Mathematics Concept & Skill Development Lecture Series: Webvideo consolidation of site lessons and lesson ideas in preparation. Price to be determined. Bright Students: Top universities want you. While many have high fees: many will lower them, many will provide funds, many have more scholarships than students. Postage is cheap. Apply and ask how much help is available. Caution: some programs are rewarding. Others lead nowhere. After acceptance, it may be easy or not to switch. Are you a careful reader, writer and thinker?
Five logic chapters lead to greater precision and comprehension in reading and
writing at home, in school, at work and in mathematics. Early High School Arithmetic
Deciml Place Value  funny ways to read multidigit decimals forwards and
backwards in groups of 3 or 6. Early High School Algebra
What is
a Variable?  this entertaining oral & geometric view
may be before and besides more formal definitions  is the view mathematically
correct? Early High School GeometryMaps + Plans Use  Measurement use maps, plans and diagrams drawn to scale.  Coordinates  Use them not only for locating points but also for rotating and translating in the plane.  What is Similarity  another view of using maps, plans and diagrams drawn to scale in the plane and space. Many humanmade objects are similar by design.  7 Complex Numbers Appetizer. What is or where is the square root of 1. With rectangular and polar coordinates, see how to add, multiply and reflect points or arrows in the plane. The visual or geometric approach here known in various forms since the 1840s, demystifies the square root of 1 and the associated concept of "imaginary" numbers. Here complex number multiplication illustrates rotation and dilation operations in the plane.  Geometric Notions with Ruler & Compass Constructions : 1 Initial Concepts & Terms 2 Angle, Vertex & Side Correspondence in Triangles 3 Triangle Isometry/Congruence 4 Side Side Side Method 5 Side Angle Side Method 6 Angle Bisection 7 Angle Side Angle Method 8 Isoceles Triangles 9 Line Segment Bisection 10 From point to line, Drop Perpendicular 11 How Side Side Side Fails 12 How Side Angle Side Fails 13 How Angle Side Angle Fails 
www.whyslopes.com >>  Volume 1A Pattern Based Reason >> Chapter 10 Responsibility Next: [Chapter 11 Accidental Patterns.] Previous: [Chapter 9 WhatisinChapters10to18.] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12][13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] Chapter 10, ResponsibilityIn this chapter, we give a short story: a conflict between the owners of a cat and a dog about who or what is responsible for an accident. The murky situation leads into a discussion of cause and effect, and then responsibility versus freedom (the limits of freedom) and the absence of liability. Finally, first principles or patterns for the assignment of responsibility and liability are stated or suggested last. Fred and FelixFelix the cat lives in a onetree park. Imagine every time Fred the dog visits the onetree park, Felix climbs the tree. On one visit, Felix steps on a rotten branch, falls and breaks a leg. In what sense is Fred the cause of this accident? In what sense is Fred the dog responsible? The argument between the owners of these animals follows Felix's owner claims that Fred is a mean, vicious dog. So Felix had to climb the tree to escape Fred. The accident would not have occurred without Fred's visit to the park. So according to Felix's owner, Fred was the cause of the accident. Fred's owner counters that Fred is a very friendly, goodnatured dog, not interested in harming Felix. Felix was perfectly safe when Fred visited the onetree park. Moreover, on the day in question, the broken leg was a result of Felix's unnecessary actions, not Fred's. Fred's owner continues: On the day in question, Fred as usual visited the park to walk about. The idea that Fred is vicious is a figment of Felix's imagination. While Felix climbed the tree every time Fred visited the onetree park, Felix was climbing the tree at his own initiative. Felix had a false fear of Fred. The cat Felix was therefore responsible by himself for climbing the tree. Felix's owner then suggests that Fred's owner is responsible for the accident since the latter should know about Felix having a natural fear of dogs. Fred's owner replies …. The argument goes on. Most of the neighbors listening to this argument agree with Felix's owner. They suggest Fred be punished. Fred's owner refuses. A year later, Felix the cat in chasing a bird climbed into the tree again, and fell on the other leg. Felix the fragile feline lived. Poor Fred was not there to be blamed. (One neighbor who missed the result of the argument wondered where or how is Fred? He did not have enough information to answer this question. Limits to FreedomHuman activities are based on regularity. In our daily lives, we know when we do a first action. Human activities are based on regularity. In our daily lives, we know when we do a first action A, then a second action B will (almost always) occur. The first action A is said to be a cause of the second B. Of course, the second event B may have another cause. That is, the second action B may occur without the first action A if there is a third action C with the property that when this third action C occurs, so does or must the second action B. As a human being, if you deliberately make a situation A happen, then you caused A to occur deliberately. The word deliberately is often omitted. It is often understood or assumed, if it is not spoken. On the other hand if you accidentally make a situation A happen, then you caused A accidentally. Are you responsible for harmful results that you accidentally caused? Your responsibility in this matter may depend on what you knew and on your local legal system. Of course, when accidental situation A appears to be good, many will claim credit if not responsibility. The removal of responsibility and liability for our actions gives greater freedom to act. For instance, when drivers are not held liable for their actions, the roads and highways become more dangerous. Damages and compensation for accidents are not automatically available. Liability and insurance here lessen the material, but not the human, consequences of accidents. Most states and countries require car drivers and owners to pass driving exams and to pay for insurance. In some states and countries, an uninsured or an uninsurable driver is allowed one accident before being forbidden to drive. In other states or countries, that represents one accident too many. So people without insurance are not allowed to drive. For the safety of myself and my neighbors, I prefer to make my home in a region where driving without insurance is forbidden. Insurance is needed so that people hurt through accidents may be compensated, that is, taken care of. In contrast to the situation with cars, the liability of businesses and industries is often removed or lessened via regulation or specially written (or loosened) laws. But the removal of legal liability also removes the enforcement of responsibility. Without this liability, reckless and uninsured drivers and their vehicles are tolerated and encouraged. If insurance is not affordable for some new industrial activity then the scale of that activity should be decreased until the price of full liability insurance becomes feasible. There should be no rush. An idea that is good today can still be pursued tomorrow. Uninsurable drivers and uninsurable vehicles should not be moving in the public domain! Principles For ResponsibilityResponsibility for actions could be based on the following principles.
No doubt the above principles can be refined or others added. All possibilities have not been considered in suggesting them. Selby A, Volume 1A, Pattern Based Reason, 1996. www.whyslopes.com >>  Volume 1A Pattern Based Reason >> Chapter 10 Responsibility Next: [Chapter 11 Accidental Patterns.] Previous: [Chapter 9 WhatisinChapters10to18.] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12][13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] 
Road Safety Messages for All: When walking on a road, when is it safer to be on the side allowing one to see oncoming traffic? Play with this [unsigned]
Complex Number Java Applet
to visually do complex number arithmetic with polar and Cartesian coordinates and with the headtotail
addition of arrows in the plane. Click and drag complex numbers A and B to change their locations.
Pattern Based ReasonOnline Volume 1A, Pattern Based Reason, describes origins, benefits and limits of rule and patternbased reason and decisions in society, science, technology, engineering and mathematics. Not all is certain. We may strive for objectivity, but not reach it. Online postscripts offer a storytelling view of learning: [ A ] [ B ] [ C ] [ D ] to suggest how we share theory and practice in many fields of knowledge. Site Reviews1996  Magellan, the McKinley Internet Directory:Mathphobics, this site may ease your fears of the subject, perhaps even help you enjoy it. The tone of the little lessons and "appetizers" on math and logic is unintimidating, sometimes funny and very clear. There are a number of different angles offered, and you do not need to follow any linear lesson plan. Just pick and peck. The site also offers some reflections on teaching, so that teachers can not only use the site as part of their lesson, but also learn from it. 2000  Waterboro Public Library, home schooling section:
CRITICAL THINKING AND LOGIC ... Articles and sections on topics such as
how (and why) to learn mathematics in school; patternbased reason;
finding a number; solving linear equations; painless theorem proving;
algebra and beyond; and complex numbers, trigonometry, and vectors. Also
section on helping your child learn ... . Lots more!
2001  Math Forum News Letter 14,
... new sections on Complex Numbers and the Distributive Law
for Complex Numbers offer a short way to reach and explain:
trigonometry, the Pythagorean theorem,trig formulas for dot and
crossproducts, the cosine law,a converse to the Pythagorean Theorem
2002  NSDL Scout Report for Mathematics, Engineering, Technology  Volume 1, Number 8
Math resources for both students and teachers are given on this site,
spanning the general topics of arithmetic, logic, algebra, calculus,
complex numbers, and Euclidean geometry. Lessons and howtos with clear
descriptions of many important concepts provide a good foundation for
high school and college level mathematics. There are sample problems that
can help students prepare for exams, or teachers can make their own
assignments based on the problems. Everything presented on the site is
not only educational, but interesting as well. There is certainly plenty
of material; however, it is somewhat poorly organized. This does not take
away from the quality of the information, though.
2005  The NSDL Scout Report for Mathematics Engineering and Technology  Volume 4, Number 4
... section Solving Linear Equations ... offers lesson ideas for
teaching linear equations in high school or college. The approach uses
stick diagrams to solve linear equations because they "provide a concrete
or visual context for many of the rules or patterns for solving
equations, a context that may develop equation solving skills and
confidence." The idea is to build up student confidence in problem
solving before presenting any formal algebraic statement of the rule and
patterns for solving equations. ...
Senior High School Geometry

Euclidean Geometry  See how chains of reason appears in and
besides geometric constructions. Calculus Starter Lessons
Why study slopes  this fall 1983 calculus appetizer shone in many
classes at the start of calculus. It could also be given after the intro of slopes
to introduce function maxima and minima at the ends of closed intervals. 