Case study research suggests that NLP influencing strategies benefit teacher effectiveness. Maths pedagogy involving higher-order questioning, challenge, problem solving and collaborative working may be a way of improving attainment in adult numeracy learning, however, such strategies may be less effective if the relationship between teacher and learner does not reflect sensitivity to attitudes, beliefs and emotions (areas in which advocates of NLP claim effectiveness).
The present study investigated these claims and the combined effect of such approaches using a pre- and post-treatment test design with 173 adult numeracy learners. Teachers were randomly allocated to three conditions, these were: (1) teachers given no training (control condition); (2) teachers trained in innovative maths pedagogy (including more frequent higher-order questioning, challenge, problem solving and collaborative learning); and (3) teachers trained in both NLP and the innovative maths pedagogy.
NLP training included suggestion using language patterns modelled from hypnosis, body language modelled from family therapy and spatial anchoring for emotional state management. A significant within-subject mean difference in maths test scores for the innovative maths pedagogy group (MD = 10. 97, t(66) = 7. 292, p< . 0005, ? 2=. 446) was nearly twice that of the control (MD = 5. 67, t(42) = 3. 099, p = . 003, ? 2 = . 186).
The Research paper on Innovative Practices in Education
Introduction The word ‘innovation’ is derived from Latin word ‘innovare’, which means “to change something to new”. In other words, we may say that ‘innovation’ means changing the regular way of doing things and involves doing the regular things in a novel way. The role of a teacher in present context has remarkably changed because of the various factors such as social, cultural, economic and ...
Although an attainment gap between pre- and post- treatment scores for the innovative treatment group alone (without NLP) appeared to close over time
post hoc between-group contrasts indicated differences between pre- and post-treatment means were not statistically significant (p = . 404 and p = . 689, respectively).
However, with the addition of NLP training, post hoc contrasts showed mean maths attainment had significantly improved compared to the control (p = . 040) with mean difference, pre- and post-treatment attainment, increased to over three times that of the control (MD = 18. 35, t(62) = 9. 552, p< . 0005, ? 2 = . 595).
CfBT Education Trust carried out this research with funding from the Learning and Skills Improvement Service. Key words: NLP, mathematics, teaching, learning, adult numeracy. Introduction Neuro-linguistic programming (NLP) publications frequently claim to have modelled the subjective experience of highly able people (particularly in relation to communication skills) in a way that enables the transfer of effectiveness both within and across disciplines (see Tosey and Mathison (2009) for an academic appraisal of the field and its development).
The earliest NLP publications originated when Richard Bandler and John Grinder (the cofounders of NLP) were a student and associate professor of linguistics at the University of Santa Cruz in California in the mid-1970s. Their early books document the use of the NLP process of modelling with hypnotherapists and family therapists such as Milton Erickson and Virginia Satir (Bandler and Grinder, 1975a; b; 1979; Bandler, Grinder and Satir, 1976; Grinder and Bandler, 1976).
These contain the first publication of their ideas about language (verbal and non-verbal), NLP approaches to the investigation of subjective experience and the internal mental processes which people are capable of perceiving. The first book to discuss teachers and classroom practice with NLP appeared in 1982 (Harper, 1982), although an earlier publication looked at the development of self-esteem with children and teenagers (Anderson, 1981).
Robert Dilts then produced a book which contained a specific chapter on NLP in Education (Dilts, 1983) originally written in 1981.
The Research paper on Business Research Study Of Wal-Mart’s Profitability
When first quarter results came in for Wal-Mart, the new CEO was not too happy and quickly recognized the challenges he would face as he strategized to increase sales. The results showed that profits decreased by 5% and that the future months were not looking good for the organization. Wal-Mart is the world’s largest retailer and has witnessed its fifth straight quarterly decline in U.S. sales ( ...
Also in that year, Sidney Jacobson published the first of three extensive volumes on NLP and education (Jacobson, 1983; 1986a; b).
Over the next 20 years, there have been over 20 more publications (see Carey et al. 2009 for a detailed review).
Drawing on the evidence in relation to communication skills and teaching (for example, Muijs and Reynolds, 2005) NLP skills have, in recent years, been increasingly associated with the teacher effectiveness (Churches and West-Burnham ,2008; 2009; Carey et al. , 2009; 2011; Vieira and Gaspar, 2012).
From an academic perspective, there has been an increasing interest in research into NLP in recent years with calls for academic commentary to become more evidence based (Tosey and Mathison, 2009) rather than speculative and theoretical. In education, there has been a significant growth in the publication of research evidence on NLP, and in 2010, CfBT Education Trust published the first systematic literature review (Carey et al. , 2010).
This reviewed the content of 111 references including studies that contain research evidence.
The authors identified 52 papers that claimed to contain confirmatory research evidence from 27 qualitative, 7 mixed-method and 18 quantitative education related studies. The review identified six quantitative studies that claim disconfirmatory evidence. None of the disconfirmatory studies was specifically in the area of adult numeracy learning, or classroom based mathematics teaching in general. There were no large-scale classroom based randomised controlled trials. Prior to the carrying out of the present research, a further search of the same databases used by Carey and colleagues in 2009 was undertaken.
Between 2009 and 2011 an additional 10 education related papers referencing NLP were published (el Gany et al. , 2010; Carey et al. , 2011; Jones, J, 2010; Kudliskis, 2009; Mohsin, 2009; Ran, 2009; Salmas-Villarreal, 2010; Saunders, 2009; Sibley, 2009; Slater et al. , 2009; Tosey and Mathison, 2010).
None of these contained evidence about the effectiveness of NLP in adult numeracy, or mathematics teaching specifically, however, two studies (Pishghadam et al. , 2011a; b) report statistically significant positive correlations between teacher success in English language teaching and NLP.
The Term Paper on Importance Of Research In School Society And Teacher
Research is important because it allows us to assess and review the quality of schools and education. It allows us to for improvement and policy change. It is help to find how research affects in your community. It is presents more information for examination. This is allow us for improvements based on better information and study. Education research is a field of inquiry aimed at advancing ...
With the exception of the NLP Spelling Strategy (Malloy, 1989; Malloy, 1995), most of the evidence in support of using NLP in education suggests benefits in relation to areas like effective communication, engagement, questioning and classroom climate rather than specific classroom pedagogy. In a perspectives paper on the potential of NLP in education Churches and West-Burnham (2008), for example, associate the potential benefits of NLP in teaching with ideas about emotional climate and the importance of this for effective learning.
Of particular relevance to this study are the 24 teacher-led action research case studies published by Carey and colleagues (2009; 2011).
The peer reviewed journal paper (Carey et al. , 2011) notes the potential benefits of teachers learning language patterns modelled from hypnosis, body language and emotional state management techniques but acknowledges the limitations of evidence provided by small scale teacher-led action research. Specifically, Carey and colleague (2011), recommend a large-scale randomised controlled trial to explore the potential of such techniques.
The present study aims to build on that recommendation. Three recent papers illustrate the need for more research into adult numeracy and effective pedagogy (McLeod and Straw, 2010; NIACE, 2010; NRDC, 2010).
In terms of progress, adult numeracy still lags behind progress in literacy in England (NIACE, 2010).
Some of the contributing factors to this are clear from a recent extensive literature review by the National Research and Development Centre for Adult Literacy and Numeracy (NRDC, 2010).
This endorsed earlier findings that suggest adult numeracy teaching is both under-researched and generally lacking a strong theoretical basis (Coben, 2003).
The CfBT Education Trust literature review into Adult Basic Skills also illustrates that there is only a limited research base currently in this area compared to other areas of adult learning, particular in relation to pedagogy (McLeod and Straw, 2010).
The Essay on Critical Pedagogy 2
The process of education is a complex one. Pedagogy, which refers largely to the style of the transmittal of education also involves a complex set of processes and procedures. There are times, however, that pedagogy is enforced and that almost all students are expected to catch up with the pedagogy. This approach can sometimes be tedious to those who have learning difficulties. For one, there ...
The NRDC review looked at academic literature, practitioner-focused publications, government reports and large-scale representative surveys.
The review noted the importance of areas such as students’ self-perceptions of their numeracy difficulties (DfES, 2003) and that the gap between assessed and perceived skills is even greater in numeracy than it is for literacy (Bynner and Parson, 2006).
In relation to the climate that teachers create in their classrooms, teachers who are effective are able to motivate learners to persist (Lopez et al. , 2007; Swain et al. , 2005) and deal with the high levels of anxiety and fear that is felt by many adult numeracy learners (Sewell, 1981; Meader, 2000).
These anxieties often originate from early childhood and can be traumatic and long-lasting (Coben and Thumpston, 1996).
Anxiety may also weaken memory, logical thinking and the ability to work methodically (Ashcraft, 2002).
The nature of the relationship between the learner and teacher itself may therefore have a significant impact with effective teachers being sensitive to the attitudes, beliefs and emotions of their learners (Cohen, 2005) and by extension it could be argued that adult numeracy teachers need the skills to deal with these areas effectively.
In terms of pedagogy, research evidence suggests that engagement and making maths meaningful is important (Salford, 2000; Baker, 2005) as is the teaching of abstract concepts not just basic numeracy (Swain et al. , 2005).
Salford, for example, drawing on Piaget argues for a constructivist approach in which learners should be allowed to work out the general rules of mathematics from exploratory situations (Salford, 2000).
‘Bad’ practice is seen as involving the application of procedures without understanding (Swain, 2005).
High levels of effective questioning, collaboration and engagement in which learners are challenged to think for themselves may therefore be more effective (see Swain and Swan, 2007).
In addition, the need to focus on the development of effective models for mathematics teaching rather than merely the identification and recruitment of the most mathematically talented is becoming increasingly clear across all education phases (Burghes and Robinson, 2009).
Principles for more innovative and effective adult numeracy teaching have been defined by the National Centre for Excellence in the Teaching of Mathematics (NCETM, 2008).
The Essay on Qualities Of A Good Teacher
Qualities of a Good Teacher In The Sandbox Experiment, Peter Sacks says [I]t really didnt seem to matter what I knew about my field when it came to teaching (Sacks 311). I disagree with him. I believe that knowledge, among many other things, is essential to being a good teacher. A good teacher is someone who is always willing to learn something new and expand their knowledge to help their students ...
These build on earlier research by Swain and Swan (2007).
These principles include the need to build on existing knowledge more effectively, expose learner misconceptions, increase the amount of higher-order questioning, more appropriate use of whole class, individual and small group work, encouraging reasoning rather than simplistic answering, the use of richer collaborative tasks and the need to make mathematics relate to the real world. The report also emphasised the appropriate use of technology, confronting difficulties rather than avoiding them, greater use of mathematical language and the need to ensure that learners
understand how they have learned things as well as what they have learned. This said there has not been any controlled research to test these claims. It would appear, from a review of the literature, that achieving effective adult numeracy pedagogy might require the inclusion of training that supports teachers to develop more effective communication skills (in order to deal with issues of learners’ anxiety, fear and motivation) as well as the types of effective pedagogy described above.
In such a context, communication skills usually found in therapeutic contexts might be useful. Formal clinical hypnosis is an increasingly established field (see Oakley and Halligan, 2009, for a review of the cognitive neuroscience evidence), however, it has also been demonstrated that hypnotic-suggestive communication can have an effect outside of formal hypnosis in contexts such as advertising (Kaplan, 2007).
The best predictor of a person’s hypnotic suggestibility is individual responsiveness to the same suggestions outside of hypnosis (Braffman and Kirsch, 1999).
Furthermore, an emerging consensus in the field of hypnosis (Kirsch et al. , 2011) acknowledges that: all suggestions experienced following induction can be experienced without it; that hypnotic inductions only slightly increase suggestibility; and that waking and hypnotic suggestibility are highly correlated. In relation to NLP one recent study also suggested evidence for a relationship between some NLP techniques and hypnotizability.
Research by Kirenskaya and colleagues (2011) showed a decrease in negative emotional intensity for both high and low hypnotizables but with autonomic activity (heart rate, skin conduction span) decline observed in high hypnotizables only. Image vividness and emotional intensity were also significantly higher in the high hypnotizability subjects. Whether NLP represents a sub-school of hypnosis, a set of techniques, or a field of study in itself remains a live debate (see Tosey and Mathison, 2009).
The Essay on Math Of Investment
MATH OF INVESTMENT: A REFLECTION PAPER At first glance, from the subject description itself, all I can defend about it was that it is all about interest and computations. And since I have loved Mathematics ever since I was born, I have loved this subject even at first heard. Solving some maths has been a challenge for me since then, but I get to see the beauty of it especially when you understand ...
This study has sought to integrate two domains: NLP influencing strategies; and innovative maths pedagogy including approaches such as higher levels of collaborative learning, challenge, engagement and higher-order questioning – both of which claim benefits, assess their combined effectiveness and the extent to which the NLP training might enhance effective pedagogy. Therefore, this research sought to contribute to both the debate about the usefulness of NLP in education and the effectiveness of NLP in general.
The present study consisted of a research design with three between-subject conditions and a within-subject pre- and post-treatment maths attainment test. The three conditions were: (1) teachers given no training (control condition); (2) teachers trained in innovative maths pedagogy (involving higher amounts of higher-order questioning, challenge, problem solving and collaborative learning); (3) teachers trained in NLP influencing skills in addition to the innovative math pedagogy training in Condition (2).
Each adult learner participant group took the same maths attainment test pre- and post-treatment. A review of the literature and subject matter content of NLP training suggested that NLP communication skills were unlikely to improve maths attainment in themselves if the quality of pedagogy being used was in question (because NLP communication skills are essentially content-free).
Rather there was more likely to be a measurable effect if a baseline of good pedagogy was established and known to be in place. The study’s design therefore allowed for the testing of two hypotheses:
Hypothesis (a) – adult learners whose teachers are trained in innovative maths pedagogy attain higher maths results than adult learners whose teachers have had no training Hypothesis (b) – training in NLP influencing skills enhances the maths attainment of adult learners whose teachers have trained in innovative maths pedagogy Method Participants Prior to participant recruitment a priori power analysis was carried out using G*Power 3. 1. 2 (Faul et al. , 2007; 2009) in order to estimate a minimum sample size for the study. No prior studies were available on which to base an effect size estimate.
An effect size of 0. 1, ? = 0. 05, ? -1 = 0. 95 (repeated measures, within-between interaction) was used in the calculation. Results indicated a recommended sample size of >207. Anticipating substantial levels of participant attrition, because of the transient nature of adult numeracy classes, the recruitment approach aimed for a target number of 300-350. Recruitment was via e-mail and presentations at networking events and targeted the teachers of adult numeracy learners across the southeast of England. Initially, 37 Further Education sector
teachers expressed interest in participating in the study, 24 teachers eventually took part with 278 adult learners completing the initial baseline testing. Offender learning was not eligible because of data sharing issues. As anticipated, there were substantial levels of participant attrition during the study. In addition (to reduce the risk of ceiling effects), the decision was taken to remove learners who scored more than 95% in the initial pre-treatment maths test. Six learners whose scores were above this cut-off point were withdrawn from the participant group following the baseline test.
In total, 173 adult learners between the ages of 16 and 70 (M = 30. 94, SD = 13. 12) completed the study, 71 males and 102 females. The following number of participants completed the post-treatment maths test: no training, n = 43; training in innovative maths pedagogy, n = 67; training in NLP and innovative maths pedagogy, n = 63 (see Table 1).
Table 1 As an incentive, teachers whose classes completed the research could attend a postresearch conference and additional training. There were no incentives for the adult learners. All participants received treatment that was in accordance with standard ethical research guidelines.
Dr Paul Tosey, University of Surrey, was consulted about the ethical application of NLP within the research design. The Skills for Life Development Centre, University of Sussex Innovation Centre monitored and controlled all data security, entry and analysis. Materials All adult learner participants received the same pencil and paper single level maths test that they completed pre- and post-treatment. Participants also completed a demographic questionnaire (e. g. age, gender).
The maths test was from the Department for Education and Skills ReadWritePlus Skills for Life Diagnostic tools in Numeracy Testing.
The test covered curriculum areas as specified in the Skills for Life Adult Core Curriculum for Numeracy: Entry 1, 2, 3 and Levels 1 to 3 (DfES, 2001).
In addition, participants completed an attitude to maths learning questionnaire, repeated pre- and post- treatment. A further research paper (currently in draft) will discuss the results from this. Procedure Prior to the administration of the pre-treatment test and demographic questionnaire the teachers were randomly allocated to one of the three conditions described above, whilst controlling for a number of background factors to ensure a similar distribution in each condition.
The controlled variables were teacher qualification level, number of years in teaching, spread of experience in teaching Skills for Life Numeracy, Functional Maths and Key Skills – Application of Number. No teachers from the same organisation/location completed the same condition to avoid the risk of ‘content sharing’ in relation to the training received and ‘contamination’ between participant groups. One criticism of NLP is that it is a form of ‘cargo cult’ psychology (Roderique-Davies, 2009).
The implication being that any effects are perceptual (or placebo) and exist only in the minds of converts – although no research has tested this hypothesis yet. In response to this criticism, the present study implemented a number of additional controls. All the adult learners were kept ‘blind’ to the purpose of the study and to the content that their teachers had, or had not, been trained in – the teachers simply adapted their practice without making any explicit references to anything that they had learned.
In relation to the teachers, the no training group remained ‘blind’ to the content that the other teacher groups had been trained in and the innovative maths pedagogy alone group remained unaware of the content of the training given to the NLP and innovative maths group. Furthermore, the NLP trained teachers did not know that they were to receive training in NLP until they arrived on the first day of the NLP training programme. All other participants remained unaware that NLP was part of the research design. No teachers whose learners completed the study had received any previous training in NLP.
The adult learners gave consent before completing the pre-treatment maths test, attitudes questionnaire and demographic questionnaire. Teachers conducted the pre- and posttreatment maths attainment tests in their own classrooms in Further Education, sixth form colleges, work-based learning providers and adult and community learning providers. There was no time limit for the test. Learners could take as much time as they needed to attempt (in one session within one lesson) as many questions as possible before handing in the test paper.
Pre-treatment tests took place in the middle to end of the autumn term and posttreatment tests at the end of the spring term/beginning of the summer term, although exact control of this variable was difficult because of the nature of adult numeracy learning and differences in weekly contact time and term dates. Where there was variation this was similar within each condition. Teachers themselves received instructions to avoid reading the maths test and simply to invigilate the test on the two occasions, collect it in and post it immediately to the project administrator. The three conditions were as follows:
(1) No training Adult learners in this group completed the maths attainment test at the beginning of the allocated time-period and again at the end, their teachers received no training (from the project) between the two testing points. (2) Training in innovative math pedagogy (involving higher amounts of higher-order questioning, challenge, problem solving and collaborative learning) Adult learners in this group completed the maths attainment test at the beginning of the allocated time-period, their teachers then received 2 days of training in innovative maths pedagogy.
The principles of effective adult numeracy teaching, as defined in the National Centre for Excellence in the Teaching of Mathematics 2008 report (NCETM, 2008), and which define a more innovative approach to pedagogy in adult learning, formed the basis for the curriculum, with a particular emphasis on higher-order questioning: ? ? ? ? ? ? ? ? ? ? ? Building on existing knowledge Exposing misconceptions Using higher-order questioning Appropriate whole class, individual and small group work Encouraging reasoning rather than answer getting Using rich collaborative tasks
Creating connection between topics, both within mathematics and to the real world Using technology appropriately Confronting difficulties rather than avoiding them Developing mathematical language Understand what has been learned and how The training the teachers received also built on ideas and approaches from the Maths4Life project (see Carpentieri et al. (2010), for a summary).
Teachers in Condition (2) were encouraged to use the online adult numeracy resources available at the Learning and Skills Improvement Service Excellence Gateway throughout the research period.
Participants also received non-NLP related mentoring support to help them to embed the training that they had received. This mentoring was carried out by the same mentors who mentored group 3 (see below) all of whom were trained to NLP Diploma level but in the case of group 2 were briefed to avoid using any NLP related techniques. At the end of the allocated time-period, the adult learners completed the same single level maths test again. (3) NLP and innovative maths pedagogy group
Adult learners in this group completed the maths attainment test at the beginning of the allocated time-period, their teachers then received the same innovative math pedagogy training as Condition (2) above. The teachers also received a further 4 days of training in NLP. The NLP training curriculum consisted of: ? ? Learning to use influential language patterns modelled from hypnosis (the Milton model (Grinder and Bandler, 1975b; 1981)) in order to formulate positive suggestions in relation to attainment, motivation and behaviour (Churches and Terry, 2007).
Specifically, the teachers were taught how to create positive presuppositions and suggestions and how to use: cause and effect and complex equivalence patterns, chained modal operators, double binds, embedded commands, linkage language, pacing and leading, universal quantifiers, yes set and yes tags. Learning to understand the effects of Satir category body language (Blamer, Placater, Leveller, Computer, Confuser) and apply appropriate categories in a ? congruent way (Bandler and Grinder, 1976; Bandler, Grinder and Satir, 1976) whilst communicating in the classroom (Churches and Terry, 2007).
This component of the training included foundation training in the development of sensory acuity and the use matching and mirroring to build rapport (Bandler and Grinder, 1979) Learning to use anchoring to support emotional state management (Bandler and Grinder, 1979) whilst teaching using spatial anchoring (Churches and Terry, 2007) Details of the training protocol are available from ac. uk. At the end of the allocated time-period, the adult learners completed the same single level maths test again.
Teachers in Condition (3) received additional NLP reading material (Churches and Terry, 2007; Terry and Churches, 2008) and the Teaching Influence cards used in previous NLP classroom case study research (Carey et al. , 2010; 2011).
They also received mentoring support from mentors trained to INLPTA NLP Diploma Level (INLPTA, 2005) to help them to embed the training they had received. Results Descriptive statistics show that the mean for the single level maths test improved from 60. 37 to 66. 05 in the no training group; from 54.
61 to 65. 58 for innovative math pedagogy group; and from 56. 49 to 74. 84 for the NLP and innovative maths group (see Figure 1 below).
Figure 1 To address hypotheses (a) and (b) paired-samples t-tests compared pre- and post-treatment adult learner maths attainment in the three conditions: no training, training of teachers in innovative maths pedagogy; training of teachers in NLP influencing strategies. Further analysis used a 3 x 2 analysis of variance with post hoc comparisons. Preliminary assumption testing used SPSS Explore.
In relation to carrying out the paired-samples ttests, pre- and post-treatment maths test within-subject data was satisfactory in relation to assumption of normality and the presence outliers. The final analysis applied post hoc tests suitable for use with unequal samples sizes. In relation to the assumptions required for the analysis of variance and between-subject post hoc comparisons, the pre-treatment data violated the assumption of homogeneity of variance, therefore the data was analysed using the Games-Howell multiple comparisons test.
Post-treatment data was satisfactory in relation to all assumptions and was assessed using Dunnett’s t. Paired-samples t-tests showed that the improvement in maths attainment in Figure 1 was statistically significant for all three of the participant groups: no training, t(42) = 3. 099, p = . 003 (2-tailed); training in innovative maths pedagogy, t(66) = 7. 292, p< . 0005 (2-tailed); training in NLP and innovative maths pedagogy, t(62) = 9. 552, p< . 0005 (2-tailed).
Partial eta squared values for all three conditions indicated they could be interpreted as having had a large effect (Cohen, 1998): control (no training), ? 2 = . 186; training in innovative maths pedagogy, ? 2=. 446; training in innovative maths pedagogy and NLP, ? 2 = .595. The largest statistically significant improvement in maths attainment was for the participant group whose teachers trained in both NLP influencing skills and innovative maths pedagogy.
Specifically, the NLP and innovative maths pedagogy group had the highest mean increase of the three participant groups (MD = 18. 35; SE = 1. 92) with an increase in maths attainment that was nearly three times that of the control condition (MD = 5. 67; SE = 1. 83) and one and a half times that of the innovative maths pedagogy alone group (MD = 10. 97; SE = 1. 50).
As can be observed in the data above, and in Table 2 below, innovative maths pegagogy alone also improved attainment with a mean difference score that was nearly twice that of the control condition.
Table 2 However, scrutiny of the confidence intervals for pre- and post-treatment means themselves (Figure 2 and Table 3 below) suggest the increase for the no treatment group would not generalise 95% of the time to the population because the post-test score for this group (66. 05) lies within the 95% confidence interval for the pre-test mean (lower bound = 53. 49, upper bound = 67. 25).
This is also the case for the innovative maths pedagogy alone results.
By contrast, the confidence interval data from the NLP and innovative maths pedagogy groups indicates that the statistical model presented by the data is likely to represent true values for the population from which the samples were drawn. Figure 2 Table 3 A 3 x 2 analysis of variance with repeated measures explored the trend seen in Figure 1, above. The dependent variable was maths attainment. The first factor was the condition (no training; innovative maths pedagogy; NLP and innovative maths pedagogy).
The second factor was the timing of the maths test (before or after treatment).
Both the main effect of level and timing (F(1,170) = 126. 37, p< . 0005) and the level x timing interaction were significant (F(2,170) = 12. 02, p< . 0005).
In order to explore the meaning of the data post hoc analysis used a series of contrasts comparing the pre- and post-treatment interaction with the three conditions. The first set of contrasts explored the differences between the levels for the pre-treatment maths tests. Because sample sizes for the pretreatment tests were unequal and Levine’s Test of Equality of Error Variance was significant the Games-Howell multiple comparisons procedure was used.
All of the contrasts between the levels were not significant (control-innovative maths, p = . 404; control-NLP and innovative maths, p = . 647; innovative maths alone-NLP and innovative maths, p = . 883).
A further series of three contrasts explored the three post-treatment maths attainment scores after the treatment phase of the research used Dunnett’s t because Levine’s Test was not significant for this data. This test also allowed for the treatment of one condition as a control (the no training group) and for the comparison of other conditions against it.
The contrast between the control condition and the NLP and innovative maths condition was significant (MD = 8. 80, SE = 4. 38, p = . 040).
As expected, from what can been seen in Figure 1 the contrast between the control condition and the innovative maths condition was not significant (p = . 689).
A final contrast with innovative maths pedagogy defined as the control, indicated a statistically significant difference between the NLP and innovative maths and innovative maths alone conditions (MD = 9. 26, SE = 3. 88, p = . 017).
A final test determined levels of significance in relation to individual participant improvement between pre- and post-treatment maths attainment (improvement was defined as ‘posttreatment test score’ minus the ‘pre-treatment score’ for each individual participant).
As expected from the 3 x 2 analysis of variance the one-way analysis of variance produced the same significant main effect (F(2,170) = 12. 02, p< . 0005).
Post hoc contrasts (Dunnett’s t) indicated a statistically significant difference between the NLP and innovative maths condition and the control (MD = 12. 67, SE = 2. 65, p
