Category Archives: education

“Pupils learn poorly when using most computer programs”

.The future: I\(I love this cartoon)

Politics 0448
.Here are two posts worth a read, showing the rheeformed way forward, and consequences

reading-between-the-lines:Obamas-testing-action-plan/
sciencedaily.com/computers_math

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Filed under competency based, education, future

GEOSTRUCT now with Save and Fetch for your constructions

Thanks to intense use of the internet I finally found a simple, understandable way of implementing Save and Fetch operations, enabling the keeping and reusing of any construction.

Here is a reminder of the application (app, program, software, whatever), with the file handling operations:

post example A
The user panel and a simple example of three points on a circle, with the bisectors of the pairs of points.

post example C
The history panel showing the actions that have been carried out

post example D
The Save popup,and, below, the resulting text file.

post example E

There is now a not quite finished Spanish option – just click “ESPANOL”

Also a modified “move object” procedure for use with a tablet,or even a smartphone.

The whole application is constructed as a web page, and to run it just click this link: geostruct

The full url is http://www.mathcomesalive.com/mathsite/geostruct/geostructforbrowser1.html

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Filed under education, geometry app, geostruct, math, math apps, teaching, web based

UK math – the National Curriculum

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)

Click to access PRIMARY_national_curriculum_-_Mathematics_220714.pdf


Key stage 3  (11 to 13)

Click to access SECONDARY_national_curriculum_-_Mathematics.pdf


key stage 4 (14,15)

Click to access KS4_maths_PoS_FINAL_170714.pdf


ans about assessment

Click to access Assessment_Principles.pdf

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.

http://www.theschoolrun.com/ks2-sats-in-2015-what-parents-need-to-know

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.

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Filed under education, INTERNATIONAL, math

Reinventing mathematics for schools

I found this today. It’s worth a read.

Author: Gary S. Stager

Link: reinventingmath.com/?p=87

Here’s an extract:

Conrad Wolfram estimates that 20,000 student lifetimes are wasted each year by school children engaged in mechanical (pencil and worksheet) calculations.
Expressed another way, we are spending twelve years educating kids to be a poor facsimile of a $2 calculator.
Forty years after the advent of cheap portable calculators, we are still debating whether children should be allowed to use one.

We are allowing education policy and curriculum to be shaped by the mathematical superstitions of Trump voters.
Educators need to take mathematics back and let Pearson keep “math.”

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Saving American Higher Education, but how?

I found the following article ” The Coddling of the American Mind” while rooting about, after finding what I was looking for.

http://www.theatlantic.com/magazine/archive/2015/09/the-coddling-of-the-american-mind/399356/

Read it, or at least some of it, as it is quite long. The fear of being upset is screwing the college sector, and my guess is that the UK won’t be far behind. “You can’t say that. We shouldn’t be reading that. Someone will be traumatised”, and so on. All must be protected. It is the death of critical thinking.

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Filed under college, critical thinking, education

Political correctness in K-12 math

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:

Click to access 07carnegie.pdf

Link found on f(t)’s blog

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Filed under abstract, algebra, CCSS, Common Core, depth, education, K-12, math, standards, teaching, tests

Mathematical discrimination in the brave new world of Common Core

Merriam Webster
discriminating
adjective dis·crim·i·nat·ing

: liking only things that are of good quality

: able to recognize the difference between things that are of good quality and those that are not

Full Definition of DISCRIMINATING

1: making a distinction : distinguishing
2: marked by discrimination:
a : discerning, judicious
b : discriminatory

Take your pick !

In the UK we used to call it prejudice, as in “racial prejudice”.

Today the perfectly good word “discrimination” has been hijacked and the old meaning has all but disappeared.

Now you ask “What’s this got to do with math?”.

We have to look at quadratic equations for an answer.

The standard quadratic equation is ax2 + bx + c = 0
It may or may not have real roots
and the sign of D = b2 – 4ac resolves this uncertainty.

D < 0 … no real roots, D = 0 … equal real roots D > 0 … different real roots

What is this D ? It is the “discriminant” of the equation.

It is used to discriminate between equations with real roots and equations without real roots.

So WHY isn’t it in the Common Core math standards. It’s about as standard a thing as is possible?

Clearly the CCSSM authors are guilty of serious discrimination in discriminating against the word “discriminant”, in order not to be accused of discrimination language. Neither “discrimination” nor “discriminant” appear in the CCSSM doc, and the result is that the poor kids ( in the little darlings sense) have to complete the square from scratch every time they have a quadratic equation ( instead of once only in order to get the discriminant formula).

So sad !

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Filed under algebra, CCSS, Common Core, education, teaching

Another “must read”, on test grading, new style(!)

When I got to the sentence

“If it doesn’t take a person with subject knowledge to score the essay, it doesn’t take a person with subject knowledge to write it.”

I thought of Todd Farley and his book “Making The Grades”‘

” Plus ca change, plus c’est la meme chose” (pardon my French, and excuse the lack of accents)

So go and read the rest : http://curmudgucation.blogspot.com/2015/06/mcgrading-mctest.html?

and then read Farley’s  book.

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Real problems with conic sections (ellipse, parabola)

So there is an oval hole in a metal casting. It’s supposed to be an elliptical hole. Is it ????? How can we find out ?????
A good start would be to find the line which would be the major axis if it was elliptical. This turns out to be an engineering problem, not a mathematical one (I cannot see a way!). If the oval curve has an axis of symmetry then the method below will find it:

Firstly, get a computer picture of the oval.
Take two circles, of different radii, and push them along until each one touches the oval in two places.

ellipse12

The line joining the two centers will be the axis of symmetry if there is one (this can be shown mathematically).

ellipse34

ellipse5

The equation of an ellipse uses the lengths of the major and minor axes. Do it !

The closeness to elliptic can be assessed in various ways. Think of one.

next…..finding the focus of a parabolic shape

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Filed under conic sections, conics, education, engineering, geometry, math, teaching

GEOSTRUCT, a program for investigative geometry

I have been developing this computer software / program / application for some years now, and it is now accessible as a web page, to run in your browser.

It provides basic geometric construction facilities, with lines, points and circles, from which endless possibilities follow.

Just try it out, it’s free.

Click on this or copy and paste for later : www.mathcomesalive.com/geostruct/geostructforbrowser1.html

.Here are some of the basic features, and examples of more advanced constructions, almost all based on straightedge and compass, from “make line pass through a point” to “intersection of two circles”, and dynamic constructions with rolling and rotating circles.

help pic 1
Two lines, with points placed on them
help pic 3
Three random lines with two points of intersection generated
help pic 6
Five free points, three generated circles and a center point
help pic 7
Three free points, connected as point pairs, medians generated
help pic 5
Two free circles and three free points, point pairs and centers generated
gif line and circle
GIF showing points of intersection of a line with a circle
hypocycloid locus
Construction for locus of hypocycloid
circle in a segment
gif002
GIF showing a dilation (stretch) in the horizontal direction
gif piston cylinder
Piston and flywheel
gif touching2circles
Construction for circle touching two circles
gif parabola
Construction for the locus of a parabola, focus-directrix definition.

 

 

 

 

 

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Filed under education, geometry, math, operations, teaching