Using symbols to support mathematics learning

Why adding symbols to mathematical vocabulary can help pupils improve understanding and make greater progress in their mathematical attainment.

Sue White , Head of Education, Widgit

Language is central to learning Maths, and the better pupils are at using Maths terminology by KS2, the better they will be able to demonstrate their Maths knowledge.

Explicit teaching of mathematical language is one of the most important and impactful aspects of developing pupils into able mathematicians. Using the right maths language helps us to have a conversation and understand what the other person means.

As well as the need to understand the mathematical concept, Maths is particularly vulnerable to misinterpretation because of the peculiarities and irregularities of many Maths words in the English language.

The Maths terminology used in class at KS1 and KS2 has meaning, but it can easily be misinterpreted by the pupils.

Steve Chinn (2004) in ‘The Trouble with Maths’ argues that the dual terminology of Maths is a real problem. The colloquial nature of some common Maths words?and phrases means that pupils may well have to cope with inconsistencies.

This is made much easier with the addition of a symbol alongside the vocabulary to explain the concept.

Visual representations are also a powerful way for pupils to access abstract mathematical ideas.?They offer the benefit of permanence, permitting pupils to process information at their own speed.

Underpinned by a ‘Structured Language Framework’, Widgit Symbols add visual support to the printed word. They are specifically designed to illustrate a single concept in a clear and concise way, and help make the connection for pupils between the word and its underlying meaning.

How the brain stores information

Both the short-term and long-term memory store information in chunks, but our short-term memories are more limited.?According to?education consultant Dr. Lynell Burmark, who writes and speaks about visual literacy, one of the easiest ways to ensure learners store information in their long-term memory is to pair concepts with meaningful images.?Visuals help pupils make sense of the content and focus attention, increasing the possibilities that learners will remember the material.

He states: “Unless our words, concepts, ideas are hooked onto an image, they will go in one ear, sail through the brain, and go out the other ear. Words are processed by our short-term memory where we can only retain about seven bits of information.

“Images, on the other hand, go directly into the long-term memory, where they are indelibly etched.”

The idea that the formation of mental images?aids?learning was used by Allan Paivio when developing his Dual Coding Theory. The theory explains how visual and linguistic information is processed in two different areas of the brain. ?

In essence, as new input enters the brain, it's stored in the short-term memory in two distinct categories.?Graphic information, images, and other sensory input are processed in the visual centre, while auditory input, words, and text are processed in the linguistic centre of the brain.

This is a great way for our brains to constantly take in both types of information, and the system works very well in the short-term. However, to actually convert new information into true learning, we need it to be saved and stored in long-term memory. ?

When we are able to blend the text input together with the images, we boost the potential for retaining the information. This means that not only are the individual words and ideas committed to long-term memory more effectively, but the associations between them are retained as well.?Pupils can understand the big ideas and concepts, and remember the vocabulary and details more consistently. ?

In addition, a related theory, the ‘Picture Superiority Effect’?refers to the phenomenon in which pictures and images are more likely to be remembered than words. This effect has been demonstrated in numerous experiments using different methods, and is based on the notion that human memory is extremely sensitive to the symbolic modality of presentation of event information. (Yuille)

The theory is supported by studies that show that blending images with text offers a stronger learning experience than using text alone.?It turns out that this boosts both the memory of the individual terms and ideas, as well as the associations and connections between the concepts.

This is why we use certain visual brain triggers in addition to using text. ?For example, a stop sign has to instantly register an idea in our brains: STOP. So, in combination with the word (text input), we also always see the same shape (graphic input) as well as the colour red (additional visual input). These blend together to send the right signal to our brains more effectively.

Key maths vocabulary

The need or desire to see in order to understand is well established, and the very fact that in English we say ‘I see’ to mean ‘I understand’ suggests a concrete link between the two.

Many schools like to display key vocabulary on ‘Maths Learning Walls’ and make this available to pupils at appropriate times during the academic year. The addition of a symbol to help reinforce the vocabulary on display will increase the pupils’ understanding of the concept and retention of the appropriate mathematical language, with subsequent improvements in attainment.

References

Burmark, Lynell (2002) Visual Literacy: Learn to See, See to Learn?1st Edition. Assn for Supervision & Curriculum.

Chinn, Steve (2004) The Trouble with Maths: A practical Guide to Helping Learners with Numeracy Difficulties. Routledge.

Paivio, Allan (1969) Mental imagery in associative learning and memory.?Psychological Review.?76?(3): 241–263.?

Yuille, John C. (2014).?Imagery, Memory and Cognition (PLE: Memory): Essays in Honor of Allan Paivio. Psychology Press.