In this article, we explore an emerging organization that unfolds during the implementation of a collaborative and practice-oriented professional development program (PD) called Action Learning. In Action Learning, local mathematics supervisors facilitate meetings where mathematics teachers collaboratively discuss and develop interventions in their own teaching. Thereafter, teachers carry out their interventions and are observed by the team, who afterwards provide feedback in an evaluation meeting, thereby taking on a central role in the PD program. Drawing on qualitative interviews of teachers, local supervisors, and school managers and observations of meetings in the PD program, we investigate what roles emerge for local supervisors, and how their contributions are framed by colleagues and school managers. This identifies three simultaneously present logics among the stakeholders, positioning the supervisors in roles as project leaders, academic beacons, and equal coaches, confronting each of them with different and mutually exclusive expectations.
The impact sheet to this article can be accessed at 10.6084/m9.figshare.16610119.
The development of a large-scale professional development project for Swedish mathematics teachers is retrospectively examined. By referring to documentation produced by stakeholders in the development process, the stakeholder’s design recommendations and underlying assumptions on teacher development are described. Seeing the development as a co-determination process explains how research-based principles appearing early in the process gradually change to become something different in the end, without the reasons for this shift ever being explicitly discussed in stakeholders’ documentations. It is discussed whether the distributed way of constructing the program might cause difficulties in sticking to an explicit theory of change.
The impact sheet to this article can be accessed at 10.6084/m9.figshare.16610113.
This paper first introduces and reviews the existing research on the well-known “students–professors (S/P) problem”, which was first formulated in 1979. Next, it presents an empirical study of Danish upper secondary students’ answers to two mathematical modeling versions of the S/P-problem; a mathematization version (296 students), and a de-mathematization version (658 students). Besides reproducing several previously reported findings, e.g., the so-called reversal error, the study identifies new error types not previously reported in the literature. The mathematical modeling perspective adopted, along with a mixed-methods design, give rise to new potential explanations of the reversal error as well as explanations of the new error types. Our study shows that interpreting the linguistic formulation of the S/P-problem statement is not only related to language but is intrinsically of a mathematical – and cognitive – nature as well. Altogether, there is still more to be said about the S/P-problem forty years after its emergence.
The impact sheet to this article can be accessed at 10.6084/m9.figshare.16610104.
In this paper, we share two conceptual replications of Hill et al.’s (2012c) study linking Mathematical Knowledge for Teaching (MKT), Mathematical Quality of Instruction (MQI), and student assessment scores. In study 1, we share data from 4th and 5th grade teachers in an urban school district. In study 2, we share data from middle school teachers in a school district with a relatively high proportion of emergent bilingual students. By varying contexts, we found that Hill et al.’s (2012c) suggested use of the MKT cutoff points was not warranted in our differing settings. Further, we found some significant relationships between MKT, MQI, and student assessments; however, we were not able to reproduce these consistently with our data. We suggest that the relationship between teaching practice and MKT may be quite sensitive to contextual factors including grade level, demographics, school effects, and assessments. We recommend that policymakers and researchers take caution when using such instruments to evaluate program initiatives and identify teachers for remediation or leadership positions.
The impact sheet to this article can be accessed at 10.6084/m9.figshare.16610080.