I was on the virtually powerless governing body of the local primary school in the UK when the first National Curriculum came out, some time in the early 80’s. Very “New Math”y. Reworked a few years later. Here is some stuff from the UK Dept for Education about the latest rewrite. The old “Back to Basics” brigade are in the ascendant, but at least the UK is not drowning under High Stakes Testing. Have a look:
Key stage 1 and 2 (ages 5 to 10)
Key stage 3 (11 to 13)
key stage 4 (14,15)
ans about assessment
Only the dedicated study math in the last 2 years.
You might find this interesting as well, just look at how little time is spent taking tests, and then only in three of the years.
Then I found this. Looks familiar !
Why the big curriculum change?
The main aim is to raise standards, particularly as the UK is slipping down international student assessment league tables. Inspired by what is taught in the world’s most successful school systems, including Hong Kong, Singapore and Finland, as well as in the best UK schools, it’s designed to produce productive, creative and well educated students.
Although the new curriculum is intended to be more challenging, the content is actually slimmer than the current curriculum, focusing on essential core subject knowledge and skills such as essay writing and computer programming.
This is definitely worth a read.
Here is a quote:
“High schools focus on elementary applications of advanced mathematics whereas most people really make more use of sophisticated applications of elementary mathematics. This accounts for much of the disconnect noted above, as well as the common complaint from employers that graduates don’t know any math. Many who master high school mathematics cannot think clearly about percentages or ratios.”
And here is the link:
Link found on f(t)’s blog
Filed under abstract, algebra, CCSS, Common Core, depth, education, K-12, math, standards, teaching, tests
It’s strange how one can read something many times and miss the complete stupidity of it, in math at any rate.
This is from the CCSSM Grade 8:
The Number System 8.NS (Grade 8)
Know that there are numbers that are not rational, and approximate
them by rational numbers.
2. Use rational approximations of irrational numbers to compare the size
of irrational numbers, locate them approximately on a number line
diagram, and estimate the value of expressions (e.g., π2). For example,
by truncating the decimal expansion of √2, show that √2 is between 1 and
2, then between 1.4 and 1.5, and explain how to continue on to get better
I need an approximation to √2. Just get me the decimal expansion, please. Oh, and I need it to 73 decimal places.
Do I have to explain to the authors of this garbage that the only way I am going to get anywhere with √2 is by a process of successive approximation, NOT THE OTHER WAY ROUND ! !
And just try doing this for pi.
“I know that there are irrational numbers”. “How do you know that?”. “Because my teacher told me”.
And where will I encounter π2 ? Or “estimate the value of pi-e”.
And when we get to High School we find:
Use properties of rational and irrational numbers.
3. Explain why the sum or product of two rational numbers is rational;
that the sum of a rational number and an irrational number is irrational;
and that the product of a nonzero rational number and an irrational
number is irrational.
I find real difficulties explaining the last point.
I am not proposing that we go as far as Cauchy Sequences or Dedekind cuts, but if they cannot do a better job than this the topic is best stopped at “√2 is irrational and here’s why”. How many students can prove that √2+√3 is irrational?
Thank you Audrey Watters for leading me to this exposure of the behaviour of testing corporations.
These two are MUST READs, and should be passed on to everybody:
“How’s your Mary doing?”.
“She’s doing well. She’s 8 now. She’s in Grade 3. She really enjoys the Pre-Algebra and the Pre-Textual Analysis.”.
I thought I had found them all, but NO.
Subtraction. Read this
Operations and Algebraic Thinking
• Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
What has subtraction got to do with taking apart ???
(The examples are all of the form 9 = 3 + 6 and so on).
Also there is NO mention at all of subtraction as a way of finding the difference between two numbers, or of finding the larger of two numbers (anywhere).
While I am in critical mode I offer two more, less awful, horrors from Grade 1:
“To add 2 + 6 + 4,…” and “For example, subtract 10 – 8″.
The poor symbols are clearly in great pain at this point. Just read aloud exactly what is written…..
Testing to destruction.
“IIHS Hyundai Tucson crash test” by Brady Holt – Own work. Licensed under CC BY 3.0
A method used in manufacturing for product testing, where the product is
designed for a single action, and is used in practice as an insurance. The
best example is vehicle air bags. To see if they work a car is driven into
a wall, and the effect on the dummy people in the car is assessed.
Unfortunately some medical procedures can have a similar effect, of course
unintended. The classic case is amniocintesis, a procedure for assessing
the presence of Down’s Syndrome in the fetus. The reality was that the
probability of a fetus having the syndrome was way smaller than the
probability of the procedure itself causing a miscarriage. Initially, and
for quite a long time this was not realised. Eventually the test was only
offered to women who had a higher chance anyway of having a syndrome baby.
Could there be a connection between this stuff and the roll out of high
stakes testing in schools. Think about it.
You should all read this, from the Washington Post October 2013.
“Why are some kids crying when they do homework these days? Here’s why, from award-winning Principal Carol Burris of South Side High School in New York”.
Here is the actual test paper (for 5-year-olds), to save you time:
the-math-test NY grade 1 Pearson
“Is” is a very overworked word, to the point of illogicality.
Technically in both cases none of them.
In everyday language we can get away with the question and accept the answer “The first one” even though it is actually a picture of the head of a dog.
In math we MUST be more precise, and ask “Which of these graphs is the graph of a function?”, or “Which of these graphs could represent a function?”.
A graph is NEVER a function, and a function is not a graph. If we actually followed the Common Core on this it would be even more troublesome, as a graph is DEFINED as a set of ordered pairs as below —
Define, evaluate, and compare functions.
1. Understand that a function is a rule that assigns to each input exactly
one output. The graph of a function is the set of ordered pairs
consisting of an input and the corresponding output.
But at least WE all know what a graph is…..or do we?
Idly passing the time this morning I thought of a – b = a + (-b).
Fair enough, it is the interpretation of subtraction in the extended positive/negative number system.
I then thought of a – (b + c)
Sticking to the rules I got a + (-(b + c))
To proceed further I had to guess that -(b + c) = (-b) + (-c)
and then, quite ok, a – (b + c) = a – b – c
But -(b + c) = (-b) + (-c) is guesswork.
I cannot see a rule to apply to this situation.
The only way forward is to use -1 as a multiplier:
So a – b = a + (-1)b = a + (-b),
and then -(b + c) = (-1)(b + c) = (-1)b + (-1)c = (-b) + (-c)
by the distributive law.
It’s not surprising that kids have trouble with negative numbers!
Do we just assert that the distributive law applies everywhere, even when it is only defined with ++’s ?