The Purpose of this Curriculum is to:
1. Allow more regular students to take up through calculus in high school.
2. Address the high math student fail rate by allowing more students to enjoy math learning success.
3. Not reduce rigor, rather, focus students on key concepts.
Every student should be able to move through the following courses: 7th Grade Math (7th grade) , Algebra I (8th grade) , Geometry I (9th grade) , Algebra II (10th grade) , Math Analysis (11th grade) , and Calculus (12th grade)
There are really only 5-7 key concepts within each of these courses.
Articulation between the courses is essential.
The 5-7 key concepts can be amply demonstrated and practiced within an 80 page text.
There is a single teacher text which contains tests and answers for all six courses.
There are three domains of knowledge: vocabulary, low-level concepts and application.
The actual curriculum duration of each course is one semester.
Passing students may move on.
Failing students can repeat in the second semester and summer and still remain on track.
The curriculum is predicated on clarity being the number one predictor of student success.
Class sets can be purchased at significant discounts over retail pricing.
7th Grade Math declarative knowledge needs to include:
Students being able to explain and use functions, rate (slope), equational, pictorial (graphing). 7th Grade Math procedural knowledge needs to include: How to calculate a rate, how to solve equations, how to draw the picture of an equation.
Algebra I declarative knowledge needs to include:
Students being able to explain and use functions, the application of a tangent line to a curve, rate (slope) of the tangent line to a curve, equations of curves and lines, critical points. Algebra I procedural knowledge needs to include: The finding of the equations of lines and the finding of critical points for curves and lines through the use of functions.
Geometry I declarative knowledge needs to include:
Students being able to explain and use length, area, volume, area under lines and curves, volume when areas are rotated. Geometry I procedural knowledge needs to include: The finding of lengths, finding areas, finding volumes, finding area under lines and curves and finding the volume when areas are rotated.
Algebra II declarative knowledge needs to include:
Students being able to explain and use life-like functions and their complex graphs with undefined portions, jumps, continuity, limits, the slope of a tangent to a curve through the definition of the derivative. Algebra II procedural knowledge needs to include: The finding of limits at infinity, the finding of slopes and equations of lines tangent to a curve through the definition of the derivative.
Math Analysis declarative knowledge needs to include:
Students being able to explain and use area under a curve with integration, volume produced by rotating the area through integration. Math Analysis procedural knowledge needs to include: The finding of area produced through integration and the finding of volume through integration.
Calculus declarative knowledge needs to include:
Students being able to explain the applicability of calculus to human infrastructure design and maintenance. Calculus procedural knowledge needs to include: The calculation of logistic problems, optimization problems, the graphing of complex functions and the determining of actual functions which represent physical behavior.
Attitudinal knowledge is enjoyment of math through success and ease.