1. Peshal Khanal, PhD
Central Department of Education
Tribhuvan University
15 February, 2013

2. Bertrand Russell has defined mathematics as the
science in which we never know what we are talking
about or whether what we are saying is true.
Mathematics has been shown to apply widely in
many other scientific fields. Hence, most other
scientists do not know that they are talking about or
whether what they are saying is true.
- Joel Cohen, “On the nature of mathematical proofs”
There are no proofs in mathematics education.
- Henry Pollak

3.  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

4. How do students learn the abstract concepts
behind differentiation and integration?
How do students learn Linear Algebra, and
how should it best be taught?

5. 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?

6.  Research title comes from …..????
 Research title comes from Research
Problem(s)

7.  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.

8.  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.

9.  From where ???????
◦ Curiosity
◦ Experience
◦ Information Gaps
◦ Social issues
◦ Controversy
◦ Replication
◦ Literature Review
◦ Other People
◦ ...???

10. 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?

11.  S – Specific
 M – Measureable
 A – Attainable
 R – Realistic
 T – Timely
 Keep it (title) short and simple

12. 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?

13. 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?

14.  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.

15.  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.

16. 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.

17. Positivism Interpretivism
Ontology 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

18. Types of Research

19.  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

20.  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

21. 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 mathematics
The use of team-based learning
Bilingual teaching and learning in mathematics
Play as a means of motivation in mathematics learning

22. When the researcher can not manipulate independent
variable; the research is conducted after variation in the
variable of interest has already been determined in the
natural 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?

23.  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?

24. Data are gathered by asking questions a group of individuals
called respondents.
Longitudinal – Panel (same subjects are surveyed at different
times), Trend (different people from the same general
population are surveyed at different times).
Cross sectional – studies a cross section of a population at a
single point in time.
To what extent does teaching staff at TU differ in terms of their
demographic characteristics?

25. A systematic attempt to establish facts and
understand the phenomena and arrive at a
conclusion 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?

26.  In-depth study of naturally occurring behaviour
within a culture or social group.
How do student-teacher interactions and relationships
affect mathematics learning?

27.  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?

28.  Discover or generate a theory grounded in
the data.
How do the children with poor cognitive
achievement cope with learning difficulties in
mathematics classroom?

29.  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?

30.  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?

31.  Blends the researcher's 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?

32.  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?

33.  Study of government policies and programs
How are policy mandates of mathematics
assessment being manifested in everyday
practices?

34.  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?

35.  Research undertaken to improve the program to be
implemented or being implemented.
What kinds of difficulties teachers face in
implementing CAS in mathematics teaching?

36.  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.

37.  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?

38.  Discourse analysis
 Systematic review
 Critical study
 ………………………
 ………………………
 ………………………

39. “Live as if you were to die tomorrow..
Learn as if you were to live forever…” -
-Gandhi
Thank You