DR. LALIT KISHORE

Title of research studyExploring and Identifying Applied Mathematics for

Action Research by School Teachers: A Research and

Development Initiative 

Applied Math (AM) and its significanceLalit Kishore (2011): AM said in cinquain – Five-line French

pattern language art form “Applied mathematics / Mathematical science with boundaries-

breaking specialized knowledge, useful mathematics for life and work / Using mathematical methods for other academic disciplines and vocations; finding applications of mathematics to make other knowledge areas precise; bridging the cross-curriculum gaps / Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry ~Wikipedia / Adapted contextual mathematics.”

Applied mathematics is able to break the abstract image of mathematics by establishing its utility in life, livelihood, professional development and other areas of study.

Overview-1Bhatt and Singh (1993), the common shortcomings of mathematics instruction

are – that it is not integrated with the curricula of other

subjects; there is a lack of technical applicability of mathematics to daily life and other courses;

– that there is an over-emphasis on conventional method of ‘chalk and talk’ that sans logical thinking.

However, there’s hope– that Mathematics has vital importance in educating

technicians, workers and commoners for its implications.

– To produce learning materials on applied mathematics right from school level.

Overview-2Wartikar and Wartikar (1987) stress the need of

identifying relevant examples and practice exercises to introduce applied mathematics for :various knowledge areas; trades; and daily life situations.

On the other hand, Dasgupta (2000) opines that applied mathematics can extend the border of

classroom and for this relevant mathematical methods should be included for learning of every subject area for an enhanced visibility of application of mathematics in them.

OVERVIEW-3Lambour and Tinker (2000) observe that

applicable mathematics is invariably included applicable mathematics is invariably included in the teaching of physical sciences at every in the teaching of physical sciences at every

levellevel

ButBut

it needs to be extended to all knowledge areas it needs to be extended to all knowledge areas and vocations tooand vocations too

Overview-5There exist rare instances of applied mathematics

for linking it to action research. According to Kishore (2009), action research and

appreciative inquiry method can be very helpful to transform teachers into learners to improve themselves and their classroom practices.

Educational institutions should promote action research to transform teachers into learners along with

the training in appropriate applied mathematics.

Methodology

The objectives of the study were as follows.To identify non- parametric statistical

techniques for action research; To formulate the analytical table for summary

of action research data; and To validate the applied mathematics

techniques with five teachers.

Method• A mini focus group was organized (N=3, time: 1

hour) to work out the useful statistics for action research. The focus group recommended that non-parametric statistics which is quick and suitable for small groups needed identification and listing out for action research and improve teaching practice.

• According to Kishore (2011), the mini-focus group method consisting of three members is being used frequently for qualitative research in which a group of well-informed professionals or respondents express their opinions, notions, precepts, and attitudes towards a concept, process, idea, or product. The method is considered appropriate for quick research like action research

Focus group: Keyword explained• Kishore further states that focus group provides

subjective data from experts with reasonable validity with low costs and quick results. He describes focus group in the form of a pedagogic cinquain as follows: – “Focus Group / Small group of three to twelve well-

informed persons, moderated specific discussion or interaction /Raising closed questions or topics, moderating discussion, recording and distilling relevant knowledge / The various kinds of focus groups are: face-to-face focus group; two-way focus group; dual moderator focus group; duelling moderator focus group; teleconference and on-line focus groups /Topics-contained informed interaction.”

Development• The scanned three book resources (Grarrett,

1981; Hildard et al., 1975; Levin & Rubin, 2001) and identified the suitable statistics which could be quick to provide the immediate feedback to the practitioner to improve himself or herself.

• The identified methods were shown to the focus group members for validation and they agreed with the identified methods and suggested for developing a mini-book as a ready-reckoner for teachers to analyze the classroom observations during teaching sessions and make recommendations to improve own practice.

Results-1On the basis of the present action research, which

involved a focus group and this investigator took 15 days with one hour daily on the work, the following results were achieved.

Quick distribution-free non-parametric statistical techniques are suitable for classroom research, teacher-designed pedagogical experiments, intervention based on theory-into-action ideas and action-research for practice improvement.

Such techniques do not require (i) setting up of precise experimental and control

groups; and (ii) a positive hypothesis.

Generally, single group of small size as a quota sample is available for the teacher to turn classroom as an educational laboratory for evidenced-based dynamic teaching. This was the concluding remark of the focus group discussion.

Results-2• Chi-square test with 2×2 contingency table of classified

observations or data is easy for a given small sample for testing independence between attributes of classification. It can address the issues like: Do boys perform better than girls in mathematics in the conventional teaching or through which method results in better performance for both boys and girls in mathematics?

• Favorability of an intervention on three point scale (favour, neutral, unfavour) as compared to those expected theoretically as equal distribution on the each point of the scale can decided using chi-square test..

Implications• Action research with use of non-parametric

statistics needs to be promoted for evidence based improvement of classroom practice of teachers. Use of applied mathematics for classroom research should be made a part of teacher development both in the pre-service and in-service teacher trainings.

• With promotion of action research by Sarva Shiksha Abhiyan, it becomes all the more desirable to include appropriate applied mathematics as a part of teacher development in a formal way. 

• The implications of this research are in the form of training of teachers in action research and field testing of the identified statistical techniques for classroom research by the investigators and action research enthusiast. Action research and statistical techniques suitable for distribution free sample giving reasonable estimates of results need to be promoted for self-development of practitioners.

Conclusion

The conclusion of the present R&D study is in the form of a recommendation that for continuous development of teachers as classroom practitioners through action research, they need be made well-versed with non-parametric statistical techniques.

ReferencesBhatt,N.R. and Singh, R.M.(1993). Applied Mathematics, New Delhi : Tata

McGraw-Hills.Dasgupta.B. (2000). Applied Mathematics, Delhi: Dorling Kindersly-Pearsons

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education. Bombay: Vakils, Feffer and SimonsHilgard, E. R. et al. (1975). Introduction to Psychology, New Delhi: Oxford &

IBH.Kishore, L. (2009), Action research helps teachers to be learners, merinews, Aug

28, www.merinews.comKishore, L. (2011), Applied mathematics: A pedagogic cinquain, cplash,

December 9, www.cplashKishore, L. (2011). Focus Group: A short note and a cinquain, cplash, December

13, www.cplashLambourne,R. and Tinker,M.(2001). Basic Mathematics for physical science,

Chickester: John Willey.Levin, R.I. and Rubin, D.S. (2001). Statistics for management, New Delhi:

Prentice-Hall of India.Wartikar, J.N. and Wartikar, P.N. (19987), Applied mathematics, Pune: Pune

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