International Journal of Yoga - Philosophy, Psychology and Parapsychology

: 2016  |  Volume : 4  |  Issue : 1  |  Page : 16--23

Efficacy of vedic mathematics and yogic breathing in school children: A pilot study

Vasant Venkatraman Shastri1, Alex Hankey1, Bhawna Sharma2, Sanjib Patra3,  
1 Division of Yoga and Physical Sciences, S-VYASA University, Bengaluru, India
2 Department of Biology, Sri Sai Angels PU College, Chikmagalur, Karnataka, India
3 Division of Yoga and Life Sciences, S-VYASA University, Bengaluru, India

Correspondence Address:
Vasant Venkatraman Shastri
S-VYASA, # 19, Eknath Bhawan, Gavipuram Circle, K.G. Nagar, Bengaluru - 560 019, Karnataka


Background: Anxiety can cause problems in examination performance, particularly mathematics. This study aimed to compare two methods of reducing math anxiety in 8th–10th standards, Yoga pranayama and Vedic mathematics (VM). We report a randomized controlled trial comparing effects of these on working memory, math anxiety, and cognitive flexibility. Subjects and Methods: Forty higher secondary students, resident at Sri Sai Angels School Chikkamagaluru were randomly assigned to Yogic Breathing, VM, and Jogging (JG) groups with 14, 13, and 13 children, respectively. Intervention: Children in Yoga breathing (YB) and VM groups attended 7-days' workshop on Pranayama and VM, respectively. Others went JG every day. Assessments: Mathematics Anxiety Rating Scale-Revised, STROOP test, Children's Cognitive Assessment Questionnaire, and digit span test were administered pre and post the intervention. Analysis: SPSS-17 was used for nonparametric pre-post comparison tests (Wilcoxon) and group comparisons tests (Mann–Whitney). Results: Math anxiety decreased most in VM (−11.77 ± 10.47; P < 0.01). Others: YB (−4.08 ± 4.99; P < 0.05); JG, (−3.75 ± 16.94). Changes in cognitive flexibility and reaction to cognitive stress were VM (++9.77 ± 5; P < 0.001); YB (+5.38 ± 5.38; P < 0.01) and JG (+8.58 ± 9.91; P < 0.05). Self-defeating cognition scores decreased in YB (−1.77 ± 1.83; P < 0.01) and VM (−1.38 ± 3.2), but not JG (+0.67 ± 1.44). Digit span scores were similar in all groups. Conclusion: VM and YB showed small improvement in cognitive skills and decrease in math anxiety compared to JG. The study suggests that a 7-day VM workshop can decrease math anxiety, which might help enhance cognitive skills. Calming effects of pranayama practices are the probable cause for YB group improvements.

How to cite this article:
Shastri VV, Hankey A, Sharma B, Patra S. Efficacy of vedic mathematics and yogic breathing in school children: A pilot study.Int J Yoga - Philosop Psychol Parapsychol 2016;4:16-23

How to cite this URL:
Shastri VV, Hankey A, Sharma B, Patra S. Efficacy of vedic mathematics and yogic breathing in school children: A pilot study. Int J Yoga - Philosop Psychol Parapsychol [serial online] 2016 [cited 2023 Sep 22 ];4:16-23
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To qualify for better career options when leaving school, good abilities in mathematics and associated cognitive skills are important. Students with math anxiety show strong tendencies to avoid mathematics, however.[1],[2] High math anxiety, low working memory, and poor math performance have been shown to be strongly correlated.[3],[4],[5] High math anxiety correlates with low self-concept, suggesting that it deeply undermines student self-confidence.[6] Math anxiety can also influence a student's decision-making abilities [7] so that stressful situations can have immediate physiological impact, for example, difficulty in breathing, increased heart rate, upset stomach, and light-headedness.[8]

Many methods have been studied and applied to reduce math anxiety or to improve math performance in school children.[8],[9] Yoga has consistently proved an effective way to reduce anxiety; the power of Yoga breathing (YB) exercises to do so has been well characterized, and they are now well understood. A completely different approach is offered by the program of Vedic mathematics (VM), which has proved popular in schools that have adopted it and is said to improve performance (James Glover, Kenneth Williams: private communication), though no quantitative results have yet been reported. Out of concern to help improve student performance on professional math examinations the present study aimed to compare the effects of VM and YB modules on math anxiety and related cognitive skills in high school students aged 13–15.

Vedic mathematics

The methods of VM were first suggested by Swami Bharati Krsna Tirtha, the Shankaracharya of Puri (1884-1960), in a posthumously published book of that title.[10] They have been applied in many schools in various different countries worldwide, and widely expanded in their possible applications. High school mathematics has long been a popular application, possibly because before becoming a monk, the Shankaracharya was a teacher of high school mathematics. He may well have tailored his cognitions so that they would have useful applications at that level. They have certainly proved popular in that context, with many students privately reporting greater enjoyment of solving math problems, even those with little previous enjoyment of mathematics.

VM consists of 16 sūtras (formulae), each of which suggests a particular pattern to solve some kind of math problem, along with 16 upasūtras (subformulae). Having learned the sutras and their possible applications, students can then choose whichever most appeals to them to solve any problem with which they are faced. One possible way that VM may help student confidence could, therefore, be by suggesting different strategies involving fewer steps to solve a given math problem. Offering such choice of alternative solutions can help students feel that math classes are entertaining. Classes can become amusing sessions of pattern finding in the form of interesting, alternative VM algorithms, appropriate to solving particular problems. These can be easily and effectively presented by school teachers, and function as teaching aids to handle math anxiety;[11] they also improve cognitive load, so certain VM techniques may be hypothesized to have a positive impact on working memory.

VM is not a new branch of mathematics, but a set of unique approaches to simplifying problem-solving. The sutras and upasutras suggest thinking patterns to help solve arithmetical, algebraic, or geometric calculations common in high school mathematics.[12] VM patterns reduce cumbersome-looking calculations in the conventional approach to simple ones.[13]

They have also been applied in digital signal processing such as construction of shortest algorithms for multipliers in circuits to optimize chip area [14],[15],[16] and other similar applications. In multiplier circuits, the pattern given in the Urdhva Tiryakbhyam sutra gives the most efficient algorithm, minimizing delays for multiplication of all types of numbers.[17] Such applications of VM algorithms improve efficiency of machines rather than mental processes.

Shortened algorithms for mental calculations may impact cognitive processes, however, eventually improving math anxiety and performance.[7] VM methods have not previously been investigated as teaching aids in educational and cognitive research. Here, we report results of using a VM module both to develop cognitive skills and manage math anxiety.

Yogic breathing (pranayama)

Yoga pranayama is well known to improve conditions in both clinical and nonclinical situations. Evidence that pranayama reduces stress levels and improves individual well-being is strong.[18] Pranayama has also been found to decrease state and trait anxiety levels.[19]

Uninostril breathing (left nostril breathing or right nostril breathing) and alternate nostril breathing (Nadishodhana pranayama) can bring positive changes in cognitive tasks.[20] They may help sharpen the critical faculty and creativity and may also bring balance between the left and right halves of the brain.[21] In addition, Kapalabhati, Bhastrika, and Nadishodhana, i.e. both fast and slow pranayamas, and Pranava (OM) chanting can be used to reduce stress levels and to improve cognitive skills, particularly working memory.[22]



Forty boys studying in 8th, 9th, 10th standards, at Sri Sai Angels School, Chikkamagaluru, were randomly assigned to: Yogic breathing group (YB – 14), VM group (VM – 13), and Jogging (JG) group (JG – 13). The design of the study was explained to parents/guardians, and signed informed consent was obtained.


Three group, pre-post random control design [Figure 1]. Randomization was performed using an internet random number generator.[23]{Figure 1}

Assessment instruments used

Mathematics Anxiety Rating Scale-Revised

This 24-item instrument is designed to measure anxiety related to involvement in statistics and mathematic courses.[24] The instrument is a revised version of a 98-item scale by Richardson and Suinn.[25] The current version is more focused on situation specific (state) anxiety, general (trait) anxiety, and test anxiety. The instrument comprises two subscales: Learning mathematics anxiety (LMA) which pertains to the process of learning of math and statistics; and evaluation mathematic anxiety (EMA) measuring anxiety over tests on math and statistics. The sum of LMA and EMA is taken as total mathematics anxiety (TMA).

Scoring - Respondents rate each item on a 5-point scale from “low anxiety” to “high anxiety.” Scores are the sum of the item ratings and range from 24 to 120 for the total scale.


The STROOP test consists of three subtasks measuring cognitive flexibility, creativity, and reaction to cognitive stress.[26] J.R. Stroop first developed it in 1935.[27] The test consists of three subtasks. The stimulus material for each of these subtasks is shown on a white sheet of paper. The 100 stimuli for each subtask are distributed evenly in a 10×10 matrix on each sheet of paper. The first subtask shows colour words in random order (red, blue, yellow, green) printed in black ink. Subtask 2 displays solid colour patches in one of these four basic colours. The third subtask contains colour words printed in an incongruous ink colour for example, the word yellow printed in red ink. The subject's task on the word subtask is to read aloud the colour words; on the colour to name the coloured patches or asterisks; and on the colour word to name the colors of the ink, ignoring the printed color word. Maximum of 45 seconds per subtask was given to the subject. Scoring was done using number of item completed on each subtask.

Children's Cognitive Assessment Questionnaire

This 40-item instrument measures self-defeating and self-enhancing cognitions associated with test-anxiety.[28] The instrument was originally developed for hypothesis testing on the relationship between cognition and test-anxiety or task performance. The theoretical perspective asserts that self-defeating thoughts inhibit performance while self-enhancing thoughts facilitate it. The Children's Cognitive Assessment Questionnaire (CCAQ) focuses on negative self-evaluations (NSEs) and positive self-evaluations as reflecting self-defeating and self-enhancing cognitions, respectively. It also assesses self-distracting thoughts (“off-task thoughts;” [OFFT]) and cognitions which focus one's attention on the task (“on-task thoughts”). The CCAQ uses these four aspects as subscales.

Scoring - Each of 40 items is answered true or false, scoring 1/0. Total score for each subscale is the number of items answered “true”, ranging from 0 to 10. Higher scores reflect more thoughts indicative of test-anxiety.

Digit span test

This test measures working memory.[29] Here, we used the 2011 computerized version of the Digit span test developed by Inquisit software.[30] Each participant is given 14 trials observing a sequence of digits (starting with three digits-level 3), presented for 1 s each, after which the participant is asked to recall the digit sequence and type the answer into a presented textbox. If the response is correct (in digits and presentation order), the participant moves up to the next level (e.g., level 4). If the response is incorrect, the same level is presented a second time. If a consecutive error occurs, the participant moves back down to a lower level, starting over.

The first time a participant makes a consecutive error, span is set to the last correctly recalled number of digits (e.g., if participant reaches level 8, but answers incorrectly both times, the span is set to 7).


YB group and VM group students attended workshops on Pranayama and VM (Appendix I), respectively, (30 min at 6.00 am and 6.30 am, respectively, every day for 7 days). Those in the JG group went for 30 min JG every day at 5.30 am.

Data extraction

Mathematics Anxiety Rating Scale-Revised (MARS-R), CCAQ, digit span test and STROOP test were given at baseline, and after the 7-day VM and YB workshops were completed.

Data analysis

The data were analyzed using SPSS 17.0 (Seattle, Washington, United States). Due to small group size, nonparametric tests were used: Mann–Whitney test for inter-group comparisons and Wilcoxon test for within group pre-post comparisons.


There were no baseline differences between the three groups in all the variables studied except offtask thoughts for the JG Group, for which the baseline score was significantly different from other two groups (P < 0.05).

Results for the three groups, YB, VM, and JG, were as follows:

Math anxiety Rating Scale

VM group showed significant pre-post differences in TMA (pre 57.85 ± 14.43; post 46.08 ± 14.38; P < 0.01), LMA (pre 34.69 ± 8; post 29 ± 9.23; P < 0.05), and EMA (pre 23.15 ± 7.8; post 17.08 ± 6.22; P < 0.01) [Table 1].{Table 1}

Yoga group showed significant differences in MARS-R in pre-post measures. Of the two subsets, EMA was significantly different between pre-post measures (pre 20.85 ± 7.35; post 17.15 ± 4.38, P < 0.05), but not LMA; TMA was still significantly lowered (pre 51 ± 14.3; post 46.92 ± 12.63, P < 0.05) [Table 1].

JG group showed no significant differences between pre-post measures [Table 1].

Comparisons of pre-post differences between the three groups: LMA and TMA differences between Yoga pranayama and VM groups were significant (P < 0.05) [Table 1]; this could have been due to lower pre values in yoga group. In contrast, the JG group was not significantly different in any of the three parameters from either of the other groups [Table 1].


VM group showed significant difference in color score (pre 61.23 ± 7.44; post 66.85 ± 10.64; P < 0.05) and color word (pre 34.15 ± 7.45; post 43.92 ± 9.06; P < 0.001). Pre-post differences in means of color word were not significant [Table 2].{Table 2}

YB showed significant difference in color word test of the STROOP test (pre 35.46 ± 5.98; post 40.85 ± 7.89; P < 0.005) [Table 2].

In JG group, significance was observed in word score (pre 86.58 ± 13.27; post 93.5 ± 12.38; P < 0.05) and color word (pre 31.33 ± 6.4; post 39.92 ± 9.03; P < 0.05) [Table 2].

No significant difference was observed between three groups on the STROOP test.

Children's Cognitive Assessment Questionnaire

VM group showed highly significant difference in pre-post values of OFFT (pre: 6.08 ± 1.61; post: 2.62 ± 2.66; P < 0.001) [Table 3].{Table 3}

YB Group showed significant improvement in lowering NSE (pre: 2.77 ± 2.01; post: 1 ± 1; P < 0.01) and OFFT (pre: 5.54 ± 2.57; post: 3.38 ± 2.36; P < 0.01) [Table 3].

JG group also showed significant difference in pre-post values of OFFT (pre: 7.42 ± 2.91; post: 5.92 ± 2.35; P < 0.05) [Table 3].

Pre-post differences analyses between the three groups suggest that YB and JG were significantly different in NSE (YB: −1.77 ± 1.83; JG: 0.67 ± 1.44; P < 0.05) [Table 3].

Digit span test

All the three groups performed equally in forward and backward digit span tests [Table 4].{Table 4}


This paper reports comparative effects of three interventions on math anxiety by MARS-R; cognitive flexibility and selective attention by the STROOP test; self-defeating and self-enhancing thoughts by CCAQ; and working memory by the digit span test. All three interventions appeared to influence the various measured parameters, to varying degrees.

Math anxiety with its two subscales, learning math anxiety, and evaluation math anxiety is the primary variable. VM brought the most benefit for math anxiety levels, followed by YB [Figure 2]. JG did not reduce Math anxiety levels to any significant extent. Why the VM group received the most benefit compared to the other groups is obvious: it directly enhances math problem-solving skills bringing confidence to students concerned about math ability.{Figure 2}

The VM group also showed the greatest improvement on the STROOP test [Figure 3]. The JG group's initial values were lower than those of the other two groups on word score, and its final (post) value did not even reach the pre-values of the other two groups [Table 2] and [Figure 3]. These measurements seem confusing and require further investigation.{Figure 3}

Scores on the CCAQ test measuring self-defeating and self-enhancing thoughts improved most for the Yoga group followed by the VM group [Figure 4]. The JG group's initial negative evaluation increased but not significantly [Table 3].{Figure 4}

The digit span test, which measures working memory and focused attention,[31] did not show significant change after any intervention, nor between any pair of groups [Figure 5]. This result may be due to low sample size and the short intervention period. It needs further investigation.{Figure 5}

Overall, VM tended to show greater results than the other interventions on all parameters. VM offers different possible strategies of mental calculation in smaller numbers of steps, bringing “a feel-good factor” to solving lengthy problems. Its methods promote pattern recognition in math,[32] introducing a fun element, possibly by stimulating “feel good” neurotransmitters release (dopamine, serotonin, and an array of endorphins).[33] Improvement in working memory, and reduction in math anxiety result.

YB practices, including repetitive chanting of A, U, M, OM, and generating a humming sound in Shambhavi Mudra, may stimulate the brain, eventually yielding stronger pattern recognition.[34] They may also stimulate the dopamine and endorphin system.[35] Cognitive flexibility, creativity, and reaction to cognitive stress and math anxiety all improve slightly.

Yogic breathing brought greater improvements in CCAQ than the other interventions, strengthens the impact of Yoga in decreasing stress and improving self-concept and self-esteem,[36] which may lead to greater self-confidence, and result in better performance.[37] This may also lead to reduction in math anxiety.

The combined effect of these practices may therefore be of value in managing math anxiety and enhancing cognitive skills. The study brings a new understanding of VM and may introduce a new domain for its application. It also offers reasons for including VM and Pranayama, individually or together, in the school curriculum.

Strength of the study

Observed improvements in working memory, math anxiety, and focused attention, resulting from learning VM are new, as are those produced by practicing pranayamṃ


As a pilot study, the sample size was too small to draw any strong conclusions. The intervention of 1 week is not enough make results conclusive.

Further research

Follow-up studies with larger group sizes are called for – one such has recently been accepted for publication;[38] also studies investigating mechanisms behind the observed changes.


The VM and YB modules were found useful in decreasing math anxiety, self-defeating thoughts and improving cognitive flexibility and self-enhancing thoughts in school children. Increasing sample size and intervention time may help generate stronger conclusions, and thus provide the grounds for implementing both techniques in school curriculṃ


We would like to thank Sri Sai Angels School for providing subjects, place, and equipment to carry out the study. We would like to acknowledge Mr. Manjunath BS for technical support during data collection.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.


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