Interpreting and Enacting the Danish Mathematics Communications Competency: The Relationship between Policy, Pedagogy, Curriculum, and Understanding
Reames, Matthew, Education - Curry School of Education, University of Virginia
Berry, Robert, Curry School of Education, University of Virginia
The purpose of this study is to examine how Danish teachers interpret the mathematics communications competency and how those interpretations are enacted in classroom practice. Denmark implemented mathematics process standards in 2003 and teachers and students in Denmark have had over a decade of working with those standards. This study provides insight into factors influencing how teachers interpret and implement oral and written mathematical communication in their classrooms. The results of this study can be used to inform mathematics communication instructional practice in the United States.
A grounded theory methodology was used to investigate two research questions: a) How do teachers interpret the Danish communications competency? and b) In what ways are those interpretations enacted in classroom practice? Data sources include observations, interviews with teachers and pupils, and classroom artifacts. Five themes emerged from the analysis of the data: understanding, communications, pedagogy, curriculum, and policy.
Two forms of mathematics understanding are described: procedural understanding – which includes understanding what to do to solve a mathematics problem, and understanding how to solve a mathematics problem, and connectional understanding – understanding why a problem is solved in a certain way. These two forms of understanding correspond directly with two levels of mathematics communications - procedural and connectional. The corresponding levels of mathematics communication influence not only the types of mathematical understanding a pupil develops but also how a teacher assesses a pupil’s degree of that understanding.
Education policies and the circumstances of teaching such as available instructional time and the structure of national assessments account for another aspect of how and why teachers interpret the mathematics communications competency. Two areas of pedagogy that relate to teachers’ views of mathematical understanding and communications are beliefs about communicating in mathematics, and beliefs about the role of the teacher and student. A key factor in the enactment of classroom mathematics curriculum is not the specific curriculum materials that are used, but how they are used, and how they are used depends on a teacher’s views of understanding.
The answer to the first research question is that teachers interpret the mathematics communications competency in a way that correspond with their beliefs and views of mathematics understanding as being either procedural or connectional. The answer to the second research question is that teachers enact the mathematics communications competency in classroom practice in ways that are largely consistent with their views of mathematics understanding as being either procedural or connectional. Mathematical communications is used in the classroom as a tool for both supporting and assessing different forms of procedural and connectional understanding. Implications of this study include reframing the discussion regarding classroom mathematics instruction as a continuum of mathematics understanding rather than one that emphasizes rote memorization and algorithms versus an expectation to teach for understanding.
PHD (Doctor of Philosophy)
mathematics understanding, mathematics communication, Denmark, competencies, process skills, communication, understanding, policy, pedagogy, curriculum, mathematics
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