Assumption 1:There are basic operations skills that must be mastered in order to succeed in everyday life. Assumption 2:There are basic "word problems" that correspond witheveryuseful "math" problem.
About "contextual learning":Although students must be able to display the following skills in a conventional standardized-test environment, we believe that students will not effectively learn these skills unless they are also represented in their real-world contexts. In order to truly learn these skills, students must see them, recognize them, explore them, discuss them, and use them to understand the real world. Afterwards, if necessary, certain skills can be reinforced using traditional "workbook-style" exercises, but only as a supplement to contextual learning.
Recognizing numbers as words to communicate quantity
Adding, subtracting, multiplying, dividing whole numbers
Simplifying expressions that have parentheses
Recognizing basic patterns and sequences
Exponents and how to use them
Order of operations and why we need rules like this one
Adding, subtracting, multiplying fractions and mixed numbers
Adding, subtracting, multiplying, dividing decimal numbers
Percents are both fractions and decimals
Comparing quantities on a number line: positive values of fractions, decimals, percents
Using negative numbers to represent reality
Adding, subtracting, multiplying, dividing negative numbers
Comparing values of different kinds of positive and negative real numbers using a number line
Using combinations of decimals, fractions, negative numbers, and the basic operations
Calculating absolute value as a function
Measurement of length, length as distance, absolute value as distance from zero
Perimeter of basic shapes
General awareness of different units, including the "English" and "Metric" systems
Converting between different units of length
Areas of basic shapes, converting between different units of area
Volumes of basic solids, converting between different units of volume
Basic angles and how to measure them
Variables and constants: why we use letters in math class instead of numbers
Expressions and equations: what's the difference and when we use each
Translating English words and phrases into math language (and back into English)
Using ratios and percents in expressions and equations
Understanding and using square roots and other roots
Understanding and using scientific notation
Gathering and organizing data
Understanding median, mode, mean (average), and standard deviation
Using charts and graphs to describe the world
Rectangular coordinates, using two-dimensional graphs (x and y axis)
Compass bearings, polar coordinates, and different coordinate systems
Assumption 2: There are basic "word problems" that correspond with every useful "math" problem.
About "contextual learning": Although students must be able to display the following skills in a conventional standardized-test environment, we believe that students will not effectively learn these skills unless they are also represented in their real-world contexts. In order to truly learn these skills, students must see them, recognize them, explore them, discuss them, and use them to understand the real world. Afterwards, if necessary, certain skills can be reinforced using traditional "workbook-style" exercises, but only as a supplement to contextual learning.
Recognizing numbers as words to communicate quantity
Adding, subtracting, multiplying, dividing whole numbers
Simplifying expressions that have parentheses
Recognizing basic patterns and sequences
Exponents and how to use them
Order of operations and why we need rules like this one
Adding, subtracting, multiplying fractions and mixed numbers
Adding, subtracting, multiplying, dividing decimal numbers
Percents are both fractions and decimals
Comparing quantities on a number line: positive values of fractions, decimals, percents
Using negative numbers to represent reality
Adding, subtracting, multiplying, dividing negative numbers
Comparing values of different kinds of positive and negative real numbers using a number line
Using combinations of decimals, fractions, negative numbers, and the basic operations
Calculating absolute value as a function
Measurement of length, length as distance, absolute value as distance from zero
Perimeter of basic shapes
General awareness of different units, including the "English" and "Metric" systems
Converting between different units of length
Areas of basic shapes, converting between different units of area
Volumes of basic solids, converting between different units of volume
Basic angles and how to measure them
Variables and constants: why we use letters in math class instead of numbers
Expressions and equations: what's the difference and when we use each
Translating English words and phrases into math language (and back into English)
Using ratios and percents in expressions and equations
Understanding and using square roots and other roots
Understanding and using scientific notation
Gathering and organizing data
Understanding median, mode, mean (average), and standard deviation
Using charts and graphs to describe the world
Rectangular coordinates, using two-dimensional graphs (x and y axis)
Compass bearings, polar coordinates, and different coordinate systems