, e.g. Maxwell’s theory, Kirchhoff’s laws, mechanics and vibrations, by showing multiple-choice concept questions using an overhead projector. The present sophisticated computer-based systems to code and display answers on a screen are at present a home-built electronics setup with a monochromatic monitor to show students’ responses. Following the experiences of Poulis and Massen, experiments with classroom electronic devices have recently spread throughout the university. QP is a second year course aimed at teaching the background and basic concepts of quantum mechanics. The course includes key historical experiments that shaped the emergence of quantum mechanics, the introduction of the Schrödinger equation and wave functions, the exploration of a number of time-independent one-dimensional potentials and introductory three-dimensional quantum mechanics, especially focusing on the H atom and the role of angular momentum. Apart from learning these quantum concepts, the application of acquired knowledge in solving problems using mathematical tools is an essential element in this course. Traditionally, QP has taken a classical instructional form of lectures and tutorials. In large group lectures (number of students; N = 30–75) theoretical insights are explained, preparing students for independent and problem solving during tutorials (N = 10–25 per group). Lecture contact hours counted for three hours a week, whereas tutorials counted for four hours weekly over a period of seven weeks. During lecture hours, the presentation and explanation of QP concepts is emphasised by the lecturer, combined with web applications, physics demonstrations and examples of the impact of QP for science and technology. Since 2010, QP has adopted an integrated instructional form of combined lectures, tutorials and self-study, using an adapted PI method and audience response devices, including individual formative feedback. This instructional setup is in contrast to the traditional setting of short separated series of lectures supported by tutorials. This course was designed and carried out as a first experiment. QP consists of a combination of educational methods in two units of four hours a week, with a total of 14 units. The structure of each unit differs according to the content of the programme. The course is given by three teachers with a small student group composition made

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Figure 1. Instructional design of Quantum Physics, showing the combination of lectures (in orange) and tutorials (in blue) in one block of four hours.

up of N = 10–20. Figure 1 provides an overview of the structure of this educational form. Key in this altered model is that students acquire new QP concepts that they can immediately apply to concrete problems and calculations within the same course unit. This is in striking contrast with the traditional approach, where concepts (lectures) and calculations (tutorials) were intrinsically separated. In the following paragraphs these, aspects of integration will be outlined further. The core value of the design of this course lies in the combination of different educational forms, e.g. interactive lectures, web application labs and tutorials to work on assignments and calculations, in one unit time and using a variation of activity learning methods. Topics are taught in short interactive lectures, in which students practise peer talk and are challenged by concept questions and quizzes that they answer with electronic feedback devices. Web animations/applications and demonstrations of the impact of quantum mechanics for physics, science and society are embedded in the lectures to illustrate content and associate with real-life situations. Interactive lectures link content from the lectures with the work that the students do during assignments in their selfstudy time. These assignments are discussed later during the interactive lectures. During their self-study time, students spend time in the preparation of lectures by doing homework, by reading textbooks for lecture preparation and by doing advanced/additional calculations to further apply the conceptual knowledge taught during lectures.

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Figure 2. Type of questions used during interactive lecture and tutorials, related to (a) updating, (b) homework/reading, (c) conceptual understanding and peer talk and (d) checking answers after performing calculations during classes.

In the Bohr-model with n = 1 and n = 2, how does the magnitude of the angular momentum L and angular frequency w compare between the two orbits? L1 > L2 w1 > w2 L1 < L2 w1 > w2 L1 > L2 w1 < w2 L1 < L2 w1 < w2 The transmission coefficient T of particles with mass m and energy E in a delta-function energy barrier given by V=+a d (x), is equal to: 1/T = 1 + (ma 2 ) / (2 2 E) 2 1/T = 1 + / (2 E ) / (ma 2) 2 1/T = 1 + / (2 E ) / (ma 2) 2 1/T = 1 + (ma 2 ) / (2 E) Figure 3.

Examples of problems used in the final examinations.

Inquiry-driven teaching has been adapted to develop questions for the interactive lectures (Beatty et al. 2006). Questions were integrated at different times during lectures and had different purposes (see also Poulis et al. 1998). For instance, the type of questions presented in Figure 2a were meant as a summary at the beginning of the interactive lecture, in this case for the teacher to see the students’ level of understanding about the previously introduced stationary wave functions of an infinite quantum well. Figure 2b represents a question on their reading homework (Introduction to Quantum Mechanics by Griffiths) as a prelude to the new concept of commutation of quantum operators. Questions like those shown in Figure 3c are not only meant to assess the conceptual understanding of the newly gained knowledge during the interactive lecture time, but also to generate discussions among students. In this particular example, a number of radial wave functions belonging to the hydrogen atom are drawn, from which the principle quantum number n should be evaluated. In addition, multiple-choice questions, as shown in Figure 2d

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(related to drawing spherical harmonics), were used to check the answers and results after the problem-solving sessions. The design of the questions has played a crucial role in the implementation of this instructional approach. The selection of quizzes as an inquiry instrument had a two-fold aim: first, the authors wanted to use a tool that serves as a quick scan and that provides an immediate overview of current deficiencies in students’ understanding. The questions, therefore, were designed to test conceptual understanding. Second, the nature of the questions asked in the quizzes requires from the students the application of that conceptual understanding in solving problems. Appropriateness of the questions is considered, according to the rationale below. The histograms, the output of software showing students’ results, serve to gain a quick and general overview of students’ learning process. To maximise students’ learning achievement, teachers capture the students’ responses on problems in QP and take immediate action to optimise content of lectures and modify the type of questions. Likewise, the exercises and problems in the final examinations represent the type of questions asked during the interactive lectures. In this sense, students are requested to apply understanding practised in the quizzes into solving problems, in which conceptual knowledge is required to answer correctly and to solve the problems properly. Figure 3 represents typical multiple-choice questions that students get in the final examinations. Note that this covers only part of the examination; the remainder of the exam is devoted to solving problems and doing calculations in the field of introductory QP. Another consideration in designing questions is the differences among students. Experience shows that there are students who learn quicker and have reached a higher level of complexity in problem solving than others. Questions to meet different students’ learning levels were consequently developed. Finally, questions were designed to meet the objectives of the different parts within one lecture block. It should be emphasised that the preparation and development of suitable questions required regular meetings and intense discussions among the teachers. Although this experience has been promising, the assumption that individual formative feedback would positively influence students’ results has been the basis for the optimisation of QP and, consequently, the integration of a feedback system. Based on this rationale, the second adjustment of the interactive design of QP was developed and launched as an experiment one year later. It included different types of refresher questions on prior knowledge at the beginning of each interactive lecture, a weekly individual formative feedback of the results of multiple-choice questions and quizzes. Feedback of students’ performance and progress through the ARS focused on the different levels of types of questions, conceptual understanding, problem solving, reading and homework exercises, and questions with the purpose of stimulating and updating students’ prior knowledge. Formative feedback was given anonymously showing scores by ID student numbers.

3.

Method

This case study has taken into account the students’ cohorts from the academic year 2006/2007 until 2011/2012. Different cohorts of second year physics students were followed, based on the end course results. Table 1 shows the number of students enrolled per year (N) along with the students’ results, i.e. the percentage of students that passed after the first and second exam. In addition, the authors were interested in gathering information on the integration of classroom response devices as a distinctively activating instrument. Therefore, the students’ opinions were collected in two ways: during the implementation of this experiment, a group of students was requested to carefully follow, analyse and provide feedback on the course, paying attention to, among others, didactical aspects such as the new clicker-pedagogy element. After the course ended, focus groups of students were organised as a major feedback and evaluation instrument.

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Table 1. Year cohort, number of students and students’ results (the percentage of students that passed after the first and/or second exam) Year cohort

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N Students’ results (%)

2007

2008

2009

2010

2011

46 70

39 79

46 65

37 88

30 93

Suggestions were used to improve and adjust not only the content material tackled in the course, but also, and more importantly, the didactical applications of the clicker as a classroom communication tool. As a result, two types of categories for problem-solving exercises were integrated for regular and advanced level of students. Students begin first with regular questions. Students who complete the exercise in a shorter time may start working on the advanced problem exercises. This was a suitable solution to meet the needs of different levels of students in the group. Regarding students’ opinions from the focus groups about the new interactive response tool, there was general level of satisfaction with the method. Suggestions to include refresher questions on prior knowledge at the beginning of each interactive lecture have been taken into consideration in the improvement of the second experiment. In addition to the suggestions of the students, the teachers have included new didactical elements around this experience, such as the individual formative feedback. Although effects on motivation of students have not been carefully studied in the case, it was observed that students’ attendance is improving. This observation was taken carefully and has been interpreted as the fact that students get direct feedback on development efforts together with the interactive educational methods used to engage them in class activities may have influenced the motivation of students to attend classes. Differences in the instructional design of the different years also include adaptations of the type of examinations used. The traditional design of QP exams in the first years included only written examinations, in which students had to solve problems. With the introduction of quizzes, exam questions (as earlier discussed, see Figure 3) were also developed to test conceptual understanding. 4.

Results

Comparing the different years, it was observed that there is an increase in students’ results along the year cohorts. Table 1 provides an overview of these results. It was also observed that there is an increase in students’ achievement, starting from the integration of interactive teaching methods in the instructional design in 2010. Increase in achievements may have also been caused by the decrease in number of students in the integration of formative feedback with the support of audience response systems. This may also explain the increase in students’ outcomes. Considering the average students results of all second year physics and mathematics courses (57% in 2007, 74% in 2008, 68% in 2009, 72% in 2010 and 78% in 2011), a slight increase in 2010 was observed, as compared to the year before, as well as an additional increase in 2011. In view of that, care should be taken in the claim that the significant increase in student’s achievements in QP is influenced only by the use of the audience response feedback system. In the discussion, this issue will be returned to. 5.

Discussion

This paper was intended to present a case study for second year physics classes that have been successful after a series of loops of adjustments and improvements. Particular characteristics of this learning environment evolving from an adaptation of PI lies in the design of a system

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of individual formative feedback. Feedback of students’ performance and progress focused on different types of questions, conceptual understanding, problem solving type of questions from homework exercises, and questions with the purpose of stimulating and updating students’ prior knowledge. The development of students’ results has been carefully followed over the last six years and a steady growth in results based on students’exams has always been appreciated. The present authors are confident that the students’ achievement levels on quiz performance are caused fundamentally by the individual feedback system as a form of rapid assessment on progress. Individual formative feedback has helped to identify gaps in learning and support students in understanding concepts. An added result of this experiment is that there is a correlation in the increase in students’gains in both conceptual understanding and in problem-solving skills. In the first version of this experiment, problem-solving questions were used in the exams. The combination of problem solving exercises and multiple-choice questions could have further influenced the increase in students’gains in 2011. Additionally, it should be pointed out that the physics level of the multiple-choice questions is, in the present authors’ opinion, equally high as for the problem solving exercises, which could be deduced from analysing the correlation between these two exam elements. It is also appreciated that, although course attendance is not compulsory, the interest in the topic and the methodology used had a high impact on students’ attendance in lectures. Although these results are promising, the present authors are still cautious in making further statements and creating a direct link between the characteristics of the instructional design of QP and the increase in student’s achievements. For example, in 2009 the department of Applied Physics has incorporated ‘intermediate diagnostic exams’ as part of the final examination, which might have had an influence in the study behaviour and thereby the scores of those students. Likewise, the study behaviour of QP students might also have been influenced since 2010, due to the introduction of the so-called ‘mandatory study advice’ that requests first-year students to compulsory earn a minimal amount of credit points before being admitted to the second year. However, the correlations between the different loops in the improvement of the design with the increase of results of end exams suggest that these instructional tailor-made pedagogical factors could have a strong positive effect on students’ gains. Furthermore, there are also other parameters that may have influenced the increase in students’ outcomes. These are, for instance, the teachers, the exam problems and exam styles, or the number of students in the class, the number of contact hours, among others. With regard to the teachers’ characteristics, the three teachers involved in teaching QP have taught this course for the past six years, both in the traditional setup as well as in the interactive version. Moreover, the teachers have been involved both in teaching the theoretical part of the course as well the problem-solving exercises in the instructions. The great experience of the teaching staff may have influenced the quality of learning. In terms of exam problems and exam styles, the evaluation carried out every year at the end of the course has a twofold objective. One is to collect information and input from students’ questionnaires and focus groups for improvement as a quality assurance policy in the Physics Department. The other is to carefully pay attention to students’ problems, which are shown in the exams. The latest students’ problems have particularly been the concern of the teachers as they have modified the exam questions according to students’ problems. While in the first year’s exam questions included only written examinations and problem-solving exercises, in the latest versions multiple-choice questions to test conceptual understanding have been added. Finally, the number of students attending the class has, most likely, been a factor affecting the quality of learning. The first experiences of QP were held in big theatre halls, with up to 75 students attending lectures, and holding tutorials in groups of approximately 20–30 students in each group. The reduction in number of students per group, around 20, and the intensive focus of the combination of interactive lectures with tutorials, along with the IT media and the support of

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the formative feedback, have undoubtedly been elements that affected the learning process and, consequently, the examination results and students’ achievements. In this venue, the increase of lecture hours embedded in the interactive classes (two × four hours per week), as compared to the traditional setup (weekly three hour lecture plus two × two hours instruction), are instructional design aspects that may also have had a positive impact on student behaviour.

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6.

Conclusions

This paper has presented and systematically described the instructional design of QP as an interactive case for a second year undergraduate course that includes interactive lectures and tutorials in a small single classroom setting. The attributes of the design are an adapted method of PI carried out in small groups, in which interactive ARS devices are combined with tailor-made individual formative feedback systems. The instructional design of QP has gone through different adjustments in the design as well as in the learning activities towards reaching an optimal model. The experience of QP has proved to be a positive interactive experiment. It is concluded, therefore, that the instructional design of QP provides a well-structured model to inspire physics teachers to create an interactive classroom learning environment. Grounded in this experience, it is confirmed that the combination of PI elements, such as peer talk, technology applications and inquiry-driven methods, together with a follow-up rapid individual feedback assessment system, are core didactical aspects of a powerful environment for upper-level undergraduate courses.

Acknowledgements The authors acknowledge and thank G.J.H. Brussaard and J.T. Kohlhepp, Quantum Physics teachers, for their valuable input and comments in the design, setup and implementation of Quantum Physics. We would also like to thank Sonja Feiner-Valkier, from the educational institute at the Applied Physics department, for her support in providing the data for the analysis of the results of Quantum Physics.

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About the authors Sonia M. Gómez Puente is Educational Advisor and Teacher Trainer at the department of Education and Training at the Eindhoven University of Technology. Key areas of expertise: research and innovation in Engineering Education; professionalisation of teachers, curriculum development and instructional design; competencies development; active teaching methods; problem/project-based learning (PBL) and design-based learning (DBL). Henk J.M. Swagten is Full Professor at the group Physics of Nanostructures within the Department of Applied Physics at the Eindhoven University of Technology. His research activities are focused on novel nanomaterials and electronic devices in the field of spintronics & nanomagnetism. Teaching activities have covered a number of Bachelor and Master’s courses.