Ignorance of Number Facts “No Barrier to Success”?

This week, a flurry of news and blog articles appeared, proclaiming that children don’t actually need to learn their number facts off by heart, as not knowing number facts doesn’t stop them from being good at maths. Is this really true?

The articles in question include these:

  • BBC News: “Sums tables ‘not needed for maths success’”
  • The Guardian’s Teacher Network Blog: “Children don’t need to know all their number facts to succeed at maths”
  •  Daily Mail’s Mail Online: “Scandal of the primary pupils  who can get full marks in maths without even knowing their times tables”
  • Independent Education Today: “Primary school children succeed at Maths without knowing their tables”
  • Yahoo UK: “Children don’t need to know number facts to be good at maths”
© iStockphoto.com/Chris Schmidt

My attention was caught by a tweet by @wanstad73 curated on my daily paper over at paper.li on September 13, linking to the Guardian article. Having taught number facts myself as a classroom teacher, and now teaching preservice teachers the importance of laying a good foundation in number facts in all 4 operations, I have a strong interest in the topic.

Let’s just say I was alarmed by a claim that memorization of number facts is unnecessary for success in primary or elementary maths. Surely, my thinking goes, without knowing number facts by heart, children will be unable to tackle later maths, not just in computation, but also in geometry, measurement, probability, algebra; pretty much all mathematics topics.

“The Development and Importance of Proficiency in Basic Calculation”

I had a look at the original article by Professor Richard Cowan at the Department of Psychology and Human Development, Institute of Education in the University of London. Surely the study’s author himself hadn’t said number facts were not necessary, as these secondary reports were saying?

It shouldn’t be a surprise that media outlets have picked on the idea that number facts are not really important. The English National Curriculum requires all addition facts to 20 to be memorized by the end of Year 3. So the idea that a research study has proven not only that Year 3 students aren’t learning all their facts, but furthermore those facts aren’t really that important could be expected to catch the interest of journalists whose bosses want to sell more advertising. But is that really what the research showed?

To summarize, Prof Cowan and his fellow authors say the following:

  • proficiency in basic addition and subtraction to 20 is a key indicator of general mathematical ability, which later leads to adult proficiency
  • students in Years 3 and 4 in the study showed above-average mathematical achievement, yet none out of 259 knew all their number facts
  • only 10% of the children themselves reported that they were recalling number facts to answer most of the questions

The report’s authors describe the differences between a traditional view of learning number facts and a progressive view. According to them, the traditional view, in vogue in the 1920s and 1930s, favours rote memorization of number facts, whereas the progressive view focuses on children ‘learning numerical principles and patterns and knowing how to use them efficiently and accurately’ (Cowan 2011, p. 4).

Rote Learning vs Developing Understanding of Numbers

A comparison is thus set up between rote learning of facts and developing understanding of mathematical principles. What can we learn from this comparison?

Traditional View Progressive View
Learning by rote (repetition) Learning through understanding
Facts learned in isolation Facts learned as connected to other facts &
Facts believed to be essential for
Facts believed to be less important than
Forgotten facts difficult to retrieve Facts not known may be derived by thinking
Memorization of number facts regarded as essential for all students The ability to work out facts from understood principles regarded as essential

Which view is better? And which one is favoured by the report authors?

Contrary to the tabloid headlines, Prof Cowan and his co-authors believe that being able to carry out basic addition and subtraction quickly (the standard used in the study was 3 seconds for a correct response) is vital for developing a wider mathematical proficiency to lay the foundations for adult mathematical skills. The authors certainly did not say that number fact shouldn’t be rapidly accessible to all students. In fact, what Prof Cowan did state (according to the Mail Online) was ‘We are not saying that fact knowledge is irrelevant’, and ‘Facts help children grasp principles, and applying principles helps children learn facts’.


  1. Children do need to know their number facts, either via memorization or via developing conceptual knowledge.
  2. While children are learning the number facts, it is quite acceptable for students to use a strategy based on conceptual knowledge to quickly work out the answer.
  3. Big media is wrong to imply that number facts aren’t important after all. Children need understanding of numbers first, and then need to memorize number facts. A more accurate headline than those chosen by editors would be “Children need to understand basic number concepts to succeed at mathematics”.
  4. Most primary age students will use a combination of strategies based on understanding and memorized facts, as they develop greater speed and proficiency. Not having the complete set memorized is not a significant flaw, provided the child has a set of tools to derive those facts that have not yet been committed to memory.


Cowan, R 2011, The Development and Importance of Proficiency in Basic Calculation, Institute of Education, London, http://www.ioe.ac.uk/Study_Departments/PHD_dev_basic_calculation.pdf [accessed 13th September 2011].

If you are interested in resources to teach number fact recall via an organised system of worksheets based around classroom-proven strategies, check out our eBook “10 Minutes a Day: Times Tables Worksheets“. If you would like to trial part I of the system, sign up to receive it; all we ask is for your email address so we can keep you updated on new resources and content as they become available. If you are ready to buy the complete eBook, visit our store where you can purchase it.

Math in the Cemetery

How can you use a field trip to a cemetery to teach mathematics?

I visited Richmond Park in London with my brother, and while there visited the East Sheen Cemetery to film a podcast.

What can  you learn in a cemetery? At first glance, this may sound like a strange or even morbid suggestion. However, provided you don’t have an issue with this (and neither do the parents of your students), there is a lot to be learned from the information a cemetery offers. In fact, the headstones or other locations where details of those who have passed are recorded form a statistical database of the community, potentially a very rich and fascinating record of the history of people who have lived in the area, and the events that have affected their lives.

Google Map

This map shows the location of the video. Zoom out to see its location in relation to the London city centre:

View East Sheen Cemetery in a larger map

The cemetery I visited is in London, which has had a number of critical events in its history that might be reflected in the records at a cemetery, such as:

  • The Great Plague (1665 to 1666; killed 60,000 people)
  • The Great Fire of London (1666; killed 16)
  • World War I (1914-1918)
  • World War II & the Blitz (1939-1945; 30,000 killed)
  • Great Smog of London (1952; 4,000 died)

[Wikipedia: History of London]

Your local cemetery will, of course, reflect the history of your local area. This opens up lots of opportunities for studies in social studies, history, civic studies, geography, and math. In fact, mathematics can be put to good use to serve studies in other disciplines, by providing tools and methods to collate and analyse the data that is collected.

As a starting point, you could ask students to record the following data from grave records for later study in the classroom:

  • date of birth
  • date of death
  • gender
  • occupation
  • cause of death, if stated
  • relationship to others buried nearby
  • other interesting information


By the way, this week I have made a few changes to the site, including removing a lot of fiddly looking links and graphics from the side menu and changing the colour scheme.
The biggest change, however, is that I have canned the audio podcast. The videos will continue, but the number of downloads of the audio was much lower, and so I’ve decided to simplify my life a bit and just produce one version of the podcast. The audio track is available from this page, if you’d like it, but it’s not part of the podcast feed for subscribers. Please let me know what you think!