Monday, May 01, 2017

direct instruction and indigenous education (version 5)

I've published an annotated contents page of my research outline at the learning evolves wiki. This has chewed up a lot of thought and time since I had hundreds of bits of paper with rough notes that had to be organised into something coherent. Well, sort of coherent. With this version I think I'm ready to look for a supervisor, to bounce ideas off, and it will provide a more focused guide to future reading / study.

RESEARCH PROPOSAL (version 5)
DIRECT INSTRUCTION AND INDIGENOUS EDUCATION: FROM THE INSIDE OUT

Sunday, April 16, 2017

Judith Curry on the current state of climate science

Judith Curry STATEMENT TO THE COMMITTEE ON SCIENCE, SPACE AND TECHNOLOGY OF THE UNITED STATES HOUSE OF REPRESENTATIVES
Hearing on Climate Science: Assumptions, Policy Implications and the Scientific Method
29 March 2017

14pp pdf, quite inspirational IMO, read the whole thing

Science is an iterative process of multi hypothesis formation, collecting data and testing that data against the variety of hypotheses

Beware of dogmatic claims (alarmists, deniers), be sensitive to the uncertainty and complexity of the climate science issue

Explanation of the how and why we have got to a bad place in climate science (page 11, extract below)

There is a war on science - not from Trump but from within the science establishment itself (page 12, extract below)
How and why did we land between a rock and a hard place on the issue of climate science?

There are probably many contributing reasons, but the most fundamental and profound reason is arguably that both the problem and solution were vastly oversimplified back in the early 1990’s by the UNFCCC, who framed both the problem and the solution as irreducibly global in terms of human-caused global warming. This framing was locked in by a self-reinforcing consensus-seeking approach to the science and a ‘speaking consensus to power’ approach for decision making that pointed to a single course of policy action – radical emissions reductions.

The climate community has worked for more than two decades to establish a scientific consensus on human-caused climate change, prematurely elevating a hypothesis to a ruling theory. The IPCC’s consensus-seeking process and its links to the UNFCCC emissions reduction policies have had the unintended consequence of hyper-politicizing the science and introducing bias into both the science and related decision making processes. The result of this simplified framing of a wicked problem is that we lack the kinds of information to more broadly understand climate variability and societal vulnerabilities. The politicization of climate science has contaminated academic climate research and the institutions that support climate research, so that individual scientists and institutions have become activists and advocates for emissions reductions policies. Scientists with a perspective that is not consistent with the consensus are at best marginalized (difficult to obtain funding and get papers published by ‘gatekeeping’ journal editors) or at worst ostracized by labels of ‘denier’ or ‘heretic.’

Policymakers bear the responsibility of the mandate that they give to panels of scientific experts. In the case of climate change, the UNFCCC demanded of the IPCC too much precision where complexity, chaos, disagreement and the level current understanding resists such precision. Asking scientists to provide simple policy-ready answers for complex matters results in an impossible situation for scientists and misleading outcomes for policy makers. Unless policy makers want experts to confirm their preconceived bias, then expert panels should handle controversies and uncertainties by assessing what we know, what we don’t know, and where the major uncertainties lie....
War on Science
With the advent of the Trump administration, concerns about ‘war on science’ have become elevated, with a planned March for Science on 22 April 2017. Why are scientists marching? The scientists’ big concern is ‘silencing of facts’. This concern apparently derives from their desire to have their negotiated ‘facts’ – such as the IPCC consensus on climate change – dictate public policy. These scientists also fear funding cuts and challenges to the academic scientific community and the elite institutions that support it.

The ‘war on science’ that I am most concerned about is the war from within science – scientists and the organizations that support science who are playing power politics with their expertise and passing off their naïve notions of risk and political opinions as science. When the IPCC consensus is challenged or the authority of climate science in determining energy policy is questioned, these activist scientists and organizations call the questioners ‘deniers’ and claim ‘war on science.’ These activist scientists seem less concerned with the integrity of the scientific process than they are about their privileged position and influence in the public debate about climate and energy policy. They do not argue or debate the science – rather, they denigrate scientists who disagree with them. These activist scientists and organizations are perverting the political process and attempting to inoculate climate science from scrutiny – this is the real war on science.

Saturday, April 08, 2017

Obama and Trump both lied

Barack Obama said he was going to do something about Assad's chemical weapons and he didn't.

Donald Trump said he wasn't going to do anything about Assad's chemical weapons and he did.

In this case, like the Syrian resistance, I prefer Trump's lies.

Tuesday, April 04, 2017

ambiguity is deeply writ

AMBIGUITY IS WRITTEN DEEPLY INTO KNOWLEDGE STRUCTURES

What puzzles me most about Direct Instruction is that it is good practice but poor theory. Part of what I mean follows.

Zig Engelmann starts with the great idea that instruction should be tidied up and made very clear but then takes that too far into the claim that in general instruction can be made unambiguous, “I didn't realise how radical the single interpretation principle was ...” (Teaching Needy Kids in our Backward System, p. 3)

We can strive for clearer instruction, that is a worthy goal, but it is not possible to achieve unambiguous instruction.

For example, when teaching the subtraction sixty two minus fifty seven (62 – 57), the DI teacher asks the students “Can we subtract 7 from 2” and the students are taught to say “No”. They then go onto rearrange 62 into 50 + 12 so as to be able solve the problem. This is good teaching, but there are other ways to solve it as well. Two take seven equals -5. Sixty take fifty equals 10. Ten – five = 5.

My aim here is not to improve DI by making it more complicated. DI works, in part, because it simplifies things. I don't deny that. But the complexity and multiple pathways are written deep into the knowledge domain of mathematics. The claim of unambiguous instruction fails. We can subtract 7 from 2. The answer is not "No". Many more examples of such oversights in DI scripts can be cited.

This is not against DI as such (which in certain contexts works better than anything else in my experience) but against the over simplified arguments often presented by advocates of DI. The idea that data provides the ultimate scientific certainty is mistaken because it is impossible to separate out data from concepts developed internally in the mind. Ambiguity is written into educational theory as well as practice.

These observations are presented here as a stepping stone towards developing a better theory of why DI often works than the unsatisfactory theory (uncritical acceptance of JS Mill's Logic) developed by Zig Engelmann and Doug Carnine.

I speculate further that this seems to tie into a critique of JS Mill, initiated by John Dewey and further developed by Hilary Putnam. JS Mill thought that a perfected science of individual psychology would be able to deliver social laws to solve social problems. This reminds me of the Zig Engelmann cult, which promotes him as the one true educational visionary amongst a sea of deceivers:
"Like Copernicus, who proofs were rejected by the church for 300 years, Engelmann remains a scorned revolutionary, anathema or simply unknown to most people in the field"
- Barbash, p. 8
I can't go along with the way that Piaget, Bruner and Dewey are rubbished in this cult war. I think they have all made valuable contributions to educational theory. Some positives, some negatives, some ambiguities. There is not one true way.

These thoughts were crystallised in thinking about these comments from Hilary Putnam about empiricism:
“Empiricism … thinks that the general form of scientific data, indeed of all empirical data, can be known a priori – even if it doesn't say so in so many words! From Locke, Berkeley, and Hume down to Ernst Mach, empiricists held that all empirical data consists of “sensations”, conceived of as an unconceptualised given against which putative knowledge claims can be checked. Against this view William James had already insisted that while all perceptual experience has both conceptual and non conceptual aspects, the attempt to divide any experience which is a recognition of something into parts is futile: “Sensations and apperceptive idea fuse here so intimately [in a 'presented and recognised material object'] that you can no more tell where one begins and the other ends, than you can tell, in those cunning circular panoramas that have lately been exhibited, where the real foreground and the painted canvas join together” (quoted in Dewey's Ethics, p. 273). Dewey continued the line of thought that James had begun, insists that by creating new observation concepts we “institute” new data. Modern physics (and of course not only physics) has richly born him out. A scientist may speak of observing a proton colliding with a nucleus, or of observing a virus with the aid of an electron microscope, or of observing genes or black holes, and so forth. Neither the form of possible explanation nor the form of possible data can be fixed in advance, once and for all...

Among the classic empiricist thinkers, the most famous ones to call before John Dewey did for the application of scientific research to the problems of society were Mill and Comte. But Comte reverted to meritocracy. He visualised handling social problems over to savants, social scientific intellectuals, a move which falls under Dewey's criticism of the idea of a 'benevolent despot'.

It might seem that this same criticism cannot be voiced against Mill, who, as much as Dewey was to do, valued active participation in all aspects of the democratic process. But as far as the application of social scientific knowledge to social problems is concerned, what Mill called for was the development of a perfected science of individual psychology, from which he thought … we would be able to derive social laws (via the hoped for reduction of sociology to psychology) which could then be applied to particular social problems. This entire program, as most would concede today, is a misguided fantasy
- Ethics without Ontology, pp. 98-100
Further reading will be required to get the bottom of this: Barbash, Shepard. Clear Teaching: With Direct Instruction, Siegrried Engelmann Discovered a Better Way of Teaching (2012)
Dewey Logic
Dewey Ethics
Dewey The Quest for Certainty
Engelmann, Zig. Teaching Needy Kids in our Backward System: 42 Years of Trying (2007)
Engelmann, Zig and Carnine, Douglas. Could John Stuart Mill have saved our schools? (2011)
Jame, William. Radical Empiricism?
Mill JS A System of Logic
Putnam, Hilary. Ethics without Ontology
Quine Two Dogmas of Empiricism

Thursday, March 23, 2017

The Origins of Modernity

Giordano Bruno (1548-1600, burnt alive by the Church) and Francis Bacon (1561-1626) put forward a clear program of domination or conquest of nature around about 1583-85, the time that Bruno visited England.
“The gods have given man intelligence and hands, and have made them in their image, endowing him with a capacity superior to other animals. This capacity consists not only in the power to work in accordance with nature and the usual course of things, but beyond that and outside her laws, to the end that by fashioning, or the power to fashion, other natures, other courses, other orders by means of his intelligence, with that freedom without which his resemblance to the deity would not exist, he might in the end make himself god of the earth … providence has decreed that man should be occupied in action by the hands and in contemplation by the intellect, but in such a way that he may not contemplate without action or work without contemplation …. when difficulties beset them or necessities reappeared … they sharpened their wits, invented industries and discovered arts … by force of necessity, from the depths of the human mind rose new and wonderful inventions.”
- Bruno, The Expulsion of the Triumphant Beast
Albert Schweitzer points out that an optimistic view of a modern world where knowledge, standard of living and health could all be improved (as compared with passive acceptance of ignorance, poverty and ill health) met considerable opposition from historical forces. Plato's ethic is world negation., Plato and Aristotle accepted slavery and so did not envisage the liberation of Humanity as a whole. The Epicureans and Stoics preached resignation.

Bacon took the moral stance that real charity involved meeting peoples needs in the full Christian sense of brotherly love. He contrasted this with the tendency of the Greeks to quarrel about opinions.

After dabbling in politics, initially without much success, Bacon took the view that invention was more useful than politics because it is felt everywhere and lasts forever.

Invention required the use of both intellect and labour, the head and the hand. The “mechanical arts” became central to Bacon's vision, he wanted the concepts spread far and wide to a thousand hands and a thousand eyes.

Bacon persistently criticised the influence of Aristotle and Plato on contemporary thinking because their mode of thinking (dialectical argument) did not support the rapid development of the mechanical arts.

Reference:
The Philosophy of Francis Bacon by Benjamin Farrington (1964), Ch 4, 5 and 6

Saturday, March 18, 2017

natural selection and Direct Instruction

Now for a pithy one liner which also happens to support Direct Instruction:
"Before there can be comprehension, there has to be competence without comprehension"
Dan Dennett, Intuition Pumps and other tools for thinking (2013), p. 105
Comprehension is a latecomer to the evolutionary process.
"Bacteria have all sorts of remarkable competences that they need not understand at all; their competences serve them well, but they themselves are clueless. Trees have competences whose exercise provides benefits to them, but they don't need to know why. The process of natural selection itself is famously competent, a generator of designs of outstanding ingenuity and efficacy, without a shred of comprehension.

Comprehension of the kind we human adults enjoy is a very recent phenomenon on the evolutionary scene, and it has to be composed of structures whose competence is accompanied by, enabled by, a minimal sort of semi-comprehension, or pseudo-comprehension - the kind of (hemi-semi-demi-) comprehension enjoyed by fish or worms. These structures are designed to behave appropriately most of the time, without having to know why their behaviour is appropriate."
- p. 105
Compare with my pithy one liner which critiques Direct Instruction:
"In Direct Instruction there is no script for those who depart from the script or who desire to write their own script"
- fork in the road options and Direct Instruction
You can't begin to write your own script until you have achieved at least a basic competence in whatever domain you are attempting to master.

Sunday, March 12, 2017

philosophers timeline

FIRST ENLIGHTENMENT

Pythagoras 560 BC - ?
Heraclitus 535 BC-475 BC
Zeno of Elea 490-430 BC
Democritus 460 BC-?
Socrates 469-399 BC
Euclid ? - 366 BC
Plato 429-347 BC
Aristotle 384 BC-322 BC
Epicurus 341-271 BC
Chrysippus 280-206 BC
Cicero 106-43 BC
Ovid 43 BC-17 AD
Seneca 1-65
Plutarch 45-120
Lucretius early to mid 1st C

NOT MUCH PROGRESS YEARS

Thomas Aquinas 1225-1274
William of Occam 1285-1347

SECOND ENLIGHTENMENT

Nicolaus Copernicus 1473-1543
Michel de Montaigne 1533-1592
Giordano Bruno 1548-1600 (burnt alive by the Church)
Francis Bacon 1561-1626
Galileo Galilei 1564-1642
Johannes Kepler 1571-1630
Thomas Hobbes 1588-1679
Rene Descarte 1596-1650
Gerrard Winstanley 1609-1676
Blaise Pascal 1623-1662
Robert Boyle 1627-1691
Christiaan Huygens 1629-1695
Baruch Spinoza 1632-1677
John Locke 1632-1704
Robert Hooke 1635-1703

ENGLISH REVOLUTION / CIVIL WAR 1642-1660

Isaac Newton 1642-1727
Gottfried Wilhelm Liebniz 1646-1716
Jonathan Swift 1667-1745
Christian Wolff 1679-1754
George Berkeley 1685-1753
Montesquieu 1689-1755
Voltaire 1694-1778
Carl Linnaeus 1701-1778
Thomas Bayes 1702-1761
David Hume 1711-1776
John Jacques Rousseau 1712-1778
Étienne Bonnot de Condillac 1714-1780
Claude Adrien Helvetius 1715-1771
Baron d'Holbach 1723-1789
Adam Smith 1723-1790
Immanuel Kant 1724-1804
Nicolas de Condorcet 1743-1794
Jeremy Bentham 1748-1832
Pierre-Simon Laplace 1749-1827
Johann Wolfgang von Goethe 1749-1832
Joseph de Maistre 1753-1821
Henri de Saint-Simon 1760-1825
Johann Gottlieb Fichte 1762-1814
Georg Wilhelm Friedrich Hegel 1770-1831
Charles Fourier 1772-1837

FRENCH REVOLUTION 1787-1799

Arthur Schopenhauer 1788-1860
Charles Babbage 1791-1871
William Whewell 1794-1866
Auguste Comte 1798-1857
John Stuart Mill 1806-73
Charles Darwin 1809-1882
Soren Kiekegaard 1813-1855
Karl Marx 1818-1883
Friedrich Engels 1820-1895
Ernst Mach 1838-1916
Charles Peirce 1839-1914
William James 1842-1910
Frederick Nietzsche 1844-1900
Georg Cantor 1845-1918
Gottlob Frege 1848-1925
Henri Poincaré 1854-1912
Giuseppe Peano 1858-1932
Edmund Husserl 1859-1938
Henri Bergson 1859-1941
John Dewey 1859-1952
Rabindranath Tagore 1861-1941
Vladimir Lenin 1870-1924
Marcel Proust 1871-1922
Bertrand Russell 1872-1970
GE Moore 1873-1958
Albert Einstein 1879-1955
Moritz Schlick 1882-1936
Otto Neurath 1882-1945
Ludwig Wittgenstein 1889-1951
Martin Heidegger 1889-1976
Hans Reichenbach 1891-1953
Rudolf Carnap 1891-1970
Mao Zedong 1893-1976
Lev Vygotsky 1896-1934
Gilbert Ryle 1900-1976
Herbert Feigl 1902-1988
Karl Popper 1902-1994
Gregory Bateson 1904-1980
BF Skinner 1904-1990
Jean-Paul Sartre 1905-1980
Raymond Aron 1905-1983
Carl Gustav Hempel 1905-1997
Kurt Godel 1906-1978
Nelson Goodman 1906-1998
Willard Van Ormon Quine 1908-2000
Isaiah Berlin 1909-1997
A. J. Ayer 1910-1989
Alan Turing 1912-1954
Wilfrid Sellers 1912-1989
Iris Murdoch 1919-1999
John Rawls 1921-2002
Imre Lakatos 1922-1974
Thomas Kuhn 1922-1996
Paul Feyerabend 1924-1994
Michel Foucault 1926-1984
Hilary Putnam 1926-2016
Marvin Minsky 1927-2016
Seymour Papert 1928-2016
Allan Bloom 1930-1992
Richard Rorty 1931-2007
Marshall Berman 1940-2013

STILL ALIVE

Noam Chomsky 1928-
Amartya Sen 1933-
Jerry Fodor 1935-
Ian Hacking 1936 -
Michael J Crowe 1936 -
Ronald Giere 1938 -
Bas van Fraasen 1941-
Larry Laudan 1941-
Paul Churchland 1942-
Daniel Dennett 1942-
Marcello Pera 1943-
Donald Gillies 1944 -
Douglas Hofstadter 1945-
Hartry Field 1946 -
Martha Nussbaum 1947-
Camille Paglia 1947-
Luc Ferry 1951-
Laura Snyder 1964-

Possibly will be updated from time to time.

The genuine refutation

"The genuine refutation must penetrate the opponent's stronghold and meet him on his own ground; no advantage is gained by attacking him somewhere else and defeating him where he is not"
- GWF Hegel, Science of Logic: Subjective Logic or The Doctrine of the Notion
Both the critics and supporters of Direct Instruction do not refute from within the others respective strongholds. That is why this quote has been playing on my mind for sometime.

Sunday, January 29, 2017

fork in the road options and Direct Instruction

An attempt at a pithy critique of Direct Instruction:

In Direct Instruction there is no script for those who depart from the script or who desire to write their own script.

I'd rather be a Robert or a Lauren, than an Alice.
Alice in Wonderland

“One day Alice came to a fork in the road and saw a Cheshire cat in a tree. ‘Which road do I take?’ she asked. ‘Where do you want to go?’ was his response. ‘I don’t know,’ Alice answered. ‘Then,’ said the cat, ‘it doesn’t matter.”
- Lewis Carroll
The Road Not Taken

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;

Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that the passing there
Had worn them really about the same,

And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.

I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.
- Robert Frost

Saturday, January 21, 2017

the pitchfork solution to world inequality

Each year Oxfam delivers a report about how the inequality in the world is getting worse and how this needs to stop. This year, I was encouraged by a marginal note from Nick Hanauer, one of the Super Rich, who warns his fellow billionarie's that:
‘No society can sustain this kind of rising inequality. In fact, there is no example in human history where wealth accumulated like this and the pitchforks didn’t eventually come out.’
- the pitchforks are coming ... for us Plutocrats
Now, what did that Oxfam report say?
  • Since 2015, the richest 1% has owned more wealth than the rest of the planet.
  • Eight men now own the same amount of wealth as the poorest half of the world.
  • Over the next 20 years, 500 people will hand over $2.1 trillion to their heirs – a sum larger than the GDP of India, a country of 1.3 billion people.
  • The incomes of the poorest 10% of people increased by less than $3 a year between 1988 and 2011, while the incomes of the richest 1% increased 182 times as much.
  • A FTSE-100 (Financial Times Stock Exchange 100) CEO earns as much in a year as 10,000 people in working in garment factories in Bangladesh.
  • In the US, new research by economist Thomas Piketty shows that over the last 30 years the growth in the incomes of the bottom 50% has been zero, whereas incomes of the top 1% have grown 300%.
  • In Vietnam, the country’s richest man earns more in a day than the poorest person earns in 10 years.
more details here

PREVIOUS BLOGS ON THIS TOPIC
Oxfam report: AN ECONOMY FOR THE 1%
the strengths and weaknesses of capitalism
Land of the Free, Home of the Poor

Sunday, January 15, 2017

RAMR Deadly Maths: Adding Fractions

The RAMR cycle originates from Chris Matthews, an indigenous man who has a PhD in maths.

RAMR is a new model for teaching maths, or at least, new to me. I've appended a link to a video at the bottom where Tom Cooper from the YuMi Deadly Centre at the Queensland University of Technology (QUT) explains the RAMR cycle. I adapted his talk to a lesson I developed about adding fractions. YuMi is a Torres Strait Islander word meaning "you and me" and Deadly is an aboriginal word meaning smart.

The RAMR acronym stands for Reality, Abstraction, Mathematics, Reflection as illustrated by this graphic:

REALITY

Teach maths the way it is created or invented. Start with a problem. The problem I posed to the class was how do you add one half and two thirds.

The elements recommended in this Reality phase of the cycle are start with a real life problem, draw on local knowledge and construct kinesthenic activities.
PIZZA DIAGRAMS half and two-thirds

Present this problem as a real life exercise. John eats half a pizza. Jermain eats two thirds of a pizza. How much pizza have they eaten altogether?

Bring real pizza into the room and cut it up. It is a recommended part of the RAMR cycle that the teacher constructs such an activity, preferably kinaesthetic.

Prerequisites: The teacher needs to be aware of prerequisite knowledge required for the problem. In this case the denominator (bottom number) tells us how many equal parts the pizza is divided into. The numerator (top number) tells us how many part of each pizza are being eaten. This had been covered in a previous lesson.

ABSTRACTION

Abstraction means moving from the real world (a pizza cut into various pieces) to a representation of that reality in words, pictures and / or symbols.

We have already begun this above by using the words, symbols and pictures for half and two-thirds. In practice the various phases of the RAMR cycle overlap as well as having some distinctiveness.

One aspect I need to improve on is that of adding in creativity by inviting students to create their own representations of fractions. I didn't do this in the class but later when running the session for trainee teachers it did energise the session with some imagination.

Can you develop your own representation of fractions?

MATHEMATICS

In this phase of the cycle we stress the formal language and symbols of mathematics, practice the concepts a lot (most students need lots of practice) and connect to other maths ideas that have been taught earlier.

When asked how to add ½ plus 2/3 many students will add the numerators and denominators to get the answer 3/5ths. Explain why this is wrong. You don't add denominators because they don't represent something that ought to be added to solve this problem. Rather they represent how many pieces each pizza has been cut into.

The trick to solving this problem is to cut both pizzas in such a way that the parts are equal. This can be solved either
(a) visually or
(b) arithmetically by multiplying the denominators or
(c) by finding the lowest common number in the two times (2, 4, 6 ...) and three times tables (3, 6 …)

So, we divide both pizzas into 6 equal parts

Now we can add the fractions 3/6 + 4/6 = 7/6 = 1 and 1/6

The denominators are not added since they represent how many pieces the pizza was cut into. The numerators are added since they represent the parts of the pizza which are eaten.

Transforming ½ into 3/6

How do we get 6 from 2? Multiply by 3.

Now if we multiply the denominator by 3 we then have to multiply the numerator by 3. ½ x 3/3 = 3/6

This doesn't change the value of the fraction since 3/3 = 1 and multiplying by 1 doesn't change the value of the number. The technical name for this is compensation, the numerator 3 compensates for the denominator 3, etc. This technique is really valuable and can be used over and over again in the future, so it needs to be reinforced. Multiplying by 1 doesn't change the value of a number.

Repeat this process to transform 2/3 into 4/6 by multiplying by 2/2

More Prerequisites: (which were covered in earlier lessons) Equivalent fractions: ½ = 2/4 = 3/6 etc.

Improper fractions (7/6) and mixed numbers 1 and 1/6

REFLECTION

The goals here are to:
  • set problems that apply the new idea back to reality
  • enable students to validate and justify their own knowledge
The concepts being covered can be extended at any point throughout the cycle. It doesn't have to be confined to the end.
Extension: Represent 7/6 or 1 and 1/6 on a clock? Answer: 70 minutes or 1 hour and 10 minutes.

Inverse: How else could the pizza have been divided b/w John and Jermain to get the same answer? ie. What other two numbers (fractions) would add up to 7/6 or 1 and 1/6?

Generalise: How could you add any two fractions? Looking for answer here about achieving a common denominator.

For the class I was teaching I found that they struggled to understand what was required for the inverse section but with prompting they got it. Overall, I was happy about the response to the challenge posed by the Reflection section.

CONCLUSION:

Maths textbooks are notoriously dull. Direct Instruction as developed by Rhonda Farkota (link to her PhD thesis) is very useful. But how do we further develop maths curriculum in a rich way once the basics are established?

I found that the RAMR cycle challenged me as a teacher to develop my delivery further. There were some elements in the cycle which made me think hard before I could deliver them. I did find that students responded well to those elements of the cycle in which I harboured a hidden belief that they may not cope with. The cycle integrates real world, creative elements and traditional elements of maths in a manner which I found very satisfactory. I think it is a very good model.

Is this maths which incorporates indigenous culture or simply good maths teaching? Good question! I think both but mainly I lean to the latter view. But really good teaching adjusts itself to take the individual needs of all the current students in the class into account. This requires more analysis and thinking. LINKS
Tom Cooper explains the RAMR cycle here: Professor Tom Cooper - YuMi Deadly Maths

Wednesday, January 11, 2017

Some books I am reading in 2017

Appiah, Kwame Anthony. Cosmopolitanism: Ethics in a World of Strangers (2007)
Dennett, Daniel. Intuition Pumps and other Tools for Thinking (2013)
Dixon, Bob. Searching for Aboriginal Languages: Memoirs of a Field Worker (1984)
Engelmann, Siegfried and Carnine, Douglas. Could John Stuart Mill have saved our schools? (2011)
Farrington, Benjamin. The Philosophy of Francis Bacon (1964)
Hofstadter, Douglas R. Metamagical Themas: Questing for the Essence of Mind and Pattern (1985)
Kenny, Robert. The Lamb Enters the Dreaming: Nathanael Pepper and the Ruptured World (2007)
McIntosh, Dennis. Beaten by a Blow (2008)
Minsky, Marvin. The Society of Mind (1985)
Osborne, Barry (Editor). Teaching Diversity and Democracy (2001)
Monk, Ray and Raphael, Frederic (editors). The Great Philosophers (2000)
Putnam, Hilary. Ethics without Ontology (2004)
Putnam, Hilary. Words and Life (1994)
Roughsey, Dick (Goobalathaldin). Moon and Rainbow: the autobiography of an aboriginal (1971)
Sarra Chris. Good Morning, Mr. Sarra: My life working for a stronger, smarter future for our children (2012)
Shapin, Steven and Schaffer, Simon. Leviathan and the Air Pump: Hobbes, Boyle and the Experimental Life (1985)
Van Fraassen, Bas. The Empirical Stance (2002)
Widdowson, Frances and Howard, Albert. Disrobing the Aboriginal Industry: The Deception Behind Indigenous Cultural Preservation (2008)
Willingham, Daniel T. Why Students don't like School: A cognitive scientist answers questions about how the mind works and what it means for the classroom (2009)

Sunday, January 01, 2017

Donald Trump's twitter feed

I guess one of my new goals in life is to try to understand Donald Trump's twitter feed.

I think this guy gets it: Staking Out The Far Edge and he predicts that President Trump will continue to twitter.
As to the tweeting of the Donald, there’s little chance that his style will become more “Presidential”. He used that style to defeat 16 Republican candidates for the nomination and to defeat Hillary Clinton. Yes, his tone may change, the Presidency has changed the tone of every man I’ve seen take on the job.

But the tweet is far too useful to Trump to ever give up. It is his direct connection to the American people, one which cannot be changed, misquoted, or slanted by the media whether favorably or unfavorably. In addition, he employs it as a most potent negotiating tool, using it to good advantage in a number of ways including staking out the far side of a discussion. So I expect little change in his use of Twitter.