Learning the Multiplication Tables with a computer - this is the original paper that shipped with the program.
In 1993, at ULTRALAB, we were interested in the fusion of ideas that might result from asking children, teachers, parents and our own software team to design a piece of software. What did children look for? What good experience might teachers bring? What did parents want? What could learning theory contribute to make it all work better? As a test we took a very simple learning outcome - remembering the multiplication tables. It was a "know that" rather than "know about" learning outcome, it was very discrete as a target but it was easily testable too and children, teachers and parents are motivated by any solution which delivers a faster learning of the tables.
So what happened, and how did "X" develop?
Firstly, the children. They had (as is typical) good experience of computer games and other 'home computing' activities. This had developed a 'climate of expectation' in them. They knew what motivated them, what delighted them and what held their attention. They were very aware as software critics and full of good ideas.
Children DID want:
- a high score record • colour, sound and great graphics
- pressure to keep them on task but also because 'racing' against a pressure environment was exciting for them.
- good rewards - something that said "well done" and had a bit of variety in it. They wanted "well done" but they didn't want it to get in the way of their 'playing' and slow everything down.
- to be able to play with others older or younger, better or worse at tables. They saw the task as a collaboritve one, not an individual one.
The children DIDN'T want:
- delays - anything that got in the way of performance was unwelcome.
- loads of 'how to text' they could see from previous experience how a game worked and wanted "X" to be equally obvious to use.
Parents DID want:
- the software to work and actually help children to learn their multiplication tables
- some way of allowing children of different ages to compete against each other even if one was on the 4 times and another on the 9 times multiplication tables.
Teachers DID want
- the software to work and actually help children to learn their tables
- some clear indicator of which numbers were being multiplied on the "table grid"
- random asking of the tables so that children could not step through adding for each subsequent answer
- an opportunity to explore the grid first before being tested on it.
- some easy way to stop and give up if things were going badly
Teachers DIDN'T want
- better sounds for "wrong" than for "well done" (too many programs that they had seen rewarded failure with the best sounds and animations!!).
Learning theory suggested that:
- children needed visual and aural cues and clues to help reinforce the memory task.
- If the clues and cues are created by the children, 'ownership' will help them learn.
pressure sequence | spoken overview | reward sequence | celebration sequence (all cartoons by Tom Smith)
intention and need were both important.
Children have a need to learn their tables. They need this learning to deflect the pressure that they suffer from not knowing them. Almost universally they are tested at school on their multiplication tables retention. If we could combine this need with personal intention then the simple learning target might be achieved very quickly. Personal motivation can be developed from the delight that a 'games' environment can offer.
So, we wrote "X".
It does MOST of what was asked of it - it doesn't yet offer aural cues and clues because we wanted to find out how the visual ones worked first it doesn't offer printouts because we decided that the learning outcome was table capability and that was what children took home or into school.
We did not want to focus on the pictures as an end in themselves, they were only a means to an end.
Initial tests suggest that it seems to work rather well. The combination of children, teachers and parents as designers showed that they all had something to offer 'learning'. Children did not sit around singly and try it, they grouped into teams - big teams - and then had great fun trying to be the one to "shout out" the answer. In doing do they heard from, and learned from, each others' answers, but also gained confidence. What was important was that the team got the answer, not who got it. Shouting out thus helped the shouter with their own self esteem, but also helped the others too - it was a collaborative activity.
(curiously, in 2012 a research report from Durham University reached a similar conclusion about "shouting out" helping the "shouters". However, with the right software, a team emphasis and a no blame culture we knew back in 1993 that it could be good learning, and fun, for everyone)
We need to look carefully at the capabilities that children have developed as computer users and seek ways of harnessing and recognising the new things that they are good at.
Interestingly the traditional way of learning multiplication tables masks how few sums actually need to be remembered - after the easy 1 to 5 and 10 times tables have been removed and allowing for commutativity (2x4 and 4x2, etc.) there are really only 10 'hard' sums to remember and four of those are square numbers that children seem to find easier to recall.
Parents (and teachers) may find it useful to help children realise from the outset that commutativity exists and that the whole task of remembering multiplication tables is manageable with only 55 sums in total to be completed. Because of the way that children traditionally learn their tables, for many there is simply no understanding that 3x7 is the same as 7x3. Ask a child who has learned their three times tables what three sevens are and they will usually say "I don't know". "X" makes commutativity explicit and for many children simply realising this seems to halve the task they have in front of them. It's a great morale booster!
Does "X" offer multiplication tables learned in a day? Try it, give it to friends and others. And please, please tell us your views. The feedback you offer is REALLY useful and helps us to develop more ideas for your children that take advantage of the new capabilities that theyve as confident computer users.
Send any views, results, research to: ULTRALAB (Project "X") Anglia Polytechnic University Sawyers Hall Lane Brentwood ESSEX. CM15 9BT (obviously this address is now gone - it's just here for history...)
Thanks. Ann, Carole, Greta, Kris, Lys, Richard, Sam, Stan, Stephen, Tom (the ULTRALAB team) and all the parents, teachers and children who have contributed so far..
technical overview: X required Apple Macintosh running System 7, HyperCard 2.1 with 2000K allocated and QuickTime installed. Happy days!
these pages last updated: Thursday, February 2, 2012 4:19 PM