Studies however, since the 1980s, show students succeed better in maths when automaticity in the basic facts is developed, leading to enhanced maths learning and problem solving. Further, neuro- and cognitive sciences explain why rote learning facts and direct instruction are essential. Cognitive load theory (CLT) adds details.
Proficiency in fields from rugby to music is built on automatized knowledge. Elite pianists often spend 15 years practising with repetition to become artists. Repetition creates long term memory. CLT refers to our working memory’s limitations with capacity for about only seven items of new information for 20 seconds. Exceeding these limits causes overload and confusion for students. Information stored in our expansive long-term memory is activated when dealing with familiar information in our working memory. The transferal of information from long-term to working memory is effortless and automatic. Learning facts is crucial in freeing up cognitive resources.
Calculator use interrupts higher level thinking processes in doing typing of eg 8x7 instead of using automatized retrieval.
Children are seldom curious about learning multiplication tables, and require direct teacher instruction and effort by the child. Our current child centered led education frowns on this, favouring children discovering and learning things for themselves through cooperation, play, fun and experimentation, an ideology called constructivism.
Recent research points to the most effective ways of achieving rote-learned tables. Flashcards trump singing and chanting the tables in order. Older students who had failed to memorize their tables were given personal packs of flashcards with answers on the back. Having daily five minute practices resulted in big improvements proving automatic retrieval from long term memory is good for reinforcing learning. Children who fail for years at learning tables, which others in their class have accomplished, can develop maths anxiety and become resistant to keep trying. The internet is awash with free ideas for the learning of tables. I have used TUX maths, Fact Freaks and Project Happy Child, also rhymes and patterns for the harder tables. For strengthening memory, called consolidation, weekly rehearsal is recommended for a while.
Curriculum writers are ill advised to ignore the tools, terminology and methods that teachers have historically used in academic disciplines, including the teaching of tables in our traditional classrooms until about 1970. Being one of a class of 50 students at mystate primary school, I observed every child by about standard three, had successfully rote learned their tables.
Teacher training programmes that tell teachers to ‘teach for understanding’ not rote learning, needs to be modernized. Of the hundreds of older primary students I tutored, all understood that multiplication was an elegant short cut adding but too many were unprepared for secondary school having not memorized even the three times table, before coming for tuition.
Teaching some children, including often the brightest, to rote-learn tables, can be laborious and frustrating. An incentive like a national test could be helpful for both teacher and student, and set standards.
The UK made statutory, in 2021/22, a simple five minute tables check, in accordance with their curriculum. This statedthat pupils aged nine years should have memorized their tables. Are we to continue to languish at the bottom of international maths assessments, from where we decline further each year? Memorizing threatens our MoE’s pet ideology, yet research, history, science and more reveal automaticity of tables helps problem solving and deep thinking.
Gaynor Chapman B.Sc, Dip.Ed., has been a private tutor for students years 0-13, and adults.
10 comments:
My technical qualifications involved maths to or near degree level. Yet I still find myself regularly drawing on the multiplication combinations learned over 70 years ago. If not immediate recall the one or two previous in the chant leads to almost instantly. Similarly adding and subtraction involves the borrow and pay back and carry ritual the theory of which is not easy to explain to a child (or anyone) but which works notably. A major problem today is the huge range of ability in classes due non failing policy and cultural and genetic differences. It is incredibly difficult for a teacher to fully occupy the able whilst hammering ritual for the not. Without some quick mental ability assessments of many practical situations, even simple shopping, are obstructed. and gross errors when using a calculator are not easily recognised.
The Ministry of Education are too busy being obsessed with school toilets – and with urinals – and with signage - and most importantly, with gender ideology to worry about maths skills.
They are using school toilets to push gender ideology. Their latest policy document proves that.
There are not many thing you need to rote learn but the multiplication table to 12 is one that takes you further than most others.
We judge experts by their ability to recall facts and procedures without having to look them up. Who would take an industrial chemist who has to look up the atomic number of hydrogen seriously? Who would want to be operated on by a surgeon who has to refer to a manual while removing your appendix?
Simple facts and procedures are rote-learnt. You have to do a lot of rote learning to become an expert.
Higher-level thinking is applied not in a cognitive vacuum but to a body of knowledge that has been built up, mainly through rote-learning. You can't solve problems unless you have a knowledge base to apply your reasoning skills to.
Long live rote learning!
While I don't want to diminish the obviously large role that the curriculum and schools have in the educational outcomes of our children, the fact is that education starts in the home and ever since we have turned into a country where families require two incomes to live comformtably, parents have been less able to do all the things in the home that help children thrive educationally.
Parents are now simply too tired and many, even very well meaning ones, are leaving their kids in front of screens instead of reading to them, and engaging in other educational activities. When I was a child we had a times tables poster up on the wall - my parents expected that they were to play a part in my learning. But my mother only worked part time for many years, and only after I started school, to ensure she was available for these parenting tasks that have now fallen away as most parents are both working full time and sending their children to day care from 6 months old. They barely have time or energy to bathe and feed their children before its bedtime.
Simply changing the schools won't stop this tide, it would require a societal and economic change of massive proportions.
Anonymous 9.01 makes a very valid point. But many of those parents who do have time, incluidng full time beneficiaries, find themselves handicapped because of moderrn obscure teaching techniques which have not provided them with understandable simple skills to pass on. Phonic reading, times tables etc
You cannot ditch rote learning of maths tables. If you don't know the basics it's a bit like trying to build a wall without knowing what a brick looks like.
To Gaynor Chapmans point about chanting and flash cards.
Away back in the middle of last century I remember a dear old Nun teaching us our times tables. At that time to most children all adults were “old”.
The method was highly effective. Reading from the booklet and simultaneously chanting the numbers. Reading and vocalising is essentially a “double dose”. Flash cards came much later I think. I can still hear it. Thirty or more children chanting in near musical rhythm: Five Fives are Twenty Five, Six Fives are Thirty, Seven Fives are Thirty Five. On and on it went.
Can’t recall the overall scheme but we probably did one set for a couple of days then moved to the next. It all settled in the memory and helped immensely with mental arithmetic in later schooling phases - and then accounting work in later years.
Gaynor is on to it. The biggest hurdle we have with our children achieving more, is the current ideology within the MoE. We need to drain the swamp and that starts with Iona Holsted, who has presided over a generational decline and achieved what? Nothing - but with the assistance of Rose Hipkins, has certainly assured a generation of under achievement. She, and her immediate cabal of like-minded incompetents need to be gone, Minister Stanford.
How does everyone learn the alphabet? Rote learning of course. Without it most of us would all probably be illiterate. So why al this pushback from education "experts" about rote learning? Hypocrites all
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