Developing Real Mathematicians (Mathematics training in school)

Schools spend time on trying to inspire their future authors, sports stars, artists, scientists, historians… and quite rightly. We book experts in those fields to visit and we reference their achievements while teaching the subjects. But what about developing the aspiration to become a mathematician?

Any mathematician will tell you that they are a seeker of patterns. Teaching children how to investigate mathematical ideas and structures is crucial to them developing a love of maths and to encourage them to be ‘a seeker of patterns’. The National Curriculum states that all children should learn how to: reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language. And the purpose of study says: ‘A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.’

I have created a planning format to support with mathematical enquiry in the form of an investigation lesson as well as a suite of resources to support teachers with how to develop real mathematicians. These investigative lessons could be delivered to children once a fortnight, for example, as an introduction or a summing up of a Unit of work.

However, in order to fully understand the ideas, the techniques need to be demonstrated and not just talked about.

Book me to work with the teachers in your school. A staff meeting will introduce the philosophy and ideas. This is then followed by lessons in each year group, over two days that are observed and reviewed.

Contact me for more details and click on this link to download the flyer:

Developing Real Mathematicians

07733 092 934          @SharonJaneDay

TES shop

I have a shop on TES. Some items for free and some for sale.

To support with Numbers and Place Value for assessment and planning there are discussion questions that could be used to observe responses (other linked areas of maths are in those documents too) and there are also examples of work from children’s maths books at ARE – both for all year groups from Year 1 to Year 6. Documents aimed at earlier year groups could be useful for assessing for gaps and to support with planning for ‘catch-up’. Each document is only £2.

I am building my products. It includes advice for Greater Depth and I am in the process of putting together exemplification at ARE for year 1, 3, 4 and 5. This should be useful for moderation purposes. Search on the TES website for Sharon Day Maths (or Sharonjaneday).

To Assessments at

Just sent this to the assessments department. Wonder if I will get a reply…

Good morning,
Regarding the KS2 mathematics SATs
It would be very helpful for schools if the cognitive domain (rated 1 to 4) could be referenced in the mark scheme, for each question, as well as the content domain . Are there any plans for this to be created? The test developers must know the cognitive domain for each question when they write them. Teachers would value having this information at their finger tips, especially when considering whether children are demonstrating thinking at Greater Depth or not.
I hope to hear from you soon.
Kind regards,
Sharon Day
of SharonDayMaths Ltd.

I got a reply. The relevant paragraph said this: ‘As you may know, the primary and sometimes (if applicable) the secondary national curriculum references are published in the live test mark schemes to inform the area of the curriculum each item intends to assess. As yet, we do not publish the cognitive domain scores in the mark scheme document. The mark scheme’s primary purpose is to guide markers on how to mark each item reliably. We could bring your suggestion to our expert review panels and consult our curriculum advisors to see what purpose they could serve if we did publish them in the mark scheme document- thank you for your suggestion.


Make angles facts and missing angles today’s focus. Work out the angles on a clock with the children (each hand goes through 30 degrees when moving from one number to another – when the hands show 3 o’clock and 9 o’clock they represent a 90 degree angle which is a quarter of 360 degrees and the two hands are also perpendicular to each other…). Revise all quadrilaterals (square, rhombus, rectangle, parallelogram, kite and trapezium) and triangles (right-angled, equilateral, scalene, isosceles). Ask: ‘Is it possible to draw a triangle with two right angles?’; ‘ If we drew a right-angled triangle which was also isosceles, what would its three angles be?’