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Basic facts under-achievement: bring on performance measures

Press Release – Doc Rainey Ltd

New research has revealed both disturbing and reassuring findings relating not to the whole of what is frequently called ‘the underachieving tail’ in NZ maths but to the small and very important part of it called basic number fact knowledge.Basic Facts Under-achievement – bring on performance measures!

Tuesday 22 November 2011, 9:45 am
Press Release: Doc Rainey Ltd
21 November 2011
For Immediate Release

Basic facts under-achievement: bring on performance measures!

New research has revealed both disturbing and reassuring findings relating not to the whole of what is frequently called ‘the underachieving tail’ in NZ maths but to the small and very important part of it called basic number fact knowledge.

But first, the situation with multiplication and division basic facts is roughly this. In their final Primary School years, 5 and 6, most students are expected to come to know basic multiplication and division facts – if not already known by Year 4 – like be able to say from memory what three twos are or how many sevens are in thirty-five – and not need to work the answers out mentally or any other way.

Traditionally teachers tried to ensure this – often a good deal earlier. They made sure children ‘learned their tables’ and repeatedly did short mental and written activities to drive facts into memory and to develop speed and accuracy.

Some say we went off the boil for a number of years. New educationist ideas saw memorisation skills despised and ‘strategic thinking’ ideas advanced at their expense. When maths performance increasingly fell off nationally, officialdom made attempts for some years to try to restore a balance. A research report to the Minister on ‘Reversal of Deficit in Basic Number Fact Knowledge’ by psychologist-consultant-inventor Dr Des Rainey suggests that at least for what is called ‘the underachieving tail’ of students, it has failed.

Across four Year 5-Year 6 classes in a low-decile school Rainey found that at the start of the year the Year 5 students averaged 7 facts per minute in correct recall of basic multiplication facts, that’s to say they took 9 seconds a fact. Greatly progressed results were expected for Year 6 students but at start-of year they averaged 9 accurate facts per minute, 7 seconds a fact. It was a negligible gain from a whole additional year of schooling. At that pace most children would not attain anything approaching the standard that the curriculum or parents desired in preparation for intermediate schooling. In fact their whole future in maths was at risk.

In the case of division achievement was at a lower level still. Year 5 students set a start-of-year benchmark of 5 accurate facts per minute or 12 seconds a fact. The corresponding Year 6 result, with the high-ability class included, was the same. There was zero gain for these students from the whole of their previous year’s maths.

School leadership expressed surprise and suggested the children weren’t used to the way the questions were presented to them and that they did in fact know their basic facts. However other tests which measured knowledge without regard to time showed otherwise. Then, when students in the following months made very substantial gains with the same teachers but with different methods of teaching, it was clear that it was neither the students nor the teachers who were responsible for the earlier results. Blame, rather, the teaching methods and ‘the system’ that provided the methods and the kind of support and monitoring that was given.

Around May the students in the study were started on the basic number facts learning programme called ‘Kiwi Maths’. It provided ‘error-free’ short sharp concentrated exercises provided that took only 5 to 10 minutes a day and did not intrude on planned maths lessons. By August the Year 5 students had moved in multiplication from 7 to 12 Accurate Facts per Minute while Year 6 students moved from 9 to 16. Scores for Maori and Pacific Island students from baseline approximately doubled. The high-ability classed moved from its earlier average of 13 to 25. It was not far from its main goal of 30 Accurate Facts per Minute and was expected soon to reach it. At the other end of the scale 20% of the Year 6 students – with only a few months of primary schooling left – scored less than 5 Accurate Facts per Minute. They needed more than 12 seconds a fact.

Division results ran parallel but in general were well behind those for multiplication. Year 5 students improved from 5 AFPM to 10 and Year 6 from 5 to 11.

All in all, although there was remarkable gain, because they started from such a low point most students along with their teachers faced an uphill struggle. A Richter-like zero to ten ‘Knowledge Scale’ measure developed by Rainey more precisely defined it. There would be one point for each known table so that, for example, a score of 5 indicated that all the facts within the 2, 3, 4 and 5 table were known. The high ability class averaged 7, was progressing well and could be expected to reach 10. One of the regular classes was not far behind. However two classes had average ratings of only 4 and 2 showing that – with Intermediate school just months away – they did not yet have recall of facts within the tables to 5.

In division, the picture was still more bleak. The high-ability class rated 7 but the others were all below 5. In one class the Year 6 students in one class had a rating of only 1, signifying that not all ‘divide by 2’ basic facts were known – perhaps because in 5 years of previous schooling the groundwork for understanding and progress in division had simply not been laid.

For such poor results as were found Rainey is emphatic that teaching methods were at fault – not the teachers – and certainly not the kids. Students made remarkable progress under the very same teachers when they adopted different teaching methods and worked towards challenging goals guided by measures that students and teachers alike understood.

Rainey believes the Minister knows well about the ‘underachieving tail’ in maths in NZ schools but know very little about the state of its basic fact knowledge and competence, which he suggests is its Achilles’ heel. That’s because it has not required schools to provide this information to the Education Review Office, ERO. Some schools volunteer it but it is not collated and examined. Neither has the Ministry developed a standard way of assessing basic facts knowledge. Schools fall back on tests they have developed themselves or on commercial products. Rainey suggests the Ministry should establish standard basic fact assessment measures and achievement standards – they will be doing it for water quality, why not for basic facts? – so schools have a good clear basis for monitoring student progress and proving to Boards and ERO and parents that they are doing their job. Many are. Some are not.

On the teaching side he thinks the Ministry should try new tacks. He shares the belief of teachers who say the Numeracy Project has’ failed the tail’ by trying to make mathematicians out of every student instead of developing basic competencies from which in due time the natural mathematicians will emerge.

If Rainey has any overall message it is to ask the Minister to take special interest in student achievement in basic number fact knowledge because it is critically important to students’ future in maths and because as of now thousands upon thousands of children will be going to Intermediate school next year lacking the capability and maths confidence that they should be bringing there. Parents and Boards, keep watch! Principals – never become rigidly anti-test! Don’t shy away from measures that show where kids are at, however unpleasantly low. Focus entirely on measuring/monitoring the progress of teachers and students to goal and to success. En route, if teaching methods aren’t working, get help, change them! It’s time we really did something about ‘the under-achieving tail’.

For the research report contact the Minister of Education or Dr Des Rainey


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