Mathematics education research encompasses a wide range of topics, including how students learn mathematics, how to develop effective teaching methods, and how to evaluate the effectiveness of different curricula. The ultimate goal of this research is to improve the teaching and learning of mathematics.

Action research is a type of research that is conducted by practitioners in order to improve their own practice. While it is sometimes used in mathematics education, it is not as common as quantitative, qualitative, and experimental research methods.

Mathematical development refers to the study of how students' mathematical thinking changes over time. This includes how they learn new mathematical concepts, how they solve mathematical problems, and how they apply mathematics to real-world situations.

Constructivism is a theory of learning that emphasizes the importance of active engagement in the learning process. According to this theory, students learn best when they are able to construct their own understanding of mathematical concepts through exploration and experimentation.

Paper-and-pencil tests are not as common in mathematics education research as performance tasks, interviews, and observations. This is because paper-and-pencil tests often do not provide a complete picture of students' mathematical understanding.

Pedagogy is the study of how teachers teach. This includes how they plan lessons, how they interact with students, and how they assess student learning. Pedagogical research is an important part of mathematics education research, as it helps to identify effective teaching practices.

Narrative design is not a common type of research design used in mathematics education. This is because narrative design is often used to study individual cases, which can make it difficult to generalize the findings to a larger population.

Ethnomathematics is the study of how students use mathematics in their everyday lives. This includes how they use mathematics to solve problems, make decisions, and communicate with others. Ethnomathematical research is important because it can help to identify ways to make mathematics more relevant and meaningful to students.

Meta-analysis is not a common type of data analysis method used in mathematics education research. This is because meta-analysis is typically used to synthesize the findings of multiple studies, which is not always necessary in mathematics education research.

Affective factors in mathematics education refer to the study of how students' attitudes, beliefs, and emotions about mathematics affect their learning. This includes how students' attitudes and beliefs influence their motivation to learn mathematics, their self-efficacy in mathematics, and their overall achievement in mathematics.

Assessment intervention is not a common type of intervention used in mathematics education research. This is because assessment interventions are typically used to improve the accuracy and fairness of assessments, rather than to improve student learning.

Cross-cultural mathematics education is the study of how mathematics is used in different cultures. This includes how different cultures use mathematics to solve problems, make decisions, and communicate with others. Cross-cultural mathematics education research is important because it can help to identify ways to make mathematics more relevant and meaningful to students from different cultural backgrounds.

The history of mathematics education is not a common type of research question in mathematics education. This is because the history of mathematics education is typically studied by historians, rather than by mathematics education researchers.

Interdisciplinary mathematics education is the study of how mathematics is used in different disciplines. This includes how mathematics is used to solve problems, make decisions, and communicate with others in different fields. Interdisciplinary mathematics education research is important because it can help to identify ways to make mathematics more relevant and meaningful to students from different disciplines.

All of the above are common types of research findings in mathematics education. These findings have been supported by a large body of research and have helped to inform the development of effective mathematics teaching practices.