Lesson 2.3 day 1
What Makes an Argument Good?
Focus: valid, sound, invalid — argument structure vs. content — the three fallacies and their connection to the four conditional forms
Day 1 has two tasks and one consolidation. Task 1 (Always/Sometimes/Never) warms up the skill of evaluating the truthiness of statements — a precursor to evaluating arguments. Task 2 (Is This a Good Argument?) is the main event: students sort nine arguments before they have vocabulary to name the categories. Consolidation names what they found. Students begin the CYU in the remaining class time. Full notes and the fallacy connection wait for Day 2.
A classroom story worth telling — the square number moment
The Always/Sometimes/Never task contains the claim: ‘A square number has an odd number of factors.’ In the first year teaching this lesson, my co-teacher and I modeled a genuine disagreement over what counts as a factor. The standard definition counts each factor once: 16 has factors 1, 2, 4, 8, 16 — five, which is odd. An alternative view pairs factors multiplicatively: 1×16, 2×8, 4×4 — where 4 pairs with itself and the count becomes different. We wanted students to see that this kind of disagreement is not an error; it is what happens when shared terms are not established.
Then a student said something none of us had thought of: ‘If we include negative numbers as factors, then every positive divisor pairs with a negative one — so the count is always even, regardless of which definition you use.’
We stopped and celebrated that. It showed that arguing carefully and respectfully can get us to a better answer than any one person reaches alone. Truth belongs to whoever makes an argument no one can find a flaw in. That is not just a nice classroom story. That is what this course is about.
This story connects directly to what comes next: the truth value of a statement depends on shared definitions. A logically valid argument can still be wrong if its premises are false. That is the lesson Day 1 is building toward.
Consolidation: Valid, Sound, Invalid:
Build the three definitions together, connecting each to the arguments students just sorted. The key insight to deliver explicitly: validity is entirely about structure. An argument can be valid even if its premises are false — even if its conclusion is false. The moon-cheese argument is valid. The unicorn argument is valid. What makes an argument valid is that the conclusion must follow from the premises, not that anything in it is actually true.
Students begin the Day 1 CYU in the remaining class time. The Day 1 CYU covers the valid/sound/invalid distinction only. Notes on argument forms and fallacies wait for Day 2.