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Teaching Uncertainty Principle by HybridApproach: Single Slit Diffraction ExperimentErdoğan Özdemir 1 and Mustafa Erol 21 Departmen of Physics Education, Graduate School of Natural and Applied Sciences,Balıkesir University, 10100, Balıkesir, Turkey.2 Department of Physics Education, Education Faculty of Buca, Dokuz Eylül University,35100, Buca, İzmir, Turkey.E-mail: erdoganozdemir_1979@hotmail.com(Received 9 June 2010, accepted 2 September 2010)AbstractA hybrid teaching model, which contains 44% peer tutoring, 26% group and class discussion, 26% problem solvingwithin group, 4% demonstration and finally some homework activities that contain problem construction and problemsolving activities, is developed and administered to teach the uncertainty principle. Pre-test and post-test controlgrouped experimental model is employed in the research with a sampling of 35 undergraduate students. Data of theresearch was collected by means of a “Single Slit Diffraction Experiment Classical Exam” which is made up of 8separate questions and a “Semi Structured Interview Form”. The content is formed through the single Slit DiffractionExperiment in order to investigate the Uncertainty Principle especially the limits of classical and quantum mechanicalregions. The data were analyzed by means of Mann Whitney U Test and Wilcoxon Signed Rank Test and additionallyqualitative analyses techniques are employed. The overall results clearly indicate that the hybrid approach is moreeffective than the conventional technique on academic achievement, retention and on building true studentconceptions.Keywords: Physics Education, Instructing Quantum Physics, Uncertainty Principle, Hybrid Teaching Approach,Single Slit Diffraction.ResumenSe muestra un modelo de enseñanza híbrido, que contiene 44% tutorías entre pares, el 26% discusión en grupo yclase, el 26% de resolución de problemas dentro del grupo, el 4% de demostración y, finalmente, algunas queactividades de tareas que contienen construcción de problemas y actividades de resolución de problemas, estádesarrollado y administrado para enseñar los Principio de Incertidumbre. El modelo experimental de pre-test y posttestde control agrupados se emplea en la investigación con una muestra de 35 estudiantes de pregrado. Los datos dela investigación fueron obtenidos a través de un "Examen del experimento clásico de una rejilla de Difracción", que secompone de 8 preguntas por separado y de un "Formato de Entrevista Semi Estructurada". El contenido está formadopor el experimento de una rejilla de difracción con el fin de investigar el principio de incertidumbre, especialmentelos límites de las regiones de la mecánica clásica y cuántica. Los datos se analizaron por medio del Test U de MannWhitney y del Test de Rango Firmado de Wilcoxon, además, se emplean las técnicas de análisis cualitativos. Losresultados globales indican claramente que el enfoque híbrido es más eficaz que la técnica convencional en los logrosacadémicos, la retención y en la creación de concepciones verdaderas del estudiante.Palabras claves: Educación en Física, Instrucción de Física Cuántica, Principio de Incertidumbre, método deenseñanza híbrida, Difracción de una rendija.PACS: 01.40-d, 01.40.Fk, 01.40.Ha ISSN 1870-9095I. INTRODUCTIONunderstand quantum physical concepts due to mainlyfollowing points: 1) Students being thought classicalIn spite of being a very well-built theory, due to being physics, based on the causality and determinism, experiencebased on probabilities and uncertainties, quantum theory is great difficulties to understand quantum physical principlescriticized by many scientists [1]. The principles of quantum based mainly on the uncertainty and probability [9]. 2)theory, which contain clear controversies with daily Quantum physics are considered to be mysteries and absurdexperiences and human observant, are very demanding and hence students believe that it is not fully understood. 3)difficult to internalize and understand [2, 3, 4, 5, 6, 7, 8, 9, Quantum physics is full of very complicated mathematical10]. Majority of the students have convinced problems to equations. 4) Students are insensible towards quantumphysical lawsLat. Am. J. Phys. Educ. Vol. 4, No. 3, Sept. 2010 473 http://www.lajpe.org

Erdoğan Özdemir and Mustafa ErolIn recent years, studies on the teaching of quantumphysics are greatly increased. These studies can becategorized under two sub-titles. Firstly, “misconceptionsand teaching difficulties” and secondly “experimentalstudies on more effective learning of quantum physics”.Searching fundamental misconceptions on teachingquantum physics highlights the following studies. Bilal andErol [2] expressed that students do not comprehend therelation between wave functions and the concepts ofprobability. Steinberg et al. [7] searched the possibleimpact of classical physics upon student learning ofquantum physical concepts and found out that students donot have scientifically acceptable models concerning waveconcepts. Mashhadi and Woolnough [8] investigated howstudents visualize electron and photon in their mind. Theysuggest that the students have a wide range of non-scientificrepresentations in their minds. Olsen [4] propounded thatstudents do not understand the structure of electron andphoton. It is also expressed that underlying cause of theseconcepts is classical physical concepts. Difficulties onteaching quantum physical concepts require identificationof factors that complicate quantum physics. Ambrose et al.[11] resolute some models structured by the students on thestructure of light and they also found out that students areunable to develop scientifically logical models aboutstructure of light. Müller and Wiesner [6] searched how tolearn the concept of atom, spatial confinement, anduncertainty principle and emphasized some learningdifficulties of quantum mechanics. Bethge and Niedderer[12] expressed that students accepted physical structure ofparticles and the relation with uncertainty principle;however they insistently carry some thoughts from classicalphysics. Aylward [13] articulated that the principle ofuncertainty caused by the technological deficiency, itmeans of absolute error and it is about single particlemeasurement. The effort of explaining quantum physicalconcepts by means of the classical concepts causes certainmisconceptions especially on understanding the uncertaintyprinciple [14]. The misconceptions can principally besummarized as follows: 1) Uncertainty principle means thatthe position and momentum of a single particle can notpossibly be measured by any means [13]. 2) Uncertaintyprinciple originates from the measurement faults. 3)Uncertainty principle also means that performedmeasurement varies the actual measured value. 4) Theuncertainty of the position is actually equal to the width ofthe confinement. 5) Position uncertainty means the spatialinterval of the position. 6) Uncertainty is caused by thetechnological inefficiency. 7) Uncertainty caused by themeasurement mistakes. 8) Uncertainty is caused by the veryfast motion of the microscopic particles. 9) x and P x arethe differences between the two measured values of theposition and momentum, respectively. 10) x is the meanvalue of the displacement at the direction of x. 11) x andP x are the mistakes of the measurements on the positionand momentum [15].Steingberg et al. [7] investigated the effects of classicalconcepts on learning quantum mechanics and concludedthat lack of classical physics knowledge causesmisunderstanding of quantum physical concepts. Ireson [5]suggested that quantum physics ought to be thoughtindependently from classical physics. Abhang [9]emphasized learning difficulties of quantum mechanicalconcepts based on uncertainty and probability withconvincing concepts from classical physics. Additionally, itis more beneficial to focus on the logical link between theconcepts. Quantum physics, it is ought to be to express limitof classical physics, to apply thought experiment and insteadof separately to explain the concept, to specify logicalrelationship between concepts.In the literature a number of studies deal with thedetermination of misconceptions and getting rid of learningdifficulties. Müller and Wiesner [16] developed acurriculum enriched with some experiments and found outthat the students learned quantum physical conceptscorrectly. Niedderer et al. [17] developed some materials onteaching quantum physics focusing on physical dimensionof the concepts rather than mathematical and also containingsome specific simulations. Bergström et al. [18] explainwave structure of electron by electron diffractionexperiments and the structure of quantum physical systemby using classical wave experiments. Johanson and Milstead[19] put forward that an effective teaching of uncertaintyprinciple can be achieved by performing the single slitdiffraction experiment. Robblee et al. [20] explored thatusing computer technology on teaching quantum physics.Rebello and Zollman [21] administered their visualcomputerized materials to undergraduate students and findout those student misconceptions is substantially reduced.Evaluation of the overall literature indicates that thefundamental gap on teaching quantum physics is more lessto perform specific experimental research on effective andconsistent conceptual learning. This study specificallyconcentrates on bridging the gap. The present workspecifically focuses on the uncertainty principle which isone of the most fundamental concepts of quantum physicsand also considered as one of the most confusing concepts.We designed a basic single slit experiment and performedthe experiment by varying the slit width and demonstratedclear shift from classical limits to quantum mechanicallimits. This shift allowed us understanding correspondenceprinciple and limitations of classical physics. So, it can behelpful to clearly understanding of Heisenberg UncertaintyPrinciple [19]. And also to support students’ attention,cooperation, sharing ideas, problem solving skills andindividual working, we performed hybrid approach consistsof 44% peer tutoring, 26% group and class discussion, 26%problem solving within group, 4% demonstration and finallyhomework containing problem construction and solving.II. RESEARCH QUESTIONSAre there any significant differences on academicachievement, retention level and misconceptions concerninginstruction of uncertainty principle between theexperimental group students trained by hybrid teachingLat. Am. J. Phys. Educ. Vol. 4, No. 3, Sept. 2010 474 http://www.lajpe.org

approach and the control group students trained byconventional methods?III. METHODA. Research ModelPre-test and post-test control grouped experimental modelis employed in the research. Independent variables of theresearch consist of hybrid model and conventional teachingmethod. Dependent variables of the study are academicachievement, level of retention and finally students’misconceptions and learning difficulties.B. Sampling of the StudyThe sampling of the research comprised of overall 35undergraduate students who all attend third grade of physicseducation department at a state university in İzmir. Thestudents were randomly divided into two groups. The firstgroup is called experimental group and comprised of 14female and 3 male students. The second group is calledcontrol group comprised of 13 female and 5 male students.In order to determine the pre knowledge and theequivalence of the groups, the classical exam test is initiallyadministered two the both groups and the result is presentedin the table I.TABLE I. Comparison of the pre measurements of theexperimental and control groups.Group N Tier Mean Tier Sum z pExperimental 17 17,50 297,50144,5 0,782 *Control 18 18,47 332,50The table I clearly confirms that there is no significantdifference concerning pre measurement points of theexperimental and control group students. It is also clear thatmean of the control group students is slightly higher thanmean of the experimental group students.C. Data Collection ToolsTeaching Uncertainty Principle by Hybrid Approach: Single Slit Diffraction Experimentthe topic of single slit diffraction. The draft copy of theclassical exam was criticized by two experts of the field andthe final form is reached by considering suggestions of theexperts. The students were given 20 minutes to answer andthe evaluation of the outcomes was carried out by means ofa pre developed Classical Exam Rubric. During thedevelopment session, the scale was administered to 26undergraduate students who all attended quantum physicscourse and the scale was evaluated twice within two mouths.The scale has a Pearson correlation coefficient of 0, 86.II- Semi Structured Interview formSemi structured interview form was developed byconsidering the answers of the students to the classical examquestions. The interview focused on the physical meaning ofthe uncertainty principle.IV. TEACHING SEQUENCEA. Content and OrderThe wave property of the particles ought to be understoodvery deeply in order to understand the uncertainty principleof the quantum physics [3, 7, 15]. One of the main factorsthat effect the instruction of the wave property of theparticles is the presence of the wave particle duality [4].This concept blocks the learning channels of the studentsrather than to easy the instruction mechanism. Its is clearthat the students have learning difficulties because they tryto understand the quantum physical concepts by simplyconsidering the classical concepts [5, 13, 22]. In order toprevent that sort of misconceptions, statistical interpretationof the quantum physics is placed within the program.Additionally, the thought experiment designed byHeisenberg is widely employed throughout the applications.The experiment explains the uncertainty of a single electron,however it would cause that the uncertainty is actually aboutonly single electron. The content is therefore structured onespecially single slit diffraction experiment rather than thethought experiment of the Heisenberg such that the studentscan compare the classical and quantum limits of theuncertainty principle. The content order is thereforestructured as follows: Uncertainty concerning single slitdiffraction experiment: a) single slit diffraction experimentat classical limits b) single slit diffraction experiment of thequantum mechanical particles.In order to explore potential answers of the researchproblem, two separate data collection tools are employed.These are “Single Slit Diffraction Experiment ClassicalExam ” and “Semi-Structured Interview Form”.I- Single Slit Diffraction Experiment Classical ExamTo investigate the relation between the independent variablethat is teaching method and dependent variables which areacademic achievement and retention levels, a ClassicalExam is prepared. The exam consists of eight questions onB. Applied Techniques and Instructional StudiesFollowing the content, a hybrid approach model isdeveloped by consideration the structure andmisconceptions on the subject. The stages, techniques,durations and percentages of the model is given by the tableII.Lat. Am. J. Phys. Educ. Vol. 4, No. 3, Sept. 2010 475 http://www.lajpe.org

Erdoğan Özdemir and Mustafa ErolTABLE II. Hybrid teaching model.Hybrid teaching modelStages Instruction Duration(min.) Percentage(%)TechniquePreparation Demonstration 5 4Instruction Peer60 44instructionInclassroomDiscussion 35 26activityProblemsolving withingroup35 26OutclassroomactivityIndividualproblemsolving andproblemdevelopment- -The stages of the developed hybrid approach can briefly besummarized as follows:Preparation: It’s crucial to use visual methods to succeedthe teaching approach [23]. Visual techniques and methodsease the learning and also motivate the students in a betterway [24]. Demonstration technique is therefore used at thepreparation stage.Instruction: It is proposed to improve the students’ socialinteraction abilities and also by entering each others“approximate progress field” it is aimed to determine theneeds of the students and to help and support them inaccordance [36]. In order to realize peer instruction, one ofthe active learning techniques, is employed [26, 27]. Thestudents are divided into groups and the group studentswere made to study the content within the group. Thefeedbacks and corrections are given simultaneously [28].In-classroom activity: The stage is made up of twostages, namely discussion and problem solving within thegroup. In the first stage, the students having efficientbackground prepares some problems by consideringcommon misconception and the developed problems arediscussed by the students within the group. The researchermaintains the frame of discussion by simply moving aroundcontinuously. A classroom discussion is realized finally toend the first session. By doing so questionnaire, analyzeand a better learning is aimed. In the second stage it’saimed to teach the mathematical bases of the concepts in adeeper manner [29]. To do so the students are asked tosolve the problems within the group and a selected studentis asked to solve the problem at the board.Out-classroom activity: At this stage the students aregiven some home works to maintain their personaldevelopments [30]. The home works contain problemsolving and problem development stages. The activities areevaluated within the week and feedbacks are given to thestudents.VI. FINDINGSA. Classical Exam FindingsIn order to investigate the effect of hybrid approach teachingon academic achievement within the experimental groupstudents the classical exam was administered before andafter the teaching season as pre and post measurements. Dueto be working on very small sampling sizes, WilcoxonSigned Rank Test and Mann-Whitney U Test were employedduring the evaluation of the data [24].TABLE III. Comparison of Pre and Post Measurements of theExperimental Group Students.Pos Test- PreTestNegative TierPositive TierEqualLat. Am. J. Phys. Educ. Vol. 4, No. 3, Sept. 2010 476 http://www.lajpe.orgN017-TierMean0,009,50*significant difference if, p

the classical exam of the control group students. It is alsoclearly seen from the tier sum points that the difference is infavor of the positive rank that means in favor of the posttest. If we investigate classical exam pre and post answersof the control group students, the following points comeforward.Investigation of the student’s answers to the classicalexam questions highlights a few points: firstly 37% of thecontrol group students acknowledged that the uncertaintyprinciple is obeyed by classical particles concerning singleslit diffraction experiments. Following the conventionalteaching, 16% of the students consistently protects theirview. Additionally, 68% of the students expressed that aGaussian distribution occurs on the screen for the classicalparticles. However, 21% of the control group studentsexpressed that classical particles obey uncertainty principleconcerning post test answers. Secondly, only 37% of thecontrol group students expressed that the interferencepattern form even the slit gap is much larger than the deBroglie wave length of the quantum mechanical particles.However 47% of the students believe that if slit gap ismuch larger than the wave length of the particle, a Gaussiandistribution is expected to occur just like classicalsituations. Some 42% of the students think that if the slitwidth and the wave length is comparable then interferencepattern is expected to occur on the screen.Teaching Uncertainty Principle by Hybrid Approach: Single Slit Diffraction Experimentdistribution occurs on the screen. These students the thinkthat if the slit width is comparable with the de Broglie wavelength of the particles then the uncertainty principlegradually becomes important and as the width gets narrowerthe uncertainty of the momentum becomes larger. Some47% of the control group students state that if the slit widthis much larger than the wave length a Gaussian distributionoccurs, however 42% of the control group students state thatin the case of comparable width and de Broglie wave lengthan interference pattern is expected to occur.The table VI indicates a insignificant difference betweenpost and delayed measurements of the experimental groupstudents concerning the Classical Exam. Consideringadditionally the difference, the difference is in favor of thenegative tier which means in favor of the post test.TABLE VI. Comparison of the post and delayed measurements ofthe experimental group students.Post-DelayedTestsNegative tierPositive tierEqualN1034TierMean7,007,00*insignificant difference , if p >0,05.TierSumz p70,0021,00 -1,717 0,086TABLE V. Comparison of the post measurements of theexperimental and control group students.Groups N Tier Mean Tier Sum z pExperimental 17 23,71 403,0056,000 0,001Control 18 12,61 227,00* significant difference if, p 0,05.The table V indicates a meaningful difference betweenexperimental and control group students’ post test resultsconcerning the Classical Exam in favor of the experimental.Additionally considering tier means, it is also clear that themean of the experimental group is much higher than themean of the control group students.Comparison of the experimental and control groupstudents’ post measurements concerning the classical exam,highlights the following points: 83% of the experimentalgroup students after the actual training expressed that theclassical particles experiencing the single slit diffractionform a Gaussian distribution and only 47% of theexperimental group students assumed that the uncertaintyprinciple is meaningless for the classical particles. Some68% of the control group students believe that the classicalparticles obey the Gaussian distribution however 21% ofthe control group students expressed that the uncertaintyprinciple gives meaningful results for the classical particles.Some 77% of the experimental group students affirmed thatif the slit width is much larger than the de Broglie wavelength of the quantum physical particles than the resultswould be very close to the classical case and a GaussianThe table VII indicates a insignificant difference betweenpost and delayed measurements of the control groupstudents’ regarding the Classical Exam. Consideringadditionally the difference, the difference is in favor of thenegative tier which means in favor of the post test results.TABLE VIII. Comparison of the control and experimental groups’delayed measurements.Groups N Tier Mean Tier Sum z pExperimental 17 22,18 377,0082,00 0,017Control 18 14,06 253,00*insignificant difference (if p >0,05)The table VIII indicates a significant difference between thecontrol and experimental group students delayedmeasurements relating to the Classical Exam. Consideringadditionally the tier means, the mean of the experimentalgroup students is considerably larger then the control groupstudents.Lat. Am. J. Phys. Educ. Vol. 4, No. 3, Sept. 2010 477 http://www.lajpe.org

Erdoğan Özdemir and Mustafa ErolB. InterviewThe classical exam findings are also supported by somestudent interviews. The interviews of the research werecarried out just before and after the actual experimentalsequence. The data of is evaluated by means of the contentanalysis. The content analysis was realized in order to reachthe specific concepts and relations that could explain theactual data. The genuine activity of the content analysis wasto group similar concepts and themes and present them in amost understandable manner. The interview focused on thephysical meaning of the uncertainty principle and thefundamental results are presented below.TABLE IX. The answers and percentages of the experimental group and control group students before and after the actual schooling session.Experimental group students’ views before the applicationSharing viewsAnswer Type Student View frequency %Student 3: “yes, we use the multi measurementsUncertainty principle deals with position and momentumof position and momentum of a single 4 66uncertainty of a single electron.electron.”Experimental group student’ views after the applicationUncertainty principle deals with position and momentumuncertainty of many identical electrons.Student 3: “we use the statistical values of themany measurements performed for differentidentical electrons.”5 83Control group students’ views before the applicationSharing viewsAnswer Type Student View frequency %Uncertainty principle deals with position and momentumuncertainty of a single electron measured many times.Control group students’ views after the applicationUncertainty is obtained from the values of manymeasurements performed on a single electron.Student 10: “Uncertainty is the average of themany simultaneous measurements of positionand momentum of a single electron.”Student 8: “we obtain the uncertainty bymeasuring the position and momentum of asingle electron at different times.”2 503 75VI. DISCUSSION AND IMPLICATIONSThe present work designed to explore the effect of a hybridteaching design on academic achievement regarding thesingle slit diffraction experiment, specifically designed toinvestigate the quantum mechanical and classical limits. It isfinally detected that the hybrid teaching method influencedthe academic achievement and also the retention levelsubstantially in comparison with the conventional techniques.The overall results are in a good agreement with the previousfindings; similarly employ a hybrid teaching approach withsome active teaching techniques [31, 32]. The success ispossibly due to the content of the hybrid teaching method inthe sense that a single slit diffraction experiment realized inthe classroom by varying the slit width in order to show theclassical and quantum limits [33].The evaluation of the classical exam papers indicate thatthe experimental group students heavily think with respect tothe control group students that the classical particles obeyGaussian distribution during the single slit diffractionexperiment however the quantum mechanical particles do notobey diffraction pattern at any case. The other aim of thepresent work was to determine the student misconceptionsand learning difficulties regarding the uncertainty principleand explore possible ways to eliminate them. The mostpronouncing detected misconception before the actualtraining for both experimental and control group students wasthat they mostly believe that the uncertainty relates to themovement of only a single electron. A very similar result wasdetermined by [13]. The students interpret the uncertaintyjust like for the classical measurements, in other words, theposition and momentum of a single electron is measuredmany times and then the standard deviation is calculated.To our view, the detected misconceptions and learningdifficulties originates from the student trend ofinterconnecting the novel quantum physical concepts withthe previous classical concepts [7]. The majority of thestudents think that the quantum physical particles havedefinite position and momentum beforehand themeasurement just like the classical cases [8, 7, 15]. Thefundamental problem here is that the students interrelate thequantum physical concepts with the previous onesmistakenly and their daily experiences and intuitive viewsmislead them eventually creating the problem.Supporting the instruction session by means of somevisualized materials and tools, thought experiments andactual physical experiments certainly helps the studentunderstanding and internalizing the difficult quantumphysical concepts [34, 35] intuitive and controversialstructure of the quantum physical concepts increase theactual need to designing an effective and understandableinstruction materialsThe other point is that the trend of linking quantumphysical concepts with the classical concepts seems to becreating challenging misconceptions and learningdifficulties. It is therefore important to especially eliminatethis trend by designing the courses in a revolutionarymanner.The overall conclusion of the research is that the hybridteaching method meaningfully increases the studentLat. Am. J. Phys. Educ. Vol. 4, No. 3, Sept. 2010 478 http://www.lajpe.org

understanding and internalizing of the quantum physicalconcepts. Hence, the research can be extended to explorethe influence of different techniques and proportions toeventually reach the perfect hybrid teaching approach.REFERENCES[1] Hooft, G., In Search of the ultimate building blocks(Cambridge University Press, Cambridge, 1997).[2] Erol, M., Philosophy and instruction of quantumphysics (QP), Balkan Physics Letters, Special Issue, 16-24(2008).[3] Bilal, E. and Erol, M., Student understanding of somequantum physical concepts: Wave function, Schrödinger’swave equation and wave-particle duality, AmericanInstitute of Physics 899, 499 (2007).[4] Olsen, R. V.,, visited in June-3-2007.[5] Ireson, G., A multivariate analysis of undergraduatephysics students’ conceptions of quantum phenomena,European Journal of Physics 20, 193-199 (1999).[6] Müller, R. and Wiesner, H., Students’ conceptions ofquantum physics, The annual meeting of NationalAssociation for Research in Science Teaching. 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Erdoğan Özdemir and Mustafa Eroland visualization instruction materials, (NationalAssociation for Research in Science Teaching, Boston,Massachusetts, 1999).[35] Redish, E. F., Steinberg, R. N. and Wittmann, C.,