ACTION RESEARCH PROJECT

“A STUDY OF PROBLEM FACED BY STUDENTS WHILE SOLVING MATHEMATICS

PROBLEMS”

Researcher

Alamelu.P.Iyer

CHAPTER

1) INTRODUCTION

2) METHODOLOGY AND DESIGN

3) DATA ANALYSIS

4) CONCLUSION SUGGESTION

ACKNOWLEDGEMENT

It is indeed a matter of great pleasure and proud privilege to present this project report. I owe a great thanks to many people who helped and supported me during the writing of this project

I would like to express thanks to Principal of R.B.T College of Education, Dombivli Dr.NAGRAJ RAO sir for providing me opportunity to conduct this research work and extending his support during my B.Ed. course.

I’m indebted to my guide Prof.KAVITA JAISWAL madam for her valuable suggestion and constant encouragement throughout this research which gave me confidence and deep gratitude and sincere thanks to her.

I would also like to thank my institution, faculty members, librarian, my friends and my family without whom this project would have been a distant reality.

1. INTRODUCTION

Mathematics plays a very important role in our daily living. It is a subject that deals with problems which involve a process of analysis, computation and other mental skills. Historically, learning mathematics and teaching it has been motivated by the belief that a study of mathematics helps individual to learn, to reason and to apply such reasoning to everyday problems. This matter, Mathematics develops the mind to think critically and analytically. It is more than counting, measuring, and computing. It is an eye opener to all sciences. As far as Mathematics instruction is concerned, the major goal is the involvement of the students in the process of discovering mathematical ideas and formulating process. One of the interesting concerns about learning Mathematics is the fact that it develops the mind to solve problemsthat need higher order thinking skills.

These problems and puzzles induced the curiosity and chalenge the ingenuity of individuals.Introducing problem solving into the classroom improves students, skills and their ability to think creatively, logically and carefully. Hugar (2011), pointed out the types of things we might think about a mathematics classroom are equations, procedures, and word problems, but in learning them, a student needs to master to solve problem. Thus, over the last couple of decades there has been a move to approach the teaching of mathematics through problem-solving.

Problem-solving as defined in the dictionary is the thought processes involved in solving a problem and it is also the area of cognitive psychology that studies the processes involved in solving problems.

The article onProblem Solving in Mathematics:

 A Tool for Cognitive Development from the University of New York,states that problem solving is

“The process wherein students encounter a problem– a question for which they have noimmediately apparent resolution, nor an algorithm that they can directly apply to get ananswer. They must then read the problem carefully, analyze it for whatever information ithas, and examine their own mathematical knowledge to see if they can come up with astrategy that will help them find a solution.

The process forces the reorganization ofexisting ideas and the emergence of new ones as students work on problems with the helpof a teacher who acts as a facilitator by asking questions that help studentsto review theirknowledge and construct new connections. As the new knowledge is embedded intoexisting cognitive frameworks, the result is an enrichment of the network of ideasthrough understanding.”

I think this in depthlook at what problem-solving is, is a greatframework for what the process entails and how the students benefit from learningmathematics this way.

In spite of the importance of Mathematics, there seems to be growing reluctanceof the student to go into subject. Many students, despite a good understanding ofmathematical concepts are inconsistent at analyzing and computing. They make errors because they misread or carry numbers incorrectly or may write numerical clearly enoughor in the correct column.

 Difficulties in solving problems in Mathematics are evident inside theclassroom. Some students were impeded in their progress in solving the problem as theydid not comprehend the problem at all. Several students also committed erroneoussolutions owing to careless computations. Students sometimes identify an appropriateoperations or sequences of operating but do not know the procedures necessary to carryout these operations accurately. Their problem particularly in solving is confounded bythe difficult terminology. These students have difficulty understanding written or verbaldirections or explanations and find word problems especially difficult to translate intomathematical form and inability to use the correct mathematics.The foregoing gave the interest to the researcher to conduct the present study dueto the difficulties of the students in problem solving.

1.2.NEED OF A STUDY

Normally we see that students have a fear towards the subject Mathematics. They are unable to understand the basic concepts of Mathematics and their technique due to various reasons. The problems that occur in the process of learning mathematics are relatively less in case of other subjects. Hence, for common students mathematics becomes a tougher subject and consequently, they try to avoid it. Problems related to mathematics occur not only in case of students but also in case of teachers. It is seen that most of the mathematics teachers are not aware of alternative simple methods of teaching mathematics and different skills of solving the same problem. Hence, there is a need to study in detail the problems faced both by students and teachers in learning and teaching mathematics. So this study has been conducted with the sole objective of identifying various problems faced by students and teachers in learning mathematics and solicits  suggestive Measure in favors of those.

Once the causes of difficulties are discovered, then it is probable to conclude and decide the remedy. The findings of this study provide greater insights into students’ thinking and difficulties as problem solvers. Difficulties are not problems to be overcome or evils to be eradicated but they are simply a part of the mathematical learning process. Thus, no one can achieve competence in any problem solving without experiencing difficulties. 

The main aim of the study is to investigate students’ ability in solving fraction word problems. The instrument for the study was a set of mathematical problems involving fractions which consists of 10 word problems. One of the observations made from the study is that almost all the students have poor mathematical communication skills. Thus, the students’ lack of concern for the mathematical syntax, grammar and semantic is a contributing factor to their difficulty in word problem solving.

Although a lot of research has been carried out relating to students performance in solving word problems, but there is very little work that has been done which dealt with mathematics as a language Students’ lack of exposure in learning the language of mathematics creates countless difficulties in learning the subject regardless of the level of education they are in. It is the root of the problem in learning mathematics especially in the area of word problem solving.

1.3.STATEMENT OF PROBLEM

“A study of problem faced by 7 thstd students while solving mathematical problems”.

1.4. AIMS

“To Study the problem faced by 7 thstd. students while solving mathematical problems.”

1.5. OBJECTIVE

1. To study the problems faced by 7 thstd. students while solving mathematical problems.

2. To find out the causes of problemsfaced by 7 thstd. students while solving mathematical problems.

3. To suggest remedies to overcome the problems faced by 7th std. students while solving mathematical problems.

1.6.OPERATIONAL DEFINITION

Word problem : “A mathematical problems that is stated in words rather than in symbols or as an equation.” ___ Mathematics Thesaurus, 2009

Study : “The devotion of time and attention to gaining knowledge of anacademic subject, especially by means of books.”

Mathematics : “The study of the measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are branches of mathematics.”

Mathematics is published by Maharashtra State Board of Secondary and Higher Secondary Education, Pune based on NCF2005.

1.7. SCOPE AND DELIMITATION OF STUDY

While teaching, the teacher is confronted with several problems for which he/she does not have any ready-made solutions. In the particular situation a befitting solution needs to be discovered by the teacher and hence he/she is led to conduct action research thereon. A classroom teacher in a particular solution faces such situations innumerable times during his course of teaching, which is quite different from problems faced by other teachers in their schools.

Scope of this research is quite broad and it has many dimensions . It deals with a complete information about subject with which research is related with people.

The study is limited to student of std. 7th of MahilaSamiti English medium , dombivli city.

The study includes students of State board of Secondary and Higher Secondary Education.

Chapter 2

METHODOLOGY AND DESIGN

“Research is an art of scientific investigation .It is regarded as a systematic efforts to gain new knowledge.”

In the broadest sense of the word, the definition of research includes any gathering of data, information and facts for the advancement of knowledge.Reading a factual book of any sort is a kind of  research. Surfing the internet or watching the news is also a type of research. Researchers organize their research by formulating and defining a research problem. This helps them focus the research process so that they can draw conclusions reflecting the real world in the best possible way.

Research methodology involves the researcher providing an alternative hypothesis, a research hypothesis, as an alternate way to explain the phenomenon.

Aims Of Research: Observe and Describe Predict Determination of the Causes Explain

The ultimate aims of research are to generate measurable and testable data, gradually adding to the accumulation of human knowledge.

Types of research: Descriptive Research Historical Research

Descriptive research is conclusive in nature, as opposed to exploratory. This means that descriptive research gathers quantifiable information that can be used for statistical inference on your target audience through  data analysis. As a consequence this type of research takes the form of closed-ended questions, which limits its ability to provide unique insights. However, used properly it can help an organization better define and measure the significance of something about a group of respondents and the population they represent.

Descriptive research has the following characteristics : Descriptive research ascertains prevailing conditions of facts in a

group or case under study. It gives either a qualitative or quantitative, or both, description of the

general characteristics of the group or case under study. What caused the prevailing conditions is not emphasized. Study of conditions at different periods of time may be made and the

change or progress that took place between the periods may be noted or evaluated for any value.

Comparison of the characteristics of two groups or cases may be made to determine their similarities and differences.

The variables or conditions studied in descriptive research are not usually controlled.

Descriptive studies, except in case studies, are generally cross-sectional, that is, it studies the different section belonging to the same group.

Historical research  is the type of research that examines past events or combinations of events to arrive at an account of what has happened in the past.

characteristics of historical research :

It is not a mere accumulation of facts and data or even a portrayal of past events.

It is a flowing, vibrant report of past events which involves an analysis and explanation of these occurrences with the objective of recapturing the nuances, personalities and ideas that influenced these events.

Conducting historical research involves the process of collecting and reading the research material collected and writing the manuscript from the data collected.

It deals with discovery of data that already exists and does not involve creation of data using structured tools.

It is analytical in that it uses logical induction. It has a variety of foci such as issues, events, movements and concepts. It records and evaluates the accomplishments of individuals, agencies or

institutions.

This research problem is related to current situation .so researcher choose descriptive method for research.

2.2. SAMPLE

A sample is a finite part of a statistical population whose properties are studied to gain information about the whole. When dealing with people, it can be defined as a set of respondents (people) selected from a larger population for the purpose of a survey. A population is a group of individual’s persons, objects, or items from which samples are taken for measurement for example a population of presidents or professors, books or students.

A simple random sample is obtained by choosing elementary units in such a way that each unit in the population has an equal chance of being selected. A simple random sample is free from sampling bias.Researcher choose 30 students as a sample from 7 th std. from Mahila Samiti English medium, Dombivli(E).

30 Students were selected as a sample by random sampling.

2.3. TOOLS OF RESEARCH

The major tools of research in education can be classified broadly into the following categories.

A. Inquiry forms Questionnaire Checklist Score-card Schedule Rating Scale Opinionnaire Attitude Scale

B. Observation C. Interview D. SociometryE. Psychological Tests

Achievement Test Aptitude Test Intelligence Test Interest inventory Personality measures etc.

QUESTIONNAIRE

List of a research or survey questions asked to respondents, and designed to extract specific information.A questionnaire is a form containing a set of questions. It serves four basic purposes:

(1) collect the appropriate data, (2) make data comparable and amenable to analysis,

(3) minimize bias in formulating and asking question, and (4) to make questions engaging and varied.

Purpose : The purpose of the questionnaire is to gather information from widely scattered sources. It is mostly used in uses in cases where one can not readily see personally all of the people from whom he desires responses. It is also used where there is no particular reason to see them personality.

CHARACTERISTICS:

1. The researcher is able to contact large numbers of people quickly, easily and efficiently using a postal questionnaire (since all he / she has to do is identify the group that will be targeted and post them the list of questions).

2. Questionnaires are relatively quick and easy to create, code and interpret (especially if closed questions are used). In addition, the respondent - not the researcher - does the time-consuming part of completing the questionnaire.

3. A questionnaire is easy to standardise. For example, every respondent is asked the same question in the same way. The researcher, therefore, can be sure that everyone in the sample answers exactly the same questions, which makes this a very reliable method of research.

4. Questionnaires can be used to explore potentially embarrassing areas (such as sexual and criminal matters) more easily than other methods. The questionnaire can, for example, be both anonymous and completed in privacy. This increases the chances of people answering questions honestly because they are not intimidated by the presence of a researcher.

5. Questions worded simply and clearly, not ambiguous or vague, must be objective

6.Attractive in appearance (questions spaced out, and neatly arranged)

7.Write a descriptive title for the questionnaire

8.Write an introduction to the questionnaire

9.Order questions in logical sequence

10.Keep questionnaire uncluttered and easy to complete

11.Delicate questions last (especially demographic questions)

12.Design for easy tabulation

13.Design to achieve objectives

14.Define terms

15.Avoid double negatives and avoid loaded questions.

16.Avoid double barreled questions 

Advantages of Questionnaire : Questionnaire are economical. In terms of materials, money and time it can supply a considerable amount of research data. • It is easier to arrange. • It supplies standardized answers • It encourages pre-coded answers. • It permits wide coverage. • It helps in conducting depth study.

Disadvantages : • It is reliable and valid, but slow. • Pre-coding questions can deter them from answering. • Pre-coded questions can bias the findings towards the researcher. • Postal questionnaire offer little opportunities to check the truthfulness of the answers. • It cannot be used with illiterate and small children. Irrespective of the limitations general consensus goes in favour of the use of questionnaire. It’s quality should be improved and we should be restricted to the situations for which it is suited.

Questionnaire prepared by researcher.Final Questionnaire considered of 20questions.

Q1. Teacher gives examples while explaining topics?Q2. Teacher gives daily life examples while teaching topics?Q3. Teacher conducts demonstrations in class?Q4. Is teacher finds any difficulty in solving problems?Q5. Teacher clears doubts in classroom itself?Q6. Teacher is loud and clear while teaching?Q7. Formulas are more difficult to understand in mathematics?Q8. Teacher uses teaching aids?Q9. Mathematics is more difficult than other subject?Q10. Teacher gives word problems to solve at home?Q11. Does Teacher explain each principles, rules and formulas one by

one?Q12. Teacher explains Theorem clearly?Q13. Teacher uses charts and pictures during explanations?Q14. Teacher takes Revision after chapter?Q15. Do you like mathematics subject?Q16. Do you understand what teacher teaches?Q17. Do you like mathematics teacher?Q18. Do you like to solve word problems?Q19. Do teacher uses various techniques while teaching?Q20. Is mathematics important in today’s life?

CHAPTER 3

DATA ANALYSIS

3.1 INTERPRETATION AND GRAPHICAL REPRESENTATION OF DATA

Q1. Teacher gives examples while explaining topics?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that teacher gives examples while explaining topics.

Q2. Teacher gives daily life examples while teaching topics?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that teacher gives daily life examples while teaching topics.

Q3. Teacher conducts demonstrations in class?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that teacher conducts demonstration in the class.

Q4. Is teacher finds any difficulty in solving problems?

FREQUENCY PERCENTAGEYES 5 17%NO 25 83%

INTERPRETATION : 83% Students are satisfied with the given statement that teacher doesn’t finds any difficulty in solving problems.

Q5. Teacher clears doubts in classroom itself?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that teacher clears doubts in the classroom itself.

Q1 Q2 Q3 Q4 Q50

102030405060708090

100

YESNO

Q6. Teacher is loud and clear while teaching?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that teacher is loud and clear while teaching.

Q7. Formulas are more difficult to understand in mathematics?

FREQUENCY PERCENTAGEYES 8 27%NO 22 73%

INTERPRETATION : 73% Students are not satisfied with the given statement that formulas are more difficult to understand in mathematics.

Q8. Teacher uses teaching aids?

FREQUENCY PERCENTAGEYES 13 43%NO 17 57%

INTERPRETATION : 57% Students are not satisfied with the given statement that teacher uses teaching aids.

Q9. Mathematics is more difficult than other subject?

FREQUENCY PERCENTAGEYES 6 20%NO 24 80%

INTERPRETATION : 80% Students are not satisfied with the given statement that Mathematics is more difficult than other subjects.

Q10.Teacher gives word problems to solve at home?

FREQUENCY PERCENTAGEYES 28 93%NO 2 7%

INTERPRETATION : 93% Students are satisfied with the given statement that teacher gives word problems to solve at home.

Q6 Q7 Q8 Q9 Q100

10

20

30

40

50

60

70

80

90

100

YESNO

Q11.Does Teacher explain each principles, rules and formulas one by one?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that teacher explains each principles, rules and formulas one by one.

Q12. Teacher explains Theorem clearly?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that teacher explains theorem clearly.

Q13. Teacher uses charts and pictures during explanations?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that teacher uses charts and pictures during explanation.

Q14. Teacher takes Revision after chapter?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that teacher takes revision after chapter.

Q15. Do you like mathematics subject?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that they like mathematics subject

Q11 Q12 Q13 Q14 Q150

10

20

30

40

50

60

70

80

90

100

YESNO

Q16. Do you understand what teacher teaches?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that they understand what teacher teaches.

Q17. Do you like mathematics teacher?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that they like mathematics teacher.

Q18. Do you like to solve word problems?

FREQUENCY PERCENTAGEYES 22 73%NO 8 27%

INTERPRETATION : 73% Students are satisfied with the given statement that they like to solve word problems.

Q19. Do teacher uses various techniques while teaching?

FREQUENCY PERCENTAGEYES 29 97%NO 1 3%

INTERPRETATION : 97% Students are satisfied with the given statement that teacher uses various techniques while teaching.

Q20. Is mathematics important in today’s life?

FREQUENCY PERCENTAGEYES 30 100%NO NIL -

INTERPRETATION : 100% Students are satisfied with the given statement that mathematics is important in today’s life.

Q16 Q17 Q18 Q19 Q200

10

20

30

40

50

60

70

80

90

100

YESNO

CHAPTER 4

CONCLUSION AND SUGGESTION

The conclusion and suggestion are drawn on basis of interpretation of the outcomes of questionaries’ conducted in the class. In the light of interpretation of data the researcher has used all the acre and caution in formulating the hypothesis. This final step of action research demands critical and logical thinking in summarizing the findings of the study and compares them with the action hypothesis formulated.

4.1 CONCLUSION

Students are satisfied with the given statement that teacher gives examples while explaining topics.

Students are satisfied with the given statement that teacher gives daily life examples while teaching topics.

Students are satisfied with the given statement that teacher conducts demonstration in the class.

Students are satisfied with the given statement that teacher doesn’t finds any difficulty in solving problems.

Students are satisfied with the given statement that teacher clears doubts in the classroom itself.

Students are satisfied with the given statement that teacher is loud and clear while teaching.

Students are not satisfied with the given statement that formulas are more difficult to understand in mathematics.

Students are not satisfied with the given statement that teacher uses teaching aids.

Students are not satisfied with the given statement that Mathematics is more difficult than other subjects.

Students are satisfied with the given statement that teacher gives word problems to solve at home.

Students are satisfied with the given statement that teacher explains each principles, rules and formulas one by one.

Students are satisfied with the given statement that teacher explains theorem clearly.

Students are satisfied with the given statement that teacher uses charts and pictures during explanation.

Students are satisfied with the given statement that teacher takes revision after chapter.

Students are satisfied with the given statement that they like mathematics subject

Students are satisfied with the given statement that they understand what teacher teaches.

Students are satisfied with the given statement that they like mathematics teacher.

Students are satisfied with the given statement that they like to solve word problems.

Students are satisfied with the given statement that teacher uses various techniques while teaching.

Students are satisfied with the given statement that mathematics is important in today’s life.

4.2 SUGGESTIONS

A. Suggestions for Students

Students should give more importance to formula They must work hard and practice to solve word problems Learn to apply rules,principles and formulas of mathematics Learn tables properly Habit of practicing sums and doing homework regularly.

B. Suggestions for Parents

Parents must motivate their wards to use mathematics in their daily life.

Parents should encourage child in participation of maths competition. Parents should check out their daily works and their home works.

C. Suggestions for Teachers

Teacher should use various teaching aids Teacher must use different ways or method of teaching Teacher should clear doubts in classroom itself Teacher should give daily life examples while teaching Teacher should take revision after teaching topics.