| 1 Introduction |
 | 1.1 The author |
| 1.2 Some suggestions and thoughts |
| 1.3 What's the problem? |
| 1.3.1 How to check |
| 2 Goals of teaching |
| 2.1 Critical and independent thinking |
| 2.2 What is education? |
| 2.3 Problems in society due to poor education |
| 2.3.1 Anti-missile missile |
| 2.3.2 JSTARS |
| 2.3.3 Depleted uranium |
| 2.3.4 Testing cars |
| 2.3.4.1 Pumping water |
| 2.4 Effort and ability |
| 2.5 How to teach |
| 2.6 Some ideas for basic approaches |
| 2.6.1 The forceful approach |
| 2.6.2 The respectful approach |
| 2.6.3 Anger |
| 2.6.4 The single-minded approach |
| 2.6.5 Rote |
| 2.6.6 Story telling |
| 2.6.7 The pleasant, intelligent approach |
| 2.6.8 Poor teachers |
| 2.6.9 Competition among teachers |
| 2.6.10 Punishments |
| 2.6.10.1 Summary punishments |
| 2.6.10.2 Indifference |
| 2.6.10.3 Understanding |
| 2.7 Piaget's theory of cognitive development |
| 2.7.1 How I explain Piaget's ideas to students |
| 2.7.2 Examples of abstract thinking |
| 2.8 Gifted children |
| 2.8.1 A gifted student |
| 2.9 Privileged adolescents |
| 2.10 Science and Mathematics |
| 2.10.1 Falsification |
| 2.10.2 Acceptance of scientific theories |
| 2.10.3 Why study science? |
| 2.10.3.1 Thoughts on the Future |
| 2.11 University professors |
| 2.11.1 Professors need high school students |
| 2.11.2 Teachers and students need professors |
| 2.11.3 20th century ideas |
| 2.11.4 Graduate assistants |
| 3 Some things to help students |
| 3.1 Abstract concepts |
| 3.2 Boredom |
| 3.3 Driving |
| 3.4 Essays and reading literature |
| 3.5 Feelings |
| 3.6 Happy students |
| 3.7 Java |
| 3.8 Languages |
| 3.9 Reading |
| 3.10 Sleep |
| 3.10.1 Breakfast |
| 3.11 Conditions at home |
| 3.12 Teaching |
| 3.13 Teaching each other |
| 3.14 Tests |
| 3.14.1 HSPA tests |
| 3.15 The Civil War |
| 3.15.1 Drums in the Civil War |
| 3.15.2 Reconstruction 1865-1877 |
| 4 Some things in science |
| 4.1 How to think about science |
| 4.1.1 Mass |
| 4.1.2 Density |
| 4.1.3 Comments |
| 4.2 Biology |
| 4.2.1 A cell is like a car |
| 4.2.2 Big words |
| 4.2.3 Pictures |
| 4.2.4 Insects |
| 4.2.4.1 Sex of spiders |
| 4.2.4.2 Butterflies |
| 4.2.4.3 Distributed brains |
| 4.2.5 Recognizing children |
| 4.2.6 Whales |
| 4.3 Birthday balloons |
| 4.4 Chemical bonds |
| 4.5 Diffraction of light and sound |
| 4.6 Forces of nature |
| 4.6.1 Forces holding things together |
| 4.6.2 Inverse square law |
| 4.7 Earthquakes |
| 4.8 Lightning |
| 4.9 Physics of driving |
| 4.10 Physics of flight |
| 4.11 Radians |
| 4.12 Science |
| 4.13 Selectively permeable membrane |
| 4.14 Size of the universe |
| 4.14.1 How big is the universe? |
| 4.15 Solar eclipse |
| 4.16 The sun |
| 4.17 Trigonometry |
| 4.18 Visualization |
| 4.19 Why do elephants have large ears? |
| 5 Studying Mathematics and Physics |
| 5.1 Mathematics |
| 5.2 Physics |
| 5.3 How to study mathematics |
| 5.4 Homework |
| 5.5 Checking your work |
| 6 Topics in physics and mathematics |
| 6.1 Black holes |
| 6.1.1 Galaxies |
| 6.1.2 Quasars |
| 6.2 Boundary conditions and waves |
| 6.2.1 Big things make deep sounds |
| 6.3 Electricity and magnetism |
| 6.4 Heat, temperature, and entropy |
| 6.4.1 Enthalpy |
| 6.5 Ideal gases |
| 6.6 Momentum |
| 6.7 Parabolas |
| 6.8 Products of vectors |
| 6.8.1 Riding a bicycle |
| 6.8.2 Work |
| 6.8.3 Energy |
| 6.9 Simple Harmonic Motion |
| 6.9.1 Period of a pendulum from dimensional analysis |
| 6.10 Resistors and capacitors |
| 6.11 Earth's orbit |
| 6.12 Quantum Mechanics |
| 6.12.1 Atoms |
| 6.12.2 Atoms and molecules |
| 6.12.3 Photons |
| 6.12.4 "An atom is mostly empty space" |
| 6.13 Statistics |
| 6.14 Symmetry and Scientific Laws |
| 6.14.1 Coordinate systems and symmetry |
| 6.14.2 Proof that symmetry is related to conservation laws |
| 6.14.3 Why Newton's Laws? |
| 7 Mentoring notes for teachers |
| 7.1 Introduction |
| 7.2 Date |
| 7.3 How to explain mathematical ideas |
| 7.3.1 The basis of mathematics |
| 7.3.2 Concrete models |
| 7.3.3 Inequalities |
| 7.3.4 Matrices |
| 7.3.5 One step at a time |
| 7.4 Internet sites |
| 7.5 What it is not |
| 7.6 Classroom management |
| 7.6.1 Computer work |
| 7.6.2 Doing |
| 7.6.3 Erasing the board |
| 7.6.4 Full Attention |
| 7.6.5 Giggling |
| 7.6.6 Homework |
| 7.6.7 Lecture direction |
| 7.6.8 Listening to the students |
| 7.6.9 Praise |
| 7.6.9.1 Observing the students |
| 7.6.10 Questioning |
| 7.6.11 Stay tuned... |
| 7.6.12 Student errors |
| 7.6.13 Student interruptions |
| 7.6.14 Student understanding |
| 7.6.15 Teacher's goals |
| 7.6.16 Team work |
| 7.6.17 Tests |
| 7.6.18 Understanding |
| 7.7 Doing problems in class |
| 7.7.1 Graphs |
| 7.7.2 Challenging |
| 7.7.3 Repetition of basic concepts |
| 7.7.4 Student faces |
| 7.7.5 Review |
| 7.8 Visibility |
| 7.8.1 Neatness |
| 7.8.2 AND, OR |
| 7.8.3 Write on one side only |
| 7.8.4 Word problems |
| 7.9 Math ideas |
| 7.9.1 Absolute values |
| 7.9.2 Addition and subtraction |
| 7.9.3 Axioms |
| 7.9.4 Closure |
| 7.9.5 Concrete ideas |
| 7.9.6 Conversion factors and units |
| 7.9.7 Cross multiply |
| 7.9.8 Domain and range |
| 7.9.9 Equality |
| 7.9.10 Equations |
| 7.9.11 Functions |
| 7.9.12 Geometric mean |
| 7.9.13 Indirect proof |
| 7.9.14 Inverse |
| 7.9.15 Isolating the x |
| 7.9.16 Lines |
| 7.9.16.1 Two points define a line |
| 7.9.16.2 Slope |
| 7.9.16.3 Parallel and Perpendicular Lines |
| 7.9.16.4 Standard Form of a Line |
| 7.9.17 Mathematical convention |
| 7.9.18 Negative numbers |
| 7.9.19 Order of operators in expressions |
| 7.9.20 Per |
| 7.9.21 Prime numbers |
| 7.9.22 Relations and functions |
| 7.9.23 Relative change |
| 7.9.24 Rounding |
| 7.9.25 Similarity |
| 7.9.26 Simultaneous equations |
| 7.9.27 Special triangles |
| 7.9.28 Term and factor |
| 7.9.29 Variables on the left |
| 7.10 Checking |
| 7.11 Percentages and blonde girls |
| 7.11.1 Example from current news |
| 7.11.2 Example from class |
| 7.12 F-C conversion |
| 7.12.1 Which is hotter, C or F? |
| 8 Teacher's actions |
| 8.1 List of things for the teacher |
| 8.2 Knowledge of the subject |
| 8.2.1 Examples of concepts |
| 8.2.2 Solving equations |
| 9 Books and quotes |
| 9.1 Corporate America |
| 9.2 Fifty Nifty Ways |
| 9.3 Human Intellegence |
| 9.4 Learned Optimism |
| 9.5 The Cheating Culture |
| 9.6 The Red Pencil |
| 9.7 The Road to Reality |
| 9.8 Science and the Retreat from Reason |
| 9.8.1 Quotes |
| 9.9 The Only Three Questions That Count |
| 9.10 Some Internet sites |
| 9.11 Some quotes |
| 9.11.1 General quotes |
| 9.11.2 Graduate education |
| 9.11.3 Imagery |
| 9.11.4 Machine thinking |
| 9.11.5 Morality |
| 9.11.6 Positive values |
| 9.11.7 Rational thought |
| 9.11.8 Science gives dignity to human existence |
| 9.11.9 Science magazine |
| 9.11.10 Scientific principles |
| 9.11.11 Thomas Jefferson |
| 9.11.12 Understanding of a problem |
© 2007 Dr. Sanford Aranoff