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 
whyslopes.com >> Parent Center Parent Center Reading Guide. 1 Speaking Skills. 2 Reading and Writing Skills. 3 Preparing for Science Studies. 4 Learning Takes Time and Effort. 5 Patience Please for Yourself and Your Charges. 6 Discipline Who is in Charge Conserving Authority. 7 Student Motivation. 8 The Effect of Negative Remarks. 9 Streaming by Student Cooperation. 10 Ends values for work study instruction. 11 Help and Defend Your Child or Teens Education. 12 Goals and Objectives For Mathematics. 13 Addition and Addition Tables. 14 Multiplication and Times Tables. 15 Counting For Parents. 16 Secondary Mathematics Tips. 17 Math Booklets for children and young teenagers. 18 Math Booklets for children and young teenagers Details. Folder Content: 19 pages. Introduction to Section Content + General AdviceSee too the general advice on helping your child or teenager in mathematics below.
General Advice For Mathematics Skill DevelopmentIn general, explain to your child or teenager that skills in mathematics and other subjects need to be seen to believed. In arithmetic and beyond, talk about the need to do and record work step by step, so that each step can be checked as done or later. Emphasize too the domino effects of errors, that is, how an error in one step leads all or most following steps to be in error as well. If local textbooks are too hard for you to follow then your child or teenager will have difficulty as well. For children or preteens ages 3+ to 12 years of aged learning mathematics, use parent friendly, Work Booklets to build or rebuild skills and confidence. Emphasize mastery arithmetic and geometry has value in adult and daily life. say this mastering is part of growing up, like learning to read exactly what is meant, and to write exactly what they mean. For children or teenagers, ages 12 and up, site material may help you check and develop skills in stronger ways that seen in school. Mastery of site material unfortunately requires adult level patience and reading abilities that most students, except for the gifted and talented do not have. So you or a tutor will have to give less gifted learners ages 13 to 19, skills and concepts to master in parallel to the skills and concepts that teachers provide in school. Site material was written to provide alternative and clearer paths for development of key skills and concept in mathematics and logic because of gaps and steps too large in the secondary level course design and delivery. The tutor or school system able follows site steps in arithmetic, geometry and algebra offers your child a firmer base for calculus and senior high school mathematics. But there is no 100% guarantee your child or will be able to follow the site program alone or with help  that remains to be seen. In the early years of secondary school, your teenager may need to be tutored to prepare them for course test and finals, besides following site steps as site material and your local school may follow two different paths. But within a year or two of effort, site steps, ends and values for skill development should help your child do well in school. But again there is no guarantee your child will be able to follow the site program  that remains to be seen. So you have explore site material or rely on the judgement of others to decide what route to follow. Good luck. If you are lucky, your local school does not follow the newage, constructivist approach to education. In it,
Teachers are further told that giving students skills and concepts to master is a substandard form of instruction. At the same time, school authorities and parents like you want their children and teenages to do well on final examinations. Such final examinations test student mastery of skills and concepts that used to be given directly instead of through hints. There is a contradiction between theories that hold students should be taught indirectly, and the practice of wanting students to do well on tests and final examinations of skills and concepts that previous educational theories and practices tried to develop directly. That being said, site material stems from the observation of gaps and steps too large or missing in the direct explanation of key skills and concepts. In particular, site material aims to remedy the foregoing by providing teachers and tutors, and the gifted or talented, clear and direct explanations likely to ease, avoid and even explain for common fears and difficulties. Clear HowTOs, ends and values for the direct explanation of given skills and concepts need to be wellknown and welldocumented before instructors, wellversed or not in mathematics and logic, are called upon to develop skills and concepts indirectly. Otherwise, indirect instruction will simple compound the shortcomings of direct instruction in skill and concepts development. The problem with constructivism is that moves the focus of education away from worldly concerns. This viewpoint of constructivistled indirect instruction stems from the perspective that arts and disciplines at home, in school and the workplace require an observable and verifiable mastery of visible and hence verifiable skills. Skills and abilities in many arts and discipline need to be seen to be shared, to be welldefined and believed. In particular, skill in cooking at home and in a restaurant may involve some thought or reflection that we cannot see, but that skill needs to be seen to believe. In general, we do not want cooks who think, we want cooks that can do. Likewise, we want cloths designers and makers, plumbers, electricians, interior decorators, construction workers, factory workers, engineers, bookkeepers, accountants, scientists and mathematicians who not only think about what needs to be done in the privacy of their own minds, but also display skill in ways that can be seen and judged. The format of that display may vary from discipline to discipline. In mathematics itself, practical concerns suggest the following ends and values. Instruction should first serve on the development of basic skills and concepts with of service in daily and adult life. Second, it should serve the needs of precollege or precalculus occupuations. Finally, it should serve the needs of calculus and precollege courses in science and technology. Calculus is required for college level studies in accounting, commerce, engineering, science, technology, mathematics and mathematics education. Here serving the first end may serve the next two, and serving the second may serve the last. Further, there is no harm in college bound students seeing skill and concepts for adult and daily life, and for precollege work destinations as a parachute or safety net as there is no guarantee that their college studies will succeeed. Mastery of logic, awareness of the domino effect of errors, and awareness of how many later skills and concepts depend on earliers could provide further ends and VALUES to guide both learning and teaching. Finally, in reaction to my description of these worldly ends and values for instruction or skill and concept development, a colleague kindly observed the absence of higher level cultural end and values here. So more thought may be required. whyslopes.com >> Parent Center 
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. 