Which Times Tables do Students Find Difficult?

There’s an excellent article on today’s Guardian Datablog looking at a computer based study (with 232 primary school students) on which times tables students find easiest and difficult.  Edited highlights (Guardian quotes in italics):

Which multiplication did students get wrong most often?

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The hardest multiplication was six times eight, which students got wrong 63% of the time (about two times out of three). This was closely followed by 8×6, then 11×12, 12×8 and 8×12.

The graphic shows the questions that were answered correctly the greatest percentage of times as dark blue (eg 1×12 was answered 95% correctly).  The colours then change through lighter shades of blue, then from lighter reds to darker reds.  It’s interesting to see that the difficult multiplications cluster in the middle – perhaps due to how students anchor from either 5 or 10 – so numbers away from both these anchors are more difficult.

Which times table multiplication did students take the longest time to answer?

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Maybe unsurprisingly, 1×1 got answered the quickest (but perhaps illustrating the hazards of speed, pupils got it wrong about 10% of the time), at 2.4 seconds on average – while it was 12×9 which made them think for longest, at an average of 7.9 seconds apiece.

It’s quite interesting to see that this data is somewhat different to the previous graph.  You might have expected the most difficult multiplications to also take the longest time – however it looks as though some questions, whilst not intuitive can be worked out through mental methods (eg doing 12×9 by doing 12×10 then subtracting 12.)

How did boys and girls differ?

On average, boys got 32% of answers wrong, and took 4.2 seconds to answer each question.  Girls, by contrast, got substantially fewer wrong, at 22%, but took 4.6 seconds on average to answer.

Another interesting statistic – boys were more reckless and less considered with their answers!  The element of competition (ie. having to answer against a clock) may well have encouraged this attitude.  It would be interesting to see the gender breakdown to see whether boys and girls have any differences in which multiplication they find difficult.

Which times table was the hardest?

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As you might expect, overall the 12 times table was found most difficult – closely followed by 8.   The numbers furthest away from 5 and 10 (7,8,12) are also the most difficult.  Is this down to how students are taught to calculate their tables – or because of the sequence patterns are less memorable?

This would be a really excellent investigation topic for IGCSE, IB Studies or IB SL.  It is something that would be relatively easy to collect data on in a school setting and then can provide a wealth of data to analyse.  The full data spreadsheet is also available to download on the Guardian page.

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Essential resources for IB students:

1) Revision Village

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Revision Village has been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams.  I would strongly recommend students use this as a resource during the course (not just for final revision in Y13!) There are specific resources for HL and SL students for both Analysis and Applications.

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There is a comprehensive Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and then provides a large bank of graded questions.  What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial.  Really useful!

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The Practice Exams section takes you to a large number of ready made quizzes, exams and predicted papers.   These all have worked solutions and allow you to focus on specific topics or start general revision.  This also has some excellent challenging questions for those students aiming for 6s and 7s.

Each course also has a dedicated video tutorial section which provides 5-15 minute tutorial videos on every single syllabus part – handily sorted into topic categories.

2) Exploration Guides and Paper 3 Resources

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I’ve put together four comprehensive pdf guides to help students prepare for their exploration coursework and Paper 3 investigations. The exploration guides talk through the marking criteria, common student mistakes, excellent ideas for explorations, technology advice, modeling methods and a variety of statistical techniques with detailed explanations. I’ve also made 17 full investigation questions which are also excellent starting points for explorations.  The Exploration Guides can be downloaded here and the Paper 3 Questions can be downloaded here.