Monthly Archives: November 2014

From Papert to Why the Lucky Stiff: What’s Out There Today for Young Programmers?

Kids should feel that computers are not mysterious devices, but can be told what to do, if only very simply. READ THIS – – – – –

Teacher Learns to Code

As the 2014 Hour of Code challenge offered by draws near (Dec. 8-12), I wanted to spend a little time with the history of what has gotten us to the place we are in today. To many educators, the ideas of edtech and coding in schools still seems far off and mysterious.  However, the innovators who embrace these ideas are incorporating them into learning experiences and seeing children become inspired and motivated by code.

From 1980 to 2003, technology moved forward, but what moved backward? Examined through the lens of two thinkers: Seymour Papert and Why the Lucky Stiff

Why the Lucky Stiff (_why) was “a prolific writer, cartoonist, artist, and computer programmer notable for his work with the Ruby programming language” (Wikipedia). Seymour Papert was a mathematician and professor at MIT. He was one of the creators of the Logo programming language (remember the turtle?) and author of…

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Common Core math testing – oh dear!

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

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Filed under arithmetic, education, language in math, teaching

Language in math, again.

“Is” is a very overworked word, to the point of illogicality.

which of these both

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 —
Functions 8.F
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?


Filed under language in math, teaching

CCSS and Standardized Testing – Who shall pass and who shall fail ?

This excerpt is from the following:

by Anthony Cody, and you should read it.

The Department of Education in New York convened a panel of educators to set cut scores on the new Pearson Common Core-aligned tests. This article  spilled the beans about the process.

Tina Good, coordinator of the Writing Center at Suffolk County Community College, said her group produced the best possible cut scores for ELA tests in grades 3 to 6 — playing by the rules they were given.

“We worked within the paradigm Pearson gave us,” she said. “It’s not like we could go, ‘This is what we think third-graders should know,’ or, ‘This will completely stress out our third-graders.’ Many of us had concerns about the pedagogy behind all of this, but we did reach a consensus about the cut scores.”

The result was that this panel of professional educators provided the state of New York with the cut scores that meant only about 30% of the state’s students were ranked proficient.

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Euclid and the Sword

If you want to know more about Euclid and his influence, especially outside mathematics, read this. It is fascinating.

Boxing Pythagoras

I have written, often, about one of my personal heroes from history, Euclid of Alexandria, who wrote a textbook called Elements which would serve as the foundation for all Western mathematics for 2000 years. You may recall that, outside of his name and a list of his writings, we know almost nothing about Euclid. We know nothing of his birth, or his schooling, or his politics. We don’t know if he traveled extensively or if he was relatively sedentary. We don’t know if he was tall, short, fat, skinny, handsome, or ugly. However, one thing we do know is that Euclid’s work, though purely mathematical, bore a tremendous influence on a wide variety of fields of knowledge.

Euclid’s Elements set out to prove the whole of mathematics deductively from very simple definitions, axioms, and postulates. Deductive logic provided a sound and absolute basis by which mathematics operated for every man…

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Radius of the inscribed circle of a right angled triangle

incircle radius with text


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Pythagoras, triples, 3,4,5, a calculator.

How to generate Pythagorean triples (example: 3,4,5), well one way at least.

Starting with (x + y)2 = x2 + y2 + 2xy and (x – y)2 = x2 + y2 – 2xy

we can write the difference of two squares

(x + y)2  –  (x – y)2 = 4xy

and if we write  x = A2 and y = B2 the right hand side is a square as well.


(A2  +  B2) 2 – (A2 – B2) 2 = 4A2 B2 = (2AB) 2

which can be written as

(A2  +  B2) 2 = (A2 – B2) 2 + (2AB) 2

the Pythagoras form.

Now just put in some integers for A and B

2 and 1 gives 3,4,5

Conjecture1: This process generates ALL the Pythagorean triples.

Conjecture2: Every odd number belongs to some  Pythagorean triple.

Have fun…….

My next post will be about finding the radius of the inscribed circle in a right angled triangle…..


Filed under algebra, geometry, teaching