Section Contents:
Keith J. Topping, Maura Kearney, Edward McGee, John Pugh
Topping, K. J., Kearney, M., McGee, E. & Pugh, J. (2004). Tutoring in mathematics: A generic method. Mentoring and Tutoring, 12 (3), 353-370.
The teaching of mathematics has been the focus of concern about standards (especially in problem-solving), discontinuity between "schooled" and "real-life" mathematics, deficits and confusions in the language of mathematics, and a failure to establish positive mathematical self-concepts in many learners. Schemes for parental involvement in mathematics have sought to ameliorate these difficulties, but are themselves subject to a number of risk factors. Rigorous evaluation has been scarce in such projects, but where it has occurred results have been encouraging. However, concerns about discontinuity and parental mathematical capability remain. Consequently there is a need for the design of tutoring procedures suitable for use by parents and other non-professional tutors which are generically applicable to the mainstream mathematics curriculum but capable of close articulation to the individualised needs of the tutee - without requiring expert mathematical knowledge on the part of the tutor. This study reports the first controlled evaluation of such a generic procedure. From a group of 30 pupils aged 9-10 years, chosen by teachers in a large primary school as of below average mathematical ability, children were randomly allocated to experimental or control conditions. Experimental tutees (n=17) were tutored in mathematics at home by their parent(s) using the Duolog Math procedure, while control children (n=13) received only normal classroom teaching. Pre- and post-test assessment of both pupil groups used a curriculum-based mathematics test in parallel forms and a scale of attitudes to mathematics. Experimental parents completed a pre-test questionnaire on attitudes to mathematics and home school links. Experimental children and parents engaged in a post-test debriefing interview. The pre-post test interval was only four weeks. On the pre-post attainment test, the experimental group gained significantly, while the control group did not gain significantly. Male tutees appeared to gain substantially more than females. No significant pre-post differences were evident on a pre-post pupil attitude questionnaire. However, interview feedback from both parents and children was generally positive. Given the brevity of the pre-post test interval, and the insensitivity of some of the measures, detecting significant differences was thought unlikely. The finding of such positive differences in attainment, especially for male tutees, was considered encouraging. Recommendations for future research were made.
Recently concern has again been expressed by Her Majesty's Inspectorate (2001) about the low level of applied problem-solving skills among children. An HMI Report (Standards and Quality in Primary Schools: Mathematics 1998-2001) noted that problem-solving skills were still the number one priority for development and improvement in primary schools.
There is also long-standing concern about the relationship between the school mathematics curriculum and the mathematical demands of everyday life and employment. A survey by Raines (1988) indicated parents were frequently critical of the relevance of the school mathematics they had learned to later life. As Nunes, Schliemann and Carraher (1993) point out in their exploration of the relationship between school mathematics and street mathematics, children can carry out quite complex arithmetical calculations in relation to their life needs without any formal teaching, while subsequently proving unable to do equivalent problems in school, where the problem is not only decontextualised but a different and singular route to the solution may be required. There is not only a lack of generalisation of school mathematics to real life, there is a lack of generalisation of the mathematics of real life to the school. What we know depends on how we know it and where we know it - cognition can be highly situated.
The survey by Raines (1988) showed that mathematics was an emotive topic for parents - even in middle class areas and schools with good home-school relations. Enjoyment of mathematics and self-concept were closely linked; very few parents who saw themselves as good at mathematics disliked doing it, whilst most of the parents who saw themselves as bad at mathematics hated it, especially at secondary school. The latter parents had strong memories of school experiences, often unfavourable. Many parents felt the aims of mathematics teaching in schools should include the development of confidence and enthusiasm as well as understanding. These findings led Raines to criticise "parental involvement in maths" schemes which were merely "shipping home the curriculum" as naively ignoring the affective and historical dimensions of parents' own reality.
From the point of view of pupils currently in school, Nicholls (1978) observed that for nine-year-olds and under, perceived effort and ability were not seen as being causally distinct. Hence the creation of self-esteem and awareness of competency in early childhood was of central importance to the development of a positive attributional style.
Discussion is crucial in developing understanding in mathematics, especially for children with learning difficulties in this area (Daniels & Anghileri, 1995). Mathematics has much specialist vocabulary, including that applied to abstract and complex concepts, as well as using some "everyday" vocabulary with more specific and restricted meanings. The linguistic aspect of learning mathematical concepts is thus of particular importance (Choat, 1981). Concept formation is aided greatly by the ability to use the related language, whilst the learning of new concepts is closely associated with the acquisition of new words which are meaningful. Children might learn words without really understanding the associated concepts, while their understanding of some concepts might be underestimated because they do not use the "official" terminology. Correspondingly, too heavy a reliance on the medium of language in the process of teaching mathematics is likely to differentially disadvantage children whose language is not well developed.
In seeking to address these concerns about standards, discontinuity, affect and language, various types of programmes to involve parents and other carers in the mathematical development of their children have become more common throughout the world.
Since the start of the 1990s in North America, reports offer a wealth of organisational detail. A series of six workshops for parents were described by Goldberg (1990), reviewing mathematical activities usable in the home with the aim of improving achievement in and attitudes toward maths for 8-12 year old children. A substantial guide for parents in Australia was developed by Costello, et al. (1991), emphasising mathematics in everyday life and the importance of discussion and language. Home activities for children aged 5 to 13 years and their parents were detailed by Kanter, Dorfman and Hearn (1992) in a booklet published by the US Department of Education, with an emphasis on communication and developing positive attitudes.
Owens (1992) produced the delightfully titled "Parent-Helper Book for Those Who Want Arithmetic Made Touchable" - which in fact also covered geometry and other areas and included detailed activity guidelines. "Natural Math" was a programme offered to pre-school and kindergarten Seminole and Chickasaw Head Start Native American and African American families (Sears & Medearis, 1992, 1993), utilising activities and games developed to relate to the home culture. The "Family Math" programme has proved very popular in the USA and Canada and has extended to parts of Australia (Onslow, 1992).
Martin (1993) focused on parents in adult literacy classes, creating take-home parent and child activity kits designed for use with everyday materials, launched via parent workshops and including instruction sheets in Spanish. Planning and organisation considerations in establishing parent-teacher partnerships in mathematics were outlined by Neil (1994). "Beyond Facts and Flashcards" was the evocative title of a parent guide produced by Mokros (1996), designed to help parents uncover the mathematics in their daily lives through everyday experiences, suggesting many activities. Similar creations had come earlier from Valentine (1992), Leonard and Tracy (1993) and Sharp, et al. (1995).
However, (with the exception of the long-standing Family Math programme), similar developments had begun somewhat earlier in the UK.
Following the surge in interest in parental involvement in reading at the beginning of the 1980s, a ripple effect became discernible in mathematics. By 1983 Jennings had published a report on parental involvement in maths with high school pupils, and a number of postgraduate research theses followed (e.g., Paskin, 1986; Risk, 1988).
Set in a deprived multi-cultural urban area of West Yorkshire, Alan Graham's "Sums for Mums" project, coupled with his book "Help Your Child With Maths" (Graham, 1985), was another major development. The project targeted women and aimed to enhance their self-esteem as mathematicians with onward transmission to their daughters, this focus attracting funding by the Equal Opportunities Commission. Although set in local schools, the workshop sessions were oriented to adult learners, and eschewed "conventional textbook maths". This was followed by PRISM (Parent Resource in Support of Maths). However, little substantive summative evaluation was reported.
The IMPACT project, widely known in the UK, involves the class teacher sending home mathematical activities which parent and child carry out together (Merttens & Vass, 1987, 1993). It is closely tied to classroom activities which the child exports to the home, often involving whole classes completing the same "homework" simultaneously. Surprisingly, given its high profile, relatively little evaluation evidence on Impact appears to be publicly available (Merttens & Vass, 1993).
The Paired Maths project in Kirklees (West Yorkshire) involved mathematical games, structured in three levels to be appropriate for Key Stage 1, 2 and 3 pupils. In an evaluation of an early years KS1 project, all the parents for the foundation year intake for that term were invited to take part, twelve of the sixteen parents accepting. The children in the next term's intake, who were not offered any project involvement, were used as a comparison group. The Quest diagnostic tests were used with all the experimental children pre- and post-project, and with the comparison children over the same eight week time interval. The project children showed a marked improvement, particularly in the areas of pattern, order and conservation. The children in the comparison group, although showing some improvement in their scores, scored significantly less well than the project children, particularly in these same areas. Pre-project scores for project children were on average below those of the comparison children, but post project this situation was reversed (Topping & Bamford, 1998a,b).
Other related projects have developed in various parts of the country (Woolgar, 1986; Perry & Simmons, 1987; Clive, 1989). One such is the Play Along Maths programme described by Cheyne (1994, personal communication), a Home School Community Tutor. The programme targets families when children are just beginning school. Activities and games (including jigsaws and peg games, all cross-referenced to the prescribed 5-14 Curriculum) are sent home, coupled with "activity cards" bearing ideas and rules prepared by volunteer parents. Much emphasis is placed on language, under the rubric of "Chat-Along", and essential vocabulary amounting to a total of 200 words is mapped out. Each game or activity is used 10-15 minutes per day for a week, then changed. Families keep diaries noting the game/activity, day, time and any comments - children adding smiley faces if they liked the game.
Neilan and Currie (1994) involved parents in a series of four workshops over a six week period, involving mathematical workbook tasks and problem solving activities which were continued at home and supplemented with number games. Pre and post norm-referenced number tests were applied to children in a mixed ability class of 18 five year olds randomly assigned to control and experimental groups. Uptake was 100% and attendance at workshops very good. In the event, despite random assignation, the experimental and "control" groups were not equivalent on pre-test scores, those of the latter being lower. Experimental group children gained more on the test than the comparison group, but the difference did not reach statistical significance. Subjective feedback from parents was very positive.
In summary, a large number of parental involvement in maths projects have been operated, but rigorous evaluations are relatively scarce. However, the results from controlled studies have been encouraging. Children involved in projects have ranged from very young primary school children to high school pupils, mostly but not exclusively those with mathematics difficulties. Gains have been demonstrated on various kinds of tests although not all gains reached statistical significance - this being elusive with small samples. Subjective feedback was ubiquitously positive. The time costs to parents of involvement was very various in different projects, and this has implications for the wider involvement of more parents.
Many projects (especially for early years children) involved parents in the mathematical development of their children at home through mathematical games. Although mathematical games have many strengths for this purpose, not least the avoidance of mindless "drill and skill", they also have some weaknesses. Most notably, concern about discontinuity remains - children enjoying the games and thinking hard but not regarding them as "real maths" (and perhaps not as maths at all), raising questions about generalisation to achievement and affect in "school" mathematics. In the later years of primary schooling, there is also concern about the capability of parents to act as effective tutors if their own mathematical knowledge is limited, narrow, out of date, or simply wrong.
Consequently there is a need for tutoring procedures suitable for use by parents and other non-professional tutors which are generically applicable but capable of close articulation to individualised aspects of the mainstream mathematics curriculum as each child's situation demands - without necessarily requiring expert knowledge of modern mathematical methods on the part of the tutor.
Tutoring procedures are most effective when thoughtfully and thoroughly scaffolded (Sharpley & Sharpley, 1981; Cohen, Kulik, & Kulik, 1982, Topping & Ehly, 1998; Topping, 2000, 2001a). The format of the structured intervention methodology in the current study took as a model the long-standing "Paired Reading" method, and was designed as a parallel generic tutoring procedure applicable to any mathematical task, but with particular relevance to problem-solving. This procedure is named "Duolog Maths".
PR is a structured method of supported or assisted reading. It is intended only for use with individually chosen, highly motivating, non-fiction or fiction books which are above the independent readability level of the tutee (but of course within the independent readability level of the tutor). However, the name has proved problematic, being widely applied by some teachers to almost anything that two people do together with a book. Of course, the effectiveness research only applies to the specific and structured technique.
In a recent review of the effectiveness of twenty interventions in reading, PR ranked as one of the most effective (Brooks, Flanagan, Henkhuzens, & Hutchison, 1998). The PR method has now been very widely disseminated all over the world, and has been demonstrated to be effective with thousands of children in hundreds of schools. It has been the subject of many research reviews (e.g., Topping & Whiteley, 1990; Topping & Lindsay, 1992). There are many controlled studies demonstrating effectiveness. Follow-up studies indicate that gains are sustained and do not "wash out" over time (Topping, 1995, 2001b).
Just as Paired Reading is a set of generalised tutoring behaviours for reading which can be applied to any book, Duolog Maths is a set of generalised tutoring behaviours which can be applied to any mathematical problem. Mathematics is a very wide ranging area, and designing tutoring procedures is considerably more difficult for mathematics than for reading.
Duolog Maths is a framework for pairs working together. Some difference in mathematical ability is desirable in each pair, but not essential. Some difference in reading ability is essential if the weaker member of the pair cannot readily read and comprehend the presentation of an extended mathematical problem. The pairs can be peers of the same or different ages, parents working with children at home, teaching assistants working with children in school, or volunteer adults (such as senior citizens) working with children in school.
A preparatory study of successful one-to-one tutoring or coaching behaviours used by professional teachers in mathematics identified 21 such discrete behaviours. Developing from this, a set of eight (much simpler and complementary) tutoring behaviours suitable for use by non-professionals was designed. This system was termed "Duolog Maths". A duologue is a dialogue between two people, and the title was selected as the preferred name by a large group of teachers in the USA - hence the American spelling.
A flowchart indicating the tutoring behaviours in the Duolog Maths system is given in section 5 of this manual. The behaviours are arranged there in a logical sequential and strategic order. It is intended that this flowchart be used in training tutoring pairs and then a copy be given to each pair in order to remind them of the interactive flow required of them. More detail concerning the definition of each tutoring behaviour follows. It is intended that this be photocopied onto the back of the flowchart, for reference by tutoring pairs.
The "Questions" and "Make It Real" sections of the latter are complex, and for this reason are also made available in simpler bulleted form as tutor prompt sheets for those specific areas (available in section 5 of this manual). These would not be issued at initial training, but could be used subsequently as necessary at the teacher's discretion. They could also be printed back-to-back as required.
A further listing of "More Tips for Tutors" is also made available in section 5 of this manual. Teachers need to use this with considerable care, given the dangers of information overload for the participants. However, it forms a useful list for reference by professionals, who might select single items from this list for discussion with participants in the light of particular problems which seem to be emerging from the monitoring of the interaction between the pairs.
Duolog Maths provides:
Duolog Maths also:
Duolog Maths aims to be:
Resources. Further information about parent and peer tutoring in mathematics and Duolog Maths will be found on the Problem-Solving project web site (www.dundee.ac.uk/eswce/research/projects/problem-solving) and in Topping and Bamford (1998a, b). These include practical resources to freely reproduce, which are also available in hard copy as a teacher's manual.
Although soundly based upon related research, the Duolog Maths system is of recent development. This study was a first modest controlled evaluation of the method. It aimed to explore the effectiveness of the Duolog Math procedure with parent tutors, in relation to mathematical tasks drawn from the mainstream school maths curriculum. Given the difficulties of measuring short-term changes in mathematical abilities and the doubtful sensitivity of norm-referenced tests of mathematics, considerable thought was given to the problem of measurement of attainment gains and a control or comparison group was considered essential. Attempts to measure gain in improvement in attitudes toward mathematics were also to be incorporated, although such measures are notoriously unreliable.
A controlled pre-post repeated measures design was adopted. The project was located in a large denominational primary school in large city in the west of Scotland at the request of the school. The school was in a predominantly home-owning area although 20% of pupils were eligible for free school meals. It had no history of parent tutoring projects, but had developed good home-school communication, including high parental participation with homework diaries and parents' evenings. Parents were also active in the parents' association and on the school board. The school's Senior Management Team worked closely together and facilitated effective communication with parents.
Thirty participant children were drawn from the Primary Six (P6) age group (9-10 years old). They were not randomly selected, but chosen by teachers on the basis of below average mathematical ability and likelihood of benefiting from the intervention. All pupils were operating below the average range in relation to the 5-14 national curriculum (post level B / pre level C). Teachers noted that the whole group evidenced difficulty with problem solving strategies, attention, motivation and maths language. More males than females were selected. The pupils were then randomly assigned to one of two groups, experimental (n=17) and control (n=13). In the experimental group there were ten males and seven females, and in the control group ten males and three females. At pre-test, the control group had the same average level but greater variability in attainment than the experimental group.
All participants received:
Training involved verbal instruction, demonstration, and a written reminder. All experimental group parents and children attended a presentation on Duolog Math and observed a demonstration tutoring session using the method (role played by two researchers). The researchers attempted to deliver the parental training programme uniformly. However, parent availability was very various, and it was eventually necessary to hold six training sessions in total. Sometimes the tutee attended a different session from their tutor.
The experimental group were asked to carry out three tutoring sessions per week, using the Duolog Math programme. Each tutoring session was expected to last twenty minutes. The pre-post research aspect lasted only four weeks. The researchers were unable to monitor the process of tutoring as it occurred within the home. There might also have been variations in the extent to which the project was prioritised by different class teachers.
A pre-test and post-test curriculum-based assessment of general mathematical competence was administered to both the experimental and control group. The nature and structure of the pre-test and post-test was very similar, but the fine detail of the content of each parallel item was different. The assessment items were selected from the 'Profile of Mathematical Skills Level 1' published by NFER-Nelson (France, 1979). A cross-section of questions of varying complexity were selected, judged suitable for pupils of the age and ability levels of the project group and Level C of the 5-14 national curriculum in mathematics which was the target curriculum area. Questions were cross-checked to ensure pre-test and post-test items were of the same standard. The pre-test and post-test each consisted of 40 questions in total, covering: addition, subtraction, multiplication, division, operations problems, money & measurement and extension questions. The assessments followed the scoring and time allocation recommended for the original by NFER-Nelson: one mark was awarded for each correct answer and a generous time allocation of forty-five minutes allowed (given that the project focus was more on accuracy and understanding than speed).
A 16-item multiple-choice attitude questionnaire sampling affective reactions to mathematics in general and doing mathematics with their parents in particular was administered to pupils in the experimental and control groups at pre- and post-test.
A questionnaire was administered to the parents of pupils in the experimental group at the end of the launch training presentation (i.e. at pre-test), to explore their general attitude to school/home links, homework and maths curriculum. This 10-item multiple-choice questionnaire requested responses on a 5-point scale to given statements, point 1 and 2 being "agree fully" or "agree mainly" with the statement. Responses were not statistically analysed, but was used to inform a post-test debriefing and feedback session for the parents and children.
Parametric and non-parametric tests of statistical significance were carried out, as the sample was not randomly drawn from a normal population. However, little difference were found between parametric and non-parametric results, and those given below are based upon Student's t-test, which is generally considered robust under less than optimum conditions.
Subjective participant feedback: parent questionnaire
The pre-test questionnaire to participating parents was completed by all participating parents (100% response rate).
Table 1: Responses to Parental Questionnaire
Statement Percentage of respondentsagreeing fully or mainly (%)
It is important for a child to have homework 83
I like to help my child with homework 75
Home/school relations are important 83
I am keen to take part in this project 83
I think maths is an important part of the curriculum 83
I believe my child enjoys maths 33
I understand the maths homework my child brings home 75
I attend parent's evenings 75
I am aware when my child has difficulties in the curriculum 75
The launch presentation informed me of something that will benefit my child 75
The parents attending the training evening were predominantly female. They showed a relatively sophisticated appreciation of home-school links and a high level of awareness of the importance of mathematical learning, and rated their own competence as potential tutors quite highly. However, only a minority felt their child's current attitude towards mathematics was positive.
An improvement in mathematical performance in both groups was evident (Table 2).
Table 2: Mathematics performance at pre- and post-test
n | mean score | mean % correct | standard deviation | significance of difference | |
Experimental Group | |||||
Pre-test | 17 | 25.88 | 64.70 | 6.95 | p<0.05 |
Post-test | 17 | 28.82 | 72.10 | 6.95 | |
Control Group | |||||
Pre-test | 13 | 26.31 | 64.80 | 6.09 | p>0.05 |
Post-test | 13 | 28.62 | 71.60 | 4.63 |
For the difference between experimental pre-test and post-test means, a significant t-value was obtained (t = -4.207, d.f. = 16, p<0.05, two-tailed). For the difference between control group pre-test and post-test means, a non-significant t-value was obtained (t = -1.358, d.f. = 12, p>0.05, two-tailed).
Although the experimental group started from a slightly lower mean point than the control group, and ended at a slightly higher point, the absolute difference between the performance of the groups was small. That one difference achieved statistical significance and the other did not probably reflects the difference in group size as much as the difference in mean differences, although the lesser post-test variance in the control group could have tended to counter-balance this.
These data indicate a modest effect size of 0.252 on mathematical performance due to Duolog Math tutoring.
Table 3 suggests an improvement in mathematical performance for both males and females in the experimental group after tutoring, but particularly in males, who started from a lower mean baseline.
Table 3: Mathematics performance for experimental males and females
n | mean score | mean % correct | standard deviation | significance of difference | |
Females | |||||
Pre-test | 7 | 29.71 | 74.3 | 3.82 | p<0.05 |
Post-test | 7 | 30.86 | 77.2 | 4.49 | |
Males | |||||
Pre-test | 10 | 23.20 | 58.0 | 7.54 | p>0.05 |
Post-test | 10 | 27.40 | 68.5 | 7.20 |
For females a non-significant t -value was obtained (t= -1.486, d.f. = 6, p>0.05, two-tailed). For males a significant t -value was obtained (t = -4.776, d.f. = 9, p< 0.05, two-tailed). This suggests that Duolog Math tutoring has resulted in a significant improvement in mathematical performance in males in particular.
Subjective participant feedback: pre-post pupil attitude questionnaire
Attitude questionnaires were returned by all the participating pupils at both pre-test and post-test (100% response rate). The overall mean score for the experimental group rose from 50.12 at pre-test to 51.35 at post-test, that for the control group from 47.92 at pre-test to 47.69 at post-test. Although the experimental group made a gain (from a somewhat higher baseline), while the control group mean actually fell, in neither case did the difference achieve statistical significance. Within the experimental group, there were no significant differences between males and females. (Experimental t = -1.430, d.f. = 16, p>0.05; experimental females t = -1.353, d.f. = 6, p> 0.05; experimental males t = -0.741, d.f. = 9, p> 0.05; all two-tailed).
Subjective participant feedback: parent and child debriefing
While the pupil attitudinal questionnaire indicated few significant changes, subjective feedback from parents in the exit group interview partly contradicted this. In this setting, many parents noted a greater inclination in their child to work collaboratively as a consequence of the intervention. They felt that their own self-expression and questioning technique had improved. However, many parents felt they had initially over-estimated their own level of competency in mathematics. Many children indicated that they would be less likely to give up on a question as a consequence of their experience with Duolog tutoring. Indeed, the tutees were very positive about the benefits of what they saw as a more dynamic and flexible form of instruction than that found in class. Both parents and children indicated that mathematical language was a difficulty for many children, and that interaction with parents afforded greater discussion and a more comfortable learning environment in which to develop adaptive strategies for problem solving.
The parental participants valued mathematics and home-school partnership highly, but a minority felt their children had a positive attitude to mathematics. On the pre-post attainment test, the experimental group gained significantly, while the control group did not gain significantly (although the absolute differences were small). Male tutees appeared to gain substantially more than females. No significant pre-post differences were evident on a pre-post pupil attitude questionnaire. However, group interview feedback from both parents and children was generally positive.
The parents attending the launch meeting were predominately female and might not have been typical of the school population. The school itself might not have been typical of other schools. Consequently, caution is needed in generalising the findings of this study.
The study also lacks implementation process data - it is not known how well or how exactly the parents implemented the Duolog tutoring method at home. A further study is need to address this question and relate process to outcomes.
Although the difference between attainment pre-test and post-test results was statistically significant for the experimental group but not for the control group, the absolute differences were not large and the associated effect size was modest. However, analysis by gender suggested a much larger effect for males than for females. Nevertheless, given that the intervention was very brief (in terms of pre-test post-test interval) and the attainment outcome measure a rather blunt instrument, it is perhaps surprising that any difference at all was evident.
The pupil attitude to mathematics questionnaire had not been piloted and its sensitivity and reliability is unknown. The lack of evidence of any significant positive shift in attitudes to mathematics from this instrument must be set against the feedback from group interviews, which indicated positive and beneficial changes in pupils' approach to mathematical problems.
Further research may wish to explore differential gender responses to Duolog tutoring. However, the current study may offer some insight into ways in which underachieving males can be supported through home school liaison.
More research is required using various methods including longitudinal studies before any firm conclusions can be drawn as to the effects of Duolog tutoring by parents. It would also be interesting to investigate the effects of Duolog with other age groups.
In this study, even very brief Duolog Math tutoring by parents appeared to lead to modest but statistically significant gains in mathematical attainment compared to a control group. This was particularly true for boys. Improved pupil attitudes to mathematics were evident from group interview feedback but not significantly from a pre-post attitude scale. The Duolog Maths method appears to hold considerable promise for improving mathematical motivation and understanding and raising mathematical attainment. Further research using the method is now needed.
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