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 >> Algebra Starter Lessons >> 3 Adding Words To Arithmetic Next: [4 A Brief Story of numbers and algebra.] Previous: [2 What is a Variable.] [1] [2] [3] [4][5] [6] [7] Words before Symbols: In the first instance, the use of letters in formulas to denote lengths or amounts stems from their shorthand role in providing a more compact description of a calculation. But that shorthand role of letters and symbols has limitations. For example, calculation of the perimeters of a triangle, quadrilateral and polygons in general may be simply given by the instruction: add the lengths of the sides. Before the introduction of algebra, that instruction can be understood and followed. In contrast, the algebraic description of the calculation of these perimeters introduces many letters and symbols, alone or with subscripts, and in doing so raises the level of complexity. That introduction of letters and symbols is has a role in the introduction of algebra but when the aim to show how to compute perimeters, algebraic expressions for perimeters are not needed. Before algebra begins, words may be also used to say when different counting or arithmetic methods lead to the same result. Here again the words may be simpler to understand and follow than the corresponding and far more complicated algebraic descriptions of the same mathematical rules or patterns. In particular, the following sequence of phrases describe common practices in primary and secondary mathematics more easily explained and understood with words. In mathematics lessons given by teachers not fully versed in algebra, the use of words in place of symbols makes instruction simpler with little or no loss of content and rigour. Explanations of why these interrelated practices work  all or some can assumed as axioms and those not assumed may explained in terms of the others. Oral Rules for ArithmeticEach rule or pattern in below has value in its own right. But the earlier ones lead to the last two. Moreover, these rules or patterns may developed and understood verbally before any algebraic description of properties of numbers, whole to real. The rules wordily given and explained reflect and extend the common knowhow in ways that may have takehome value.
The first two of the last three rules or patterns imply that sums and products of terms and factors may calculated and grouped (carefully) in different ways even before algebra begins. The distributive property of arithmetic with real numbers is introduced elsewhere with the aid of geometry and coupled with a column methods for calculating products of sums. See using geometry in algebra. Mastery of the algebraic form of properties of real numbers etc may be left to courses in pure mathematics. The modern mathematics course designs seen in my student days emphasized the algebraic form of arithmetic properties, but presented as axioms for real numbers etc. The use of algebra in that manner raise the level of complexity beyond the level of many students and teachers. Furthermore, in the senior high school development of mathematics, the necessary extensions to aid if not justify polynomial addition, subtraction, multiplication were indicated orally and not written algebraically. Thus the use of oral rules to justify if not explain has been part of secondary mathematics previously, that being for ease of exposition. With the expansion of the role of words before and in algebra to expand and enrich the common knowhow or knowledge in mathematics, Upper high school mathematics and calculus instruction may have balance the verbal and algebraic description of arithmetic properties of numbers, whole to real or complex. Course design and delivery will have to adjust. www.whyslopes.com >> Algebra Starter Lessons >> 3 Adding Words To Arithmetic Next: [4 A Brief Story of numbers and algebra.] Previous: [2 What is a Variable.] [1] [2] [3] [4][5] [6] [7] 
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. 