We’ve now gone through all the algebra – more accurately, “algebra” – sections of ACARA’s new mathematics curriculum. Parallel to our Worst Number Lines post, the following is our list of the worst algebra lines. Once again, it is important to note that these few lines do not begin to convey the unrelenting stupidity and triviality of the curriculum.
8 ÷ 2(2 + 2) = ?
This is really a PoSWW. Except, there are a lot of words.
Above is one of those stupid BODMAS things, which appear in the media about once a month. Except, this one has just been sorted by a couple of Canadian Maths Ed professors, in a Conversation article titled The Simple Reason a Viral Math Question Stumped the Internet. Regular readers will be aware of our method of resolving such questions, but we think there are aspects of the Conversation article that warrant specific whacks.
Courtesy of frequent commenter Red Five, a maddening and absolutely hilarious article:
Guessing C For Every Answer Is Now Enough To Pass The New York State Algebra Exam
My student, River, spent more time in the courtroom than the classroom last year. One Friday night in September, a drunk friend called and asked for a ride home from a party. River obliged. That’s a problem when you’re 14 years old. On his excellent adventure with his drunk friend, River drove over the landscaping of several local businesses and ended with his car in the woods caught in a web of maple sugaring lines. Things spiralled from there. Continue reading “RatS 24: Ed Knight – Guessing C on a NY Algebra Test”
We have the bigger projects (AC, ITE, SD) in the works, plus an FOI appeal to do, plus 2000 words for a lefty magazine due in a couple weeks. We’re kinda busy. But, we’ll try to keep the general posts ticking along. This one is some fun, plus some history and a couple of puzzles.
One of the all-time great maths scenes is Abbott and Costello’s famous bit, where Lou Costello proves that 7 x 13 = 28:
It’s Greg Ashman‘s fault. It’s always Greg Ashman’s fault.
A couple days ago Ashman had an excellent post, on Jo Boaler and her California Dreamin’ curriculum. That draft curriculum has been, let’s say, hammered, particularly by mathematicians. Not that such criticism slows Boaler:
“We understand education, and they have no experience studying education. Mathematicians sit on high and say this is what is happening in schools.” Continue reading “PoSWW 23: Jo Boaler is Challenged”
OK, hands up who thought there was ever gonna be a second NotCH?
We’re not really a puzzle sort of guy, and base ten puzzles in particular tend to bore us. So, this is unlikely to be a regular thing. Still, the following question came up in some non-puzzle reading (upon which we plan to post very soon), and it struck us as interesting, for a couple reasons. And, a request to you smart loudmouths who comment frequently:
Please don’t give the game away until non-regular commenters have had time to think and/or comment.
Start by writing out a few terms of the standard doubling sequence:
1, 2, 4, 8, 16, 32, 64, etc. Continue reading “NotCH 2: A Digits Puzzle”
More or less by accident, this post is the beginning of a new series: Not Crap Here.
A couple of people have suggested that we could occasionally include Dr. Jekyll material on this blog. You know, helpful stuff. It’s a decent idea, if our current thoughts weren’t so influenced by misanthropic disgust and murderous rage. Still, we’ve received two specific requests for the same old Jekyll material,* and which entailed some digging. Having finally dug, we’ve decided to post the material here, for whomever is interested. Whether or not there will ever be a NotCH 2 is anybody’s guess.
The following are Year 10 Number-Algebra content-elaborations in the current curriculum:
Apply the four operations to simple algebraic fractions with numerical denominators
expressing the sum and difference of algebraic fractions with a common denominator
using the index laws to simplify products and quotients of algebraic fractions
Solve linear equations involving simple algebraic fractions
solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution
representing word problems, including those involving fractions, as equations and solving them to answer the question
Not essential for all students to learn in Year 10.
God only knows how one develops fluency with expressions that cease to exist.
The previous A-Crash consisted of everything we could find in the Daft Curriculum on the algebraic treatment of polynomials and polynomial equations. This companion A-Crash consists of everything we could find in the Year 10 draft on the same material.
CONTENT (Year 10)
expand and factorise expressions and apply exponent laws involving products, quotients and powers of variables. Apply to solve equations algebraically
reviewing and connecting exponent laws of numerical expressions with positive and negative integer exponents to exponent laws involving variables
using the distributive law and the exponent laws to expand and factorise algebraic expressions
explaining the relationship between factorisation and expansion
applying knowledge of exponent laws to algebraic terms, and simplifying algebraic expressions using both positive and negative integral exponents to solve equations algebraically
CONTENT (Year 10 Optional Content)
numerical/tabular, graphical and algebraic representations of quadratic functions and their transformations in order to reason about the solutions of
connecting the expanded and transformed representations
deriving and using the quadratic formula and discriminant to identify the roots of a quadratic function
identifying what can be known about the graph of a quadratic function by considering the coefficients and the discriminant to assist sketching by hand
solving equations and interpreting solutions graphically
recognising that irrational roots of quadratic equations of a single real variable occur in conjugate pairs