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# Applied logic: A mastery learning approach

This presentation describes the use of a mastery learning approach with a content-heavy course of applied logic. Practical tips are shared.

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### Applied logic: A mastery learning approach

1. 1. John Blake University of Aizu Applied logic: A mastery learning approach https://xkcd.com/1570/
2. 2. Overview 02 • Heavy content load • Mastery learning • Active learning activities • Tests • Student feedback • Practical take-aways
3. 3. Examples of complex concepts and technical terminology covered 03 Reasoning • deductive, inductive, abductive, … Valid propositional forms: • modus ponens, modus tollens, hypothetical syllogism,… Formal fallacies: • affirming the consequent, undistributed middle term,… Informal fallacies: • ad hominem, ad populum, equivocation,… Causes: • proximal, distal, necessary, sufficient,… Paradoxes: • Liar, Sorites, Heap,… Cognitive biases: • Confirmation, Anchoring, Framing,… Mean TOEIC score: c.350 Heavy-content load Actual input + nα Comprehensible input + α
4. 4. Expected detail for written analysis 04 If Hillary is speaking, she is lying. She is lying. Therefore, she is speaking. Structure: Premise 1 Premise 2 Conclusion The conclusion follows the logical indicator therefore. Reasoning: deductive Truth value: uncertain Evidence: none Formal fallacy: affirming the consequent Proof of fallacy: P = Hillary is speaking Q = she is lying. P --> Q Q P This argument is also a form of ad hominem or personal attack. Heavy-content load learning 50 students x 7 weeks x 2 koma
5. 5. 05 Mastery learning Literature Students master lower-level concepts prior to higher-level concepts. (Bloom, 1971, 1985; Slavin, 1987; Guskey, 2007) Example 1 x 2 = ?  1 x 12=?  12 x 12=?  13 x 125 =? Steps Bloom, B. S. (1971). Mastery learning. In J. H. Block (Ed.), Mastery learning: Theory and practice (pp. 47–63). New York: Holt, Rinehart & Winston. Bloom, B. S. (1985). Developing talent in young people. New York: Ballantine Books. Guskey, T. R. (2007). Closing the achievement gap: Revisiting Benjamin S. Bloom’s “learning for mastery.” Journal of Advanced Academics, 19, 8–31. Slavin, R. E. (1987). Mastery learning reconsidered. Review of Educational Research, 57, 175-213. Study level 1 Testfeedback If pass test, i+ 1 list concepts 2 sequence concepts 3 create concept chains 4 create input activities 5 create output activities
6. 6. 06 Mastery learning: Step 1 Inventory
7. 7. True False Truth value Declarative statement Premise Conclusion Logical indicator Inference Inference bar 07 Mastery learning: Step 2 Sequence 1. This is red. 2. Red Grass is green Green is blue Therefore, grass is blue
8. 8. antecedent consequent true false deny affirm Denying the antecedent Affirming the consequent 08 Mastery learning: Step 3 Chain
9. 9. 09 Active learning (Communication gap) Work in pairs. Use the vocabulary below to name the type of causes (C1, C2, C3, C4) that lead to effect, E1. proximal, distal, sufficient, necessary, rival, common, root
10. 10. 10 Work in pairs (student A and student B). Discuss the figure and complete the table. Do not allow let anyone see your table. Term Example Description C1 First cause in a series Common cause C2 & C3, C4 Competing causes Necessary cause Sufficient cause One of the possible causes Distal cause C3, C4 Cause near the effect Student A Active learning 2 (Information gap)
11. 11. 11 Read the example to your group who try to name the fallacy. Read the definition to your group who name the fallacy Read the name of the fallacy to your group who explain it. Active learning 3 (Information gap)
12. 12. 12 Active learning 4 (student created materials/tests) Argument 1 If Java language is running, then the function of C++ language is used. If the function of C++ language is used, then we can utilize C language. Therefore, If Java language is running, we can utilize C language. Argument 2 In a programming course students must solve problem A or problem B. Most of the students selected to solve question A, so I also chose to solve that problem. Evaluate and name the following short arguments. Identify the conclusion, evaluate the truth value of the statements and validity of the argument. If a fallacy is present, name it.
13. 13. 13 Tests Paired review start with course review; end with lesson/unit review, e.g. Formative test Determine progress Summative test Assess mastery Assessor: Self, Peer, Teacher, Online Test (Basic knowledge) Type Mode Participant Assessor #1 List concepts formative paper individual self #2 Label concept descriptions formative paper pairs peer #3 Write concept descriptions summative paper individual teacher #4 Discuss concepts formative live/video pairs/threes teacher #5 Explain concepts summative audio rec individual peer #6 Multiple-choice quiz formative online individual software #7 Explain concepts summative live individual teacher P Q R S a M M a P U  P P  U P  P 1. Inductive 2. Deductive 3. Abductive
14. 14. 14 A tale of two students Student A masters the concept earlier and moves on to the next concept. Student B masters the concept on the third summative assessment. Tests 2 Student A #1 #2 #3 Student B #1 #2 #3 #4 #5 #6 #7
15. 15. 15 Tests 3 #3 Write concept descriptions No further test Explained these. To clarify these #5 Example artefact 30-second audio recording assess and re-purpose Chewar, C. and Matthews S J. (2016). Lights, Camera Action! Video Deliverables for Programming Projects. Journal of Computing Sciences in Colleges, 31(3), 8-17Thanks for the reference
16. 16. 16 Tests 4
17. 17. 17 Student feedback Students liked • Paired reviews • Clarity of 108-item mastery list e.g. 3 invalid arguments • Multiple chances to get 100% e.g. Live vs. recorded e.g. Discussion vs. presentation • Not having to take tests once concept is mastered “I can know what I need to doing”[sic] • Ability to self-evaluate using checklist “I can know what I need to doing”[sic] -4 -2 0 2 4 6 8 10 -8 -6 -4 -2 0 2 4 6 8 10 Low challenge High challenge LowsupportHighsupport EL317 cohort n=40 (range -10 to +10) Students did not like • 9am tests • Missing 9am tests Csikszentmihalyi (1993) Flow theory High challenge + high support  in the zone/flow Csikszentmihalyi, M. (1993). The evolving self: A psychology for the third millennium (Vol. 5). New York, NY: HarperCollins publishers.
18. 18. 18 Practical take-away tips 1. Write clear assessment guidelines (or aims/objectives) 2. List knowledge, skills and behaviours required 3. Knowledge is easiest to create mastery learning syllabus 4. Write clear rubrics 5. Provide measurable objectives 6. Include paired reviews 7. Get students to create artefacts. Digital artefacts are easier to re-purpose, e.g. text, video or audio files 8. Assess artefacts using clear criteria 9. Create materials and tests from artefacts 10. Would mastery learning help your Japanese?
19. 19. Any questions, comments or suggestions? jblake@u-aizu.ac.jp