About This Chapter
Who's it for?
This unit of our High School Geometry Homeschool Curriculum course will benefit any student who is trying to learn about critical thinking and logic in mathematics. There is no faster or easier way to learn about logic in mathematics. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn about conditional statements in math and logical math connectors.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a mathematics curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and the Logic in Mathematics unit exam confirm understanding or identify any topics that require review.
Logic in Mathematics Unit Objectives:
- Learn about disjunctions and conjunctions.
- Explain circular reasoning and hasty generalization.
- Study propositions and truth values.
- Learn about the format of a formal proof.
- Provide examples of premises, logic and conclusion.
- Find applications for direct proofs.
- Learn about hypotheses and conditional propositions in mathematics.
1. Critical Thinking and Logic in Mathematics
Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.
2. Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice
Watch this video lesson to see how you can identify cases where logic is not sound. Learn the characteristic traits of hasty generalization, circular reasoning, false cause, and limited choice.
3. Logical Fallacies: Appeals to Ignorance, Emotion or Popularity
Watch this video lesson to see examples of the logical fallacies of appeals to ignorance, emotion, and popularity. You will also see how to identify them.
4. Propositions, Truth Values and Truth Tables
Watch this video lesson and learn what truth values are and what a truth table looks like. Learn how to go from a proposition to its negation and how that affects the truth values and the truth tables.
5. Logical Math Connectors: Conjunctions and Disjunctions
Watch this video lesson to learn how to identify conjunctions and disjunctions. Also learn the connectors that are used with each. Learn how you can use them to make statements.
6. Conditional Statements in Math
Sometimes, what is true in the mathematical world of logic is false in the real world. Check out this lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.
7. Logic Laws: Converse, Inverse, Contrapositive & Counterexample
Logical statements can be useful, but only if we are able to determine their validity. In this lesson, we'll look at the various forms of a logical statement and see how they relate to each other.
8. Direct Proofs: Definition and Applications
In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.
9. Geometric Proofs: Definition and Format
Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.
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Other chapters within the High School Geometry: Homeschool Curriculum course
- Foundations of Geometry: Homeschool Curriculum
- Geometric Figures: Homeschool Curriculum
- Properties of Triangles: Homeschool Curriculum
- Triangles, Theorems & Proofs: Homeschool Curriculum
- Parallel Lines & Polygons: Homeschool Curriculum
- Similar Polygons: Homeschool Curriculum
- Quadrilaterals: Homeschool Curriculum
- Circular Arcs and Circles: Homeschool Curriculum
- Focus & Directrix: Homeschool Curriculum
- Geometric Solids: Homeschool Curriculum
- Analytical Geometry: Homeschool Curriculum
- Introduction to Trigonometry: Homeschool Curriculum