Types of Research Designs: A Comprehensive Guide for Advanced Mathematics Students

Question 1

Which research design involves observing and recording data without manipulating an independent variable?

Accepted Answer

Observational Design

Answer

Experimental Design

Answer

Quasi-experimental Design

Answer

Mixed Methods Design

Question 2

Which research design randomly assigns participants to groups and exposes them to different treatments while controlling for other variables?

Accepted Answer

Experimental design

Answer

Quasi-experimental design

Answer

Non-experimental design

Answer

Mixed methods design

Question 3

What is a key benefit of using a mixed methods research design?

Accepted Answer

Enhanced understanding of the research topic through the convergence of qualitative and quantitative data.

Answer

Reduced time and cost compared to other research designs.

Answer

Straightforward analysis process compared to other research designs.

Question 4

What is the main difference between experimental and non-experimental research designs?

Accepted Answer

Experimental designs use random assignment, while non-experimental designs do not.

Answer

Experimental designs can use both quantitative and qualitative data, just like non-experimental designs.

Answer

Experimental designs can be used for both hypothesis testing and exploratory research questions, as can non-experimental designs.

Answer

Experimental designs do not necessarily require large sample sizes, and neither do non-experimental designs.

Question 5

Which research design involves manipulating one or more independent variables to observe their effect on a dependent variable?

Accepted Answer

Experimental research

Answer

Survey research

Answer

Correlational research

Answer

Observational research

Question 6

Which research design is used to investigate the relationship between variables without manipulating them?

Accepted Answer

Correlational research

Answer

Observational research

Answer

Experimental research

Answer

Survey research

Question 7

Which research design is primarily used to provide a detailed description of a phenomenon?

Accepted Answer

Descriptive research

Answer

Correlational research

Answer

Experimental research

Answer

Survey research

Question 8

Which research design involves studying a phenomenon in its natural setting over an extended period?

Accepted Answer

Ethnography

Answer

Grounded theory

Answer

Phenomenology

Answer

Narrative inquiry

Question 9

Which type of research design aims to develop a theory based on the analysis of data?

Accepted Answer

Grounded theory

Answer

Narrative inquiry

Answer

Phenomenology

Answer

Ethnography

Question 10

Which research design is used to examine the experiences of individuals over time?

Accepted Answer

Narrative inquiry

Answer

Grounded theory

Answer

Ethnography

Answer

Phenomenology

Question 11

Which research design involves conducting multiple studies that build upon each other in a sequential manner?

Accepted Answer

Sequential mixed-methods research

Answer

Multi-phase mixed-methods research

Answer

Concurrent mixed-methods research

Answer

Transformative mixed-methods research

Question 12

Which research design strategy involves collecting data from multiple sources to enhance the validity and reliability of findings?

Accepted Answer

Triangulation

Answer

Generalisation

Answer

Saturation

Answer

Replication

Question 13

Which research design involves collecting data from the same participants multiple times over a period of time?

Accepted Answer

Longitudinal

Answer

Experimental

Answer

Cross-sectional

Answer

Quasi-experimental

Question 14

Which of the following is a key strength of using a mixed methods research design?

Accepted Answer

Provides a more thorough and multifaceted understanding of the research question than either qualitative or quantitative methods alone.

Answer

Requires a smaller sample size.

Answer

Is less time-consuming than other designs.

Question 15

Which of the following is a limitation of qualitative research designs?

Accepted Answer

Findings may be difficult to generalize to a larger population.

Answer

Require a large sample size.

Answer

Are not suitable for exploring complex research questions.

Question 16

What is the main purpose of a control group in an experimental research design?

Accepted Answer

To provide a comparison group that is not exposed to the experimental treatment.

Answer

To increase the sample size of the study.

Answer

To ensure that the results are statistically significant.

Question 17

Which type of research design is most suitable for studying the experiences and perspectives of a specific individual or small group in depth?

Accepted Answer

Case study

Answer

Survey

Answer

Experiment

Answer

Mixed methods

Question 18

Which of the following is a fundamental ethical principle in research involving human participants?

Accepted Answer

Obtaining informed consent from all participants prior to their involvement in the study.

Answer

Using a large sample size.

Answer

Publishing the results of the study in a reputable journal.

Answer

Conducting the research in a timely manner.

Question 19

Which of the following is a characteristic of a valid research design?

Accepted Answer

Produces results that are accurate and representative of the population being studied.

Answer

Uses a variety of data collection methods.

Answer

Is easy to implement.

Answer

Requires a large sample size.

Question 20

Which type of research design involves collecting data by observing participants in their natural settings without manipulating or controlling the situation?

Accepted Answer

Observational

Answer

Mixed methods

Answer

Survey

Answer

Experimental

Question 21

Which of the following is a potential bias that can occur in research when participants are aware that they are being observed?

Accepted Answer

Hawthorne effect

Answer

Sampling bias

Answer

Response bias

Answer

Selection bias

Question 22

A researcher aims to investigate the effectiveness of a new teaching method on student achievement in algebra. Which research design would be the most appropriate for this study?

Accepted Answer

Experimental design

Answer

Case study

Answer

Grounded theory

Answer

Descriptive survey

Question 23

Which research design involves an in-depth examination of a specific individual, group, or event to understand its unique characteristics and gain insights into a broader phenomenon?

Accepted Answer

Case study

Answer

Phenomenological research

Answer

Action research

Answer

Correlational research

Question 24

A researcher wants to examine the relationship between students' mathematical problem-solving skills and their overall academic achievement. Which research design would be most appropriate?

Accepted Answer

Correlational research

Answer

Historical research

Answer

True experimental design

Answer

Action research

Question 25

Which of the following is NOT a strength of a cross-sectional research design?

Accepted Answer

Ability to establish cause-and-effect relationships

Answer

Cost-effectiveness

Answer

Efficient data collection

Question 26

A researcher wants to investigate the ways in which students develop their understanding of mathematical concepts. Which research design is most suitable for this purpose?

Accepted Answer

Qualitative research

Answer

Quantitative research

Answer

Mixed methods research

Question 27

A researcher uses a control group and a treatment group to compare the effects of two different teaching methods on student learning. This is an example of what type of research design?

Accepted Answer

True experimental design

Answer

Quasi-experimental design

Answer

Pre-experimental design

Question 28

Which research design involves developing theories or models based on the systematic analysis of data, often using inductive reasoning?

Accepted Answer

Grounded theory

Answer

Ethnographic research

Answer

Action research

Answer

Case study

Question 29

A teacher wants to implement a new approach to teaching geometry in their classroom and evaluate its impact on student learning. Which research design is most appropriate?

Accepted Answer

Action research

Answer

Historical research

Answer

Descriptive research

Answer

Experimental design

Question 30

Which of the following is a key characteristic of a longitudinal research design?

Accepted Answer

Data collection over an extended period to observe changes over time

Answer

Experimentally manipulating variables

Answer

Focus on data collection at a single point in time

Question 31

A researcher studying the evolution of mathematical thinking throughout history would most likely use which research design?

Accepted Answer

Historical research

Answer

Ethnographic research

Answer

Grounded theory

Answer

Action research

Question 32

A researcher wants to investigate the effectiveness of a new teaching method for solving quadratic equations. They randomly assign students to two groups: one receiving the new method and the other receiving the traditional method.  What type of research design is this?

Accepted Answer

Experimental Design

Answer

Correlational Design

Answer

Descriptive Design

Answer

Case Study

Question 33

A researcher wants to examine the relationship between students' scores on a standardized mathematics test and their attitudes towards mathematics. What type of research design would be most appropriate?

Accepted Answer

Correlational Design

Answer

Case Study

Answer

Experimental Design

Answer

Survey Design

Question 34

A researcher wants to understand the experiences and perspectives of students who have successfully overcome a learning difficulty in mathematics. What type of research design would be most appropriate?

Accepted Answer

Case Study

Answer

Action Research

Answer

Grounded Theory Design

Answer

Survey Design

Question 35

Which of the following is NOT a characteristic of a qualitative research design?

Accepted Answer

Emphasis on numerical data

Answer

Focus on understanding meaning and experiences

Answer

Use of open-ended questions

Answer

Exploration of complex social phenomena

Question 36

A researcher wants to investigate the impact of a new online learning platform on students' engagement in mathematics. They collect data from a group of students using the platform over a semester.  What type of research design is this?

Accepted Answer

Longitudinal Design

Answer

Cross-Sectional Design

Answer

Grounded Theory Design

Answer

Action Research

Question 37

A researcher wants to investigate the differences in problem-solving strategies used by students in different countries. They collect data from a sample of students in each country at the same time. What type of research design is this?

Accepted Answer

Cross-Sectional Design

Answer

Action Research

Answer

Longitudinal Design

Answer

Ethnographic Design

Question 38

A researcher wants to investigate the effectiveness of a new teaching method for solving algebraic equations. They implement the new method in their own classroom and collect data over time. What type of research design is this?

Accepted Answer

Action Research

Answer

Case Study

Answer

Experimental Design

Answer

Ethnographic Design

Question 39

Which of the following is a key advantage of using a mixed methods research design?

Accepted Answer

Combines strengths of both qualitative and quantitative approaches

Answer

More easily generalizable to larger populations

Answer

Requires less time and resources

Question 40

A researcher wants to study the social dynamics and cultural practices in a mathematics classroom. What type of research design would be most suitable?

Accepted Answer

Ethnographic Design

Answer

Case Study

Answer

Grounded Theory Design

Answer

Survey Design

Question 41

A researcher wants to develop a theory about the process of students' mathematical problem-solving. They collect data through interviews and observations and analyze it to identify emerging patterns and themes. What type of research design is this?

Accepted Answer

Grounded Theory Design

Answer

Case Study

Answer

Action Research

Answer

Ethnographic Design

Question 42

Which research design is characterized by the researcher manipulating an independent variable to observe its effect on a dependent variable?

Accepted Answer

Experimental design

Answer

Descriptive design

Answer

Qualitative design

Answer

Correlational design

Question 43

A research design that seeks to describe and interpret a phenomenon as it occurs in its natural setting is:

Accepted Answer

Ethnographic design

Answer

Grounded theory design

Answer

Case study design

Answer

Narrative inquiry design

Question 44

Which type of research design involves collecting data from a large sample to generalize findings to a wider population?

Accepted Answer

Survey design

Answer

Correlational design

Answer

Experimental design

Answer

Case study design

Question 45

A research design that allows the researcher to explore a research question in depth is:

Accepted Answer

Case study design

Answer

Experimental design

Answer

Survey design

Answer

Correlational design

Question 46

Which research design involves studying a single group of participants over time?

Accepted Answer

Longitudinal design

Answer

Case study design

Answer

Cohort study design

Answer

Cross-sectional design

Question 47

A research design that investigates the relationship between two or more variables without manipulating them is:

Accepted Answer

Correlational design

Answer

Experimental design

Answer

Longitudinal design

Answer

Survey design

Question 48

Which research design involves collecting data from a non-random sample?

Accepted Answer

Convenience sampling

Answer

Random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Question 49

A research design that uses a combination of qualitative and quantitative methods is:

Accepted Answer

Mixed methods design

Answer

Action research design

Answer

Quantitative design

Answer

Qualitative design

Question 50

Which research design is appropriate for studying the effects of a new teaching method on student achievement?

Accepted Answer

Experimental design

Answer

Descriptive design

Answer

Qualitative design

Answer

Correlational design

Question 51

A research design that investigates the relationship between two or more variables by manipulating one variable and observing its effect on the other is:

Accepted Answer

Experimental design

Answer

Qualitative design

Answer

Correlational design

Answer

Descriptive design