RESEARCH IN MATH RESEARCH IN MATH EDUCATION-3EDUCATION-3

CONTINUE…CONTINUE…

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QUANTITATIVE AND QUALITATIVE QUANTITATIVE AND QUALITATIVE

APPROACHESAPPROACHES

So far we learned that research consists of the So far we learned that research consists of the six steps.six steps.

We will learn another fact that research can be We will learn another fact that research can be design in two ways: quantitative and design in two ways: quantitative and qualitativequalitative

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In this lesson we will;In this lesson we will; explore how these approaches differ explore how these approaches differ

througthroughhout the six steps out the six steps define quantitative and qualitative define quantitative and qualitative

research,research, explain the main ideas and paradigms that explain the main ideas and paradigms that

influenced the development of influenced the development of quantitative and qualitative research; quantitative and qualitative research;

ideidenntify simitify simillarities and differences arities and differences between these two research approaches in between these two research approaches in terms of the six steps;terms of the six steps;

see the factors useful in deciding whether see the factors useful in deciding whether quantitative or qualitative research is best quantitative or qualitative research is best for studying our problem;for studying our problem;

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Quantitative ResearchQuantitative Research• Positivist traditionPositivist tradition• ObjectivistObjectivist• TestingTesting• DeteDeterrminingmining• GeneralizingGeneralizing• Numerical dataNumerical data• Statistical techniquesStatistical techniques

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Quantitative Research…….Quantitative Research……. We can summarize the characteristics of We can summarize the characteristics of

quantitative research as below:quantitative research as below: focusing on collecting and analysing focusing on collecting and analysing

information in the form of numbers;information in the form of numbers; testing cause and effect relationship;testing cause and effect relationship; comparing different groups with regard to comparing different groups with regard to

differendifferentt variables; variables; designing experimental inquiries—pre-post designing experimental inquiries—pre-post

test and control-experimental groups.test and control-experimental groups.

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Qualitative ResearchQualitative Research RelativistRelativist SubjectivistSubjectivist UnderstandingUnderstanding Views, ideas, values as dataViews, ideas, values as data ThemesThemes as findings as findings

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Qualitative Research…….Qualitative Research……. We can summarize the characteristics of We can summarize the characteristics of

qualitative research as below:qualitative research as below: focusing on themes coming from participants’focusing on themes coming from participants’

views;views; collecting data from the settings people live and collecting data from the settings people live and

work;work; sharing researcher’s ideas, comments, values sharing researcher’s ideas, comments, values

and assumptions within the research report;and assumptions within the research report; interpreting qualitative data for not testing interpreting qualitative data for not testing

hypothesis or conjectures.hypothesis or conjectures.

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Similarities and Similarities and Differences……Differences……

What are the similarities and fifferences of qualitative and What are the similarities and fifferences of qualitative and qualitative esearch?qualitative esearch?

1. Identifying research problem1. Identifying research problem

quantitativequantitative qualitativequalitativeProblem requires a Problem requires a description of trends or description of trends or explanation of the explanation of the relationship among variables relationship among variables

We know much about We know much about particular variables in the particular variables in the setting.setting.

Problem requires;Problem requires; an exploration in which little is an exploration in which little is known about the issue,known about the issue,A detailed understanding of a A detailed understanding of a central phenomenon.central phenomenon.

We don’t know much about We don’t know much about variables in the settingvariables in the setting

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Similarities and Similarities and Differences……Differences……

What are the similarities and fifferences of qualitative and What are the similarities and fifferences of qualitative and qualitative esearch?qualitative esearch?

2. Reviewing the literature2. Reviewing the literature

quantitativequantitative qualitativequalitative

The literature plays a major The literature plays a major role;role;for especially ensuring that for especially ensuring that the problem orithe problem origginal and inal and unique,unique,to be objective and,to be objective and,to generalize conjectures or to generalize conjectures or hypothesishypothesis

The literature plays a minor role The literature plays a minor role for justifying that the problem is for justifying that the problem is unique and oriunique and origginal.inal.

Literature review provides Literature review provides speculative ideas rather than speculative ideas rather than objective resultsobjective results

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Similarities and Similarities and Differences……Differences……

What are the similarities and fifferences of qualitative and What are the similarities and fifferences of qualitative and qualitative esearch?qualitative esearch?

3. Specifying a pupose of research3. Specifying a pupose of research

quantitativequantitative qualitativequalitative

The purpose statement;The purpose statement;is specific and narrow;is specific and narrow;Seeks to describe Seeks to describe measurable and observable measurable and observable data on variables.data on variables.

The purpose statement;The purpose statement;•is general and broad;is general and broad;•seeks to understand the seeks to understand the participants’ experiences participants’ experiences

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Similarities and Similarities and Differences……Differences……

What are the similarities and fifferences of qualitative and What are the similarities and fifferences of qualitative and qualitative esearch?qualitative esearch?

4. Collecting data4. Collecting data

quantitativequantitative qualitativequalitative

The data collection consists of;The data collection consists of;using instruments with preset using instruments with preset questions and responses;questions and responses;gathering numeric data; gathering numeric data; Gathering information from a Gathering information from a large number of individual.large number of individual.

The data collection consists of;The data collection consists of;using forms with general using forms with general questions, open-ended questions, open-ended questions to permit the questions to permit the participants to generate participants to generate responses;responses;gathering words, pictures, gathering words, pictures, symbols;symbols;Obtaining information from a Obtaining information from a small number of individuals.small number of individuals.

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Similarities and Similarities and Differences……Differences……

What are the similarities and fifferences of qualitative and What are the similarities and fifferences of qualitative and qualitative esearch?qualitative esearch?

5. Analyzing and interpreting data5. Analyzing and interpreting data

quantitativequantitative qualitativequalitative

The data analysis consists of;The data analysis consists of;statistical inferstatistical inferrring;ing;describing trends; describing trends; comparing groups’ differences;comparing groups’ differences;relating variablesrelating variablesgeneralizing conjectures.generalizing conjectures.

The data analysis consists of;The data analysis consists of;text analysis;text analysis;developing an understanding;developing an understanding;iidentifying themes;dentifying themes;stating the larger meaning of stating the larger meaning of the findings (speculation)the findings (speculation)

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Similarities and Similarities and Differences……Differences……

What are the similarities and fifferences of qualitative and What are the similarities and fifferences of qualitative and qualitative esearch?qualitative esearch?

6. Reporting and evaluating research6. Reporting and evaluating research

quantitativequantitative qualitativequalitative

Report uses standard, fixed Report uses standard, fixed structures and evaluative structures and evaluative criteria.criteria.Researchers take an objective Researchers take an objective and unbiand unbiaased manner in sed manner in presenting findingspresenting findings

Report uses a flexible structure Report uses a flexible structure and evaluate criteria.and evaluate criteria.Researchers take a subjective Researchers take a subjective (reflective) position and b(reflective) position and biiased ased approach.approach.

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QuantitativeQuantitative StepsSteps QualitativeQualitative

Description and explanation Description and explanation orientedoriented

Major role, justification for the Major role, justification for the research problem, research problem, specification for the need for specification for the need for the studythe study

Specific and narrow, Specific and narrow, measurable and observable measurable and observable datadata

Predetermined enstruments, Predetermined enstruments, numerical data, large number numerical data, large number of peopleof people

Statistical analysis, Statistical analysis, description of trends, description of trends, comparision of groups, comparision of groups, relationship among variablesrelationship among variables

Standard and fixed, objectivist Standard and fixed, objectivist and unbiasedand unbiased

Identifying Identifying research problemresearch problem

Reviewing Reviewing literatureliterature

Specifying purposeSpecifying purpose

Collecting dataCollecting data

Analyzing and Analyzing and interpreting datainterpreting data

Reporting and Reporting and evaluating evaluating researchresearch

Exploratory and understanding Exploratory and understanding orientedoriented

Minor role, justification for the Minor role, justification for the research problemresearch problem

General and broad, General and broad, understanding participants’ understanding participants’ experiencesexperiences

İnterviews, observations, text, İnterviews, observations, text, pictures, symbols, small pictures, symbols, small number of peoplenumber of people

Text analysis, thematic Text analysis, thematic organisation, understanding organisation, understanding meaningsmeanings

Flexible and emerging, reflexive Flexible and emerging, reflexive and biasedand biased

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What are the research designs associated with What are the research designs associated with quantitative and qualitative research?quantitative and qualitative research?

It is not enough to know the steps differ in quantitative and qualitative It is not enough to know the steps differ in quantitative and qualitative procedures,procedures,

We also need to go into detail to see how research designs differ in both We also need to go into detail to see how research designs differ in both approaches.approaches.

Research designs differ for quantitative and qualitative research.Research designs differ for quantitative and qualitative research.

Experimental designExperimental design Correlational designCorrelational design Survey designSurvey design Grounded theory designGrounded theory design Ethnographic designEthnographic design Narrative designNarrative design Mixed methods designMixed methods design Action research design (teacher as researcher)Action research design (teacher as researcher)

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Quantitative research designsQuantitative research designs Qualitative research designsQualitative research designs Combined quantitative Combined quantitative and qualitative research and qualitative research designsdesigns

Intervention Intervention ResearchResearch

Non-Non-intervention intervention ResearchResearch

Exploring Exploring common common experiences of experiences of individuals to individuals to develop a theorydevelop a theory

Exploring the Exploring the shared culture shared culture of a group of a of a group of a peoplepeople

Combining quantitative and Combining quantitative and qualitative data to best qualitative data to best understand and explain a understand and explain a research problemresearch problem

Using qualitative and Using qualitative and quantitative data for quantitative data for individuals’ practicesindividuals’ practices

within an educational within an educational

SettingSetting

Mixed methodsMixed methods

ResearchResearch

Explaining whether an Explaining whether an intervention influences intervention influences an outcome for one an outcome for one group as opposed to group as opposed to another groupanother group

Describing Describing trends for a trends for a population of population of peoplepeople

Exploring Exploring individual stories individual stories to describe the to describe the lives of peoplelives of people

Narrative Narrative ResearchResearch

Action ResearchAction Research

Associating or relating Associating or relating variables in variables in apredictable pattern for apredictable pattern for one group of individualsone group of individuals

Ethnographic ResearchEthnographic Research

ExperimentExperimental Researchal Research

CorrelationalCorrelational ResearchResearch

Survey Survey ResearchResearch

GroundeGrounded theory d theory ResearcResearc

hh

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Experimental DesignExperimental Design Some researchers seek to test whether a particular practice has any effect Some researchers seek to test whether a particular practice has any effect

on individuals. For exampleon individuals. For example, , in education, doesin education, does problem solving based problem solving based teaching has any effect on students’ cognitive development?teaching has any effect on students’ cognitive development?

In this case, an experimental design is suitable for you. In this case, an experimental design is suitable for you. In experimental design, researchers try to determine whether an activity or In experimental design, researchers try to determine whether an activity or

materials make difference in results for participants.materials make difference in results for participants. You assess this impact by giving one group set of activities (You assess this impact by giving one group set of activities (called an called an

intervention) intervention) and keeping another group out of activities and keeping another group out of activities (called non-(called non-intervention)intervention)

Experimental-control groupsExperimental-control groups Pre-and-post testPre-and-post test Dependent and independent variablesDependent and independent variables Testing hypothesisTesting hypothesis

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Correlational DesignCorrelational Design In sIn some inquiries,ome inquiries, you may be unable to provide an intervention or to you may be unable to provide an intervention or to

assignassign individual to groups, but you want to focus on examining the individual to groups, but you want to focus on examining the relationship of one or more variables. relationship of one or more variables.

In this case, you need to conduct a correlational study.In this case, you need to conduct a correlational study.

Correlational design is a procedure in quantitative research in wich Correlational design is a procedure in quantitative research in wich researcher tries to measure the degree of relationship between two or researcher tries to measure the degree of relationship between two or more variables by using the statistical procedures of correlational analysis.more variables by using the statistical procedures of correlational analysis.

Correlational statistics: whether the two variables are related or whether Correlational statistics: whether the two variables are related or whether one can predict another. one can predict another.

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Survey DesignSurvey Design Survey is another form of quantitative research.Survey is another form of quantitative research.

You may not want to test an activity (you don’t have any way to You may not want to test an activity (you don’t have any way to interventinterventionion) or may not be interested in the relations) or may not be interested in the relationshhips among ips among variables.variables.

Instead, you may want to seek to describe trends in a large population of Instead, you may want to seek to describe trends in a large population of people.people.

In this case, a survey is a good procedure for you to use.In this case, a survey is a good procedure for you to use.

In this procedure, you use questionnaire with some group of people In this procedure, you use questionnaire with some group of people (called (called sample) sample) in order to identify trends, attitudes, opinions, views, believes or in order to identify trends, attitudes, opinions, views, believes or behaviours of a large group of people behaviours of a large group of people (called population).(called population).

Choosen sample must present every aspects of the populationChoosen sample must present every aspects of the population

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Grounded Theory DesignGrounded Theory Design Instead of studying a single group, you may want to examine a number of Instead of studying a single group, you may want to examine a number of

individuals.individuals. In this case, you need to conduct a grounded theory design.In this case, you need to conduct a grounded theory design. It is a form of qualitative research.It is a form of qualitative research. This design enables you to generate a broad theory about phenomenon This design enables you to generate a broad theory about phenomenon

grounded in the data.grounded in the data. As a systematic procedure, it is used by a wide range of educational As a systematic procedure, it is used by a wide range of educational

researchers to generate a general explanation that explains a process, researchers to generate a general explanation that explains a process, action or interaction between people.action or interaction between people.

In this process, researcher uses interview (or clinic interview) as a data In this process, researcher uses interview (or clinic interview) as a data collection tool.collection tool.

Researcher focuses on categories and themes emerged from the Researcher focuses on categories and themes emerged from the qualitative data.qualitative data.

These categories and themes help researcher to construct predictive These categories and themes help researcher to construct predictive statements about the experiences of individualsstatements about the experiences of individuals

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Ethnographic DesignEthnographic Design You may be interested in;You may be interested in;

• studying one group of individuals,studying one group of individuals,• examining them in the natural setting where they live and work;examining them in the natural setting where they live and work;• developing a portrait of how they interact.developing a portrait of how they interact.

In this case, it is good for you to use ethnographic design as a qualitative research.In this case, it is good for you to use ethnographic design as a qualitative research. Ethnographic design is a qualitative procedure for describing, analyzing and Ethnographic design is a qualitative procedure for describing, analyzing and

understanding a cultural group’s shared patterns of behaviours, believes, values and understanding a cultural group’s shared patterns of behaviours, believes, values and language that developed over time.language that developed over time.

Ethnographic research provides a detaled picture of the culture of group drawing Ethnographic research provides a detaled picture of the culture of group drawing from various sources of information.from various sources of information.

Researcher describes the group within their natural setting, explores themes, Researcher describes the group within their natural setting, explores themes, meanings and issues that develop over time as the group interact, and presents a meanings and issues that develop over time as the group interact, and presents a detaled picture of the group.detaled picture of the group.

While doing these researcher also put him/herselves into the report with his/her While doing these researcher also put him/herselves into the report with his/her biases and conceptions.biases and conceptions.

Entring the field as observer as participantsEntring the field as observer as participants

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Narrative DesignNarrative Design You may not be interested in describing, explaining or interpreting the You may not be interested in describing, explaining or interpreting the

actions, ideas, behaviours or experiences of people within their own culture actions, ideas, behaviours or experiences of people within their own culture and setting as researchers do in grounded theory research and and setting as researchers do in grounded theory research and ethnographic designs.ethnographic designs.

Instead, you may want to tell the stories of one or two individuals.Instead, you may want to tell the stories of one or two individuals.

Or you may want to tell some thing about the lives of individuals.Or you may want to tell some thing about the lives of individuals.

In this case, it is good for you to use narrative design as a form of In this case, it is good for you to use narrative design as a form of qualitative research. qualitative research.

Researchers collect detailed information about these individuals and tell Researchers collect detailed information about these individuals and tell stories about these individuals’ lives and write personstories about these individuals’ lives and write personaal narratives. l narratives.

In education, these stories often relate to school classroom experiences or In education, these stories often relate to school classroom experiences or activities in schools.activities in schools.

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Mixed Methods DesignMixed Methods Design If you decide to collect both quantitative and qualitative data, it is good for If you decide to collect both quantitative and qualitative data, it is good for

you to use a mixed methods design.you to use a mixed methods design.

This design may provide a better understThis design may provide a better understaanding of a research problem nding of a research problem than one type of data alone.than one type of data alone.

This design as a procedure links both quantitative and qualitative data in a This design as a procedure links both quantitative and qualitative data in a single study.single study.

It is important that you should decide how you integrate and connect two It is important that you should decide how you integrate and connect two kinds of data during the process of data analyzing.kinds of data during the process of data analyzing.

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Action Research DesignAction Research Design Like mixed methods design, action research design often utilizes both Like mixed methods design, action research design often utilizes both

quantitative and qualitative data. But it focuses on procedures useful in quantitative and qualitative data. But it focuses on procedures useful in explaining practical problems take place in schools and classroom settings.explaining practical problems take place in schools and classroom settings.

Action research design is a systematic procedure used by teachers as Action research design is a systematic procedure used by teachers as researcher within actual settings.researcher within actual settings.

While teaching the researcher tries to obtain qualitative and quantitative While teaching the researcher tries to obtain qualitative and quantitative data through intervention or non-intervention. I mean that teacher as a data through intervention or non-intervention. I mean that teacher as a researcher can continue his/her inquiry without changing anything in the researcher can continue his/her inquiry without changing anything in the setting or can study any innovation put into the setting.setting or can study any innovation put into the setting.

Through this type of designs, teachers as researchers have an opportunity Through this type of designs, teachers as researchers have an opportunity to obtain first hand data about what is going on within the setting in terms to obtain first hand data about what is going on within the setting in terms of learning and teaching.of learning and teaching.