Peshal Khanal, PhDCentral Department of Education Tribhuvan University 15 February, 2013
Bertrand Russell has defined mathematics as thescience in which we never know what we are talkingabout or whether what we are saying is true.Mathematics has been shown to apply widely inmany other scientific fields. Hence, most otherscientists do not know that they are talking about orwhether what they are saying is true. - Joel Cohen, “On the nature of mathematical proofs”There are no proofs in mathematics education. - Henry Pollak
Short, Sharp and Meaningful describing what the research is about. In qualitative research It may also be a ‘working title’ that the researcher will revise as his/her project develops. Example of poor title An Investigation of a Survey and Analysis of the Influence of Program X on the Attitudes, Teaching Methodology, and Evaluative Techniques of Randomly Selected Male and Female Physical Education Teachers in Public High Schools in Kathmandu district A qualitative inquiry into how 7th graders develop problem solving skills in mathematics at selected public schools in Morang district Better title Influence of Program X on Physical Education teachers’ attitude, teaching methodology and evaluation techniques (A qualitative inquiry into ) the development of problem solving skills in mathematics (among 7th graders) The use of technology in the teaching and learning of mathematics Transition from school to college mathematics
How do students learn the abstract conceptsbehind differentiation and integration?How do students learn Linear Algebra, andhow should it best be taught?
1. Does the title precisely identify the area of the problem?2. Is the title clear, concise, free from jargon, and adequately descriptive to permit indexing the study in its proper category?3. Does the title identify the key variables and provide some information about the scope of the study?4. Are unnecessary words, such as “a study of,” “an investigation of,” and “an analysis of” avoided?5. Do nouns, as opposed to adjectives, serve as the key words in the title?
Research title comes from …..???? Research title comes from Research Problem(s)
A research problem is a DISCREPANCY between what one knows and ought to know to solve a problem or to understand a phenomenon. Research problems are EDUCATIONAL ISSUES OR CONCERNS studied by researchers. A SITUATION OR CIRCUMSTANCE THAT REQUIRES A SOLUTION to be described, explained, or predicted. It is an unsatisfactory situation that wants you to confront. A research problem refers to some DIFFICULTY that a researcher experiences in the context of either a theoretical or practical situation and wants to obtain a solution for the same. Research problems are QUESTIONS THAT INDICATE GAPS in the scope or the certainty of our knowledge. They point either to problematic phenomena, observed events that are puzzling in terms of our currently accepted ideas, or to problematic theories, current ideas that are challenged by new hypotheses.
Einstein: If I have one hour for solving the problem on which my life depends, I will devote 40 minutes to study the problem, 15 minutes to analyse it, and only 5 minutes to solve it.
From where ??????? ◦ Curiosity ◦ Experience ◦ Information Gaps ◦ Social issues ◦ Controversy ◦ Replication ◦ Literature Review ◦ Other People ◦ ...???
In selecting the research question consider whether or not it is: easible: in terms of time, place, money, equipment, subjects etc. nteresting : The question has to be interesting to the investigator, but should also be interesting to others. ovel: Has this study been done before? Does it add to the current body of knowledge? thical: Can the study be done in a way that does not subject subjects to excess risks? elevant: Will it further knowledge in the related field? Will the results change practice, policy or point towards further avenues of research?
S – Specific M – Measureable A – Attainable R – Realistic T – Timely Keep it (title) short and simple
1. Is there a difference in the science achievement of boys and girls exposed to the same science activity?2. Should we teach sex education in elementary school?3. What happens if the school day becomes longer?4. How do students adjust in a school environment?
2. What is the difference in knowledge and attitude of fifth graders taught sex education compared to fifth graders who are not taught sex education?3. What is the relationship between length of the school day and learning achievement of high school students? Are the following questions researchable? Is democracy a good form of government? Should values clarification be taught in public schools? Can crime be prevented? Should physical education classes be dropped from the high school curriculum?
A paradigm is a “worldview” or a set of assumptions about how things work. “shared understandings of reality”; a set of beliefs about reality and knowledge that provides the researcher with a broad overview and direction of the research. A paradigm encompasses three basic components – ONTOLOGY, EPISTEMOLOGY and METHODOLOGY.
Ontology is the starting point of all research after which one’s epistemological and methodological positions logically follow. An individual’s ontological position is their answer to the question – What is the nature of reality and what constitutes reality.
Epistemology – what is knowledge? What is the relationship between knowledge and reality and between knower and would-be-knower? If there were no human beings, would there still be three basic types of rock? , Did the unconscious exist before Freud?Methodology – procedural strategy for acquiring knowledge about the phenomena under study.
Positivism InterpretivismOntology Naïve realism (only one reality that Relativism (multiple is observable, measureable) reality)Epistemology Dualism/objectivism (the Subjective/transact researcher and research ional; Created participants and the topic are findings independent to each other, findings (knowledge is independent of the researcher socially constructed)Methodology Controlled, ‘scientific’ experiment, Hermeneutical/dial measurement ectical, interaction
ONTOLOGICAL ◦ Existence of objective, absolute truths ◦ Focus on operational definitions and rational explanations EPISTEMOLOGICAL ◦ Researcher (knower) and object of study (known) independent – focus on objectivity ◦ Assumption that inquiry can approximate objectivity (value-free); disagreements between observers due to errors and/or observer biases METHODOLOGICAL ◦ Replicability as a means for testing truth ◦ Focus on generalization ◦ Criteria – notions of internal/external validity
ONTOLOGICAL ◦ Reality is local and specific ◦ Constructions cannot be absolutely true or correct (but can be less sophisticated/informed) ◦ Reality actively constructed rather than discovered EPISTEMOLOGICAL ◦ Researcher and object of study inherently dependent ◦ Inquiry inherently value-bound ◦ Multiple interpretations can be equally valid METHODOLOGICAL ◦ Focus on induction ◦ Relative lack of emphasis on generality – use purposive samples ◦ Criteria – trustworthiness, credibility, transferability, confirmability
A scientific investigation in which the researcher manipulates one or more independent variables, controls any other relevant variables, and observes the effect of the manipulations on the dependent variable(s).Peer tutoring and cooperative learning in undergraduate mathematicsThe use of team-based learningBilingual teaching and learning in mathematicsPlay as a means of motivation in mathematics learning
When the researcher can not manipulate independentvariable; the research is conducted after variation in thevariable of interest has already been determined in thenatural course of events. Do the students who work during their college year have lower grades than students who do not work? What is the effect of single-parent homes on achievement?
No manipulation, the researcher investigates how scores on one variable or variables rise or fall as scores on other variables rise or fall. To what extent is there a relationship between preschool attendance and academic achievement in first graders?
Data are gathered by asking questions a group of individualscalled respondents.Longitudinal – Panel (same subjects are surveyed at differenttimes), Trend (different people from the same generalpopulation are surveyed at different times).Cross sectional – studies a cross section of a population at asingle point in time. To what extent does teaching staff at TU differ in terms of their demographic characteristics?
A systematic attempt to establish facts andunderstand the phenomena and arrive at aconclusion about the past. How has mathematics changed in the past 50 years, and how does this change how it should be taught? How do the school textbooks during the Panchayat period (2017 – 2047BS) portray nationalism and patriotism?
In-depth study of naturally occurring behaviour within a culture or social group. How do student-teacher interactions and relationships affect mathematics learning?
An in-depth study of a bounded system or unit such as a person, family, club, program, community etc; sometimes a longitudinal study. How do the first-graders develop computation skills in arithmetic?
Discover or generate a theory grounded in the data. How do the children with poor cognitive achievement cope with learning difficulties in mathematics classroom?
Understanding the essence of experiences as perceived by the participants. How do adults in an ethnic community experience mathematics in their everyday lives? How do adults having no formal schooling develop their own systems of learning and teaching mathematics in their everyday lives?
Extensive interviews with individuals to collect first person narratives about their lives or events in which they participated. How do adult learners experience mathematics learning at various stages of their lives?
Blends the researchers own experience with scholarly research in order to present an idea, point, or argument about a particular topic. How do my struggles with learning mathematics correspond to those of others?
Challenges the basic structures and ideologies that oppress women; goal – empowerment and emancipation of women. To what extent do mathematics textbooks manifest gender-based stereotypes and biases?
Study of government policies and programs How are policy mandates of mathematics assessment being manifested in everyday practices?
Assessment of the effectiveness of a program/To make decision about a program. To what extent do parents satisfied with the mathematics learning of their children? If not, what are the reasons? To what extent has the mathematics curriculum accomplished its objectives?
Research undertaken to improve the program to be implemented or being implemented. What kinds of difficulties teachers face in implementing CAS in mathematics teaching?
An emergent inquiry which includes designing and testing particular interventions. Interventions embody specific theoretical claims about teaching and learning, and reflect a commitment to understanding the relationships among theory, designed artefacts and practices. Continuous cycle of conceptualisation, design, enactment, analysis and redesign. ◦ Devising a computer-based mathematics curriculum for blind children.
Small-scale study carried out by the practitioners to solve problems or improve practices within their own institutions/programs. Why do five ethnic children achieve poor grades in a mathematics achievement test despite introducing a remedial teaching for them?