Teaching considerations

When developing teaching and learning programs for students working with perceptual strategies, teachers need to consider:

Strategy development

Students working with perceptual strategies have limited approaches for solving number problems. Teachers should provide a wide range of activities which encourage students to develop more sophisticated strategies, regularly discussing why developing increasingly efficient and sophisticated strategies are useful and desirable. Activities that develop visual recognition skills should be regularly implemented.

Teachers should ensure that students are not hindered in the development of strategies because they have a limited range of understandings in other number areas such as number word sequences, numeral identification and pattern and number structure.

Language development

Students need to be taught the explicit mathematical language to be able to describe learning activities and the strategies they are using and/or learning about. Additionally the naming of number words in the “teens” can be difficult for all students and particularly for students from non-English speaking backgrounds. For example, number words such as fourteen and forty sound very alike. Students need a great deal of experience with the number words within the teen range.

Within the range of 11-20, there are a number of ways of verbally representing a group of ten. Thirteen to nineteen use “teen” to show there is a ten, however, we say the unit value first (in nineteen for example we say “nine”, the units value, before we say “teen”), and as such, reversals are very common. The suffix “-teen” comes from Old English and means “ten more than”. Eleven and twelve present different ways and representing “ten” as does “ty” which means “group/s of ten”. Sharing this knowledge with students may help them understand the difference between words such as “thirteen” and “thirty”.

Language such as: count, counting, forward, backward, more than, less than, the number words (zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty), is the same as, is equal to, equal, count forwards, count backwards, before, after, combines with, joins, take away, how many more, altogether, makes, how much, amount, total, sum, add, subtract, ten-frame, represent, dice, domino, pattern, fingers, match, number word, order, sequence, item, collection, group, the ordinal number words, etc. are examples of the language students need to learn about and incorporate into their vocabulary.

Students need learning opportunities that support their skills in describing, classifying, generalising, sorting, comparing and contrasting in order to support their mathematical understandings. In order to communicate, reason and problem solve, students need explicit teaching in how to recall, recount, justify, speculate, explain, question, hypothesise and respond using mathematical language. 

Numeral identification

Activities for developing numeral identification can be modified to cater for the student by limiting the range of numerals targeted.

The Number Zero

When children count backwards from 10, some learn to finish the backward count with “zero” and others with “blast off”. Although there is value in counting down from 10 to 0, a problem arises when some children begin a forward count from zero. In developing a one-to-one match between objects and counting words, children can allocate the word “zero” to the first object counted. For this reason, the descriptions of the levels of the counting words do not include zero. Students do, however, need to meet the number zero. It could be presented with an empty five frame or ten frame, showing empty containers, no fingers, no clapping or discussing what happens when you take all the items away.

An ever-increasing range of representations

Students need to be exposed to as many representations of an amount as possible as this awareness is vital to understanding the flexibility that exists within mathematics and numbers. Students should be able to use a vast array of concrete and visual representations of amounts, varying colour, shape, size, object and orientation. Numerals and number words need to be presented and discussed using a range of font types, colours and contexts. Discussions about the similarities and differences between representations should be regularly included in learning opportunities.

For students working with perceptual strategies it is important to introduce numbered dice as well as dot dice during games and activities. This is important as perceptual counters need to move to recognising numerals as a completed count. Often students will continue to rely on counting the dots one-by-one even when they know a more efficient strategy.