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

1. John Blake
University of Aizu
Applied logic:
A mastery learning approach
https://xkcd.com/1570/

2. Overview
02
• Heavy content load
• Mastery learning
• Active learning activities
• Tests
• Student feedback
• Practical take-aways

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. 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. 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. 06
Mastery learning: Step 1 Inventory

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. antecedent
consequent
true
false
deny
affirm
Denying the antecedent
Affirming the consequent
08
Mastery learning: Step 3 Chain

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
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
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
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
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
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
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
Tests 4

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
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. Any questions, comments or
suggestions?
jblake@u-aizu.ac.jp