Tag Archives: fundamental understanding

Mundane Maths?

I will not take this for an answer. Maths is not mundane. It is not tedious. Most of all, it is not boring! I have learned this only from teaching maths in my professional practice and still then I was not 100% confident maths could be full of fun and adventure. However, now, having completed the Discovering Mathematics module, my fun with maths is only just beginning.

Maths does not have to be a chore. It does not have to be the dreaded subject for a learner to approach. But this is up to you, the teach, the educator, the facilitator, the mathematician! I think it is important that in order for a learner to enjoy learning mathematics, the content delivery should be engaging, intriguing and taught with an approach oozing motivation and love for learning maths. Otherwise, what’s the point? You’ll be bored teaching it and you’ll be fed up learning it. Make it fun, it’s down to you to get involved.

Piaget (1953) expresses his view of learning maths:

“It is a great mistake that a child acquires the notion of number and other mathematical concepts just from teaching. On the contrary, to a remarkable degree he develops them himself independently and spontaneously. When adults try to impose mathematics concepts on a child prematurely, his learning is merely verbal; true understanding of them comes only with his mental growth.”
(p. 74)

My interpretation of this, is Piaget is saying maths does not solely have to be learned from the teacher teaching the subject content; honest understanding and real learning of maths happens through experience out-with the classroom, as well as in the class environment. I can vouch for this and state that I completely agree with this statement. I have learned through the course of Discovering Mathematics that maths can in fact be discovered and learned successfully by independent research and development. By development, I mean I have developed an appreciation for maths more than I had prior to this module. The way I have learned maths and been taught maths has made it intriguing maths rather than mundane, which is immensely important to note.

Bruner (1964) makes a valid point:

“Any idea or body of knowledge can be presented in a form simple enough so that any particular learner can understand it”.
(p. 44)

To me, this summarises and clarifies what fundamental mathematics is all about – why we talk about it, why we learn about it and why we use it to teach. It is so important to know about.
Prior to this module, I did not have a clue what ‘fundamental mathematics’ was. I mean, I could take somewhat-aimless guesses at what it meant, but I did not know how to approach understanding what it entailed and meant in the classroom context. Bruner (1964) suggests any content of learning has the ability to be translated in its notion, in order to allow learners to understand it at the appropriate level. In other words, abstract and ‘scary’ maths – which is commonly the root of maths anxiety (pardon the pun) – can be taught, delivered or learned in a different form, one that is more simple or fundamental, for the learner to have an easier understanding.


Bruner, J. S. (1964) Some theorems on instruction illustrated with reference to mathematics. In E.R. Hilgard (Eds.), Theories of Learning and Instruction: The sixty-third yearbook of the National Society for the Study of Education (NSSE) Chicago: The University of Chicago Press.

Mason, J., Burton, L. and Stacey, K. (2010) Thinking Mathematically (2nd ed.). Harlow: Pearson Education Ltd.

Piaget, J. (1953, reprinted 1997) The origins of intelligence in the child. Abingdon: Routledge.

Look around you! (continuation – tessellation)

Since my last blog post about tessellation – “Look around you!“, I have reflected deeper on what tessellation is and, more specifically, where the fundamental mathematics lies within.
You can read ‘Look around you!’ at:

Harris (2010) discusses the prior knowledge a learner must have acquired, in order to understand the mathematical concepts behind tessellation. The following is content the child should understand prior to learning about tessellations:

  • A whole turn around any point on a surface is 360°;
  • The sum of the angles of any triangle is 180°;
  • The sum of the angles of any quadrilateral is 360°;
  • How to calculate or measure the inner angles of polygons (a plane figure with at least three straight sides and angles.

He continues to explain children are required to know about the angle properties of all polygons – regular and irregular – in order to understand the maths in tessellation (2010, p. 4).

So, having read this report by Harris: “The Mathematics of Tessellation” (2010), I now know there is more fundamental elements than I previously assumed. Prior to reading Harris’ work, I thought the only fundamental maths in tessellation was knowing the shapes in use. I did have an awareness of the angles having an importance, but as I knew the shapes I demonstrated worked in tessellation anyway, I did not think twice about needing to know the angles of the shapes.

If you would like to find out more about the mathematics in tessellation, follow the link below!


Dickson, R. (2015) Look around you! Available at: https://blogs.glowscotland.org.uk/glowblogs/teachingjourney/2015/12/05/look-around-you/

Harris, A. (2010) The Mathematics of Tessellation. Available at: https://my.dundee.ac.uk/bbcswebdav/pid-4544087-dt-content-rid-2917269_2/courses/ED21006_SEM0000_1516/Tessellation.pdf. Last Accessed: Dec 5 2015.