The scoundrel, David Gonski

In one of his last acts as Prime Minister, Tony Abbott and his Minister for Education Chris Pyne appointed one of their mates from big business to review how schools were funded. He brought to the review his experience of attending one of Sydney’s most expensive grammar schools and being Chairman of the Board of Trustees there. He’s a good friend of Rupert Murdoch though, and owns a house worth over $5 million (and sold a penthouse for $14 million). A real battler for the disadvantaged.

Unsurprisingly the review he just handed down entrenched strong funding for the sort of private schools he attended and presided over. A “sector blind” approach basically sneaks in a school voucher system. Commentators on the left are livid and are planning to run a sharp campaign to demand that the government prioritise public schools in the funding model.

No, I’m kidding. This was actually 2010, and Prime Minister Kevin Rudd and his Minister for Education Julia Gillard appointed David Gonski. But the rest of the facts are the same. Oh and except for the howling on the left. Under the cloak of supporting Labor (and not giving ammunition to a strong Abbott opposition) the left was mostly supportive of the Gonski model. Perhaps it’s also just realpolitik – substantial new money in education is a good price for silence on how it should be allocated? It’s hard to figure out how the consensus arose to largely be silent on Gonski’s flaws.

David Gonski seems a good man, and genuinely cares about giving disadvantaged student groups in Australia a fair shot in life, but there are significant right-wing, business, private-schooled values are clear in the model bearing his name. These don’t get enough press, particularly by groups you’d expect would devour anyone proposing any of these things by themselves.

The biggest blow to the predominantly public system that these people talk about wanting is the whole “sector-blind” approach. This is the idea that funding is per-student and gets allocated with minor caveats regardless of the system that the student is in*, effectively following each student. Come on – if this was introduced as a standalone policy anywhere else, we’d call a spade a spade and say it’s basically a school voucher system. Sure private school funding trails off as parent contributions increase, but the real change is that it makes low-fee private schools competitive with their public counterparts. Given the decreased accountability and rules for private schools (in curriculum, industrial relations etc.) this is close to sneaking in a charter school system to Australia through the backdoor. Sure, it is a tapered school vouchers system, and a low fee charter-wannabe would have to get some parent contributions or significant fundraising. The Victorian Government is happy to help out though, with their policy to raise the minimum floor of government contributions from 10% to 25%.

In the biggest change to funding that 5 years later is left to be implemented and will probably stand for over a decade when its (if ever) introduced, it’s just surprising that the progressive voices concede such a huge entrenchment of government funding. A small pip in The Age today reminded me to publish this, is this the start of a conversation in the right direction (if you’re so inclined that way)?

Overstating results: “Stop yelling at kids”

There’s a new article on The Conversation this week, reporting the results of a US study comparing “negative parenting” tactics against student results (full text available, no paywall!).

The article actually summarises the study really – a sample size 500, a survey of parents of what they would hypothetically do if students had below-expected results at school, then comparing that to math and literacy achievement five years later. The results are that parents who endorsed “negative parenting” tactics five years earlier are on average the parents of the worse performing students. The conclusion of the study – “parental endorsement of punitive strategies in response to bad grades has negative effects on adolescents’ reading and math achievement and this is generalizable to the broader population given the use of a nationally representative study”.

Sigh. Vomit.

What’s the obvious problem here? That usual nemesis to social science, correlation and causation. Are “negative parenting” tactics causing poorer results or something else? What really annoys me about this study is that the authors wrote a really long list of all the ways this results could be non-causal or confounded (literally every objection I thought of before reading the paper was already described there), but the researchers then ignore that discussion and act as if “negative parenting” causes bad grades. Maybe it does, but this study certainly doesn’t show it.

Let’s go through the points the authors themselves bring up:

Firstly, the study doesn’t actually measure parenting tactics: it’s a self-reported scale about a hypothetical scenario at the start of middle school, compared to performance across the next 5 years. It would be interesting to measure whether parents would even fill out the survey the same way across those 5 years, as a 11-13 year old approaches adulthood and the child’s personality and relationship to their parents changes. The study’s authors note that “prior research demonstrates that parents generally underreport the level of their punitive parenting”. So any conclusion to “stop yelling” has to be tempered by the fact that even in the supposedly successful households, some level of negative parenting happens. The important point here is that the measure for negative parenting underreports, may change over time, and may be completely different than what actually happened.

The second confounder is that parents were asked what they would do if a student brought home a report below expectations. There was no control in the study at all for what parents expected of their kids. It’s all very well to ask a parent what they’d do “if” but if the student comes home with a D and the parents don’t react, it’s a completely different scenario to the old joke that a B+ is an “Asian fail”. Again, because the study doesn’t measure actual parenting, these differences confound the data. A parent pushing their kid with negative or positive strategies will get different results than a family that hypothetically would do something but doesn’t. There’s variations on this theme with parents who stay involved during the whole year vs. those who react to a twice-yearly report card.

The third problem is race and ethnic group confounding. The racial group most famous (or infamous) for high academic outcomes with strict parents are Asians (indeed the study itself references Amy Chua, the Tiger Mom). What percentage of the sample was Asian? 1%. Remember the authors words were “this is generalizable to the broader population given the use of a nationally representative study”. Instead the study is dramatically overweight towards African Americans, who are 12% of the US population and 44% of the sample here. Oh, by the way, African Americans “were more likely to endorse punitive parenting practices [than White parents]”, and of course tend to underperform relative to White students in schools for a range of reasons. It’s hard to look at the study and not at least think that they’ve merely found a variable (negative parenting survey) that simply correlates to academic performance by race for 90% of their sample (African American and Whites together).

I think I’ve made my point but let’s complete this. A good teacher knows that depending on exactly what a students is doing and why, a range of behaviour management strategies are appropriate. The authors of the Conversation article state “the main reason that “punitive parenting” strategies like those are unlikely to work is that they do not directly address the underlying problems that lead to the poor result”. This only true if students are getting bad grades for some other reason than “not putting in enough effort”. We can debate about whether parents should address a students extrinsic or intrinsic motivation but the negative tactic “restricting activities” i.e. grounding could plausibly work in some situations. The study authors talk about this: because the survey was hypothetical, parents are making assumptions about the cause and “they may endorse alternative types of parenting strategies if the reason for the poor grade was a result of the child not understanding the content.”

Here’s the most important line in the paper, ignored 3 paragraphs later in the conclusion:

“this study is correlational in nature and even though we accounted for important covariates related to achievement, it is still possible that we did not identify an important construct accounting for the outcomes”

Why Harvard can lose to a prison debate team

The story of how a debating team from Harvard got trounced by a team formed from prison inmates is getting thrown around at the moment. Here’s CNN, The Guardian and the Wall Street Journal. It’s a stellar win, particularly with the inmates have to study without internet access and delays or difficulties in written materials. I thought it was unbelievable when I first heard about it – here’s why it’s not.

It’s not “the average person from Harvard” vs. “the average person in prison”. I definitely caught myself stereotyping the types of people on both sides at first glance, and if the match-up was “the average person” from both sides, of course Harvard would win. Instead the inmates are from a highly selective program (doing very good work in those institutions). For instance, at minimum participants need a high school diploma and then rise above a very competitive process where applicants are selected “on their ambition and willingness to work hard”. There are only “ten applicants for each available spot” (not that they’re drawing from the same pool, but that’s still not as exclusive as Harvard). Some inmates from the program went on to study at Yale and Colombia themselves. So it’s less a Stand and Deliver situation as much as picking out a combination of near-Harvard-eligible inmates (oh and one of them was at least 10 years older than the Harvard team if you think life experience and that counts).

It’s an incredible achievement – winning a debate of that calibre – just less counter-intuitive than I first thought.

Fact-checking: Maria Montessori, “3 time Nobel Peace Prize nominee”

I was reading this article, and in a minor point, the author defends Maria Montessori, founder of the Montessori approach to education, by stating that among other achievements “she was nominated for the Nobel Peace Prize.”

I was surprised because I was under the impression that nominees for the Nobel Prizes were never announced. Unlike Oscars or Emmys, I didn’t think Nobel Prizes offered the title of “nominee” as a sort of runner-up or title of its own merit e.g. “3 time Oscar nominee, Johnny Depp“.

It turns out the Nobel Foundation do release a list of people nominated, but only 50 years after the fact purely for “research in intellectual history” (in 2015 we don’t have any information about nominees after 1964). Nevertheless Maria Montessori is indeed a nominee, nominated in 1949, 1950 and 1951.

The trouble is “Nobel Peace Prize nominee” is not a particularly exclusive title. In 2015 the number of nominees for Best Actor in the Oscars was 5. In 2015 the number of nominees for the Nobel Peace Prize was 273. This is because unlike the Oscars, where the list of nominees is already a select shortlist, “Nobel Peace Prize nominee” is literally anyone whose name was mailed to the Committee by an eligible nominator and “eligible nominator” is also a wide category. Eligible nominators include any “professors of social sciences, history, philosophy, law and theology” or any “members of national assemblies and governments of states”. So if you’d like to be a “Nobel Prize Nominee” start petitioning your local MP, they can make you one!

Who nominated Maria Montessori? In 1949, it was 2 professors from Utrecht, the Viscount Lambert in the UK’s House of Lords, and Maria Jervolino, an Italian MP. It was Maria Jervolino who went on to nominate Maria Montessori again in 1950 and 1951. Did I mention that Maria Jervolino was Vice-President of the international Montessori association and president of the Italian Montessori association at the time? There isn’t anything wrong with a nomination process where the vice-president of the Adam Sandler fan club can make him an Oscar nominee, but I might not value the title “nominee” very highly.

Maria Montessori has had a large impact on education over a very long time and is indeed technically a nominee for the Nobel Peace Prize, but it’s not a title that means very much.

It does though, elevate her amongst the ranks of other Nobel Peace Prize nominees, including:

  • Josef Stalin
  • Adolf Hitler (nominated once, satirically)
  • Benito Mussolini
  • The Argentinian dictator Juan Peron and his wife Eva Peron
  • Vladamir Putin
  • Fidel Castro
  • Hugo Chavez

Is a “good” teacher really 1 year of learning better than a “bad” teacher?

“If you get one of the best teachers, you will learn in six months what an average teacher will take a year to teach you. If you get one of the worst teachers, that same learning will take you two years.” – Dylan William, talk at ALT-C 2007 

This quote about teacher effectiveness or some variant of it still gets a lot of traffic from a number of sources. For a line with such wide and prominent use, the original research behind it seems thin and inapplicable for the general comments about teachers it is used for now.

The quote appears to derive from a study by Eric Hanushek in 1992. In his later writings on teacher quality e.g. Hanushek (2014), he himself phrases it as:

“In one study of mine, teachers near the top of the quality distribution got an entire year’s worth of additional learning out of their students compared to those near the bottom. That is, a good teacher will get a gain of 1.5 grade level equivalent while a bad teacher will get 0.5 year during a single academic year” (sic)

I’m not sure where Wiliam finds an extra 6 months of performance out of the “best teachers” in his quote (maybe they attended one of his workshops!).

Surprisingly, the quote is only a side-note in the original paper which was actually designed to study something else. The sample used doesn’t support the wide and general use that the quote is put to today. The study uses a small, non-representative sample – classes of under-performing, low-income all-minority students in one district. Another result from the study is that the white teachers performed on average “significantly worse” than their black colleagues, possibly due to selection effects or a racial dynamic between teachers and students.

It is unclear what the definition of “good” and “bad” are for the quote. Footnote 16 in a 2006 book chapter by Hanushek and Rivkin suggest that they refer to a comparison between teachers at the 5th and 95th percentiles. However the original paper suggests that it was between 1 standard deviation above and below the mean for teacher effects (which would be 16th to 84th percentile if teacher effects followed a normal distribution, which it may not have). In his other publications citing this work, Hanushek just uses the term “good” and “bad” without clarification. It’s not clear that other people using it, certainly at the school level, understand the definition or the implication of it applying at different percentiles.

As far as I can tell, it hasn’t been replicated in the 23 years since, which is the most alarming fact. At best I think it’s overly cited for its credibility, at worst it describes a local, old or deeply exaggerated effect. Using one (1!) result from a poor, US district in the 90s with race confounders to make a statement about current teachers in the UK or Australia seems ridiculous.

What are your thoughts? Put them in the comments below.

“Ideology trumps evidence”, hardly…

It’s critical that teachers have a high enough level of literacy themselves to do their job – how can you teach what you don’t know? There’s been a bit of press e.g. this from the Herald Sun recently raising concerns that some teachers aren’t up to scratch in this regard. If its true, it is a really critical issue affecting our children in important ways.

Or it’s just a beat up on the teaching profession, another attack by politicians, some researchers and the media to weaken the respect and standing of overworked, under-appreciated teachers. Monash University’s David Zyngier tweeted out the article below by Eileen Honan from the University of Queensland who has been studying the issue.

“Ideology trumps evidence” he crows! Except not really.

To start with, in the second paragaph of the article Eileen says “This blog post is a report on our ongoing research. We haven’t finished yet.” As in, as you read the article its pretty clear that the evidence in insufficient and inconclusive (which is why Eileen is bothering to do the good work of further research in the field).

Are literacy levels for teachers actually falling? A lot of the evidence is anecdotal. Attempts to directly measure teaching students’ literacy has only been done in narrow or small studies (one of which was the basis for the Herald Sun article above). Is it enough to act on? Maybe not but I can also sympathise with anyone involved who is impatient to wait for the 5 years for a deep research base to make a solid call.

What is clear however is that the university entry requirements for teaching are falling, simply due to supply and demand as universities have been allowed to open up a lot more education places after the Gillard Government’s change to demand-driven higher education system. It’s not unreasonable to assume that ATAR is correlated with literacy and therefore the average teaching student is worse than those who have come before. The counter-argument is that not all those who are accepted into teacher courses finish and get hired, and declining entry scores were only measured at the undergraduate level (so this will be hard to track without deliberate effort now that most teaching courses are going post-graduate). Or just that correlation with literacy doesn’t translate into less ability to teach primary school how to read.

But it’s certainly got some stakeholders advocating for stricter entry standards:

“It’s further evidence that we need to strengthen standards and rigour with respect to initial teacher education”.

Who are these teacher-bashers? Well it’s the AEU, making a sensible argument that “teaching is a specialist profession”.

So “ideology trumps evidence”, except the ideology isn’t a beat up by media or politicians; it’s the AEU defending teaching being a complex profession requiring skilled workers, and the evidence base is thin, probably trending towards a decline in standards but exactly how that affects students is deeply unclear.

If you want politicians fiddling with schools, go “public education”

“I’m shocked, shocked to find that gambling is going on in here” – Captain Renault, Casablanca

It is a simple fact of public education that for long periods of time, people whose values you fundamentally disagree with will have strong control over schools and teaching. No matter which party you vote for “the other side” are going to have their way for years, sometimes over a decade. Even 1 term in government by the “bad guys” whoever you think they are, is almost a quarter to a third of a child’s education, at the state level it’s at least 1 swing at an EBA negotiation and enough to do a bit of damage. This is the reality of public education in a democracy.

I’m trying to keep it open about which side of politics we’re talking about because the argument does work both ways but honestly most “public education” advocates are on the left side of politics. There are some very valid complaints about the NSW government banning Gayby Baby, the Federal Government pushing an autonomy and independent public schools agenda or direct instruction, or the previous Coalition government in Victoria gutting the regions. People were pleasantly surprised that Donnelly and Wiltshire didn’t send the History curriculum back to the white-washed 1950s – we dodged a bullet there.

But I never see anyone point out the obvious – this is what you sign up for in a government-run system.   No matter how successful a government, at some point cracks start appearing internally or voters get tired, for whatever reason, you hand the keys to the other party. There’s a weird rhythm to government cycles, no party seems to be able to hold power indefinitely and generally when there’s a change it’s rare that someone only lasts 1 term (Victoria being a recent counterexample).

Is there a way for schools and teachers escape the inevitable? Maybe it’s worth pointing out that charter schools were originally conceived by the head of a teachers union as a way to offer trust and autonomy to respected, professional teachers and free them from controls of bureaucratic and political masters.

“I took the one less traveled by, And that has made all the difference” is wrong

I found this article on Hacker News, about Robert Frost’s famous poem starting “Two roads diverged in a yellow wood…”. The article itself is a bit too long, so I’m summarising the parts I find most interesting here.

So this classic, inspirational poem isn’t actually advice to go against majority opinion or tradition by taking “roads less travelled”; it’s really talking about how we rewrite our own history, inflating the importance of equal choices to spin a narrative.

The first thing to note is that the two roads from the first line are actually described (twice) as equal travelled:

“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.”

The final verse is usually interpreted as representing the narrator’s eventual choice, and its impact. This is the quote that everyone remembers I think:

“Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.”

But the full verse is below. The narrator is commenting on what he will say in the future about his eventual choice – overstating his contrarian virtues and the impact on his life – though now he recognises both roads are equal. Now that it has been pointed out to me I struggle to understand how ever I saw it the other way.

“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.”

I’ve left the full (beautiful) poem below, and again you can read the full article by David Orr here.

“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.”

 

No such thing as a kinaesthetic learner in math

There is no such thing as a kinaesthetic learner in mathematics. There are lots of other articles about how “visual-auditory-kinaesthetic” learning styles have been well-refuted by research.

Yet some teachers still think they’ve seen a kinaesthetic learner: “I had a student struggling to grasp fractions written as numbers but finally got it when they worked with physical objects.”

This student isn’t kinaesthetic, they’re just at a low stage of development. Rather than supporting the student to be kinaesthetic mathematician for the rest of their life, its the teacher’s role to move them away from this dependence on the real and concrete.

Rather than VAK, the correct model is the Concrete-Pictorial-Abstract (CPA) continuum. The Singaporeans renamed Jerome Bruner’s enactive-iconic-symbolic sequence in the 1980s and its been a cornerstone of their success in mathematics education ever since.

Students can engage with concepts at different levels. The concrete stage is the observation or manipulation of physical objects and therefore has very little abstraction. As students develop, they can handle the same knowledge drawn as a diagram or picture (pictorial) or as pure symbols (abstract). Each layer steps further away from reality, trading faithful representation for what Bruner calls economy and power. Economy means that, by using diagrams or beyond that symbols, students can reduce the amount of information needed to process the same idea – consider how compact  \dfrac{5}{4} + \dfrac{2}{15} is compared to any diagram or physical mode. Power is the idea that alternative representation can unearth new insights beyond the surface level, bringing out patterns and connections to other ideas.

So the goal for a teacher is to take someone reliant on the “kinaesthetics”, and give them the ability to move past it. Students can’t remain “kinaesthetic” learners of quadratic equations or matrices. For, say, 95%+ of the curriculum past Year 8 students are expected to be beyond the kinaesthetic level and teachers introduce concepts at a purely pictorial level to bridge symbolic understanding. The mistake many a novice Year 7 teacher makes is to ignore the kinaesthetic because some students are ready to live without it.

The end goal of course isn’t abandoning the concrete for the abstract, it’s a flexible ability to use any representation and move between them. The physicist Richard Feynman had a tactic of drawing new, complex ideas back to concrete examples, which he used to prank mathematicians by appearing to understand everything about their fields:

“I had a scheme, which I still use today when somebody is explaining something that I’m trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terrific theorem, and they’re all excited. As they’re telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball)–disjoint (two halls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, “False!” “

I encourage my students to do this when they get tangled up in the application of a formula or a counterintuitive step to solve an equation – “Ask yourself, what does it really mean?” or “Throw some numbers at it and see what works”. Most teachers get students to “draw a diagram” before jumping back to pure symbols.

If you do see a real kinaesthetic learner in the wild, be sure to send me a blurry picture.

Patterson–Gimlin_film_frame_352

A Year 7 maths problem that confuses Year 7 teachers

The modern approach to teaching mathematics is that students should understand more about what they’re doing – for instance instead of giving students a formula, students should see how it works and why (whether they construct it themselves or a teacher explains is a different debate). So here’s an example of a very simple formula that most teachers I spring this on struggle to justify:

Explain why the formula for the area of a triangleA = \dfrac{1}{2}bh is true.

The immediate but glib answer I normally get is: “Because it takes up half of the area of a rectangle you draw around it”. You get partial marks, but this is incomplete.

It is obviously true for this triangle:

Triangle1

For a Year 7, this next triangle causes a few seconds of pause before they notice you can split the triangle in two, and each part is half of its part of the whole rectangle:

Triangle2

How about this triangle?

Triangle3

 

Does A = \dfrac{1}{2}bh hold, where b is the base of the triangle andh is its height? (The answer is in the comments.)

To be fair to the teachers, most of them can work it out, the point is it’s not something they’d considered, nor something they knew offhand (and certainly not something they were introducing to their students). Which begs the question – if a bunch of maths teachers didn’t need this “conceptual understanding”, why do students? Do they?