In a challenging and constantly changing world, students are required to develop advanced thinking skills such as critical systematic thinking, decision making and problem solving. This challenge requires developing critical thinking abilities which are essential in unfamiliar situations. A central component in current reforms in mathematics and science studies worldwide is the transition from the traditional dominant instruction which focuses on algorithmic cognitive skills towards higher order cognitive skills. The transition includes, a component of scientific inquiry, learning science from the student's personal, environmental and social contexts and the integration of critical thinking. The planning and implementation of learning strategies that encourage first order thinking among students is not a simple task. In an attempt to put the importance of this transition in mathematical education to a test, we propose a new method for mathematical instruction based on the infusion approach put forward by Swartz in 1992. In fact, the model is derived from two additional theories., that of Ennis (1989) and of Libermann and Tversky (2001). Union of the two latter is suggested by the infusion theory. The model consists of a learning unit (30h hours) that focuses primarily on statistics every day life situations, and implemented in an interactive and supportive environment. It was applied to mathematically gifted youth of the Kidumatica project at Ben Gurion University. Among the instructed subjects were bidimensional charts, Bayes law and conditional probability; Critical thinking skills such as raising questions, seeking for alternatives and doubting were evaluated. We used Cornell tests (Ennis 1985) to confirm that our students developed critical thinking skills.

In a challenging and constantly changing world, students are required to develop advanced thinking skills such as critical systematic thinking, decision making and problem solving. This challenge requires developing critical thinking abilities which are essential in unfamiliar situations. A central component in current reforms in mathematics and science studies worldwide is the transition from the traditional dominant instruction which focuses on algorithmic cognitive skills towards higher order cognitive skills. The transition includes, a component of scientific inquiry, learning science from the student''s personal, environmental and social contexts and the integration of critical thinking. The planning and implementation of learning strategies that encourage first order thinking among students is not a simple task. In an attempt to put the importance of this transition in mathematical education to a test, we propose a new method for mathematical instruction based on the infusion approach put forward by Swartz in 1992. In fact, the model is derived from two additional theories., that of Ennis (1989) and of Libermann and Tversky (2001). Union of the two latter is suggested by the infusion theory. The model consists of a learning unit (30h hours) that focuses primarily on statistics every day life situations, and implemented in an interactive and supportive environment. It was applied to mathematically gifted youth of the Kidumatica project at Ben Gurion University. Among the instructed subjects were bidimensional charts, Bayes law and conditional probability; Critical thinking skills such as raising questions, seeking for alternatives and doubting were evaluated. We used Cornell tests (Ennis 1985) to confirm that our students developed critical thinking skills.

Critical thinking (CT) is one of the desirable skills to be taught in school. It is not only considered an important 21st century skill for living in a democratic society, but also important for a deep understanding of domain-specific content. Despite its importance, studies show that students often lack the ability to think critically. Moreover, there is a lack of clear theory, supported by empirical findings, for developing domain-specific teaching-learning sequences to promote students’ CT. This makes teaching CT challenging for teachers. To address this gap, the presented study has two goals: to identify design principles for instruction that promotes critical thinking and to develop an exemplary instructional unit in particle physics on this basis. Particle physics is chosen because of its abstractness and complexity, as well as student interest in the subject. Another basis is a definition of CT that can be readily applied in the context of teaching physics. For this purpose, Halpern’s classification of CT strategies and their measurable outcomes is used. Furthermore, a distinction is made between general CT skills that provide a framework for CT, such as understanding the need to define terms precisely, and domain-specific CT skills that represent the application of general CT skills in a specific domain and require domain-specific expertise, such as distinguishing between the concepts of mass and matter in the context of particle physics. This study examines the development of both general and domain-specific CT. The teaching-learning sequences about antimatter (10 to 12 lessons) are developed for students in grades 10, 11, and 12 using the Design-Based Research (DBR) approach. Analysis of the data from pilot studies provides guidance for further development of the antimatter course and the creation of a teacher package that supports teachers both methodologically and in terms of content when implementing the antimatter course. In the main study, the course is implemented in 3 classes in different federal states of Germany. To evaluate the effectiveness of the course in promoting students’ CT, the perspectives of students as well as of teachers are examined. To evaluate the effectiveness of the course from the students’ perspective, the video and audio data, the students’ works, students’ interviews or questionnaires are inductively analyzed using the constant comparative method to identify the students’ learning processes. The results show that students apply content knowledge, apply CT skills, and demonstrate a disposition toward CT. This corresponds to a developed CT. Further analysis is conducted to relate the design skeleton facets of the course (materials, activity structure, and participant structure) to the learning processes, using the conjecture map framework to support the results from the constant comparative method. A Particle Physics Critical Thinking (PPCT) test is also developed to triangulate the results. The results of administering the PPCT test as a posttest are consistent with the qualitative findings on the effectiveness of the course. A questionnaire is developed for teachers to elicit their perceptions of the relevance, practicality, and effectiveness of the course in promoting students’ CT. The results show a positive perception. Combining all the results shows that the antimatter course is an effective course in promoting CT. The design principles applied contribute to the theory of designing effective CT instruction. Furthermore, data analysis reveals the challenges students face in critical thinking and provides teachers with heuristics for designing a domain-specific course. Based on the findings, a model for teaching CT is developed. This work leads to implications for teaching, in addition to other research questions. These include, for example, developing domain-specific CT instruction using 6 principles empirically tested in this study, considering heuristics for designing domain-specific CT instruction, and using the course materials for the purpose of developing CT. In addition, the PPCT can guide the development of other domain-specific CT tests.:Abstract i Kurzfassung iii Table of Contents v 1 Introduction 1 1.1 Importance of critical thinking and its teaching 1 1.2 Research goals 2 1.3 Structure of the work 4 Part I Theory 7 2 What is critical thinking? 9 2.1 Definition of critical thinking 9 2.2 Commonalities between different definitions 20 2.3 Nature of critical thinking: general and domain-specific 28 2.3.1 Nature of critical thinking in physics 30 2.4 Students’ challenges in critical thinking 32 2.4.1 Verbal reasoning skill 33 2.4.2 Argument analysis skill 33 2.4.3 Thinking as hypothesis testing skill 34 2.4.4 Likelihood and uncertainty analysis skill 35 2.4.5 Decision making and problem solving skill 36 2.5 Teachers’ perspective on critical thinking and teaching critical thinking 37 2.5.1 Teachers’ perspective on critical thinking 38 2.5.2 Teachers’ perspective on teaching critical thinking 41 2.5.3 Rationale for developing supportive materials for teachers 41 3 Teaching critical thinking 43 3.1 Challenges of teaching critical thinking 44 3.1.1 Teaching critical thinking as a general or domain-specific skill . 45 3.1.2 Teaching critical thinking implicitly or explicitly 46 3.1.3 Valuing disposition alongside teaching critical thinking 48 3.2 Design of critical thinking (CT) instruction 49 3.2.1 First component of CT instruction: Critical thinking model 50 3.2.2 Second component of CT instruction: Appropriate instructional design theory 52 3.2.3 A proposal for CT instruction 56 3.3 Evaluation of CT instruction 57 3.3.1 Evaluation criteria 58 3.3.2 Evaluation approaches 63 4 Design-based research 69 4.1 Design-based research (DBR) and its features 69 4.2 Conducting DBR in education: Design and evaluation of an instruction 71 4.2.1 Analysis and exploration phase 73 4.2.2 Design and construction phase 74 4.2.3 Evaluation and reflection phase 79 4.3 Summary 89 Part II Empirical Study 91 5 Research questions 93 6 Design and methodology of the study 95 6.1 Design and development of instruction according to Design-based research 96 6.1.1 Analysis and exploration phase 97 6.1.2 Design and construction phase 100 6.1.3 Evaluation and reflection phase 111 6.2 Evaluation of effectiveness of instruction 114 6.2.1 Constant comparative method for qualitative evaluation 114 6.2.2 Description of instruments for quantitative evaluation 119 6.3 Relating design skeleton facets to valued outcomes 133 6.4 Description of instrument for evaluating teachers’ perspective 134 7 Evaluation of effectiveness of the antimatter course 139 7.1 Participants 139 7.2 Evaluation of structure fidelity of implementation 141 7.2.1 Adherence 141 7.2.2 Duration 145 7.3 Results of qualitative data analysis 146 7.3.1 Likelihood and uncertainty analysis skill in the positron discovery context 147 7.3.2 Argument analysis skill in the Big Bang context 162 7.3.3 Verbal reasoning in the context of analysing the scenario of scene of “Illuminati” 173 7.3.4 Thinking as hypothesis testing in the antimatter trap context 184 7.4 Conclusion on the effectiveness of antimatter course 200 7.5 Development of critical thinking skills: a model proposal 202 7.5.1 Model proposal on developing likelihood and uncertainty analysis skill 202 7.5.2 Model proposal on developing argument analysis skill 204 7.5.3 Model proposal on developing verbal reasoning skill 205 7.5.4 Model proposal on developing thinking as hypothesis testing skill 206 7.5.5 An underlying model on developing critical thinking 207 8 Relating design skeleton facets to valued outcomes 213 8.1 Design skeleton facets of antimatter course 213 8.1.1 Materials 214 8.1.2 Activity structure 214 8.1.3 Participant structure 215 8.2 Relation of design skeleton facets to valued outcomes 218 8.2.1 Materials 218 8.2.2 Activity structure 220 8.2.3 Participant structure 221 8.3 Conclusion and discussion 225 9 Teacher perception of the antimatter course 227 9.1 Participants 227 9.2 Perceived relevance 228 9.3 Perceived practicality 232 9.4 Perceived effectiveness 234 9.5 Conclusion and discussion 239 10 Triangulation of findings 241 10.1 Participants 241 10.2 Evaluation of general critical thinking skills 242 10.3 Evaluation of domain-specific critical thinking skills 244 10.4 Conclusion and discussion 244 Part III Conclusion 247 11 Summary and discussion 249 11.1 Empirical study 249 11.2 Contribution to theory 253 11.2.1 Theory of instructional design 254 11.2.2 Evaluation of critical thinking instruction 256 11.2.3 Model on developing critical thinking 257 11.3 Limitations 257 12 Outlook 259 12.1 Implications for teaching critical thinking 259 12.2 Future research 263 Appendix 265 Research instruments 267 A Student information and prior knowledge questionnaire 267 B Particle Physics Critical Thinking (PPCT) test 270 C Student questionnaire 289 D Teacher information 290 E Teacher questionnaire 291 Antimatter course materials 292 F Worksheet 1: Critical Thinking 292 G Worksheet 2: Illuminati 295 H Worksheet 3: Anderson’s cloud chamber photograph 296 I Worksheet 4: Big Bang 298 J Worksheet 5: Search systematically 299 K Worksheet 6: Trapping antimatter 302 L Worksheet 7: Individual work “Illuminati” 305 M Worksheet 8: Group work “Illuminati” 306 List of tables 309 List of figures 313 References 315 Acknowledgements 329 Statement of Authorship 331 / Kritisches Denken (KD) ist eine der wünschenswerten Fähigkeiten, die in der Schule vermittelt werden sollten. Es gilt nicht nur als wichtige Kompetenz des 21. Jahrhunderts für das Leben in einer demokratischen Gesellschaft, sondern auch als wichtig für ein tiefes Verständnis von fachspezifischen Inhalten. Trotz dieser Bedeutung zeigen Studien, dass es den Lernenden oft an der Fähigkeit fehlt, kritisch zu denken. Zudem fehlt es an einer klaren, durch empirische Befunde gestützten Theorie für die Entwicklung von fachspezifischen Lehr-Lern-Sequenzen zur Förderung der KD-Fähigkeiten von SchülerInnen. Dies macht den KD-Unterricht zu einer Herausforderung für Lehrkräfte. Um diese Lücke zu schließen, verfolgt die vorgelegte Studie zwei Ziele: Die Identifikation von Gestaltungsprinzipien für einen Unterricht, der die Fähigkeit zum kritischen Denken fördert, und die Entwicklung einer exemplarischen Unterrichtseinheit in Teilchenphysik auf dieser Grundlage. Die Teilchenphysik wurde aufgrund ihrer Abstraktheit und Komplexität sowie des Interesses der Schüler ausgewählt. Eine weitere Grundlage ist eine Definition von KD, die sich gut im Rahmen des Physikunterrichts anwenden lässt. Hierzu wurde Halperns Klassifizierung von KD-Strategien und ihre messbaren Ergebnisse verwendet. Darüber hinaus wird unterschieden zwischen allgemeinen KD-Fähigkeiten, die einen Rahmen für KD bilden, wie z. B. das Verständnis für die Notwendigkeit, Begriffe genau zu definieren, und domänenspezifischen KD-Fähigkeiten, die die Anwendung allgemeiner KD-Fähigkeiten in einer bestimmten Domäne darstellen und domänenspezifisches Fachwissen erfordern, wie z. B. die Unterscheidung zwischen den Konzepten von Masse und Materie im Kontext der Teilchenphysik. Diese Studie untersucht die Entwicklung sowohl der allgemeinen als auch der domänenspezifischen KD. Die Lehr-Lern-Sequenzen über Antimaterie (10 bis 12 Unterrichtsstunde) werden für SchülerInnen der Klassenstufen 10, 11 und 12 mit Hilfe des Design-Based Research (DBR) Ansatzes entwickelt. Die Analyse der Daten aus den Pilotstudien liefert Anhaltspunkte für die Weiterentwicklung des Antimateriekurses und die Entwicklung eines Lehrerpakets, das Lehrkräfte methodisch und inhaltlich bei der Umsetzung des Antimateriekurses unterstützt. In der Hauptstudie wird der Kurs in 3 Klassen in verschiedenen Bundesländern Deutschlands durchgeführt. Um die Wirksamkeit des Antimateriekurses bei der Förderung des KD der SchülerInnen zu evaluieren, werden sowohl die Perspektiven der SchülerInnen als auch die der LehrerInnen untersucht. Um die Wirksamkeit des Kurses aus der Perspektive der SchülerInnen zu evaluieren, werden die Video- und Audiodaten, die Schülerarbeiten, das Schülerinterview und der Fragebogen induktiv mit der Constant Comparative Methode analysiert, um die Lernprozesse der SchülerInnen zu identifizieren. Die Ergebnisse zeigen, dass die SchülerInnen inhaltliches Wissen und KD-Fähigkeiten anwenden und eine Disposition zeigen, die gemeinsam einer entwickelten KD entsprechen. Zusätzlich werden mit Hilfe von sog. „Conjecture Maps“ die Gestaltungsfacetten des Kurses (Materialien, Aktivitätsstruktur und Teilnehmerstruktur) mit den Lernprozessen in Beziehung gesetzt, um die Ergebnisse aus der Constant Comparative Methode zu stützen. Ein Particle Physics Critical Thinking (PPCT) Test wurde ebenfalls entwickelt, um die Ergebnisse zu triangulieren. Die Ergebnisse der Durchführung des PPCT-Tests als Posttest stimmen mit den qualitativen Erkenntnissen über die Wirksamkeit des Kurses überein. Ferner wurde ein Fragebogen für Lehrkräfte entwickelt, um ihre Einschätzung der Relevanz, Praktikabilität und Wirksamkeit des Kurses bei der Förderung des KD der SchülerInnen zu erheben. Dieser zeigte eine positive Wahrnehmung. Die Kombination aller Ergebnisse zeigt, dass der Antimateriekurs ein effektiver Kurs zur Förderung des KD ist. Die angewandten Gestaltungsprinzipien tragen zur Theorie der Gestaltung eines wirksamen KD-Unterrichts bei. Darüber hinaus zeigt die Datenanalyse die Herausforderungen auf, denen sich die SchülerInnen beim kritischen Denken gegenübersehen, und liefert den Lehrkräften Heuristiken für die Gestaltung eines domänenspezifischen Kurses. Auf der Grundlage der Ergebnisse wird ein Modell für den KD-Unterricht entwickelt. Diese Arbeit führt neben weiteren Forschungsfragen auch zu Implikationen für den Unterricht. Dazu gehören z. B. die Entwicklung eines domainspezifischen KD-Unterrichts unter Verwendung von 6 Prinzipien, die in dieser Studie empirisch getestet wurden, die Berücksichtigung von Heuristiken für die Gestaltung eines domainspezifischen KD-Unterrichts, und die Verwendung der Kursmaterialien zum Zweck der Entwicklung von KD. Darüber hinaus kann der PPCT Test die Entwicklung anderer domainspezifischer KD-Tests anleiten.:Abstract i Kurzfassung iii Table of Contents v 1 Introduction 1 1.1 Importance of critical thinking and its teaching 1 1.2 Research goals 2 1.3 Structure of the work 4 Part I Theory 7 2 What is critical thinking? 9 2.1 Definition of critical thinking 9 2.2 Commonalities between different definitions 20 2.3 Nature of critical thinking: general and domain-specific 28 2.3.1 Nature of critical thinking in physics 30 2.4 Students’ challenges in critical thinking 32 2.4.1 Verbal reasoning skill 33 2.4.2 Argument analysis skill 33 2.4.3 Thinking as hypothesis testing skill 34 2.4.4 Likelihood and uncertainty analysis skill 35 2.4.5 Decision making and problem solving skill 36 2.5 Teachers’ perspective on critical thinking and teaching critical thinking 37 2.5.1 Teachers’ perspective on critical thinking 38 2.5.2 Teachers’ perspective on teaching critical thinking 41 2.5.3 Rationale for developing supportive materials for teachers 41 3 Teaching critical thinking 43 3.1 Challenges of teaching critical thinking 44 3.1.1 Teaching critical thinking as a general or domain-specific skill . 45 3.1.2 Teaching critical thinking implicitly or explicitly 46 3.1.3 Valuing disposition alongside teaching critical thinking 48 3.2 Design of critical thinking (CT) instruction 49 3.2.1 First component of CT instruction: Critical thinking model 50 3.2.2 Second component of CT instruction: Appropriate instructional design theory 52 3.2.3 A proposal for CT instruction 56 3.3 Evaluation of CT instruction 57 3.3.1 Evaluation criteria 58 3.3.2 Evaluation approaches 63 4 Design-based research 69 4.1 Design-based research (DBR) and its features 69 4.2 Conducting DBR in education: Design and evaluation of an instruction 71 4.2.1 Analysis and exploration phase 73 4.2.2 Design and construction phase 74 4.2.3 Evaluation and reflection phase 79 4.3 Summary 89 Part II Empirical Study 91 5 Research questions 93 6 Design and methodology of the study 95 6.1 Design and development of instruction according to Design-based research 96 6.1.1 Analysis and exploration phase 97 6.1.2 Design and construction phase 100 6.1.3 Evaluation and reflection phase 111 6.2 Evaluation of effectiveness of instruction 114 6.2.1 Constant comparative method for qualitative evaluation 114 6.2.2 Description of instruments for quantitative evaluation 119 6.3 Relating design skeleton facets to valued outcomes 133 6.4 Description of instrument for evaluating teachers’ perspective 134 7 Evaluation of effectiveness of the antimatter course 139 7.1 Participants 139 7.2 Evaluation of structure fidelity of implementation 141 7.2.1 Adherence 141 7.2.2 Duration 145 7.3 Results of qualitative data analysis 146 7.3.1 Likelihood and uncertainty analysis skill in the positron discovery context 147 7.3.2 Argument analysis skill in the Big Bang context 162 7.3.3 Verbal reasoning in the context of analysing the scenario of scene of “Illuminati” 173 7.3.4 Thinking as hypothesis testing in the antimatter trap context 184 7.4 Conclusion on the effectiveness of antimatter course 200 7.5 Development of critical thinking skills: a model proposal 202 7.5.1 Model proposal on developing likelihood and uncertainty analysis skill 202 7.5.2 Model proposal on developing argument analysis skill 204 7.5.3 Model proposal on developing verbal reasoning skill 205 7.5.4 Model proposal on developing thinking as hypothesis testing skill 206 7.5.5 An underlying model on developing critical thinking 207 8 Relating design skeleton facets to valued outcomes 213 8.1 Design skeleton facets of antimatter course 213 8.1.1 Materials 214 8.1.2 Activity structure 214 8.1.3 Participant structure 215 8.2 Relation of design skeleton facets to valued outcomes 218 8.2.1 Materials 218 8.2.2 Activity structure 220 8.2.3 Participant structure 221 8.3 Conclusion and discussion 225 9 Teacher perception of the antimatter course 227 9.1 Participants 227 9.2 Perceived relevance 228 9.3 Perceived practicality 232 9.4 Perceived effectiveness 234 9.5 Conclusion and discussion 239 10 Triangulation of findings 241 10.1 Participants 241 10.2 Evaluation of general critical thinking skills 242 10.3 Evaluation of domain-specific critical thinking skills 244 10.4 Conclusion and discussion 244 Part III Conclusion 247 11 Summary and discussion 249 11.1 Empirical study 249 11.2 Contribution to theory 253 11.2.1 Theory of instructional design 254 11.2.2 Evaluation of critical thinking instruction 256 11.2.3 Model on developing critical thinking 257 11.3 Limitations 257 12 Outlook 259 12.1 Implications for teaching critical thinking 259 12.2 Future research 263 Appendix 265 Research instruments 267 A Student information and prior knowledge questionnaire 267 B Particle Physics Critical Thinking (PPCT) test 270 C Student questionnaire 289 D Teacher information 290 E Teacher questionnaire 291 Antimatter course materials 292 F Worksheet 1: Critical Thinking 292 G Worksheet 2: Illuminati 295 H Worksheet 3: Anderson’s cloud chamber photograph 296 I Worksheet 4: Big Bang 298 J Worksheet 5: Search systematically 299 K Worksheet 6: Trapping antimatter 302 L Worksheet 7: Individual work “Illuminati” 305 M Worksheet 8: Group work “Illuminati” 306 List of tables 309 List of figures 313 References 315 Acknowledgements 329 Statement of Authorship 331

Teaching mathematics means teaching learners to think – wrote Polya in How to Solve It? 1957. This paper intends to offer mathematics teachers suggestions for incorporating reading, writing, and speaking practices in the teaching of mathematics. Through explicit examples and explanations we intend to share ways of engaging students in deep learning of mathematics, especially using and producing written and oral texts. More specifically, we plan to broaden and deepen teachers’ understanding of strategies for guiding students’ thinking so that they grasp mathematical concepts and processes, and also bridge the divide between mathematical processes, and written and oral communication. This paper presents a core math lessons which provides numerous opportunities for the students to get actively engaged in the lesson and think about the new concepts, algorithms and ways of solving problems/ exercises. The lesson was designed for the 7th graders (13 year-olds). It was chosen to illustrate teaching by using reading and writing for understanding math processes. The teacher’s reflections after the lesson and some samples of the students’ work and feedback are included in the paper. The material in this paper is based on the author’s own extensive teaching experience; and her work in the Reading and Writing for Critical Thinking project in Romania.

Teaching mathematics means teaching learners to think – wrote Polya in How to Solve It? 1957. This paper intends to offer mathematics teachers suggestions for incorporating reading, writing, and speaking practices in the teaching of mathematics. Through explicit examples and explanations we intend to share ways of engaging students in deep learning of mathematics, especially using and producing written and oral texts. More specifically, we plan to broaden and deepen teachers’ understanding of strategies for guiding students’ thinking so that they grasp mathematical concepts and processes, and also bridge the divide between mathematical processes, and written and oral communication. This paper presents a core math lessons which provides numerous opportunities for the students to get actively engaged in the lesson and think about the new concepts, algorithms and ways of solving problems/ exercises. The lesson was designed for the 7th graders (13 year-olds). It was chosen to illustrate teaching by using reading and writing for understanding math processes. The teacher’s reflections after the lesson and some samples of the students’ work and feedback are included in the paper. The material in this paper is based on the author’s own extensive teaching experience; and her work in the Reading and Writing for Critical Thinking project in Romania.