Jo Boaler’s article was interesting (Britain’s Maths Policy Simply Doesn’t Add Up) and prompted me to blog. She shows concern about girls’ math achievement in Britain:

* “**But when I sat with the PISA team recently, I was horrified to see that of 64 countries assessed, Britain has the biggest gender gap in ‘maths mindset’. Simply put, the data showed that British boys believe they can do well in maths; girls don’t.”*

I was curious whether the claim was true and I checked PISA reports, summaries and Excel tables. She was right. **Boys not only outperform girls in math but also have higher confidence and are more likely to pursue math-related careers. **

She shares Maryam Mirzakhani’s story – the first woman to have received Fields Medal – where Maryam almost turned away from mathematics when she was 11:

*“In the first year of “middle school”, she struggled in maths and her teacher decided she was not very capable. By her own account, at that point Maryam ‘lost her interest in maths’. This experience is not unusual.”*

However, I do not entirely agree on that what she thinks is the core problem responsible for this gap:

*“(…) the testing and levelling culture that has taken hold in British schools, which has turned mathematics into a subject of speed, memorisation and procedural thinking.”*

If that is the reason, then one must assume boys are better at all three (speed, memorization, and procedural thinking). Which contradicts the idea “there is no maths person” that she brings up in the same article.

I love Jo Boaler’s view on the teaching of mathematics and have repeatedly tweeted her videos, conferences, articles. But I think some claims are too strong.

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**CURRICULUM and TEACHER KNOWLEDGE are key**

My question was, “What could possibly account for this gap?”, and two answers came to mind:

**Girls really don’t “get” math**(with some exceptions)**beyond basic or average levels**. (Don’t shoot me – playing devil’s advocate is good for thinking).**There is something in the system**(curriculum, teaching methods, teacher subject knowledge)**and/or culture**(girls’ mindset, teacher bias).

What also makes me sensitive to the topic is that, as a primary school teacher, I saw no differences between student achievements in math gender-wise. The ratio of girls-boys who both achieve in and enjoy math has always been balanced in my classes for nearly 20 years now. **What happens from primary to high school that changes this proportion?** Could it be that arithmetic is easier, more concrete, than algebra?

If that is the case (as explained in The Psychology of Learning and Teaching Mathematics above), that would result in girls being less able to deal with abstract thinking (which is my point 1). Hm, is this hypothesis true?

So I read and read dozens of reports.

First, in this report on gender achievement in math from PISA, it is stated:

“In most countries and economies, girls underperform boys in mathematics; and among the highest-achieving students, the gender gap in favor of boys is even wider.”

However, why is it that (from the same report),

” The **average** **girl** in Shanghai-China scores 610 points in mathematics, **well above boys’ average performance in every other country and school system** that participated in PISA.”

And we are talking about “the average” girl. Had she been less able in math she couldn’t have possibly outperformed boys. That score, then, says something about **the SYSTEM and its elements – curriculum, methodology, teacher subject knowledge**. Something that is under teacher and school control. While *methodology* varies between countries (see China, Japan, and Finland for comparison – at extremes in terms of direct instruction vs. more progressive methods) and it is difficult to track, I sought to find more transparent elements that would explain why top achieving countries that are so different get such results.

One answer: **more exposure to formal mathematics** (as opposed to applied math – real-world problems) **AND to advanced mathematics content** correlates to higher scores. Formal mathematics was the only one that correlated positively at three levels (student, school, country performance), and word-problems as found in books did “correlate with positive performance but not as strongly.”

In other words, that “average” girl that outperforms boys has **no** problem understanding mathematics – it is that she is exposed to different math learning opportunities.

The exposure to **applied mathematics (real-world context) only correlates positively up to a point after which it affects performance** – in other words, it is good only if it is balanced with formal mathematics and word problems (see where applied mathematics is used “frequently” the performance drops).

Being aware of the dangers of “authenticity” is also found in The Handbook of Research on the Psychology of Mathematics Education (2006) that warns that “realistic problems may, in fact, steer pupils away from the underlying mathematical structure of a problem”.

See the difference between the **mathematics level** (on a scale 1-6) across different countries.

While applied mathematics do have their role in math performance, it is suggested that balancing formal-applied math is necessary.

This is important because, in our noble attempt to make math “interesting” for girls we might actually harm: dumb down, if you want me to put it simply. The very fact that girls in Japan or Singapore outperform boys in other countries signals that girls *are* capable of doing advanced math. Also, making math slightly easier or more concrete is self-defeating: your message to girls is that they *are* incapable of doing “normal” math. There is the cultural aspect here (growth mindset), but one cannot understand truly to what extent it affects girls. We can, however, see what stable elements – such as curriculum and teacher knowledge – influence their achievement.

Aside from **curriculum** (see exposure to more advanced math content and formal math), I think **teacher subject knowledge** plays a huge role. It is difficult to discuss math in primary beyond lesson plan ideas and math games – at least on Twitter. Not many primary school educators have a solid grasp of mathematics as content and principles, as well as psychology of mathematics – how students make sense of math. We might very well look at this aspect and see how we can change – see Finland where the competition for becoming a teacher is fierce. It is a highly professionalized career.

**Methodology**, as said before, is difficult to track and analyzed as these top-performing countries show extreme variation (from direct, sequenced instruction to more progressive, student-centered teaching). However, it is interesting to notice that, for instance, in the U.S. teachers help too much and do not allow students to struggle, they do not pose open-ended problems like in Japan and so forth – the TIMSS video study is very relevant as to how teachers across countries actually teach.

Just a sample of their reports (which you can find and download ) – how much time is devoted to high complexity problems in Japan vs. the U.S.

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**Girls’ – boys’ performance differences are NOT that dramatic**

The difference between girls and boys performance is striking ** only on Level 6** (6 levels of difficulty as measured by PISA). For the rest of the levels (1-5) they are insignificant.

And we are talking about *averages* here. Some countries **narrowed the achievement gap** (e.g. Russian Federation, where girls performance improved by 20 score points while boys’ performance did not change), and in others (e.g. Iceland) **girls outperform** boys. Perhaps it is a good idea to see how these countries implemented policies that brought about these changes.

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References:

PISA – Gender International Version

PISA – A Profile of Student Performance

PISA – Measuring Opportunities in Learning Mathematics

More links at – Key Findings – OECD

TIMSS – Video Study (scroll to Reports, Data, Instruments)

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