

ORIGINAL ARTICLE 

Year : 2017  Volume
: 49
 Issue : 2  Page : 5362 

Impact of pranayama and vedic mathematics on math anxiety and cognitive skills
Vasant Venkatraman Shastri^{1}, Alex Hankey^{1}, Bhawna Sharma^{2}, Sanjib Patra^{3}
^{1} Division of Yoga and Physical Sciences, SVYASA University, Bengaluru, Karnataka, India ^{2} Department of Biology, Sri Sai Angels PU College, Chikkamagaluru, Karnataka, India ^{3} Division of Yoga and Life Sciences, SVYASA University, Bengaluru, Karnataka, India
Date of Web Publication  7Dec2017 
Correspondence Address: Vasant Venkatraman Shastri SVYASA, No. 19, Eknath Bhawan, Gavipuram Circle, K.G. Nagar, Bengaluru  560 019, Karnataka India
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DOI: 10.4103/ym.ym_13_17
Context: Many children have low selfconfidence in mathematics, leading to math anxiety, disturbed cognitive skills, and reduction of the quality of their educational experience. Aims: This study aimed to compare methods of reducing such anxiety and improving cognitive skills using pranayama; and second, introducing pattern recognition in problem solving, using methods of Vedic Mathematics. These methods were chosen because pranayamas are wellestablished, standardized means of anxiety reduction for any stressful condition, offering a precise standard for comparison, while, Vedic Mathematics shortens and facilitates calculations. Settings and Design: The study design was a randomized controlled trial with three groups: Yoga pranayama (YP), Vedic Mathematics (VM), and controls (CG) taking 12^{th} grade students from a private preuniversity college in India. Method: Intervention was 15 days each of 30 min daily instruction in either selected YP or VM for the two experimental groups. All the three groups received conventional math training every day. Exclusion criteria were major psychological problems. Assessments used the Mathematics Anxiety Rating Scale Revised and Children's Cognitive Assessment Questionnaire. Statistical Analysis Used: SPSS 19.0 was used for statistical analysis. Results: The experimental groups improved on all subscales of both tests, p < 0.001: the VM group improving more on the first test and the pranayama group performing better on the second test. Controls showed no improvements. Conclusion: Introducing pranayama and VM methods as teaching aids would improve cognitive skills and reduce math anxiety and offer a means to improve examination results, as later demonstrated. Keywords: Cognitive skills, math anxiety, pattern recognition, pranayama, Vedic Mathematics
How to cite this article: Shastri VV, Hankey A, Sharma B, Patra S. Impact of pranayama and vedic mathematics on math anxiety and cognitive skills. Yoga Mimamsa 2017;49:5362 
How to cite this URL: Shastri VV, Hankey A, Sharma B, Patra S. Impact of pranayama and vedic mathematics on math anxiety and cognitive skills. Yoga Mimamsa [serial online] 2017 [cited 2018 Jan 19];49:5362. Available from: http://www.ymkdham.in/text.asp?2017/49/2/53/220183 
Introduction   
Many children have less interest in mathematics (Frenzel, Goetz, Pekrun & Watt, 2010), and find learning mathematics very difficult. Why this is may not be clear, because many children find wellpresented mathematical ideas inspiring (Hohenwarter, Hohenwarter & Lavicza, 2008; Tatar, 2013). Demands of science and mathematics can turn school into an unpleasant experience (Kihwele, 2014). Anxiety caused by daily mathematics lessons starts in elementary school (Ramirez, Gunderson, Levine & Beilock, 2013) and becomes a dominant feature of their school experience (Maloney, Risko, Ansari & Fugelsang, 2010), causing math anxiety (Taylor & Fraser, 2013) and leading to poor performance in mathematics. A specific anxiety rating scale for math anxiety developed by Richardson & Suinn (1972) was revised and validated (Plake & Parker, 1982). One problem it causes is decrease in working memory (Maloney et al., 2010), a skill important for performing calculations in class exercises, tests, and examinations (Ashcraft & Krause, 2007). Of many papers on math anxiety (Ashcraft & Krause, 2007; Ashcraft & Moore, 2009; Maloney & Beilock, 2012; Wang et al., 2014), few show how to reduce it (Bellinger, DeCaro & Ralston, 2015; Brunyé et al., 2013).
How to remedy these problems? This study compares two methods of reducing math anxiety and improving cognitive skills: Vedic Mathematics (VM), a system offering students choice of ways to carry out calculations (Ismail & Sivasubramniam, 2010), and yoga pranayama (YP), a wellresearched means of anxiety reduction (Khalsa, HickeySchultz, Cohen, Steiner & Cope, 2012; Nemati, 2013; Sharma & Haider, 2013) and benchmark for doing so.
Yoga Pranayama
The first method investigated to reduce student's overall anxiety was YP (Cramer, Lauche, Langhorst & Dobos, 2016; Goldstein et al., 2016), already well researched at many different institutions (Cramer, Lauche & Dobos, 2014) and shown to be highly effective against anxiety (Varambally & Gangadhar, 2016; Uebelacker & Broughton, 2016).
Traditionally, pranayama (Nagendra, 2005) is used as preparation for meditation (Brown & Gerbarg, 2009) because it has a delightful settling influence on mind and body, while at the same time enlivening certain levels of “subtle energy” within the tissues (Sharma, Hankey, Meenakshy & Nagendra, 2014). Its settling influence has been much studied, including test anxiety reduction, test performance(Nemati, 2013), perceived stress reduction, and cardiovascular and respiratory parameters (Bhavanani, Raj, Ramanathan & Trakroo, 2016; Sharma et al., 2013).
Universally, high levels of stress, elevating levels of disease, make application of pranayama to decrease the effects of stressful situations an acute need of our times. Learning its practice in school offers children a life skill with lifelong benefits. It was of central interest here because competitive examination systems providing elimination procedures for those entering professional education have put new pressures on schoolchildren (Kadapatti & Vijayalaxmi, 2012). Also, more countries today are seeking to become knowledgebased societies (Gilbert, 2005), offering citizens more interesting work than drudgery of employment in mines and factories. However, some argue that examinationoriented education systems pressure children unnecessarily.
Introducing children to stressreducing techniques of yoga offers great potential benefit. By steadying the breathing process, pranayama steadies the mind itself. Everything passing through the mind can be “seen” and understood more clearly (Jerath & Barnes, 2009). Conversely, when a person performs a steadying series of yoga breathings, their emotions are steadied (Gilbert, 1999), negative thoughts tend to decrease (Arch & Craske, 2006), and their thinking patterns become clearer and more positive. Problemsolving abilities and mental efficiency improve (Sharma et al., 2014). YP also promotes positive health among adolescents (Singh, 2015).
Vedic Mathematics
VM gives students a choice of method to solve problems by selecting specific patterns of calculation (Muehlman, 1998). It shortens many calculations, directly improving examination results. Previously, mediocre students start scoring 90% or higher. Various researchers have demonstrated the intuitive and holistic nature of VM (Muehlman, 1998).
VM (Tirthaji Maharaja & Agarwala, 1992) seems to have been developed by Bharathi Krishna Tirtha (1884–1960) and by Shankaracharya of Puri, who said that it effectively formed an appendix to Atharva Veda. Previously, a teacher of high school mathematics demonstrated many applications at that level which have since been greatly expanded (Nicholas, Williams & Pickles, 2010).
The Shankaracharya's methods prove popular with children learning them (Ismail & Sivasubramniam, 2010). They develop abilities to visualize patterns of calculation for solving problems. Imagining hidden pictorial or algebraic patterns leads to enjoying the process (Zazkis & Liljedahk, 2002). Performing calculations becomes more like a game.
Professional mathematicians use similar powers of mental cognition in understanding and creating mathematics. VM methods have been applied professionally, for example, to shorten algorithms for multiplier circuits and decrease chip areas (Anjana, Pradeep & Samuel, 2015; Bansal & Madhu, 2016).
This led to the choice of tests employed in this study; the Mathematics Anxiety Rating ScaleRevised (MARSR) aims to assess benefits of learning VM, while the Children's Cognitive Assessment Questionnaire (CCAQ) was chosen to demonstrate benefits of the chosen sequence of pranayamas and related yoga breathing as summarized in [Table 1].
Method   
Participants
A total of 168 students, aged 17.0–18.5 years, studying in 12^{th} standard at a PreUniversity College in Chikkmagaluru, Karnataka, India, were randomly assigned to: YP (59 students, 34 male, 25 female), VM (59 students, 16 male, 43 female), and controls (CG – 50 students, 22 male, 28 female).
Design
The three groups employed prepost randomized controlled design [Figure 1]. Randomization used an online random number generator (Psychic Science, n.d.). G*Power analysis on a pilot study yielded n = 23.  Figure 1: Study design. Participants were divided randomly by a random number generator into three groups: Vedic Mathematics, yogic breathing, and controls. Baseline data were collected and respective interventions were administered for 15 days. Postdata collection was carried out after the intervention
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Informed consent
The study purpose and design were explained to parents/guardians who signed informed consent forms.
Interventions
Students in the experimental groups attended workshops lasting 30 min/day for 15 days during their regular mathematics classroom periods. The YP group received instruction in yoga breathing while the VM group received instruction and exercises in VM. Controls continued their usual maths classwork during the same classroom periods. Thirty minutes daily instruction was given to all the three groups at different times by the first author who is expert in YP, VM, and conventional mathematics teaching methods. The YP and VM groups also attended conventional mathematics classes after the 30 min intervention class.
The YP intervention consisted of a sequence of yoga breathing listed in the right column of [Table 2]. The first two (Kapalabhati and Bhastrika) are yoga kriyas and cleansing techniques, the third is deep breathing technique, while the last three are forms of pranayama. Each technique was first demonstrated, and then the class imitated the demonstrator, each member being carefully corrected for mistakes. After mastery of the first technique, instruction moved to the second technique, etc., until all were confident in performing the techniques in sequence. In each workshop, verbal instructions were given to start each technique and students with difficulties were helped. After each allotted 5 min time period, the group began performance of the next technique. Each workshop ended with Bhramari pranayama, the 6^{th} technique listed in [Table 2] (right column).
The VM intervention comprised instruction in 12^{th} standard mathematics, taught by standard procedures for VM instruction. Examples are given in [Table 2], with details of three explained in Appendix, for example, solutions to simultaneous equations were demonstrated using VM sutras, “vertically and crosswise,” “transpose and apply,” and “addition and subtraction,” offering alternative strategies to solve equations related to specific examples. Example 1 solves two simultaneous equations using “vertically and crosswise.” Example 2 demonstrates the use of “transpose and apply” to simplify integration of the reciprocal of a factorable quadratic function. Both problems cause less gifted students conceptual problems, time loss, and errors. Example 3 presents a multiple choice question on integration of nonfactorizable quadratic functions, the most difficult problem in Indian preuniversity maths, requiring understanding functions less familiar to the student [Appendix 1].
These examples show how VM methods shorten 12^{th} grade maths calculations used in differential and integral calculus, coordinate geometry, algebra, trigonometry, vectors, and 3D geometry. The above topics were taught to all the three groups participating in the study, but only the VM group learned to solve problems by VM procedures.
Assessments
Mathematics Anxiety Rating ScaleRevised (Plake & Parker, 1982)
This 24item instrument is designed to measure anxiety incurred in maths and statistics courses. It is a revised version of a 98item scale by Richardson & Suinn (1972), and is more focused on situationspecific (state) anxiety, general (trait) anxiety, and test anxiety. It contains two subscales: learning mathematics anxiety (LMA) concerning processes of learning of maths and statistics and evaluation maths anxiety (EMA) measuring anxiety from maths and statistics tests. LMA plus EMA form the total maths anxiety (TMA).
Scoring: Respondents rate each item on a 5point scale from “low” to “high anxiety.”
Scores are the sum of item ratings, ranging from 24 to 120 for the total scale.
Children's Cognitive Assessment Questionnaire (Zatz & Chassin, 1983)
This 40item instrument measures selfdefeating and selfenhancing cognitions associated with test anxiety. It focuses on negative selfevaluations and positive selfevaluations, reflecting selfdefeating and selfenhancing cognitions. It also assesses distracting, “offtask thoughts,” and “ontask thoughts,” focusing attention on task. These four constitute CCAQ subscales.
Scoring: Each item is answered true or false. Scores on the four subscales are the number of items answered “true,” ranging from 0 to 10. The first two subscales more reflect thoughts associated with test anxiety, while the last two subscales reflect less test anxiety.
Data analysis
IBM SPSS Statistics for Windows, Version 19.0, manufactured by IBM Corporation, Armonk, NY (IBM Corp., 2010) software was used, and Kruskal–Wallis, Mann–Whitney, and Wilcoxon tests were also used for data analysis.
Results   
Seven students in the VM group and eight in YP group failed to give postintervention data, and were listed as dropouts. Data were therefore analyzed for the remaining 52 students in VM, 51 in YP group, and 50 in CG. Baseline demographic data were not significantly different between the three groups.
Test results are presented in [Table 1] and [Table 3], [Table 4], [Table 5]. [Table 3] presents means and standard deviations of the scores on MARSR for the three groups, pre and postinterventions, while [Table 4] and [Figure 2] summarize prepost differences, giving statistical significances of differences between experimental and CGs. The VM group showed consistent improvements on both LMA and EMA subscales, p < 0.001, while the YP group showed consistent improvements on both subscales at p < 0.01. Controls showed no change in scores.  Table 4: Comparison of prepost differences between experimental and control groups  MARSR
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 Figure 2: Math anxiety postpre mean score comparisons for yoga pranayama, Vedic Mathematics, and controls. Math anxiety postpre difference comparisons for the three study groups from Mathematics Anxiety Rating ScaleRevised. Decrease in math anxiety for yoga pranayama and Vedic Mathematics is significant as compared to controls; p < 0.01 and p < 0.001, respectively. All bars and attached error lines represent means ± standard deviations
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For CCAQ results, [Table 5] presents prepost values of means and standard deviations for the three groups, pre and postintervention period. As hypothesized, both experimental groups showed significant prepost differences, p < 0.001. Significance was less for the On Task subscale, where the YP group attained p < 0.05, while the difference for the VM group was only p = 0.06 only, showing a trend; interestingly, values for controls improved on every scale, but did not reach significance on any.
[Table 1] and [Figure 3] compare the groups' prepost differences showing that relative improvements between CG and the YP groups were significant for the first three subscales, reaching p < 0.01 for the Off Task subscale and p < 0.05 for negative and positive evaluation subscales, but not for the fourth subscale, On Task. Prepost differences were significantly different for positive evaluation between VM and CGs (p < 0.05).  Figure 3: Children's Cognitive Assessment Questionnaire postpre mean score comparisons for yoga pranayama, Vedic Mathematics, and controls. Comparing Children's Cognitive Assessment Questionnaire postpre differences among the three groups. Yoga pranayama group shows significant reduction in negative evaluation (p < 0.05) and Off Task thoughts (p < 0.01) as compared to controls. Yoga pranayama and Vedic Mathematics groups improved significantly in positive evaluation (p < 0.05) as compared to controls. All bars and attached error lines represent means ± standard deviations
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Discussion   
Results confirm experimental hypotheses with good statistical significance, math anxiety reduces most in the VM group (Cohen's d = 0.57 for TMA in VM), and seemingly less in the YP group, though betweengroup differences were not significant. Scores on CCAQ improved most in the YP group, less in the VM group, but not in CG – with a similar caveat (Cohen's d varies from 0.35 to 0.95 for various CCAQ parameters for YP). The immediate scientific question is why should such results obtain?
Systematic reviews of randomized controlled trials (RCTs) of yoga provide much evidence for benefits of YP for anxiety (Sharma & Haider, 2013; Weaver & Darragh, 2015). Changes observed in the YP group are consistent with such predictions and G*Power analysis. Changes observed in the VM group may be attributed to the intervention. Similarly, studies comparing yogic practices to eyesclosed rest obtain different results for experimental and CGs: eyesclosed rest showing little change (Travis & Wallace, 1999). Positive effects observed in the YP group are therefore due to the intervention.
Reasons for using YP comparison group may still require comment. YP practices can be taken as a benchmark with which to compare other methods of anxiety reduction. They are effective for any kind of stressful condition. Evaluation of their comparative ability to reduce math anxiety is therefore relevant.
This study represents the first full study of effects of using the VM approach to maths teaching, though a single case study has recently been published (Pagedar, 2015). Many studies concern effects of regular practice of yoga in the classroom (FerreiraVorkapic et al., 2015). In India, introducing yogic practices is intended to improve the quality of life of schoolchildren, as well as, help decreasing anxiety and depression generated by emphasis on exam performance. Any study providing evidence for benefits to schoolchildren of particular yoga practices is therefore of potential value.
Another angle of investigation is provided by a study of 1345 Filipino engineering students aged 15–25, which showed that, when learning trigonometry, anxiety measured by the Academic Emotion Questionnaire – Mathematics correlates negatively with positive emotions, pride, and enjoyment (Villavicencio & Bernardo, 2016). Findings from our data are parallel to those Spearman's rho between the three subscales of MARSR and the four subscales of CCAQ ranged from ρ = 0.273 to ρ = 0.450, with all highly significant (p < 0.0001). Although the correlations may be expected, since both tests concern quality of emotion experienced by participants, it is of value to see the extent of the correlations.
Conclusion   
This study obtained good statistical significance in all subscales of both tests except the fourth subscale of CCAQ, On Task. These observed prepost improvements were significant at p < 0.05, but did not reach significance between groups. Improvements on other subscales for both VM and YP groups suggest considering VM as a potential teaching aid and yogic breathing as an activity to improve cognitive skills in schoolchildren.
Strengths
The study was a RCT with 59 in VM, 59 in YP, and 50 in CGs. It obtained significant results on all subscales of both tests except CCAQ's 4^{th} subscale.
Weaknesses
The first author is an experienced teacher of both VM and YP. Whether reported results depend on teacher's personal qualities may require further study. However, he also conducted mathematics classes for controls; their lack of improvement tends to discount teacher's personal qualities as the cause of improvements in experimental groups.
Future research
Being the first quantitative study of the effects of VM on math anxiety, results need to be verified by further research. Followup studies including more test variables have been planned.
The first author introduced VM as a means to improve mindfulness (Shastri, Hankey, Sharma & Patra, 2017) and student performance on finalyear professional examinations. A 6year assessment is being made of examination results at the school where the study was performed.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]
