[CrossRef] 5. Satake, E.; Murray, A.V. Teaching an Application of Bayes' Rule for Legal Decision-Making: Measuring the Strength of Evidence. J. Stat. Educ. 2014, 22. 

[CrossRef] 6. Hoffrage, U.; Hafenbrädl, S.; Bouquet, C. Natural frequencies facilitate diagnostic inferences of managers. Front. Psychol. 2015, 6, 642. 

[CrossRef] Mathematics 2022, 10, 1558 28 of 31 7. Kahneman, D.; Slovic, P.; Tversky, A. (Eds.) Judgment under Uncertainty: Heuristics and Biases, 1st ed.; Cambridge University Press: Cambridge, UK, 1982; ISBN 978-052-128-414-1. 8. Gigerenzer, G.; Hoffrage, U. How to improve Bayesian reasoning without instruction: Frequency formats. Psychol. Rev. 1995, 102, 684-704. 

[CrossRef] 9. McDowell, M.; Jacobs, P. Meta-analysis of the effect of natural frequencies on Bayesian reasoning. Psychol. Bull. 2017, 143, 1273-1312. 

[CrossRef] 10. Cosmides, L.; Tooby, J. Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition 1996, 58, 1-73. 

[CrossRef] 11. Eddy, D.M. Probabilistic reasoning in clinical medicine: Problems and opportunities. In Judgment under Uncertainty: Heuristics and Biases; Kahneman, D., Slovic, P., Tversky, A., Eds.; Cambridge University Press: Cambridge, UK, 1982; pp. 249-267. ISBN 978-052-128-414-1. 12. Gigerenzer, G. Calculated Risks: How to Know When Numbers Deceive You; Simon & Schuster: New York, NY, USA, 2002; ISBN 074-320-556-1. 13. Schneps, L.; Colmez, C. Math on Trial: How Numbers Get Used and Abused in the Courtroom, 1st ed.; Basic Books: New York, NY, USA, 2013; ISBN 978-046-503-292-1. 14. Stine, G.J. Acquired Immune Deficiency Syndrome: Biological, Medical, Social, and Legal Issues; Prentice Hall: Upper Saddle River, NJ, USA, 1996. 15. Johnson, E.D.; Tubau, E. Comprehension and computation in Bayesian problem solving. Front. Psychol. 2015, 6, 938. 

[CrossRef] 16. Hoffrage, U.; Krauss, S.; Martignon, L.; Gigerenzer, G. Natural frequencies improve Bayesian reasoning in simple and complex inference tasks. Front. Psychol. 2015, 6, 1473. 

[CrossRef] 17. Binder, K.; Krauss, S.; Bruckmaier, G.; Marienhagen, J. Visualizing the Bayesian 2-test case: The effect of tree diagrams on medical decision making. PLoS ONE 2018, 13, e0195029. 

[CrossRef] 18. Brase, G.L. Pictorial representations in statistical reasoning. Appl. Cogn. Psychol. 2009, 23, 369-381. 

[CrossRef] 19. Binder, K.; Krauss, S.; Bruckmaier, G. Effects of visualizing statistical information—An empirical study on tree diagrams and 2 × 2 tables. Front. Psychol. 2015, 6, 1186. 

[CrossRef] 20. Sirota, M.; Kostovičová, L.; Vallée-Tourangeau, F. How to train your Bayesian: A problem-representation transfer rather than a format-representation shift explains training effects. Q. J. Exp. Psychol. 2015, 68, 1-9. 

[CrossRef] 21. Van Merriënboer, J.J.G.; Kirschner, P.A. Ten Steps to Complex Learning: A Systematic Approach to Four-Component Instructional Design, 2nd ed.; Routledge: New York, NY, USA, 2013; ISBN 978-020-309-686-4. 22. Zhu, L.; Gigerenzer, G. Children can solve Bayesian problems: The role of representation in mental computation. Cognition 2006, 98, 287-308. [CrossRef] 

[PubMed] 23. Borovcnik, M. Multiple Perspectives on the Concept of Conditional Probability. Av. Investig. Educ. Mat. 2012, 2, 5-27. 

[CrossRef] 24. Böcherer-Linder, K.; Eichler, A. The Impact of Visualizing Nested Sets. An Empirical Study on Tree Diagrams and Unit Squares. Front. Psychol. 2017, 7, 2026. 

[CrossRef] 25. Leinhardt, G.; Zaslavsky, O.; Stein, M.K. Functions, Graphs, and Graphing: Tasks, Learning, and Teaching. Rev. Educ. Res. 1990, 60, 1-64. 

[CrossRef] 26. Ayalon, M.; Wilkie, K.J. Exploring secondary students' conceptualization of functions in three curriculum contexts. J. Math. Behav. 2019, 56, 100718. 

[CrossRef] 27. Thompson, P.W.; Carlson, M.P. Variation, covariation, and functions: Foundational ways of thinking mathematically. In Compendium for Research in Mathematics Education; National Council of Teachers of Mathematics: Reston, VA, USA, 2017; pp. 421-456. 28. Niss, M.; Højgaard, T. Mathematical competencies revisited. Educ. Stud. Math. 2019, 102, 9-28. 

[CrossRef] 29. Wild, C.J.; Pfannkuch, M. Statistical Thinking in Empirical Enquiry. Int. Stat. Rev. 1999, 67, 223-248. 

[CrossRef] 30. Gal, I. Adults' Statistical Literacy: Meanings, Components, Responsibilities. Int. Stat. Rev. 2002, 70, 1-25. 

[CrossRef] 31. Buckman, R.A. Breaking bad news: The S-P-I-K-E-S strategy. Community Oncol. 2005, 2, 138-142. 

[CrossRef] 32. Brinktrine, R.; Schneider, H. Juristische Schlüsselqualifikationen: Einsatzbereiche—Examensrelevanz—Examenstraining; Springer: Berlin, Germany, 2008; ISBN 978-354-048-698-5. 33. Bromme, R.; Nückles, M.; Rambow, R. Adaptivity and anticipation in expert-laypeople communication. In Psychological Models of Communication in Collaborative Systems; Brennan, S.E., Ed.; AAAI Press: Menlo Park, CA, USA, 1999; pp. 17-24. ISBN 978-157-735-105-4. 34. Frerejean, J.; Merriënboer, J.J.G.; Kirschner, P.A.; Roex, A.; Aertgeerts, B.; Marcellis, M. Designing instruction for complex learning: 4C/ID in higher education. Eur. J. Educ. 2019, 54, 513-524. 

[CrossRef] 35. Krauss, S.; Weber, P.; Binder, K.; Bruckmaier, G. Natürliche Häufigkeiten als numerische Darstellungsart von Anteilen und Unsicherheit—Forschungsdesiderate und einige Antworten. J. Math. Didakt. 2020, 41, 485-521. 

[CrossRef] 36. Kleiter, G.D. Natural Sampling: Rationality without Base Rates. In Contributions to Mathematical Psychology, Psychometrics, and Methodology; Fischer, G.H., Ed.; Springer: New York, NY, USA, 1994; pp. 375-388. ISBN 978-038-794-169-1. 37. Brase, G. What facilitates Bayesian reasoning? A crucial test of ecological rationality versus nested sets hypotheses. Psychon. Bull. Rev. 2021, 28, 703-709. 

[CrossRef] Mathematics 2022, 10, 1558 29 of 31 38. Böcherer-Linder, K.; Eichler, A.; Vogel, M. The impact of visualization on flexible Bayesian reasoning. AIEM 2017, 25-46. 

[CrossRef] 39. Böcherer-Linder, K.; Eichler, A. How to Improve Performance in Bayesian Inference Tasks: A Comparison of Five Visualizations. Front. Psychol. 2019, 10, 267. 

[CrossRef] 40. Binder, K.; Krauss, S.; Schmidmaier, R.; Braun, L.T. Natural frequency trees improve diagnostic efficiency in Bayesian reasoning. Adv. Health Sci. Educ. 2021, 26, 847-863. 

[CrossRef] 41. Sloman, S.A.; Over, D.; Slovak, L.; Stibel, J.M. Frequency illusions and other fallacies. Organ. Behav. Hum. Decis. Processes 2003, 91, 296-309. 

[CrossRef] 42. Eichler, A.; Böcherer-Linder, K.; Vogel, M. Different Visualizations Cause Different Strategies When Dealing With Bayesian Situations. Front. Psychol. 2020, 11, 1897. 

[CrossRef] 43. Khan, A.; Breslav, S.; Glueck, M.; Hornbæk, K. Benefits of visualization in the Mammography Problem. Int. J. Hum.-Comput. Stud. 2015, 83, 94-113. 

[CrossRef] 44. Bea, W. Stochastisches Denken: Analysen aus Kognitionspsychologischer und Didaktischer Perspektive; Lang: Frankfurt am Main, Germany, 1995; ISBN 363-148-844-0. 45. Chow, A.F.; van Haneghan, J.P. Transfer of solutions to conditional probability problems: Effects of example problem format, solution format, and problem context. Educ. Stud. Math. 2016, 93, 67-85. 

[CrossRef] 46. Kurzenhäuser, S.; Hoffrage, U. Teaching Bayesian Reasoning: An evaluation of a classroom tutorial for medical students. Med. Teach. 2009, 24, 516-521. [CrossRef] 

[PubMed] 47. Ruscio, J. Comparing Bayes's theorem to frequency-based approaches to teaching Bayesian reasoning. Teach. Psychol. 2003, 30, 325-328. 48. Sedlmeier, P.; Gigerenzer, G. Teaching Bayesian reasoning in less than two hours. J. Exp. Psychol. Gen. 2001, 130, 380-400. 

[CrossRef] 49. Starns, J.J.; Cohen, A.L.; Bosco, C.; Hirst, J. A visualization technique for Bayesian reasoning. Appl. Cognit. Psychol. 2019, 33, 234-251. 

[CrossRef] 50. Steckelberg, A.; Balgenorth, A.; Berger, J.; Mühlhauser, I. Explaining computation of predictive values: 2 × 2 table versus frequency tree. A randomized controlled trial ISRCTN74278823. BMC Med. Educ. 2004, 4, 13. 

[CrossRef] 51. Talboy, A.N.; Schneider, S.L. Improving Accuracy on Bayesian Inference Problems Using a Brief Tutorial. J. Behav. Dec. Mak. 2017, 30, 373-388. 

[CrossRef] 52. Wassner, C. Förderung Bayesianischen Denkens: Kognitionspsychologische Grundlagen und Didaktische Analysen; Franzbecker: Hildesheim, Germany, 2004. 53. Maggio, L.A.; Cate, O.T.; Irby, D.M.; O'Brien, B.C. Designing evidence-based medicine training to optimize the transfer of skills from the classroom to clinical practice: Applying the four component instructional design model. Acad. Med. J. Assoc. Am. Med. Coll. 2015, 90, 1457-1461. 

[CrossRef] 54. Wopereis, I.; Frerejean, J.; Brand-Gruwel, S. Information Problem Solving Instruction in Higher Education: A Case Study on Instructional Design. In Information Literacy: Moving Toward Sustainability, Proceedings of the Third European Conference, ECIL 2015, Tallinn, Estonia, 19-22 October 2015; Revised Selected Papers; Kurbanoğlu, S., Boustany, J., Špiranec, S., Grassian, E., Mizrachi, D., Roy, L., Eds.; Springer: Cham, Switzerland, 2015; pp. 293-302. ISBN 978-331-928-197-1. 55. Sarfo, F.K.; Elen, J. Developing technical expertise in secondary technical schools: The effect of 4C/ID learning environments. Learn. Environ. Res. 2007, 10, 207-221. 

[CrossRef] 56. Martinez-Mediano, C.; Rioperez Losada, N. Internet-Based Performance Support Systems in Engineering Education. IEEE Rev. Iberoam. Tecnol. Aprendiz. 2017, 12, 86-93. 

[CrossRef] 57. Costa, J.M.; Miranda, G.L.; Melo, M. Four-component instructional design (4C/ID) model: A meta-analysis on use and effect. Learn. Environ. Res. 2021, 2021, 1-19. 

[CrossRef] 58. Van Merriënboer, J.J.G.; Clark, R.E.; Croock, M.B.M. Blueprints for complex learning: The 4C/ID-model. Educ. Technol. Res. Dev. 2002, 50, 39-61. 

[CrossRef] 59. Van Merriënboer, J.J.G.; Seel, N.M.; Kirschner, P.A. Mental Models as a New Foundation for Instructional Design. Educ. Technol. 2002, 42, 60-66. 60. Clark, R.C.; Nguyen, F.; Sweller, J. Efficiency in Learning: Evidence-Based Guidelines to Manage Cognitive Load; John Wiley & Sons: Hoboken, NJ, USA, 2011; ISBN 978-111-804-674-6. 61. Renkl, A. The Worked Examples Principle in Multimedia Learning. In The Cambridge Handbook of Multimedia Learning, 2nd ed.; Mayer, R.E., Ed.; Cambridge University Press: Cambridge, UK, 2014; pp. 391-412. ISBN 978-113-954-736-9. 62. Van Merriënboer, J.J.G.; Kester, L. The Four-Component Instructional Design Model: Multimedia Principles in Environments for Complex Learning. In The Cambridge Handbook of Multimedia Learning, 2nd ed.; Mayer, R.E., Ed.; Cambridge University Press: Cambridge, UK, 2014; pp. 104-148. ISBN 978-113-954-736-9. 63. Kirkwood, B.R.; Sterne, J.A.C. Essential Medical Statistics, 2nd ed.; Blackwell Publishing: Malden, MA, USA, 2003; ISBN 978-144-439-284-5. 64. Mayer, R.E. (Ed.) The Cambridge Handbook of Multimedia Learning, 2nd ed.; Cambridge University Press: Cambridge, UK, 2014; ISBN 978-113-954-736-9. Mathematics 2022, 10, 1558 30 of 31 65. Mayer, R.E. Applying the Science of Learning: Evidence-Based Principles for the Design of Multimedia Instruction. Am. Psychol. 2008, 63, 760-769. 

[CrossRef] 66. Ainsworth, S. DeFT: A conceptual framework for considering learning with multiple representations. Learn. Instr. 2006, 16, 183-198. 

[CrossRef] 67. Eichler, A.; Vogel, M. Teaching Risk in School. Math. Enthus. 2015, 12, 168-183. 

[CrossRef] 68. Rey, G.D.; Beege, M.; Nebel, S.; Wirzberger, M.; Schmitt, T.H.; Schneider, S. A Meta-analysis of the Segmenting Effect. Educ. Psychol. Rev. 2019, 31, 389-419. 

[CrossRef] 69. Mayer, R.E.; Wells, A.; Parong, J.; Howarth, J.T. Learner control of the pacing of an online slideshow lesson: Does segmenting help? Appl. Cognit. Psychol. 2019, 33, 930-935. 

[CrossRef] 70. Schneider, S.; Beege, M.; Nebel, S.; Rey, G.D. A meta-analysis of how signaling affects learning with media. Educ. Res. Rev. 2018, 23, 1-24. 

[CrossRef] 71. Mayer, R.E.; Fiorella, L. Principles for Reducing Extraneous Processing in Multimedia Learning: Coherence, Signaling, Redun dancy, Spatial Contiguity, and Temporal Contiguity Principles. In The Cambridge Handbook of Multimedia Learning, 2nd ed.; Mayer, R.E., Ed.; Cambridge University Press: Cambridge, UK, 2014; pp. 279-315. ISBN 978-113-954-736-9. 72. Ayres, P.; Sweller, J. The Split-Attention Principle in Multimedia Learning. In The Cambridge Handbook of Multimedia Learning, 2nd ed.; Mayer, R.E., Ed.; Cambridge University Press: Cambridge, UK, 2014; pp. 206-226. ISBN 978-113-954-736-9. 73. Sweller, J. Cognitive Load Theory. In The Psychology of Learning and Motivation, 55, Cognition in Education; Mestre, J.P., Ross, B.H., Eds.; Academic Press: San Diego, CA, USA, 2011; pp. 37-76. ISBN 978-012-387-691-1. 74. Schnotz, W. Integrated Model of Text and Picture Comprehension. In The Cambridge Handbook of Multimedia Learning, 2nd ed.; Mayer, R.E., Ed.; Cambridge University Press: Cambridge, UK, 2014; pp. 72-103. ISBN 978-113-954-736-9. 75. Schnotz, W.; Mengelkamp, C.; Baadte, C.; Hauck, G. Focus of attention and choice of text modality in multimedia learning. Eur. J. Psychol. Educ. 2014, 29, 483-501. 

[CrossRef] 76. Kulgemeyer, C. A Framework of Effective Science Explanation Videos Informed by Criteria for Instructional Explanations. Res. Sci. Educ. 2020, 50, 2441-2462. 

[CrossRef] 77. Spanjers, I.A.E.; van Gog, T.; Wouters, P.; van Merriënboer, J.J.G. Explaining the segmentation effect in learning from animations: The role of pausing and temporal cueing. Comput. Educ. 2012, 59, 274-280. 

[CrossRef] 78. Guo, P.J.; Juho, K.; Rob, R. How video production affects student engagement: An empirical study of MOOC videos. In Proceed ings of the L@S 2014: First (2014) ACM Conference on Learning @ Scale, Atlanta, GA, USA, 4-5 March 2014; pp. 41-50, ISBN 978-145-032-669-8. 79. Ouwehand, K.; van Gog, T.; Paas, F. Designing effective video-based modeling examples using gaze and gesture cues. Educ. Technol. Soc. 2015, 18, 78-88. 80. Van Wermeskerken, M.; Ravensbergen, S.; van Gog, T. Effects of instructor presence in video modeling examples on attention and learning. Comput. Hum. Behav. 2018, 89, 430-438. 

[CrossRef] 81. Hertwig, R.; Benz, B.; Krauss, S. The conjunction fallacy and the many meanings of and. Cognition 2008, 108, 740-753. [CrossRef]

[PubMed] 82. Böcherer-Linder, K.; Eichler, A.; Vogel, M. Die Formel von Bayes: Kognitionspsychologische Grundlagen und empirische Untersuchungen zur Bestimmung von Teilmenge-Grundmenge-Beziehungen. J. Math. Didakt. 2018, 39, 127-146. 

[CrossRef] 83. Rushdi, A.M.A.; Serag, H.A.M. Solutions of Ternary Problems of Conditional Probability with Applications to Mathematical Epidemiology and the COVID-19 Pandemic. Int. J. Math. Eng. Manag. Sci. 2020, 5, 787-811. 

[CrossRef] 84. Batanero, C.; Borovcnik, M. Statistics and Probability in High School; SensePublishers: Rotterdam, The Netherlands, 2016; ISBN 978-946-300-624-8. 85. Díaz, C.; Batanero, C. University Students' Knowledge and Biases in Conditional Probability Reasoning. Int. Elect. J. Math. Ed. 2009, 4, 131-162. 

[CrossRef] 86. Mathan, S.; Koedinger, K.R. Recasting the Feedback Debate: Benefits of Tutoring Error Detection and Correction Skills. In Artificial Intelligence in Education: Shaping the Future of Learning through Intelligent Technologies; Hoppe, U., Verdejo, F., Kay, J., Eds.; IOS Press: Amsterdam, The Netherlands, 2003; pp. 13-149. ISBN 978-158-603-356-9. 87. Binder, K.; Krauss, S.; Wiesner, P. A New Visualization for Probabilistic Situations Containing Two Binary Events: The Frequency Net. Front. Psychol. 2020, 11, 750. 

[CrossRef] 88. Bruckmaier, G.; Binder, K.; Krauss, S.; Kufner, H.-M. An Eye-Tracking Study of Statistical Reasoning with Tree Diagrams and 2 × 2 Tables. Front. Psychol. 2019, 10, 632. 

[CrossRef] 89. Gigerenzer, G.; Multmeier, J.; Föhring, A.; Wegwarth, O. Do children have Bayesian intuitions? J. Exp. Psychol. Gen. 2021, 150, 1041-1070. [CrossRef] 

[PubMed] 90. Hoffrage, U.; Gigerenzer, G. Using natural frequencies to improve diagnostic inferences. Acad. Med. 1998, 73, 538-540. [CrossRef]

[PubMed] 91. Barbieri, C.A.; Booth, J.L. Mistakes on Display: Incorrect Examples Refine Equation Solving and Algebraic Feature Knowledge. Appl. Cogn. Psychol. 2020, 34, 862-878. 

[CrossRef] 92. Loibl, K.; Rummel, N. Knowing what you don't know makes failure productive. Learn. Instr. 2014, 34, 74-85. 

[CrossRef] 93. Dick, W. Formative Evaluation. In Instructional Design: Principles and Applications; Briggs, L.J., Ackermann, A.S., Eds.; Educational Technology Publications: Englewood Cliffs, NJ, USA, 1977; pp. 311-336. ISBN 978-087-778-098-4. Mathematics 2022, 10, 1558 31 of 31 94. Ashdown, H.F.; Fleming, S.; Spencer, E.A.; Thompson, M.J.; Stevens, R.J. Diagnostic accuracy study of three alcohol breathalysers marketed for sale to the public. BMJ Open 2014, 4, e005811. [CrossRef] 

[PubMed] 95. Steib, N.; Büchter, T.; Eichler, A.; Krauss, S.; Binder, K.; Böcherer-Linder, K.; Vogel, M. How to boost performance and communication in Bayesian situations among future physicans and legal practitioners—A comparison of four training programs. submitted. 96. Büchter, T.; Steib, N.; Krauss, S.; Eichler, A.; Binder, K.; Böcherer-Linder, K.; Vogel, M. A new take on Bayesian Reasoning: Teaching understanding of covariation. submitted. 97. Bayesian Reasoning. Available online: http://bayesianreasoning.de/en/bayes_en.html (accessed on 14 March 2022). 1. De Finetti, B. Theory of Probability: A Critical Introductory Treatment, 1st ed.; John Wiley & Sons: Chichester, UK; Hoboken, NJ, USA, 2017; ISBN 978-111-928-637-0. 2. Gelman, A. Bayesian Data Analysis, 3rd ed.; CRC Press: Hoboken, NJ, USA, 2013; ISBN 978-143-984-095-5. 3. McGrayne, S.B. The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, & Emerged Triumphant from Two Centuries of Controversy; Yale University Press: New Haven, CT, USA, 2011; ISBN 978-030-018-822-6. 4. Ashby, D. Bayesian statistics in medicine: A 25 year review. Stat. Med. 2006, 25, 3589-3631.