Author: Richard

Balancing Squares and Cubes

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BALANCING SQUARES AND CUBES

John ruptured the silence as he leapt to his feet and heaved the chair towards the corner of the room.

Year 7 students enjoy squiggling ancient Egyptian numerals—at least for a short time. It was Hay in the seventies. Ten minutes into my lesson, on early number systems, a sharp knock sounded at the door. An enthusiastic youngster, with a voice reminiscent of a boat horn, stuck her head in the classroom.

“Sir, John’s gotta go to reading”. Like a shaken bottle of lemonade, John exploded. He resented leaving the group to improve his language know-how.

Without basic reading skills, however, other classroom content becomes formidable. Mathematics is no exception. A problem couched in words often belies the simplicity of the sums involved.Adding

I did teach kids with reading difficulties who learnt to decipher the required sum from the presentation of the digits. For example, a question containing a string of numbers might suggest an addition is needed. Alternatively, two numbers, one large and one small could be a division. The problem is, you don’t travel far with these dubious techniques.

But back to John whose demeanour had darkened in a twinkling. He freewheeled from amiable to aggro, tipping his table forward, and sending pens and pencils flying—a tantrum that left us all gobsmacked.

Everybody waited. Nobody said a word.

His dilemma? Being withdrawn from mainstream lessons labelled John as “special”. This had overtones of “different” even “abnormal” and hey, no one wants to be a square in a room of cubes. Additional assistance in the classroom might have proved a suitable alternative.

And John? Having upended both his desk and seat, packed up his belongings and made a hasty exit.

“Then the silence closed upon us”: appropriate sentiments from the pen of Rudyard Kipling. To put it bluntly—silence is not only golden, but a relief.

“Children learn to read by being in the presence of books. The love of knowledge comes with reading …”  Horace Mann (1796-1859) American Education Reformer 

Notes

  • “Then the silence closed upon us,” quoted from the poem, ‘In the Neolithic Age’ by Rudyard Kipling (1865-1936) English short-story writer, poet, and novelist.
  • A cube is a Platonic solid named after Plato (428-348BC) although some credit Pythagoras (570-495) with their discovery. It is also called a hexahedron because it is a polyhedron that has 6 (hexa- means 6) faces.

Short Story Post#3

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High Five Duncan

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High Five Duncan

Duncan froze, too scared to accept his certificate–or perhaps his feet were nailed to the stage stairs.

Presentation Days are an inside affair, but Duncan preferred the outdoors. He reminded me of a white-skivvied ‘Wiggle’ as daily he aided the General Assistant. Together they toiled through a host of school chores.

The WigglesBright-eyed but shy, he would greet acquaintances with a robust ‘high five’. Today, however, the packed assembly hall represented unfamiliar territory–a daunting experience for the young man.

It had been an epic journey. Intellectually handicapped, Duncan had not experienced the smoothest transition from the junior classes to the senior ranks. Nonetheless, caring staff members had prepared him for this gathering.Skivvy

The pupils in our Support Group, of which Duncan was a member, represented an essential part of the school. They joined the student body for recess, lunch and assemblies. Athletics and swimming carnivals were included in their favourite activities. The presence of these teenagers encouraged a community of understanding and acceptance. We considered ourselves fortunate.

Today though, Duncan and his colleagues in the academic stream would be presented with their Year 12 Certificates. Dignitaries, teaching staff, fellow students, parents and friends filled the hall on this auspicious occasion. But Duncan’s runners were riveted to the highest tread.

Conscious of his hesitation, I read his name slowly. How could his anxiety be alleviated? With only a second to act, I shuffled around the lectern, stepped forward, and raised my hand. Duncan’s face lit up like a surprised contestant who had just won a ten kilogram advantage at the ‘Biggest Loser’ weigh-in.

Jumping onto the stage, he gave me a ‘High Five’ I will never forget. Classmates cheered. The audience clapped. His mum cried.

And Duncan, displaying the true grit of John Wayne and Jeff Bridges combined, accepted his certificate.

“It is not our disability that is the problem, but rather it is the way our disabilities are viewed by others.” Drexel Deal – American, Member of the Disabled Persons Organization.

Notes:

  • A Skivvy is a name used in the United States and Australasia for a turtle-necked top.
  • The Wiggles are an Australian children’s music group. They are known, among other things, for their brightly coloured skivvies.
  • The Biggest Loser is a reality television show in which overweight contestants attempt to lose weight.
  • ‘True Grit’ is the title of two movies, each of which is an adaption of the Charles Portis 1968 novel of the same name. The first movie, from 1969, starred John Wayne and the second, released in 2010, saw Jeff Bridges in the lead role.

Short Story Post#2

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The Die is Cast

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‘ALEA IACTA EST’ (The Die Is Cast)

Zen masters live a life of meditation.

I wonder if any has contemplated the question, “If a die falls in the classroom and no one hears it, does it make a sound?”

Search me. With today’s bunch, detecting a pin drop or hearing a pail of pins hit the floor is unlikely.

Besides, a single dotted cube amongst thirty teenagers does not constitute an effective learning experience. Then again, thirty dice with the same group is thwart with complications.

Like big Julie tippy-toeing into the river Rubicon, once I embark on my probability lesson, hesitation is futile—‘the die is cast’.

Classroom StoryI am well prepared with dice and graph paper. A primeval over-head projector sits on the front desk and my chalk sticks are crossed in the hope it behaves. My hand-outs have emerged from the photocopy room. Sure, ‘maths-speak’ cannot be avoided, but I maintain my carefully worded instructions constitute everyday English.

My introduction to the lesson is in its embryonic stage, when the banter begins.

“Sir, chuck us a dice.”

Doh! Despite telling my group that ‘dice’ is plural of ‘die’, I know Jonathon is asking for one. It’s a small point and not worth mentioning.

Once the chitchat starts, though, others want in.DICE

“I want the yellow ones, Sir. Not those lame white things.”

“Can we use the ones that go up to eight, Sir.”

“Dice don’t go up to eight, ya dummy.”

“Yes they do, we’ve used ‘em before. You tell ‘im sir.”

Bothermacready! And on paper, my lesson displayed potential.

Close to one hour rolls by—literally. I am annoyed with certain individuals who consider the desktop insufficient room to toss and land a die.

Nonetheless, final results—individual and collective—have been recorded and graphed.  The discussion ensures my charges draw the appropriate conclusion, that is, when a die is tossed, each of the six numbers has an equal chance of being on the top face. All this in fifty-six minutes. Yes-siree-bob—‘I love it when a plan comes together’.

The bell rings. Only one die has disappeared—collateral damage. I am modestly pleased with the lesson outcome. OK, I’m experiencing a warm smug feeling.

That is, until Jonathon stops as he leaves the room. “Sir, I didn’t get to toss my dice many times.”

My response? “Surprise, surprise.”

“And I got more sixes,” he continues. “So I still reckon tossing a “six” is easier than any other number.”

I shake my head, perhaps I should have remained in the drafting office.

“Coincidences, in general, are great stumbling blocks in the way of that class of thinkers who … know nothing of the theory of probabilities.” Edgar Allen Poe (1809-1849) American author, poet.

Notes:

  • ‘Alea iacta est’ is a Latin phrase attributed to Julius Caesar, spoken as he crossed the Rubicon River, Italy, in 49BC. Leading his army, it was the start of a civil war against Pompey. The phrase is used today to indicate proceedings have passed the point of no return.
  • ‘I love it when a plan comes together’ comes from the Eighties TV series ‘The A-Team’. These words were often spoken by John “Hannibal” Smith played by actor George Peppard.

Short story #1This picture contains six errors. Some are easy to spot, others are more difficult. If you wish to post the mistakes you discover, include them as a comment. The six errors will be posted at the same time as the next story and will be found on the ANSWERS PAGE (Click here).