A Study Of The Use Of Mathematics Laboratory For Teaching Mathematics By Developing A Strategy And Testing Its Effectiveness
November 4th, 2010 | 
Author: A Study Of The Use Of Mathematics Laboratory For Teaching Mathematics By Developing A Strategy And Testing Its Effectiveness
Guide: Dr.S.S.Chaugule, Reader & Head Special Project Research Centre, YCMOU, Nasik, Maharashtra
Research student: Donnipad Manjunath
INTRODUCTION:
Mathematics, according to National Education Policy 1986, should be visualized as the vehicle to train a child to think, reason, analyze and articulate logically. Apart from being a specific subject, it should be treated as a concomitant to any subject involving analysis and reasoning. With the introduction of computers in schools, educational computing and emergence of learning through understanding of cause-effect relationships and the interplay of variables, the teaching of Mathematics will be suitably redesigned to bring it in line with modern technological devices so that learning takes place effectively.
Learning often takes place best when students have opportunities to express ideas and get feedback from their peers. But for feedback to be most helpful to learners, it must consist of more than the provision of correct answers. Feedback ought to be analytical, to be suggestive, and to come at a time when students are interested in it. And then there must be time for students to reflect on the feedback they receive, to make adjustments and to try again- a requirement of mathematics education that was neglected, due to rigorous practice of traditional methods of teaching. It was also observed that; students who frequently try to solve exercises related to new mathematics topics by finding the inter-connections and who discuss practical problems related to everyday life tend to score good in mathematics examinations. Teachers, who use of active learning strategies like students working on mathematics projects, connecting mathematical knowledge to everyday life when solving mathematics problems and actively participating in peer-group interaction have always significantly contributed to good performance in mathematics.
The traditional didactic methods of teaching are no longer adequate to meet the demands of mathematics education in line with National Education Policy 1986. In the light of National Education Policy 1986, to develop the skills reiterated in the policy and to provide practical experience of mathematical concepts, assumptions, assertions and rules, an appropriate method of instruction or a strategy for teaching mathematics and a suitable platform to use such strategy is the need of hour. “Any idea or a concept presented in a simple & appropriate form and the way that is suitable to learner’s ability and aptitude provides the best of understanding of it (Bruner 1966)”.
Every student has a unique way of thinking, learning and making sense of what he/she listens or observes. Their active imagination constantly builds new connections and assimilates new information. If the teacher is active speaker and persistently using traditional methods, the learning takes backseat and in the process some faulty ideas can also form and lead to several learning gaps. These learning gaps need to be identified, questioned and corrected before they result into misconceptions. These misconceptions lead to low self- efficacy among students resulting low performance in the subject of mathematics. Learner learns faster, when he is influenced by his peer group and developing a sense of positive interdependence, besides reducing the role of teacher to facilitator. However, reducing the role of a teacher to facilitator and creating an atmosphere of positive interdependence among students, a change in methods of teaching is inevitable requirement. In a normal course of teaching mathematics in a classroom, creating such atmosphere as mentioned above is not possible.
So, a strategy for teaching mathematics in a different but suitable atmosphere that would transform the position of the teacher to facilitator of learning from an authoritarian and active speaker’s role was the need of the hour. Hence this experimental study was taken up.
OBJECTIVES:
1. To find out various methods being used in teaching Mathematics in regular classes
2. To find out teachers views about Mathematics Laboratory
3. To develop a strategy to be used in a Mathematics Laboratory set – up.
4. To test the effectiveness of the strategy developed for teaching in Mathematics Laboratory set-up
5. To suggest recommendations for the development of Mathematics Laboratory and training of Mathematics teachers
HYPOTHESIS
There was no difference between teaching Mathematics through Traditional Methods of teaching to that of teaching through a strategy developed for teaching mathematics in Mathematics Laboratory atmosphere.
ASSUMPTION
Teachers were not using Mathematics Laboratory as a platform for teaching Mathematics
LIMITATIONS OF STUDY
The study was limited to only Kendriya Vidyalayas’ functioning in & around Nasik district and schools governed by State Government and affiliated to Central Board of Secondary Education as well. The students’ sample of study was limited to class 10th students of Kendriya Vidyalaya, AFS Ojhar Nasik District, while teachers’ sample was limited to schools functioning in and around Ojhar, Nasik District. The investigation did not develop any standardized tests or psychological tests for the purpose of study, but prepared a questionnaire and got validated by experts from Department of Education, Yashwantrao Chavan Mahrashtra Open University.
VARIABLES OF THE STUDY
INDEPENDENT VARIABLE
Use of Strategy evolved to teach mathematics in a Mathematics Laboratory
DEPENDENT VARIABLE:
Performance of students and improvement in their result
SAMPLE OF THE STUDY
For this experimental study purpose, two different samples were chosen namely students’ sample and teachers’ sample. The students’ sample of the study consisted of a total of 80 students of class X standard of Kendriya Vidyalaya, Ojhar and while teachers’ sample consisted of 100 teachers of mathematics working in schools in & around Ojhar Nasik District
The sample of 80 students was divided into two groups’ viz., controlled and experimental group. The two groups were matched on the basis of their marks obtained in class IX on the basis of Continuous & comprehensive evaluation, a criteria being used in all Kendriya Vidyalayas’ for assessing the performance students at the end of an academic year.
The sample of 100 teachers from Primary to senior secondary level was chosen. However, 80% of teachers chosen were secondary teachers who handled class 10th Mathematics.
TOOLS
Tools like questionnaire, Visits, Observations and Interviews were used in the study. Various Mathematics Laboratories located different parts of country were visited and observations were recorded, besides visiting online Laboratory at Lower Columbia College, Washington State University, USA. Mathematics Laboratory at NCERT, New Delhi, Ramanujam Institute of Mathematics Learning Chennai, Mathematics Laboratory in Mysore based schools functioning at Bangalore and Mathematics Laboratory at Homi Bhabha Science Education Centre, Mumbai and Department of Mathematics, IIT, Powai, Mumbai were visited and Interviews were conducted on various strategies and techniques being employed to carry out the activities in Mathematics Laboratory. Based on recorded observations and Interviews from Head, DESM, NCERT, Laboratory curators at Chennai and Bangalore questionnaire consisting of 18 questions was prepared to administer among 100 teachers selected as teachers’ sample study.
RESEARCH DESIGN
The research design of the study was “Two Groups Posttest Experimental Design”. Two groups namely, Control group and Experimental group were taken with each of them having a total of 40 students. The Research Methodology was Quasi Experimental Research Methodology.
STRATEGY EVOLVED FOR TEACHING MATHEMTAICS IN A MATHEMATICS LABORATORY
A strategy consisting of three different methods namely; Expository method, Cooperative Learning Method and Problem Solving method coupled with Modelling was evolved. These three methods were administered as one unit but in three stages while teaching mathematics in a Mathematics Laboratory. Each stage was defined with specific input and anticipated output. The role of teacher was active during first stage as teacher teaches mathematics using Expository method and during later two stages where Cooperative Learning at 2nd stage and problem solving coupled with modelling at 3rd stage the role of teacher is a facilitator of learning. At 3rd stage teacher’s role is not only a facilitator of learning but also ensures a learning outcome viz., social relevance of knowledge being assimilated by students.
PROCEDURE OF THE RESEARCH
¬ Mathematics Laboratories functioning at NCERT, New Delhi and few other Laboratories located in different part of the country were visited to record the observations on the use of Mathematics Laboratory in day-to-day teaching leaning process. Interviews of Heads and Laboratory curators were carried out. ¬ Laboratories functioning abroad visited online and observations were made. Interviews were also carried out with a Lab Head-cum-Teaching assistant of college of Lower Columbia, USA. ¬ Suggestions and guidance seeking mail correspondence was done with a senior Lecturer, Department of Mathematics Education, Education, School of Education, University of East Anglia Norwich. These suggestions and guidance were sought before preparing the questionnaire and formulating the strategy for teaching mathematics. ¬ On the basis of observations and interviews, a questionnaire consisting of 18 questions was prepared and was validated by two experts, Department of Education, Yashwantrao Chavan Maharashtra Open University, Nasik ¬ Questionnaire was administered among those 100 teachers selected to gather their views and opinion on use of Mathematics Laboratory, various Teaching Methods and use of software in teaching mathematics. ¬ On the basis of responses; a statistical analysis and interpretations were drawn and then, a strategy consisting of three methods; viz., Expository method, Cooperative Learning Method and Problem Solving method coupled with Modelling was developed. ¬ The strategy evolved was used for 10 weeks on the Experimental group to teach mathematics in a Mathematics Laboratory atmosphere. The control group was taught the same mathematics content using normal classroom teaching. ¬ The methods of teaching mathematics to control group were Traditional methods. The lesson plans (excluding the method of teaching and Mathematics Laboratory), worksheets and modules were the same to both control and Experimental groups. ¬ At the end of 10 weeks; a Posttest was administered to both groups to evaluate and assess the performance of students. Meanwhile the data gathered through Questionnaire administered on teachers of mathematics and posttest administered on students was analyzed and Hypothesis was tested using statistical test of significance. ¬ Hypothesis was rejected on the basis of statistical inference drawn and concluded that; the strategy evolved to teach mathematics in a mathematics laboratory was effective than the traditional methods of teaching.
FINDINGS
¬ Teachers who were trained through behaviourist model were not aware of methods like cooperative Learning; guided-Expository and problem-solving method integrated with modelling. So, these methods were less preferred to teach mathematics as compared to traditional didactic methods like Lecture; Lecture-Demonstration methods ¬ Mathematics laboratory is not an integral part of curriculum framework in Maharashtra. ¬ Mathematics laboratory cultivated research attitude among students, when it was integrated with strategy evolved ¬ Mathematics Laboratory and its utility were given less importance during teaching degree pursuit. Majority of in-service teachers lack the knowledge of the modus-operandi using mathematics laboratory for teaching mathematics at school level. ¬ Majority of teachers were not given in-service training in using computers and software to teach mathematics. ¬ Use of computer and mathematical software to teach and provide conceptual knowledge of mathematics in a Mathematics Laboratory yielded positive reinforcement among students. ¬ Use of computers and allied software was not in the curriculum of teaching degree pursuit. Hence teachers of mathematics were not aware of using computer and allied software to teach mathematics. ¬ Strategy evolved to teach mathematics helped in effective content management. ¬ Computer and mathematical software used in Mathematics Laboratory has provided hands-on experience of mathematical knowledge taught ¬ The strategy evolved has also helped students to know the social relevance of knowledge learnt. ¬ 3rd stage of the strategy helped teacher to create learning problems and situations that will actively involve students and stimulate interest in how mathematics is applied in real life situations. ¬ There is significant difference between the mean scores of Experimental Group and Control group. The t-test revealed that the t-value statistically arrived was 5.59 for the degree of freedom 78. When t-value was compared with 0.05 level and 0.01 levels of significance for the same degree of freedom, the t-value arrived was significantly greater than both levels of significance. So, the strategy evolved for teaching mathematics in a mathematics laboratory was effective than didactic traditional methods.
RECOMMENDATIONS
¬ The teachers of mathematics shall the newly developed methods or strategies to teach mathematics instead of following age-old methods of teaching. ¬ The teachers shall use the strategy evolved for teaching mathematics in mathematics laboratory to enrich their teaching experiences. ¬ Mathematics laboratory should be made an integral part of curriculum of mathematics ¬ Mathematics Teaching could be carried out in a Mathematics Laboratory by integrating mathematics laboratory into regular curriculum. ¬ A specific curriculum in the form of credits shall be prescribed as regular syllabi for Mathematics Laboratory and could be made it mandatory to students to complete. ¬ Process of Evaluation and Assessment shall be based on minimum number of credits completion. Completion of this minimum number of mandatory credits by each student at each class could be made mandatory. Promotion to next class could be linked with this mandatory completion. ¬ Process of Evaluation and Assessment techniques shall be changed to a different format such as making rubrics for positive interdependence, group investigation skills etc., so that; academic performance of students could be improved along with social skills and peer interaction. ¬ Teaching through computers shall be introduced in the Basic teaching degree pursuit. All the pre-service teachers shall get ample exposure in using embedded atmosphere to teach mathematics. ¬ All In-service teachers shall be given training in Information & Communication Technologies, so that; the teaching experiences could be enriched. Pre-service teacher-students be given an exposure to Mathematics Laboratory and its usage in teaching mathematics. Techniques or strategies to integrate it ICT shall be taught during their teacher education programme. ¬ Addition human resources with mathematics background could be given for mathematics laboratory so as to enable the students to use the laboratory not only during their allotted periods, but also during leisure periods ¬ In every school Mathematics Laboratory shall be established and teaching of mathematics shall be carried out through mathematics laboratory.
EDUCATIONAL IMPLICATIONS
This study has an influence on the initiation of using mathematics laboratory in teaching of mathematics at secondary level. As the need for good strategy for teaching mathematics so as to improve the result and performance of students in board examinations, the study has thrown a light on the use of appropriate strategy that is the integration of three methods of teaching namely Expository, Cooperative and Problem Solving method coupled with Modelling in a laboratory atmosphere. As per this study, use of strategy evolved for teaching mathematics in a Mathematics Laboratory as described there are States like Mahrashtra where Mathematics laboratory is not an integral part of curriculum framework. So this study signifies that, mathematics laboratory could be made an integral part of curriculum framework and create mandatory use of lab for teaching mathematics. The ultimate result of the study revealed that; strategy was more effective instructional paradigm for teaching mathematics as compared to traditional methods of teaching. Furthermore, mathematics laboratory appeared to be a befitting platform for creating positive interdependence as compared to classroom.
CONCLUSION
The study established that; traditional didactic methods of teaching do not facilitate learning by understanding nor provide opportunities to students to relate their knowledge with real life, besides making low performers in the subject of mathematics. It was further established that, use of strategy evolved integrating three different methods for teaching mathematics in a Lab atmosphere yielded improved performance of students. So, the study found a positive and significant correlation between the academic achievement of secondary school students and the use of different methods of teaching in a Laboratory atmosphere. Hence, teachers teaching mathematics shall use Mathematics Laboratory as a platform and by using the strategy or any method other than didactic methods to make a significant impact in the knowledge construction so as to improve the performance of secondary school students.
REFERENCES:
Alyas Qadeer Tahir, (2005), “A Comparative Study of the Effect of use of Information and Communication Technology in Varied Teaching Approaches on Achievement and Retention of Students of Mathematics, Gomal University, Pakistan. Anderson, H (1989). The mathematics Teaching Around the World, Mathematics Teacher, 5 (I), 13 – 17 Bhalwankar, A.G. (1985); A Study of Effects of Expository and Guided Discovery Methods of Teaching Mathematics on the Achievement of Students of Different Levels of Intelligence; Pune University, Pune Bharadwaj (1987); Standardization of Comprehensive Diagnostic Test and preparation of Remedial Material in Mathematics for Middle Standard students of Haryana; Kurukshetra University. Bernard Cohen, Sidney M. Edelstein Lecture, Baylor School, Kenneth Tobin, Research on Science Laboratory Activities: In Pursuit of Better Questions and Answers to Improve Learning, School Science and Mathematics, 90 (5), May/June 1990, p. 414. Buch M.B., Fourth Educational Survey (1983-1988), Volume – I, published by NCERT, Ministry of Human Resources Development, Government of India, New Delhi Buch M.B., Fourth Educational Survey (1988-1992), published by NCERT, Ministry of Human Resources Development, Government of India, New Delhi Dave, R.H., & Saxena, R.C. (1965), Curriculum & Teaching of Mathematics in the Higher Secondary Schools, NCERT, New Delhi David, W. Johnson (1994): Learning Together; Westport press, Connectuit, London Dutta, A., (1986), Bruner, J. (1966). Toward a Theory of Instruction. Cambridge, MA: Harvard University Press. Iqbal Muhammad (2004); Effect of Cooperative Learning on Academic Achievement of secondary school Students in Mathematics; University of Arid Agriculture, Rawalpindi Jain, S.L.; Burad. G.L. (1988) for Rajasthan Secondary Education Mathematics; Kasat, B.S. (1991) for Palghat Tehsil Chel, M.M.; (1990) for West Bengal Secondary Education Mathematics; Fifth Educational Survey (p.371 – p.375) Prof. Ramanujam, R. Dr. Ravi Subramanian & Group (2006) Position Paper – National Focus Group on Teaching of Mathematics – National Curriculum Framework (2005), NCERT publications, New Delhi Methods of Communication, A book for M. Ed students of YCMOU Nasik Mathematics Laboratory – Guidelines to Schools, Central Board of Secondary Education (2005), New Delhi Lulla, B.P., Shah, G.B.; & Darji, D.R.; (1966); An Investigation into the Academic Causes of Backwardness in Mathematics at the Elementary Stage (Classes I – VII); Centre of Advanced Study in Education ; Baroda
Working as a teacher in Christian missionery schools functioning in India. Teaching standard K – 12 Mathematics. Doing research work in Mathematics Eduacation.
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Question by canonize: Should all high school students have classes geared toward college entrance?
All high school students in my school district in California are being forced to take a college preparatory list of classes for graduation including advanced mathematics, English, and laboratory science. Almost no shop, work preparation, or skill based classes are offered. Do you feel we should do this or should we offer a lower academic level of classes for graduation for students who do not plan on entering a 4 year university?
Best answer:
Answer by drip
NO! Just because a student does not plan on attending a four year college doesn’t mean these classes will not enrich and help them in what they do end up doing.
What do you think? Answer below!
Posted in Mathematics Laboratory
I suppose the good thing about it is that the students who do go to college will be better prepared to do so. And…at least they aren’t learning how to take standardized tests – they’re actually learning something which in this day and age isn’t just good, it’s great!! I teach at a university and some of the people who go through my classes have never really been prepared for the rigors of collegiate life – but they know how to take a standardized test – so kudos to your school district for at least preparing them. However, as you point out, despite the fact a college degree is a necessity to get ahead in the world, there are people who are going to become mechanics, plumbers, electricians, and sad to say, those who work at the counter at McDonald’s. These students – I’m assuming there is some sort of aptitude test given at some point – who are more skilled at working with their hands and who possess poor study habits that will probably never be changed deserve the same consideration as their college-bound classmates. Let’s face it, where would we be without those mechanics etc.? I know I’d be up that proverbial creek without a paddle since I know nothing about automobiles and if I attempted to do my own electrical work I could probably burn the house down in a matter of minutes not to mention flooding the place if I tried to do plumbing. These are people who are important to our well-being and way of life and for a school district to arbitrarily assume that everyone is going on to college isn’t right. Although I work in education, I find some of my colleagues to be deadly boring when it comes to conversation and at times its easier to talk to the guy who comes to fix my air-conditioning and where would we be without them? Overall, it would seem your school district has its heart in the right place and has good intentions, but hasn’t taken into consideration the need for people to work in these service-oriented fields and they are just as important as we are – and in some respects, maybe more important!!
I used to think black and white, clear cut, everyone should take classes that will prepare you for college. You say you don’t want to go to college? Well, some day you might, so suck it up and take Chemistry and English 4.
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Since moving to my current district, however, my views have changed somewhat. I now teach in an extremely low income, rural area in a very low ranked school with all of the attendant problems. Over 90% of our students receive free or reduced lunch and many of them only come to school for that reason. All of the time I have teachers tell me that I’m lucky that I teach 11th grade because our drop out age is 16 and “most of the bad ones (and low scorers) have been weeded out by then.” I also teach a state tested EOC class with a curriculum that would stymie many a college student (seriously, check out http://www.ncpublicschools.org/docs/curriculum/socialstudies/secondary/honorsushistory.pdf and imagine trying to learn all of that in 85 days).
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I so hesitate to say, yes, we should lower our expectations for some students, not all of them can or should go to college, but the reality is, most of mine can’t or wont. Or if they do get in they will never be able to graduate. I wish that our school district would still expect students to take most of those college preparatory classes (in the core subjects) but, instead of offering electives like Music Appreciation and Teen Living, that they would aggressively foster relationships with local companies and offer students the opportunity to complete internships in various fields for course credit. I guess I’m kind of wishing for the best of both worlds here, rigorous academic classes and opportunities for vocational growth and networking all put together. I think it is possible, but it would require a serious re-imagining of how we expect our schools to function and how we measure them.
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Interestingly, this subject comes up every semester in my classes when we discuss the Booker T. Washington v. W.E.B. DuBois debate. The class almost always comes down on the side of DuBois, insisting that everyone in school should get a college prep education. I don’t know if that says something profound, or if it just says that they have absorbed the ideals of our school systems well enough to be able to spit them back at me.
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However you look at it, this is a problem that, to me, has no really satisfactory solution.
Layyla, I personally don’t believe that every child, or even up to half of the children in school are geared towards higher educational goals. So my answer is no. many school districts now are recognizing this and designing charter schools and programs that suit a wider range of abilities and goals.
In our school district a child may decide to become a bricklayer, carpenter plumber or general contractor. Working with their respective unions, the schools offer apprenticeship programs beginning in 10th grade. If a child wants to pursue engineering, the arts or or other creative program, specific charter schools will help him reach those goals. What this has done is focussed the entire college prep program including the exam on those children who truly want to go on to college. It is a much more cost effective way to deliver targetted educational results to specific and highly individual needs.
Those who are slated to be tested have the added bonus of field trips to nearby universities and parent/child weekends at their prospective colleges of choice. It seems to me this type of tailored programming is very beneficial for our children.
Not everyone is meant to go to college. I’m not sure about offering a lower academic level for students not going to a 4 year college but I also don’t want to see kids dropping out because they can’t handle those college prep courses.
Now as to why I don’t agree with everyone taking the prep courses, I raised three children. Our oldest is a great person, loving husband, fantastic father and very successful at his job, who never, ever was meant to go to college. He is one of those people who works with his hands and is fantastic. He can build furniture, build a house, grow a garden, repair anything that needs fixing, repair a car, take an engine apart, I could go on and on, and some of his friends in high school were the same. Those boys went on to become fire fighters, refrigeration techs, police officers and many other occupations. Yes, further education was needed but not all sat for a 4 year college.
I truly believe putting everyone on a college track diminishes the importance of trades and jobs which we most definitely need in our lives. Plumbers, electricians, masons, painters, some of these people are the most intelligent, awesome people I’ve ever met.
Now my other two children, a son and a daughter, both went to college. #2 Son found his way through the college experience and guess what, he works with his hands as well as his head now. He has a very successful business of his own and it’s expanding every year. So college worked for him but so does working with his hands. My daughter was very successful in college, so that worked for her. Again, it doesn’t work for everyone.
Although a college degree is becoming more and more necessary for getting some jobs these days, there are still those jobs that a student would be better-off going to a vocational school for (or need no post high school education at all for).
The problem is that many high school students continually change their mind as to what vocation they are aiming for, and many of them don’t really know until years after they’re out of high school (and perhaps even half-way through college in a major that they ultimately wish they’d never gotten into!).
What your school district in California is trying to do, I think (I, too, live in California–but am not familiar with my local school district’s requirements), is to make sure that everybody has the background to go to college should they decide to eventually pick a vocation in which a college degree is required.
The only problem with this idea is that many “non-academic” courses (like art, music, shop, drama, etc.) have been dropped due to lack of state funding, and so many students who might eventually prefer to seek employment in these fields never even get a chance to “test them out”, whereupon they might therefore decide that it would be better to go to an art or music school, etc., instead of college.
Part of my answer is derived from my own experience, even though I’m from an era when high schools still had a full slate of courses available (and were also “chauvinistic”–with the boys being required to take a shop class, and the girls being required to take a “home economics” class!). My parents made me take what was then called an “Academic” major in high school–consisting primarily of math and science courses added to the basic required ones (even though I was more interested in art and writing)–as they wanted me to go to college, and that was the only major that prepared you. I did go to college and got my degree as expected, only to find out too late that, for my interests, I should have gone to a dedicated school of fine arts (my major was “art” in college; however, since you were required to take so many non-art classes as well, you just didn’t get the concentrated training in the subject that you would have in a dedicated school).
My best advice would be for parents to monitor their children’s interests over the years wherein they have control of them, and do their best to help guide him or her onto the right path, regardless of what the school system’s requirements are.