Abstract

In New Zealand, many primary teachers of children from Year 3 upwards, begin mathematics learning sessions with a ‘Quick Ten’ of some form. This is an activity where the teacher may write on the board, or call out one by one, a number of questions that must be answered at speed. . This paper examines the effects of this widespread teaching practice, through the study of children who are currently participating in a 3-year case study research project which seeks to investigate the importance of student affect in children’s learning of mathematics. It has been found that, by the end of their fourth year at school, children in the group have come to believe that the Quick 10 is a very important part of mathematics learning. It defines for them what mathematics actually is, and is used by them as the primary gauge by which they determine their own and others’ ability in mathematics.

‘Ten Mental’ was a common feature of arithmetic lessons of past generations. It was designed to increase the agility of children’s minds in the rapid recall of important arithmetic facts, and give children practice in the application of these facts in the mental computation of ‘sums’ such as how much it would cost to buy seven ice-creams if one ice-cream cost three pennies.

In many respects, the activity served to socialise or enculturate us into a mathematics belief system, where individual achievement was measured by the yardsticks of speed, accuracy and completion. Bishop (1991) argues that, like other ‘cultures’, ‘mathematics culture’ is based on a number of underlying beliefs and values. The practice of teachers’ giving of a quick-fire test at the beginning of every maths lesson is a good example of ‘cultural’ beliefs enshrined in everyday routines &emdash; beliefs that a good grasp of basic facts is essential for all other learning in mathematics, that speed of recall is of vital importance, that children must work alone when finding answers, that there is only ever one right answer, that the answers are more important than the methods of finding them, that a child’s ability to perform in basic facts tests is a good indicator of their overall mathematics ability, that frequency of testing will increase learning for all children, that children are all ready for this kind of activity at a certain age, that it is the teacher’s role to choose the questions for the children and the teacher’s role to determine the pace of questioning, that sharing scores with the rest of the class is good for children and that a degree of pressure and public exposure helps children to learn.

If the everyday routines and practices form an important part of a child’s world with which s/he interacts and through which meaning is negotiated and constructed, as a growing body of social researchers suggest (Berger and Luckman, (1996) Douglas (1970), Weigert (1981)) then it would seem reasonable to assume that the everyday practices and routines associated particularly with mathematics teaching have a significant influence on children’s processes of construction of meaning about mathematics. Sociologists of education draw attention to this hidden curriculum that everyday practices reinforce. (Meighan and Siraj-Blatchford, 1998).

A group of ten children were selected, all from different schools, and their learning in mathematics tracked for a three year period from age seven years through to age nine years, to determine how they developed their ideas about mathematics. The prevalence of the use of testing activities requiring rapid recall of answers is summarised in the following table:

Child	Year 3 (7 years old)	Year 4 (8 years old)	Year 4 (9 years old)
Rochelle	Daily - ‘Quick 15’, Bingo or Buzz game (teacher calls)	Daily: ‘Daily 20’	Daily: ‘Daily 20’
Fleur	Daily: ‘Quick Ones’ (20) (teacher calls)	School A: Daily: ‘10 Basic Facts’ (from board)   School B: Daily: ‘Quick 10’(from board or teacher calls)	20 or 50 Quick Questions
Toby	Weekly test &emdash; ‘all the sums done in 10 minutes’	Daily 4x4 basic facts array (from the board)	Daily Morning Maths sheet
Peter	Daily ‘Quick 10’ (from the board)	Daily ‘Quick 10’ (from the board)	Daily ‘Quick 10’ (from the board)
Mitchell		Daily ‘Quick 10’ (teacher calls)	Daily ‘Quick 10’ (teacher calls)
Jessica	Occasional: Around the World (teacher calls)	Daily: ‘Quick 10’ or similar basic facts activity (teacher calls)	Weekly basic facts test (on a sheet)
Georgina	Daily: 10 questions (from board or teacher calls) Monthly: Speed test (worksheet)	Daily: ‘Daily Questions’ (10) (teacher calls) Monthly: Speed test (worksheet)	Daily 10 Questions (teacher calls)
Liam	Occasional: Around the World game (teacher calls)	Daily: ‘20 Quick Questions’ (teacher calls), Around the World game (teacher calls)	Daily 15 Questions (teacher calls)
Dominic	Daily: ‘Daily 10’ (teacher calls)	Daily: Maths Challenge and Shoot Out type games Weekly: basic facts speed test (worksheet)	Daily Drill (10 questions from the board) Weekly basic facts speed test
Jared	Daily: Around the Clock individual public performance or competitive team basic facts games (teacher calls)		Weekly basic facts test, (on a sheet) occasional speed maths games (teacher calls)

Table: The frequency and style of quick-fire question mathematics activities

The children in the study group responded in a range of different ways to these routine tests. Rochelle, Toby, Liam and Dominic said they enjoyed the speed activities. They usually finished in the given time and scored highly with few mistakes. Liam, Toby and Dominic are also very keen on competitive sports and their parents and teachers have remarked on their enthusiasm and success in this area. The competitive aspect of the Quick Ten seemed to appeal to them. Here are some revealing excerpts from the researcher’s conversations with these children:

Researcher: How do you feel about the Quick Twenty?

Liam: Good.

Researcher: OK. Why do you feel that?

Liam: ‘Cause it’s a competitive thing and I like to compete.

Researcher: What about Buzz? You said earlier that you didn’t like that as much.

Liam: No, I can’t compete with it.

(End of Year 4)

Researcher: Do you ever talk about maths with your friends?

Dominic: Um, probably just after our basic facts tests, like when we talk about our scores and stuff.

Researcher: How do you feel about those [the weekly basic facts tests]?

Dominic: I feel real good when we have those. Because I always get stickers and stuff.

(End of year 4)

Rochelle, who also enjoys the ‘Daily Twenty’, seems to regard it as a reassuring and satisfying measure of personal success and as a demonstration of compliance with teacher expectations. Her teachers have remarked on how Rochelle is ‘eager to please’ and for Rochelle, ‘getting answers right’ would appear to fall into this category.

Researcher: What do you like most about maths, Rochelle?

Rochelle: Daily Twenty.

Researcher: What is it about Daily Twenty that you like?

Rochelle: You get to answer questions.

(Later)

Researcher: Why do you think you’re pretty good at maths, Rochelle?

Rochelle: ‘Cause in the Daily Twenty, I can get nearly all the questions right.

(Middle of Year 4)

Rochelle, it seems, has come to believe that mathematics is mostly about finding the one right answer for each given question. The questions always come from an outside source &emdash; the teacher, a textbook or a worksheet.

Toby is also keen and competent at the speed activities but does say when asked whether he feels comfortable doing maths: ‘If we have to get this ..like, something done in a certain time, I don’t feel too comfortable, I have to hurry up, and well, if it doesn’t matter how long it takes, I feel comfortable.’ (End of Year 4)

Georgina, Jessica, Fleur, Callum, Mitchell and Peter are less positive about basic facts activities but they all believe that these are extremely important. Over the two years of the study, Georgina has expressed her dislike of, and lack of confidence with, mathematics. On our first meeting, before we had even been introduced, she approached me and spontaneously burst out with: ‘I hate maths because I only only get three or four, (out of ten in the daily questions) ‘cause it’s really hard!’ (Early Year 3)

The daily speed affair has become a real problem for her and it is important to note that over the two and a half years I have been observing Georgina engaging in these speed tests, there has been minimal progress. The back of her mathematics book tells the tale. Day after day, Georgina gets ‘three or four’. For her, the Quick Tens serve only to reinforce, on a daily basis, her sense of failure.

Researcher: When the teacher says ‘Ok, it’s time for maths now, how do you feel?’

Georgina: Ugh! (grimaces) We have to do this 20 or 10 question thing and Mrs Cayo calls out the questions and you have to write the answer and she goes really fast now and I can’t do it.

(Middle of Year 4)

Given concrete materials and opportunities to talk about her mathematics, but above all more time, Georgina demonstrates understanding and creativity in the subject. As her Year 4 teacher said: ‘Georgina has more ability than the assessments show.’ And yet Georgina feels that she is no good at mathematics, and pinpoints her ‘failure’ in basic facts tests as the reason.

Researcher: What subjects that you learn at school do you think you’re the worst at?

Georgina: Maths.

Researcher: What makes you think that?

Georgina: Because I never get my basic facts right. (Daily test)

(Later)

Researcher: What makes someone good at maths do you think?

Georgina: They learn all their times tables and learn all the, um, take aways and, um, pluses.

(End of year 4)

Jessica, too, says she is no good at mathematics by the end of year 4. Mathematics games with quick-fire questions have helped to create, and reinforce, her feelings of inferiority and for her, are far from fun.

Researcher: Do you think there are people in the class who are better than you at maths?

Jessica: Way better!

Researcher: Okay, how do you know they’re better?

Jessica: Well, because we do Around the World, things like times tables, adding and dividing and there’s this boy, he goes around and he’s, like, really, really good. He’s made it, like, three-quarters of the way around.

Researcher: How do you feel when he comes around to stand by you?

Jessica: Not Good. I feel kinda nervous. Because there’s the whole class there and stuff.

(End of Year 3)

Researcher: What makes a person good at maths do you think?

Jessica: If you practise quite a lot. And the little girl Alison with the curly hair and glasses, she’s really good at maths, she got a hundred and five out of a hundred and five this time (Basic facts speed test) ‘cause she’s really smart, but I don’t think it’s, like she practices or anything, well she probably does, but I don’t think it’s really that reason, I think it’s because she was just born like that. And some people are born differently than others.

(Later)

Researcher: How do you feel about the tests?

Jessica: I feel nervous, …’cause if you don’t get very many, we’ve got these graphs (of their basic facts scores) and mine starts up there and then it goes down, up a bit, but down and up… So somebody could tell as soon as they saw it, so they can tell you got a low score.

Researcher: Does anyone else see your graph?

Jessica: Some people do but they’re not really supposed to look at it.

Researcher: Do people know each other’s scores or is it private to you?

Jessica: It’s meant to be private but some people go ‘What did you get?’ (Uses a wheedling voice).

(End of Year 4)

Mitchell is experiencing learning difficulties in all areas of his schooling and is trying to make sense of the activities that he is expected to do in mathematics time. It is the daily basic facts tests that most stand out for him.

Researcher: What is maths do you think?

Mitchell: Like ten plus one.

Researcher: Is there any other thing you do in maths?

Mitchell: We have to do a sheet (of basic facts questions) and Miss Upton times us and you have to put your hand up and it’s really short, like for three minutes.

(Later)

Researcher: Are there some people in the class who are better than you at maths do you think?

Mitchell: Yep.

Researcher: How do you know they’re better?

Mitchell: Because they’re doing it right and I got some of them wrong. (basic facts test)

Researcher: How do you know you’ve got them wrong?

Mitchell: Because there’s Xs by them.

(End of Year 4)

Jared began his third year at school by being quite positive and confident about doing mathematics. His attitude had changed by the end of the year. This was directly linked to the mathematics games that were a regular feature of his classroom.

Researcher: What about that game I saw you playing last time? People would stand up in front of the times table clock and they would have to go as fast as they could. How did you like that?

Jared: It was hard.

Researcher: How did you feel when Miss Wai said it was your turn?

Jared: I hated it.

(End of Year 3)

Like Georgina, Fleur was feeling the pressure of speed in the basic facts activities and was reporting diminishing confidence in, and enjoyment of, the subject.

Researcher: Are there any people in the class who are better than you at maths?

Fleur: Ella.

Researcher: How do you know Ella’s good at maths?

Fleur: ‘Cause she can get to finish all her times tables and take aways and pluses all right most of the time. She’s a lot faster than me too.

Researcher: How many do you have to do?

Fleur: We get a hundred, in fifteen minutes.

(Later)

Researcher: How does maths time usually start?

Fleur: We usually start with times tables or take aways. She says, like, ‘Six take away seven’ (sic) and we write them down in the back of the (maths exercise) book and sometimes she mixes them all up… She calls it ‘Quick Ones’.

(End of Year 3)

Researcher: Do you usually start with ten questions in the back of your book? (as I had just observed)

Fleur: We usually do one of those tests (points to yellow times tables achievement chart on classroom wall) or else just questions like five take away five and stuff like that.

Researcher: I see, and does the teacher call those out?

Fleur: Yes.

Researcher: How do you feel about that?

Fleur: Sometimes she goes too fast and I get a little bit sad… If she goes a bit slower, I can usually get ten out of ten.

(Middle of Year 4)

Peter, in spite of having had lots of help and encouragement at home, Quick Ten from the whiteboard every morning for two years and a basic facts speed test every Friday for most of Year 4, is not feeling entirely happy with his own progress. He is one of those children who work methodically, carefully, accurately but slowly!

Researcher: Is there anything you’ve done in maths that you really haven’t liked much?

Peter: Um, times tables.

Researcher: What makes the times tables not so good for you?

Peter: Because they’re hard.

(Later)

Researcher: Is there anything that we could do to make maths better for you?

Peter: Um, learn more times tables and learn them all.

Researcher: What would help you to learn them all do you think?

Peter: Just getting a piece of paper and writing them all down then copy the answers and just looking at them for ten minutes or something.

Researcher: Yes? Do you get enough time to do that in class do you think?

Peter: No.

(End of Year 4)

 

Teachers’ Beliefs

When asked what a typical mathematics session would look like in their classroom, teachers all mentioned some form of time-constrained basic facts component. The rationales they gave for this teaching practice were varied. For Jessica’s teacher, the focus is recall.

Researcher: What would a typical maths lesson look like in your class?

Jessica’s Teacher: We start off with some, um, basic facts recall. This morning I just did the Quick 10, other mornings I do problems on the board, word problems and things like that, so some sort of recall of basic facts.

(Early Year 4)

Because some children in the class are very enthusiastic about competitive mathematics games, teachers can wrongly assume that all the children love such games. Jared’s teacher had no idea that Jared ‘hated’ them. For the last term of Year 3, she placed him in a special class for children who were slow at mathematics and language.

Researcher: What would a typical maths lesson look like in your class? From the start ?

Jared’s Teacher: A game, we mostly do a game …they really, really like the game that we played (the competitive game I saw while observing the class) so I play it heaps &emdash; yeah, basic facts all through, pretty well.

(Middle Year 3)

Some teachers appeared to use the Quick Ten as a management tool.

Researcher: What would a typical maths lesson look like? How would it start?

Peter’s Teacher: We come (children sit at group tables) and we have Quick Ten which is so basic and easy, but that’s really just to settle down. ‘Get your book out, turn to the back, do those’ and then we do ‘Hurry up, Peter’ (a chanting ‘game’ to get slow children to hurry onto the mat) and then we do table practice.

(Early Year 4)

Teachers rarely expressed an awareness of, or concern about the pressure they were applying to children through their routine basic facts testing and game-playing. Neither did they question the effectiveness of these practices in terms of children’s actual learning.

Even when there had been an attempt by advisers to change one teacher’s attitudes, it was hard for her to abandon her familiar strategies. This young teacher was in her second year of teaching and had just been on an inservice mathematics course.

Researcher: What would a typical maths lesson look like in your class?

Fleur’s Teacher: Normally we start off the day, there’s ten questions on the board. I went on a maths course where the lady said, ‘Don’t do it. Don’t put questions on the board because if they don’t know it, they’re going to feel like they’re failing, and if they do know it, they don’t need to practise it. And I thought ‘Oh, that might be a really good point and I came back and thought about it and then I thought, ‘But often it’s reminding them of things we’ve done’.

(Middle Year 4)

Teachers were observed moving children on to multiplication algorithms with two-digit factors before children had a good understanding of the concept of multiplication and on the basic multiplication facts. The exasperation is clear in this teacher’s comment:

Jared’s Special Class Teacher:

That’s why I’m having a blitz on the times tables. They’ve just got to know it, they’ve got to learn it by rote &emdash; memorise it &emdash; there’s no other way.

This teacher did not appear to have made any attempt to discuss patterns in the ‘two times table’ that she was teaching that day, to place them in context, or to discuss with children some effective methods for memorising them.

Conclusion

These case studies serve to illustrate that in many classrooms, learning of basic facts dominates mathematics teaching in the middle primary years. The children in these classrooms have come to believe that answering basic facts questions is mathematics. They believe this because their teachers, through their everyday practices, seem to value the skills of rapid recall of basic facts more than any other aspect of mathematics. Basic facts test results are frequently the most recorded of teachers’ assessment practices.

In most cases, basic facts speed activities are being used as the ‘opener’ to the daily mathematics session. They often take the form of a written time-constrained ‘test’. which is always marked and scores allocated. Often, children are asked to ‘publicise’ their scores by standing or raising their hands if they got 10 out of 10, 9 out of 10 etc or by calling out their scores which the teacher then records in the mark book.

Basic facts speed activities also often take the form of competitive, pressurising games in which the players are exposed to peer scrutiny. To answer wrongly is to lose, or be eliminated. Harmless, sound even, as these daily routines may seem, these practices can only be described as inhumane when, as this small sample shows, a significant proportion of the children are saying that they feel nervous, scared, or that they hate those parts of the mathematics time. Even some of the competent children in the study group expressed anxiety about having to keep producing good scores.

Because of basic facts dominating routine classroom practices, children in this study conclude that ‘knowing your tables’ must be the most important mathematics skill to have. They come to believe that anyone who is ‘no good at basic facts’ is no good at mathematics. They identify class members whom they believe to be good at mathematics by the speed with which they finish and the scores that they achieve in regular timed tests.

The children were seldom given opportunities to share in question-asking in basic facts learning. The teacher controled the questioning process by selecting the questions and calling them out, or by choosing the textbook, worksheet or test paper for the children. This made some of the children feel disempowered and alienated.

The children were seldom encouraged to learn together, and are sometimes even ‘told off’ for sharing methods or answers. They can come to believe that mathematics is about solo performance. They were exposed to the judgement of peers. This made even the most competent children a little anxious, and the less competent, fearful and self-deprecating. The children were frequently discouraged from using concrete aids, even fingers, in the completion of timed tests. For many, this meant that the mathematics required was inaccessible to them.

There is an urgent need to change teacher’s attitudes and beliefs about mathematics learning. Teachers need to be challenged about the ways in which they undermine children’s confidence and security in mathematics. After all, in most new curricula of recent years, promotion of children’s confidence and enjoyment in mathematics are given as important aims of mathematics teaching. Teachers are making assumptions about the way children learn. When the teacher always controls the questioning and assessment process, children are disempowered and vulnerable.

Alternatives must now be sought for the entrenched use of quick-fire questions.. Children need to be asked about how they learn best, about what helps them to understand and retain knowledge, and how the classroom sessions can be arranged to best accommodate a range of learning needs and preferences.

Instead of ten quick fire questions, mathematics lessons could start with a Thinking Exercise &emdash; one problem to solve instead of 10 timed, random, contextless basic facts, and children’s strategies could be discussed and evaluated. If teachers ask every day ‘Who came up with a strategy that worked? Explain it to us,’ instead of ‘Who got ten out of ten?’ then children may begin to think that problem-solving is what mathematics is all about rather than rapidly producing answers and gaining scores. And if schools send the message home that mathematics education is shifting emphasis from ‘mere recall’ to ‘thinking, figuring out and understanding’, then parents can join the teachers in helping to change our limited and limiting mathematics culture.

But it is not until we change our routine, familiar, taken-for-granted everyday practices in primary school classrooms, I believe, that we will begin to see a change in children’s confidence and enjoyment in mathematics, and an accompanying improvement in real achievement for all children.

References

Bishop, A. (1991) . Mathematical Enculturation: A cultural perspective on mathematics education, Kluwer: Academic Publishers.

Berger, P. and Luckman, T. (1966). The Social Construction of Reality, Penguin.

Douglas, J.D. (1974) . Understanding Everyday Life, Routledge and Kegan Paul Ltd, London.

Meighan, R. and Siraj-Blatchford, I. (1998) . A Sociology of Educating, Cassell: London.

Weigert, A.J. (1981) . Sociology of Everyday Life, Longman.