Monday, January 2, 2017

Comparison of Algebra 2 textbooks

A look at Algebra 2 textbooks (as promised a month ago):

Dolciani (1977)
Heath (1998)
Pearson (2012)
Chapter 1
Vocabulary and the Operations of Algebra (Expressions, operations, solving 1 variable equations)
Review of Basic Algebra (Operations, Solving 1 variable equations, inequalities, absolute value equations and inequalities)
Expressions, Equations, & Inequalities (including absolute value)
Chapter 2
Properties of Real Numbers (including compound inequalities)
Linear Equations (Graphing, slope, 2 variable inequalities, absolute value graphs)
Functions, Equations, and Graphs (linear and absolute value)
Chapter 3
Linear Open Sentences (Graphs, slope, linear equations, systems of equations & inequalities)
Systems of Linear Equations and Inequalities
Systems of Equations and Inequalities (linear only)
Chapter 4
Functions & Polynomials (linear functions, direct variation, multiplying and dividing polynomials, synthetic division—optional)
Matrices and Determinants
Quadratic Functions and Equations
Chapter 5
Factoring Polynomials (GCF, quadratics—factoring and solving)
Quadratic Equations and Parabolas (Solving, graphing, quadratic formula, completing the square, complex numbers, quadratic inequalities)
Polynomials and Polynomial Functions (including the fundamental theorem of algebra, remainder theorem, rational root theorem)
Chapter 6
Rational Expressions
Functions (Operations, inverse functions, transformations of function graphs, recursive functions)
Radical Exponents and Rational Functions
Chapter 7
Radicals and Irrational Numbers
Powers, Roots, and Radicals
Exponential and Logarithmic Functions
Chapter 8
Quadratic Equations and Functions (Solving, complex numbers, quadratic formula)
Exponential and Logarithmic Functions
Rational Functions
Chapter 9
Quadratic Relations and Systems (Distance formula—yes, I know! Perpendicular slope, conics, solving quadratic systems)
Polynomials and Polynomial Functions (operations, division, synthetic division, fundamental theorem of algebra, remainder theorem, rational root theorem)
Sequences and Series
Chapter 10
Exponential Functions and Logarithms
Rational Functions
Conic Sections
Chapter 11
Sequences and series
Quadratic Relations (conics)
Probability and Statistics
Chapter 12
Permutations, Combinations, and Probability
Sequences and Series
Chapter 13
Trigonometric Relations and Functions
Periodic Functions and Trigonometry
Chapter 14
Trigonometric Graphs, Equations, and Identities
Trigonometric Identities and Equations
Chapter 15
Trigonometric Identities and Formulas
Probability and Statistics

Chapter 16
Circular Functions and their Inverses (Radians, inverse trig functions)

The largest takeaway is how today’s textbooks rush ahead into more difficult concepts. Quadratic Functions waits for a later time in the old texts while the current textbook pushes them early and moves ahead. It is also noteworthy that in years past, classes rarely reached the last two or three chapters in the book, which were an advance look at the next course. It was no problem back then as there was no standardized test to contend with and the following year, the new teacher picked up where the old teacher had ended.

It is hard to understand the demand of Common Core mathematics looking at these textbooks. They cover all the topics under the Algebra 2 umbrella. You will only really understand what has taken place when we take a look at Algebra 1 (which I will have to do some work to report as I don’t have access to a current textbook.) But here’s the gist: so much of Algebra 2 has been moved to Algebra 1 that most of the year (in Florida) the students are reviewing what they were supposed to learn earlier.