Reciting tables ‘not requisite’ in learning math

By Wachira Kigotho

Teachers may be forced to abandon traditional methods of teaching primary school mathematics, where pupils’ learning progress is measured by ability to recite multiplication tables and memorise other basic calculation solutions.

Basic education researchers at the University of London’s Institute of Education have discovered primary school children can make progress in maths even if they do not know their tables by heart.

"Incomplete ignorance of number facts is not a barrier to success in maths," says Richard Cowan, lead researcher.

According to Cowan, conceptual knowledge of principles was found to be superior in solving simple calculations than learning facts and memorising tables. However, most primary school syllabuses in many countries are based on traditional view that expects children to know answers to basic calculation problems by end of Class Three.

Teaching is often through rapid mental calculations and pupils’ progress is measured on how quickly they are able to answer basic mathematical questions.

Number facts

"This mode of teaching equates proficiency with having solutions to basic calculations stored in long-term memory as number facts that can be quickly and accurately retrieved," says Cowan.

However, if teachers and parents want to help their children to learn maths properly, then they should encourage them to use their knowledge of principles to solve problems and not merely to memorise the answers to problems like little parrots.

According to David Geary, an educational psychologist at the University of Missouri, the best way to teach maths is to let pupils to understand numbers and the quantities that those numbers represent.

Reporting findings of a study ‘Cognitive Predictors of Achievement Growth in Mathematics’, in the recent issue of the Developmental Psychology journal, Geary said understanding numbers and quantity is key to laying the foundation for success as a pupil progresses to more complex topics.

The most important finding of Geary’s study is that mathematical knowledge is incremental and is not founded on isolated facts. In the five-year study, Geary and his team noted that pupils that can go back and forth easily and quickly in translating numerals into quantities and in breaking complex problems into smaller parts had a good headstart.

The new interest on how pupils make progress in mathematics is based on the fact that understanding of the subject has become critical towards success in many fields. However, once pupils fall behind, it is almost impossible to get them back on track.

Nevertheless, children differ in their mathematical performance at the end of primary school and hence the importance to improve their basic understanding of the subject.

"Teachers have to know what to instruct as these are factors that would make a difference in the first years of schooling beyond pupils’ inherent intelligence," says Geary.

For most pupils, performance at primary school predicts subsequent mathematical achievement and ability to manage numerical demands of everyday life and adulthood.

"Consequently, understanding what causes individual differences and what will help primary children develop could yield long-term benefits," says Cowan.

Whereas educational researchers are aware child attainment in maths could be influenced by family and school characteristics, there are indicators that a child’s individual differences are the ones that are strongest and could be improved upon.

Child level variables that are related to mathematical performance include cognitive factors that correlate with general educational achievement — general ability, memory functioning, processing speed, and oral language — and socio-emotional functioning.

Fear for maths

However, the main worry is that as a result of poor teaching techniques, many pupils have come to fear maths. In such circumstances, a large number of pupils leave schooling without ability to calculate even the most basic sums needed for everyday life, such as calculating household bills.

"As a result, victims of poor teaching of maths continually keep on worrying about basic arithmetic and numbers," says Cowan.

The situation can be averted if teachers realise mathematical performance can be improved if pupils are made to understand basic principles and patterns of numbers. There is logical connection between simple and complex arithmetic and achievement in basic calculation is central to understanding higher maths.

But while the debate still rages, as to whether pupils should memorise their tables or not, the situation on the ground is that around one in five adults globally have problems understanding basic maths and have below functional levels of literacy. Perhaps, the time is now for teachers to change tact and adopt new strategies in teaching methods.