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Conceptual Knowledge & Skills (pdf file)
Task Group
Progress Report
January 11, 2007
While there is agreement to the sequence of particular concepts and skills in PreK-8 mathematics (e.g. whole numbers), this is not true with algebra. Therefore the following list of essentials should not be considered a linear sequencing of these topics.
Elements of Algebra
Symbols and expressions
Geometric sequences and series
Polynomial expressions
Rational expressions
Radical expressions
Arithmetic and geometric sequences and series
Linear Relations
Fundamental relationships between linear equations and the graphical representations of such equations
Solving problems with linear equations
Linear inequalities and their graphs – to include compound inequalities
Graphing and solving systems of simultaneous linear equations
Quadratic Relations
Factors and factoring of trinomials with integer coefficients
Factors and factoring of polynomials
Completing the square in quadratic expressions
Quadratic formula and factoring of general quadratic polynomials
Using the quadratic formula to solve equations
Functions
Quadratic functions – solve problems involving quadratic functions
Fundamental relationships between quadratic functions and their graphs
Polynomial functions (know graphs of basic functions)
Simple nonlinear functions (e.g. square and cube root functions; absolute value)
Rational exponents and exponential functions
Logarithmic functions
Rational functions
Trigonometric functions
Fitting simple mathematical models to data
Polynomials
Roots and factorization
Complex numbers and operations
Fundamental theorem of algebra
Binomial coefficients (and Pascal’s triangle)
Mathematical induction and the binomial theorem
Combinatorics and finite probability
Connections between algebra and other areas (e.g. linear functions and best fit in statistics; similarity relationships and distance in geometry)
________________
Panelists Contributing
– Francis (Skip) Fennell, Task Group Chair
– Larry Faulkner
– Liping Ma
– Wilfried Schmid
– Tyrrell Flawn, Staff
Other Contributors
– Hung-Hsi Wu
– Joan Ferrini-Mundy
– Sandra Stotsky
– Outside Reviewers - several
(copied from the documents Lynn posted on the 18th)
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6 comments:
I will absolutely be looking for more information about the sequence of topics in high school algebra.
Should one teach just a few rules about "moving x" and then immediately introduce "solve for x"? or is it better to develop super facility with everything that can be done to a polynomial before solving for x. Jacob's, for example does it one way. But I've found an older book that does it differently.
I'll be eager to hear.
This topic is being taught as a complete jumble at IMS.
What is the older book?
I have a question.
This is algebra 1 & algebra 2, right?
It's from a 1950's algebra book, college level. Probably not so relevant to high school but that's an ongoing argument going on at my house right now. LOL.
My husband is saying that there was a lot of selection bias concerning who took algebra to begin with, even in high school, so they were able to cover harder topics more in depth than is possible today.
I just blogged on the book in my most recent blog entry. It's probably not that relevent.
oh great - I'll go find it - or do you want to post a link?
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