Misconceptions in maths

Freya has been struggling with some of her maths and we have been painstakingly going back through the year 1 syllabus to find and identify the route of her misconception.

Not surprisingly for teachers out there, it was to do with her understanding of place value and the quantitative value of numerals in different columns of a number.

To help reteach her this we have been doing lots of practical maths with concrete materials.

Yesterday we had a ‘click’.

Freya had been counting in 2s and, as is usual, was getting her ‘thirteen’ and ‘thirty’ words confused.

I started by modeling what she was saying in a grid: 2, 4, 6, etc laying it out so that 12 was under 2, 14 under 4 etc using invisible columns to demonstrate the value of the tens and ones.

We then talked about the pattern she could see in the numbers.

To help reinforce what each digit was worth I got out the abacus – I know! A what?

Yes, an abacus… what a great way to show the volume of 2 versus 12 versus 22 easily.

We repeated this and she continued to add numbers to the grid I had started making the numbers on the abacus as she went.

We went onto one more and one less and ten more and ten less on the abacus writing down the corresponding numbers so she could see which numeral in which column increased as she added the beads.

Finally, she practiced making the ‘teen’ numbers and the ‘ty’ numbers on the abacus to show her understanding.

We are going to repeat in various ways (bead strings, abacus, drawing) for the next two weeks until she is completely secure, then start building up again from there.

Fascinating as a teacher, upsetting as a mum, that such a basic building block of maths has been ‘skipped’ over and not embedded. Glad we caught it now and can build up her confidence again.

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