I have worked with children who struggled with some concepts despite having memorised the terminology for the subject. In dealing with the problem, I changed my own approach to teaching some subject vocabulary. This entry is an example of this approach: teaching number names (Australian Curriculum, Mathematics, Number and Algebra,Number and Place Value ) in Foundation and Year 1, to prevent problems in Year 4 and above

Remember that items grouped together in time are linked together in memory.

Remember that items grouped together by name-form are linked together in memory – and that this form linkage aids rapid learning of items within the group, particularly if the name-form is meaningfully linked to the item’s qualities.

Remember that items linked together by pattern are remembered together.

**Common practise:** We can count on our fingers and thumbs, making it easy to prompt 1,2,3, … 10. Most classroom displays go 1 to 10, 11 to 20, etc.

**Problems:** Where is zero? What concept of zero are is developed, when it appears as part of “10” and “20” but not alone except in special mentions. Where does it fit in the number name pattern? Why did the children I helped remember 10 as a single concept-shape, not splitting the 1 and 0, grouping it with 1 to 9, not 20 to 90? Why do they jump from 49 to 60, or 47 to 58?

Zero by itself seems taboo, a scary thing with great powers not to be approached by the uninitiated. As Gahan Wilson asked,

**Alternative teaching approach:** Counting practice starts with zero : zero, 1,2,3,4,5,6,7,8,9.

Ten is brought in with 11 to 19. If both hands are used, 1 full set of digits and zero more (yes, it is a pun) is 10, ten; and one more, 11, eleven…

Twenty is a word introduced with two, twin, and twice. Twin-ty for twin tens makes sense. Then the number is “2 tens and zero left over.” So we write the 20 group of the 10s family 20 to 29 …. and they count 2 tens and zero left over is twenty, twenty-one, twenty-two … twenty-nine (We have all 9, next is a 10 – how many tens now? 2+1 is 3…) The digit form and verbal form are explicitly linked with the physical as we go (an example of manipulatives for this is below.)

Thirty is introduced with three, and third place, and twenty – if it ends in “ty” it is part of the tens-family

Forty follows (fourth place) and then they can guess fifty to ninety-nine.

**Manipulatives** emphasise zero (none there) and limit group size to 9 objects – e.g. Linear Arithmetic “Blocks” like these:

The pieces are lengths of pipe, with washers for the smallest. 10 of the lesser are as long as 1 of the next length. The rods hold only 9 of the pieces. The organiser serves a similar purpose to the place value chart often used with MAB, holding pieces of the same size together and representing the left-right spatial arrangement of decimal numeration. (Beware – you must be looking from the front!)

Also, if there are ten or more pieces of any one size they will not fit onto the appropriate rod and so ten of them must be exchanged for a single piece of the next highest value. They can see how 100 must be written before they know the name for certain.

To emphasise the infinite nature of number, I have a very long pipe (as long as 10 of the largest) to show that the next rod would be too long for the classroom.

In later years, for introducing decimals, I also use pieces of paper to show that the next smaller rod would be too small to use in class, and then “zoom in” by introducing a blob of bluetack as the decimal point. As multiplying / dividing by 10 “Zooms” by bluetack movement, the place value/decimal continuity becomes clear.

I would like to see the big “Educational” display manufacturers making their posters show 0-9, 10 – 19, … and go up to 109 rather than 100.

Tags: LAB, linear arithmetic, manipulatives, place value, teaching, teaching the concept of place value

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