Optimal thought and optimal fitness through reason, logic, science, passion, and wisdom.
Logic For Future Teachers
Logic For Future Teachers

Logic For Future Teachers

Enroll on Outschool, or contact me to set up a course or workshop for you, for a small group, for your school, or for your company.

We will learn ideas and techniques that are deep, fundamental, and powerful — yet found nowhere else (or rarely anywhere). They will benefit any teacher or thinker of any age.

You love teaching and want the best for your students, now or in the future. Make sure you have the tools to be your best and to help your students and other teachers. A confused teacher makes confused students — remember the teacher who, at least sometimes, had the heart but couldn’t explain? Let’s all be the best we can be, heart and mind.

We will study logic in context of education: the subjects, the academics, the teaching, the learning, the assessment of learning, the assessment of learners, the assessment of self. Dig deep. Martin Luther King, Jr. wanted a better education for us. Thomas Edison wanted a better education for us. (See below for some of their thoughts.) Let’s help achieve that dream. You and your students deserve it. This course will benefit anyone of any age and any level of experience teaching.

Enroll on Outschool, or contact me to set up a course or workshop for you, for a small group, for your school, or for your company.

In studying such logic skills as concept-formation, definition, induction, and integration, we will learn:
-how to explain well
-how to build concepts and help students build concepts
-how to use question-and-answer to drive thinking and learning
-how to analyze and correct errors and misunderstandings
-what understanding is and how to achieve it and teach it
-lots more!

Chief topics covered to achieve those goals:

  1. Q&A: thinking as asking and answering questions
  2. Thinking: knowing and understanding, not merely memorizing words
  3. Concretes & concepts: keeping it real, keeping it efficient
  4. Definition: knowing what we are talking about
  5. Classification: keeping our minds flexible, organized, and adaptable
  6. Induction: drawing meaningful conclusions on our own; checking other people’s
  7. Integration: making our knowledge useful and keeping everything connected

Enroll on Outschool, or contact me to set up a course or workshop for you, for a small group, for your school, or for your company.

We will learn, practice, digest, and work toward some mastery of some techniques of logic used in teaching. Time will be spent in all or most classes working through examples and going over homework.

We will use a combination of lecture, interactive discussion, Q&A, homework, and in-class work. Be prepared to think, to learn, to take notes, and to have new horizons open up for both yourself and your future students.

Tentative Schedule (will be tailored to the class participants’ level and interests)
Week 1: Teaching, Q&A, and thinking for yourself.

Day 1.
Intro. Aims of course: what we will cover, and what we will not cover. What is teaching. A few knowledge issues in teaching. The need for logic. What logic is. Defining truth and knowledge. Reason RX: repairing broken hierarchy, faulty generalizations, poorly formed concepts.

Day 2.
Getting down to basics: thought and thinking. Memorizing words or following authority vs thinking and knowing. Independent thought. How thinking for yourself is beneficial for you and everyone else. The evidence of the senses. Content: it’s about reality.

Day 3.
Thought revisited. Using Q&A. What questions to ask. Digging into the questioning process and its uses.

Week 2: Q&A, and concepts and concretes

Day 1.
Q&A revisited. Thinking as Q&A. The Five Whys. Stages of learning. Content: it’s about reality. Practice and exercises from education and its subjects.

Level one of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

We will be continuing to look at some of these examples step-by-step and in more depth as we progress in the course, even while we bring in some new examples and exercises.

Day 2.
What a concept is. How we use them. Content: it’s about reality. Meaningful concretes. How we think rationally and logically.

Level two of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

Day 3.
Some rules for forming concepts. How we form concepts. Similarity and difference. Work through examples and exercises.

Week 3: Concepts and concretes

Level two of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

Day 1.
Some rules for forming concepts. How we form concepts. Degrees of abstraction. Work through examples and exercises.

Day 2.
Some rules for forming concepts and how we form concepts, continued. Combining the rules. Work through examples and exercises.

Day 3.
Some rules for forming concepts and how we form concepts, continued. Combining the rules. Work through examples and exercises.

Week 4: Definitions 1

Level three of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

Day 1.
What a definition is. Logical definitions vs. dictionary definitions. Why they are important. How we use them. Formulating definitions. Context.

Day 2.
Rules of definition: genus and differentia. Work through examples and exercises.

Day 3.
Rules of definition: genus and differentia. Work through examples and exercises.

Week 5: Definitions 2

Level three of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

Day 1.
Rules of definition: stating the essence. Work through examples and exercises.

Day 2.
Rules of definition: neither too wide nor too narrow. Work through examples and exercises.

Day 3.
Rules of definition: combining the rules. Work through examples and exercises.

Week 6: Classification

Level four of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

Day 1.
What is classification. Why it is important. How we use it in life, learning, teaching, and education. Degrees of abstraction. Rules of classification. Work through examples and exercises.

Day 2.
Rules of classification: mutually exclusive, jointly exhaustive; consistent; essential characteristics. Work through examples and exercises.

Day 3.
Rules of classification: mutually exclusive, jointly exhaustive; consistent; essential characteristics. Work through examples and exercises.

Week 7: Induction 1

Level five of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

Day 1.
What induction is. Induction vs. deduction. How induction (i.e., generalization) works. How inductions are formed. How to do it right. Reduction. Work through examples and exercises.

Day 2.
Theory-building. Sequencing learning. Stages of learning. Hierarchy diagrams. Induction diagrams/maps. Work through examples and exercises.

Day 3.
The evidence of the senses. Meaningful concretes. Causality. Causal analyses. Context. Content: it’s about reality. The nature of things. Why to teach animals and plants instead of starting with DNA. Work through examples and exercises.

Week 8: Induction 2

Level five of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

Day 1.
Rules of induction. Context. Contrast. Think like a baby. Think like a historian. Work through examples and exercises.

Day 2.
Rules of induction. Context. Contrast. Think like a baby. Think like a historian. Work through examples and exercises.

Day 3.
MIll’s Methods. Work through examples and exercises.

Week 9: Integration 1

Level six of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

Day 1.
What cognitive integration is: connecting ideas, especially to the big picture. Why it is important (e.g., in wisdom). Notice that it has been in everything we’ve done! Top to bottom. Characteristic of all human knowledge. Examples of how it is not practiced as much as it should be. Examples of its use. Work through examples and exercises.

Day 2.
Integration in the history of science. Some advice on using it in your thinking. Work through examples and exercises.

Day 3.
Integration in the history of science. Some advice on using it in your thinking. Work through examples and exercises.

Week 10: Integration 2

Level six of working through examples selected from (but not limited to): education, teacher, student, learning, teaching, thinking, understanding, logic, adverb, preposition, subordinate clause, sentence diagramming, poem, synecdoche, literary device, force, motion, acceleration, projectile, electricity, heat, energy, sound, atom, reaction, acid, base, lifting, jumping, running, walking, deadlift, sport, kinetic chain, forest, lake, habitat, predator, prey, food chain, food web, cell cycle, photosynthesis, government, society, economy, number, ratio, equation, quadratic equation, sine, cosine, proof, trigonometry, limit, derivative.

Day 1.
Interdisciplinary work: if you don’t practice it and teach it, your students probably won’t learn how. Tell stories to integrate. Tell, e.g., physics as story so it makes sense, so students get the discovery and proof process, and so it is easier to remember. Use etymology, grammar, step-by-step development, etc. Connect geometric proof to reasoning in all other areas. Develop step by step in writing essays: length, complexity, logic, grammar, consideration of audience, purpose, etc. Work through examples and exercises.

Day 2.
Integration in education. Dr. Maria Montessori. Some advice on using it in your thinking. Work through examples and exercises.

Day 3.
Telling stories: concretes and abstractions; making connections. Building knowledge. Making connections. Stages of learning. Degrees of complexity. Sequencing curriculum. Thinking about The OODA Loop. Work through examples and exercises.

Week 11: Hierarchy, Context, Understanding

Day 1.
Hierarchy. What it is. Notice that it was in everything we did! Hierarchy mapping. Stages of learning. Sequencing. What builds to what builds to what. Simple tasks come together into more complex. Identify a topic, drill it, mix it in with other similar things, add it to other tasks, increase complexity. Work through examples and exercises.

Day 2.
Context. What it is. Notice that it was in everything we did! Student context versus your context. Our context develops. Stage of learning. Degree of abstraction. Work through examples and exercises. (Including maybe “What must we know before we learn any grammar and sentence diagramming?”, “What is needed for someone to learn to write longer and longer essays that are more and more complex?”, “What must we know before we get physics?”, “Of what must we be capable before we do something in physical fitness?”) Work through examples and exercises.

Day 3.
Understanding. What it is. Three characteristics of understanding. Measuring it. Stages of learning. Work through examples and exercises.

Week 12: Explanation (or continue topics in weeks 1-11 so we get understanding)

Day 1.
Explanation. What it is. Making it relevant to your audience. Considering audience background. Feynman in using “energy” to explain — or not. Related to DNA. Rules of explanation. Work through examples and exercises.

Day 2.
Rules of explanation. Analogies. Using evidence. Work through examples and exercises.

Day 3.
Rules of explanation. Finding causes. Problem-solving. Error analysis. Causal analysis. Identifying a problem. Work through examples and exercises. Conclude course.

Enroll on Outschool, or contact me to set up a course or workshop for you, for a small group, for your school, or for your company.

Examples can be pulled from what you suggest, as well as the whole, huge field of education:

physics, chemistry, literature, earth science, mathematics, sociology, anthropology, language, history, economics, government, civics, geography, political science, philosophy, psychology, sociology, anthropology, physical education, athletics, art, music, dance. theatre, computer science, technology, engineering, medicine

mnemonics as tools of integration, Walden, Newton’s Laws, Bernd Heinrich, history of physics, history of chemistry, history of language, concept-formation and vocabulary, integration and vocabulary, induction, physics and math and reasoning and logic, math as measurement, definition of proposition, math and thinking, Aristotle and biology, Aristotle and logic, get hierarchy right in chem and physics, simplify, diagram in physics, diagram in mathematics

crawling, throwing, climbing, catching, hitting; know sun and its warmth and its importance to life before know anything about light and the entire production process of Vitamin D; climax species, succession; animal gait, animal track, running, flying; cat, mammal, animal, fission-fusion; animal intelligence, animal emotion, pain, pleasure, problem-solving; ecology, habitat, lifestyle, species-appropriate; integration: how climate and geology interact; get hierarchy right in physics; tell physics as story so it makes sense and get discovery process and easier to remember; electromagnetism, universal gravitation; planet, star, sun, earth, moon, white dwarf, moon; electricity, lightening, magnet, electric charge, electric current; electron, proton, atom, nucleus; mass, velocity, distance, momentum, rotation; heat, temperature, latent heat

equations of motion, the Coriolis effect; getting the hierarchy right in chem; metal, iron, water, nonmetal, gas, liquid; period, periodic table; atomic radius, bonding, covalent, ionic, metallic; concept-formation and vocabulary, integration and vocabulary; grammar, vocabulary, reading; adjective, adverb, noun, preposition, part of speech, sentence, clause, phrase, prepositional phrase; step by step in writing essays: develop complexity, logic, grammar, considering audience, purpose, writing an essay, The Tygre; rock, igneous, metamorphic, tectonic plate, glaciation, mountain, valley, desert, ocean, lake, river, stream, climate, weather, freeze, snow, rain, hail, cloud, lightening

math and reasoning and logic, math as measurement, math and thinking, diagram in mathematics, opposite vs adjacent sides and angles, how to do a proof, how to derive the area formulas, how to divide by a fraction, how to add fractions with unlike denominators; history of physics, history of chemistry, history of language; government, legislature, capitalism, communism, socialism, monarchy, money, barter, finance; Confucius, Aristotle. Plato. Dewey. Kant. morality, aesthetics, epistemology, politics; SAT/ACT work

Many have pointed out the need for logic and the opportunities for us in education to grow and improve. Let’s listen and improve.

1. Martin Luther King, Jr wrote: “At this point, I often wonder whether or not education is fulfilling its purpose. A great majority of the so-called educated people do not think logically and scientifically. Even the press, the classroom, the platform, and the pulpit in many instances do not give us objective and unbiased truths. … Education must enable one to sift and weigh evidence, to discern the true from the false, the real from the unreal, and the facts from the fiction.”

2. Thomas Edison wrote: “The present system does not give elasticity to the mind. It casts the brain into a mold. It insists that the child must accept. It does not encourage original thought or reasoning, and it lays more stress on memory than on observation. The result of accepting unrelated facts is the fostering of conservatism [in thinking]. It breeds fear, and from fear comes ignorance.”

3. David Epstein, in his recent book Range: How Generalists Triumph in a Specialized World wrote: “Science students learned the facts of their specific field without understanding how science should work in order to draw true conclusions.”

4. Rachel Evans, wrote in the Biomedical Odyssey Blog: “But educators at the Johns Hopkins Bloomberg School of Public Health assert that memorization alone does not a scientist make — above all, students must be critical, creative thinkers who are honest and responsible with data. In order to train scientists as critical thinkers, the R3 Graduate Science Initiative was recently created in the Department of Molecular Microbiology and Immunology (MMI), led by director Gundula Bosch, Ph.D.” Let’s give our students and our world the best we can be, the best we can teach, and the best education they can receive.

Enroll on Outschool, or contact me to set up a course or workshop for you, for a small group, for your school, or for your company.

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