The Secret Question (Are We Actually Good at Math?)

Posted on the AMS Blogs on September 1, 2015 by Ben Braun

“How many of you feel, deep down in your most private thoughts, that you aren’t actually any good at math? That by some miracle, you’ve managed to fake your way to this point, but you’re always at least a little worried that your secret will be revealed? That you’ll be found out?”

Over half of my students’ hands went into the air in response to my question, some shooting up decisively from eagerness, others hesitantly, gingerly, eyes glancing around to check the responses of their peers before fully extending their reach.  Self-conscious chuckling darted through the room from some students, the laughter of relief, while other students whose hands weren’t raised looked around in surprised confusion at the general response.

Preterm Birth Linked With Lower Math Abilities and Less Wealth

September 1, 2015
For Immediate Release
Contact: Anna Mikulak
Association for Psychological Science
amikulak >>at<<

People who are born premature tend to accumulate less wealth as adults, and a new study suggests that this may be due to lower mathematics abilities. The findings, published in Psychological Science, a journal of the Association for Psychological Science, show that preterm birth is associated with lower academic abilities in childhood, and lower educational attainment and less wealth in adulthood
“Our findings suggest that the economic costs of preterm birth are not limited to healthcare and educational support in childhood, but extend well into adulthood,” says psychological scientist Dieter Wolke of the University of Warwick in the UK. “Together, these results suggest that the effects of prematurity via academic performance on wealth are long term, lasting into the fifth decade of life.”

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Latest speech by Nick GIbb

Nick Gibb speaks at the Researchers in Schools celebration event, 25 August 2015.

What follows are paragraphs from the text containing the words maths or mathematics.

The Researchers in Schools programme prioritises recruiting teachers in STEM subjects, in particular mathematics and physics. Nobody needs reminding that British employers face ongoing skills shortages in these areas.

One in 10 state schools have no pupils progressing to either further maths or physics at A level, and 1 in 3 physics teachers have themselves not studied the subject beyond A level.

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The Quadratic Formula in Malta’s Learning Outcomes Framework

What I see as a deficiency of the Learning Outcomes Framework is that it does not specify learning outcomes in a usable way.

There are several references to quadratic equations in Levels 8–10, for example

Level 8
Number – Numerical calculations
18. I can solve quadratic equations by factorisation and by using the formula.

If a student from Malta comes to my university (and I have had students from Malta in the past, I believe), I want to know what is his/her level of understanding of the Quadratic Formula.

There are at least 7 levels of students’ competencies here, expressed by some sample quadratic equations:

(a) x2 – 3x +2 =0
(d) x2 – 1 = 0
(c) x2 – 2x +1 = 0
(d) x2 + sqrt{2}*x – 1 = 0
(e) x2 + x –  sqrt{2} = 0
(f) x2 + 1 = 0
(g) x2 + sqrt{2}*x + 1 = 0

These quadratic equations are chosen and listed according to their increasing degree of conceptual difficulty: (a) is straightforward, (b) has a missing coefficient (a serious obstacle for many students), (c) has multiple roots, (d) involves a surd, but no nested surds in the solution, (e) has nested surds in the answer, (f) has complex roots, although very innocuous ones, and (g) has trickier complex roots. Of course, another list  can be made, with approximately the same gradation of conceptual difficulty.

I would expect my potential students to be at least at level (d); but LOF tells me nothing about what I should expect from a student from Malta.

And one more comment: a comparison of the statements in the LOF Level 10:

I can solve quadratic equations by completing a square

and in the LOF Level 8:

I can solve quadratic equations by factorisation and by using the formula.

apperars to suggest that at Level 8 the Quadratic Formula is introduced to students without proof or proper propaedeutics which appear only at Level 10. In my opinion, this should raise concerns: at Level 8, this approach has a potential to degenerate into one of those “rote teaching”  practices that make children to hate mathematics for the rest of their lives.

Malta’s Learning Outcomes Framework: a Discussion

Malta’s new Learning Outcomes Framework for school mathematics is an important case study of the European Union’s approaches to implementation of its education policies in member countries. For that reason the Framework deserves a close attention.

The original post of 13 August generated more responses than it was anticipated, and it is useful to collect them all at a single page.

The Great Mystery of Malta’s Learning Outcomes Framework

Important update below: it is no longer a mystery.

Malta’s new Learning Outcomes Framework is an important case study of the European Union’s approaches to implementation of its education policies in member countries. For that reason the Framework deserves a close attention.

An attempt to study the official website

immediately leads to a question:

Who had actually developed the Framework?

According to Wikipedia, population of Malta is about 445,000. When compared with the City of Manchester (about 514,000), it becomes clear that development of the Framework is a job beyond capabilities of a small nation.

So, external consultants were hired, some institutions or companies from English speaking parts of Europe. Taking into consideration traditional cultural connections, this part of Europe is likely to be the UK.

Added 24 August 2015:  Indeed I could not locate contractor’s names using advanced Google search on,but  serendipitously discovered their logos in the document Joint Venture Presentation dated 28  Jan 2015:

IoE_24Aug15Outlook Coop is a company on Malta specialising in project management with expertise in EU funded projects. 

East Cost Education Ltd is a small private company based in Northumbira with specialism, judging by their website,  concentrated mostly in vocational education and training. In recent years, they worked on Malta on several projects in vocational training.

Institute of Education, London, is

the world’s leading centre for education and applied social science.

The Inspection Paradox is Everywhere

From a brilliant blog by Allen Downey:

The inspection paradox is a common source of confusion, an occasional source of error, and an opportunity for clever experimental design.  Most people are unaware of it, but like the cue marks that appear in movies to signal reel changes, once you notice it, you can’t stop seeing it.

 A common example is the apparent paradox of class sizes.  Suppose you ask college students how big their classes are and average the responses.  The result might be 56.  But if you ask the school for the average class size, they might say 31.  It sounds like someone is lying, but they could both be right.

The problem is that when you survey students, you oversample large classes.  If are 10 students in a class, you have 10 chances to sample that class.  If there are 100 students, you have 100 chances.  In general, if the class size is x, it will be overrepresented in the sample by a factor of x.
That’s not necessarily a mistake.  If you want to quantify student experience, the average across students might be a more meaningful statistic than the average across classes.  But you have to be clear about what you are measuring and how you report it.