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The gist of this episode might read: Neural networks, anyone?

Neural networks are commonplace, but we might not be aware of them. They are used when Facebook suggests tags for photos, a diagnostic lab analyses cell samples for cancer, or a bank decides whether or not to offer a loan.

So knowing what neural networks are and how they work are important. However, this episode provided only a small taste of both with this schematic.

My marked up version of the PBS/CrashCourse graphic on a basic neural network schematic.

Marked up version of the PBS/CrashCourse graphic on a neural network schematic.

If the input layer is a query we might have and the output layer is an answer, the black box is where rules and algorithms break down and process the input.

What happens in the black box is still a mystery. We might not care how exactly a social media system knows what tags to suggest for a photo, but we probably want to know why a financial system denies us a loan.

Perhaps the next episode might shed more light on the black box.

Here is segment that one might call News We Need Right Now. It is about an autistic, near non-verbal boy who went “Wow!” at the end of a classical music concert.


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When I started teaching, all I hoped from my students were “Oh!” or “A-ha!” as expressions of realisations. As an educator of 30 years, perhaps I should aspire to “Wow!”

You know what? I would rather that my learners go “Hmm…”

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This video pit students against teachers in a mathematics test. But what was the point?

Neither party did well, so was the message about the state of mathematics learning was in the US? The PISA findings already told us that.

Was the point that test-worthy mathematics was not relevant to both schooling teens and working adults? If you collect enough anecdotes it becomes data. If you analyse that data, you might come to the same conclusion.

Was Buzzfeeed reaching for low-hanging fruit (we hate mathematics but we want to feel good about it) so it made a video to ingratiate itself and its audience? It’s Buzzfeed — that is their modus operandi.

The subtle point is that nuance is difficult and undesired. It is hard to show that mathematical thinking (not just going through the motions of using formulae) is what is important.

An academic test is just that — it results in a score to sort and possibly remediate before subjecting the student to another test. But passing a test does not guarantee that the student has mastered mathematical thinking. Passing a test shows that the student is good at taking tests.

Trying to showcase such nuance does not make for good viewing. Reality TV and video producers focus on the heightened or controversial for entertainment. Educators on the other hand need to look at the everyday and mundane to make mathematics relevant. Sadly, such videos do not have as many hits as Buzzfeed ones.


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This needs to be said: No one should assume that movies depict teachers and teaching accurately.

No one should learn from movie depictions of the same, except to critique said depictions. All that said, there are two truths about such representations:

  1. Movies often do not show how teachers decompress. This is mirrors life and is boring or ugly, so viewers seeking entertainment might reject it.
  2. The best teachers listen first, listen again, and listen some more, before offering anything of substance.

Like many things, written and spoken language evolves. The video below highlights a few changing standards and “standards” in written language.


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The thing it hints at is context. We speak and write differently in different contexts. What some students are not taught (or not taught sufficiently) is when and how to switch.

If students are not taught to identify contexts first, they might see the different rules and standards as a burden. They might opt to use the form of language they are most comfortable with regardless of context.

Like it or not, this is a failure of teaching and learning.

If we consider the SAT, the prime test for entrance to US universities, what does that test actually measure?

The video below provides insights into the history and design of the SAT.


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It concludes with this sobering thought:

The SAT was created in the pursuit of precision. An effort to measure what we’re capable of — to predict what we can do. What we might do. What we’ve forgotten is that, often, that can’t be untangled from where we’ve been, what we’ve been through, and what we’ve been given.

The same could be said about practically any other academic test taken on paper.


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The USA (not America) celebrated its Independence Day last week. It has lots to celebrate and it still has a lot to work on.

M(US)AGA, anyone?


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