Perspectives on Scholarship and Research Methods

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Perspectives on Scholarship and Research Methods

• By Lindsey Gerber

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Math Sciences Education as a Field of Study

• E.G. Begees diagram of school math illustrates
  the interrelationship of the components in the
  schooling process and the need for multiple
  perspectives and procedures.

SOCIETY
SCHOOLING MATERIALS ORGANIZATIONS
SUBSETS
STUDENTS
TEACHERS
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Activities of Researchers

• Research refers to the things one does, not
  objects one can touch and see.
• Research cannot be viewed as a mechanical
  performance or a set of activites, so we are
  going to go through a process that

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10 Steps(Research Activities)
1. Phenomenon of interest
Situating your ideas (most important)
2. Preliminary model
What kind of evidence and how to do it
3. Relate to others ideas
4. Questions or Conjectures
5. Select research strategy
6. Select research procedure
7. Gather evidence
8. Interpret evidence
Making sense of the info and interpreting for
others
9. Report results
10. Anticipate actions of others
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Model for research and curriculum development.
Teacher Knowledge
Teachers Decisions
Classroom instruction
Students cognitions
Students Learning
Students behaviors
Teacher Beliefs
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Scholarly Communities

• A group in which the researcher follows specific
  lines to answer a particular group of questions,
  methods and procedures.
• Thomas Kuhn argues there is a dominant approach
  called Normal Science, which is a product of a
  network of personal contacts that has been termed
  an invisible college.
• Communities determine what is being researched.
  There are two interactive features between
  researchers and social problems
• Scholars are pressured socially and politically
• To increase the understanding of the problem or
  improve practice.

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Ideology and Paradigms

• We must understand the history of the development
  of scientific theories and natural sciences.
• During the past century, our natural sciences
  have adopted positivism to attempt to build
  theories in social behaviors.
• In 1913, J.B. Watson, the father of behaviorism,
  says psychology as the behaviorist views it, is
  a purely objective experimental branch of natural
  science. Its theoretical goal is the prediction
  and control of behavior.
• Changing because of W.P. Weimer.
• Non-Euclidean Geometry
• Karl Popper on testing theoretical propositions
• Social Science and educators reject the physical
  sciences model close to their discipline.

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Different Ideology Perspectives

• These are reflected in a groups assumptions
  about the knowledge that is to be taught, the
  work of students and how learning occurs, the
  work of teachers and professionalism, and the
  social organization and technology of the
  classroom and schools.
• Different approaches viewed by
• Empirical-Analytic, symbolic and critical paradigm

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Empirical-Analytic Paradigm

• Starts with ones goal to explaining the
  relationship between human and the natural world
  and uses the knowledge to gain intellect or
  control of the world. (only by observing)
• Popkewitz argues there are 5 other reasons to be
  in this group
• Theory universal, not bounded by specifics.
• Theory to describe the relationships of facts.
• Social world exists variables.
• Knowing facts and being organized prior to
  research
• Rely on Math for variables to construct.
• In Math Education, it is translated to facts,
  concepts, procedures, etc.

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Symbolic Paradigm

• This research is to understand how humans relate
  to the social world they have created.
• This world is created by rule making.
• In education, this perspective translates to
• Knowledge is situational and personal
• Pupils learn by construction a a consequence of
  experiences.
• That the job of teaching is to create
  instructional experiences for students
• Understanding gained from experience
• Experience rich and meaningful wih teachnology.

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Critical Paradigm

• To demystify the patterns of knowledge and social
  conditions that restrict our practical
  activities.
• Basic assumptions with this view is that humans,
  through thought and action, can improve the
  social world in which they live.
• The impact in school
• reflection on how humans can improve solcial
  conditions
• Pupils learn through reflection and action
• Job of teaching is to get the students to reflect
  on the social world in which they live.

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Failure of Novices

• Novices, such as Graduate Students, do not think
  it is important to use the work of others.
• Failure results from
• Skip the problem of interest to designing a study
  and collecting data.
• Results are open and can be interpreted in a
  variety of ways, which leads to this study being
  of little real value.

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Methods Used By Researchers

• The scholar must decide(5-10)
• What evidence is needed to address the question
  or conjectures raised
• How to gather, analyze, and interpret that
  evidence
• How to report the findings to others
• These are a result from Activities 1 4
• 2 things to understand from the use of the term
  Research Methods
• specific methods discussed in research on
  collecting, presenting and analyzing
• 5 factors for gathering information world view,
  time orientation, existence of situation,
  anticipated source, and judgement of results

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Methods used with Existing Evidence

• There are three methods used and in these methods
  a researcher can not change or alter any results,
  they must depend on the given information.
• Historiography Deeper and fuller understanding
  of the past
• Content analysis Investigate in the present time
• Trend analysis Use past and present information
  to predict future results.

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Methods Used When a Situation Exists and Evidence
Must be Developed

• Researchers have control on how this is collected
  and interpreted.
• Retrospective Survey Using questions from the
  past to re-interview participants.
• Mass-Descriptive Survey to study
  present-oriented questions
• Structured Interviews Not as many participants
  are used as above and researchers listen to
  responses
• Clinical Interviews Like previous but questions
  change upon response.
• Projective Surveys Make predictions from surveys
• Structured observations Study groups and their
  interactions with different members

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Continuation

• Clinical Observations Study group behavior
• Longitudinal Study Study of change over time
• Cross-Sectional Design Study change but by
  finding equivalent data and making assumptions
• Casual Modeling Used to investigate complex math
  educational situations
• Case Studies Organize and report information
  about the actions, perceptions, and beliefs of an
  individual or group under specific conditions
• Action Research Is a research strategy used to
  investigate schooling situations, where the
  researcher assumes a problem that has evolved and
  document observations
• Ethnography Study complex culture of schools,
  use culture as a reason how people live.

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Experiments

• There are three approaches used in Education
• Teaching Experiments developing new teaching
  techniques by creating a hypothesis about
  teaching strategy and reasons for effectiveness
  are determined.
• Comparative Experiments used to determine if a
  specific set of actions performs the desired
  results
• Interrupted time-series experiments comparing
  the outcomes before and after a treatment.

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Evaluations

• It is common for people or groups of people
  create new products for teaching.
• Four stages of development process product
  design, product creation, product implementation,
  and product use.
• Four general methodologies of evaluations
• Needs Assessment (By researcher)
• Is there a need for this product?
• Will it fulfill the need?
• What priority does the product have?
• Formative Evaluation (By evaluator)
• Is the content of the product high quality?
• Are intended performance outcomes reached?
• Are unintended performance outcomes identified?
• Are necessary support services for installations
  provided?
• Summative Evaluation (By researcher)
• How is the content different from competitors
• What performance differences?
• What cost difference?
• Have provisions been made for maintaining product
  use?
• Illuminative Evaluation
• Field research to determine if the product is
  useful.

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3 Important Aspects Associated with Each Method

• Objectivity A researcher should be personally
  interested in the topic and investigation. If
  they were not interested in the topic then their
  information might not be trusted. Therefore a
  researcher must be objective in gathering
  evidence, examining and reporting results.
• Quality of Evidence Make sure the evidence is
  valid and also make sure the evidence is
  reliable.
• Validity Evidence is often difficult to
  demonstrate so researchers might use indicators
  to identify results.
• Reliability accuracy on gathering evidence
• Can you believe something that can not be backed
  up?
• Generalizability Predicting on probability of
  similar studies.

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TRENDS

• Hard to describe the past quarter-centurys
  research on teaching and learning trends.
• But there are at least 5 broad trends in social
  the social sciences that can be described.

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Trend 1 Growth of Research

• Teaching and learning research has grown in the
  last 30 years.
• Four factors that have contributed to a faster
  growth in research in education.
• Availability of Research Funds
• In 1960s, established National Science Foundation
  and the Office of Education.
• Increased social demands for reform of schooling,
  resulting in an increase of scholars research
  that are not in the education field.
• A variety of research journals, research
  organizations, an meetings dedicated to
  educational research.
• Research centers dedicated to math education
  research in Universities.

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Trend 2 Growing Diversity in Research Methods

• As more scholars get involved with research in
  math education the variety of methods also grows.
• In 1963, most research was conducted by
  experiments to verify or clear a concern with the
  hypothesis.
• In 1973, experimentations was still a large part
  of research but they have elaborated and more
  organized.
• Today, studies to compare and experiments are
  commonly used but scholars are creating different
  strategies and methods. ( research teams)

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Trend 3 A Shift in Epistemology

• a branch of philosophy that investigates the
  origin, nature, methods, and limits of human
  knowledge
• Three aspects to understanding authentic
  knowledge
• Understand the difference between knowledge
  (basic) and record of knowledge (more in depth
  understanding)
• Changes in math due to new technology which
  allows us to look at elaborate, complex problems.
• What is unique in learning and teaching of any
  subject?

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Trend 4 A Shift in Learning Psychology

• New view is cognitive science which has grown in
  the last decade.
• 7 notions on how the mind works
• Processing with the experience
• Either stored in working, short term, or longer
  term memory
• Try to process to much information at one time so
  it is harder to store in long term unless
  organized called schemata
• New experiences related to old or forced to
  change a schema
• Naturally occurring experience that might not
  consciously realize
• Learning trough preorganized and structured
  experiences
• Schemata is never fixed
• If students do not have the structured organized
  schemata they look for it through experiences.

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Trend 5 Growth of Political Awareness

• Educational research is both scientific and
  political
• Our schools are governed by 16,000 local school
  districts and by state regulations and federal
  mandates.
• The MSEB was created to provide a national voice
  for math education in Washington, D.C.
• Researchers must be a part of the political
  battles to help create new policies that will be
  made. They must contribute.