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"Mathematics teaching"
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Flipped classroom as a reform-oriented approach to teaching mathematics
Innovative methods can change the paradigm of teaching mathematics and inspire teachers to espouse new ideas and gain new experiences. The flipped classroom (FC) is currently an innovative pedagogical approach that has high potential to transform the teaching of mathematics. In the case study described in this paper, we investigated one mathematics teacher's transformation of teaching in two mathematics classrooms through implementing interventions based on FC methods; furthermore, we identified several key points of FC design as well as challenges and opportunities afforded by teaching mathematics in FCs. The results of the study showed that the tasks posed by the teacher, the implemented discourse, teacher feedback and scaffolding, and the teaching-learning environment were changed in FCs, although the approaches used by the teacher to analyze the tasks and students' learning were similar to those used in non-FCs, which points out the strengths of traditional teaching approaches. The study indicates that although teaching mathematics in FCs created some difficulties for teaching, well-designed FCs offered a great opportunity to promote students' mathematical thinking and understanding. Overall, the results highlight that through FC, teachers can develop students' mathematical potential with FCs. [Author abstract]
Journal Article
The quality of mathematics teaching from a mathematics educational perspective: what do we actually know and which questions are still open?
In this survey paper we focus on aspects of the quality of teaching mathematics from several perspectives. We differentiate between effective aspects that are empirically proven and more normative ones that constitute “good teaching” but that are highly dependent on context. High quality of mathematics teaching includes characteristics from a generic point of view as well as those that rely upon more subject- and topic-specific features. In the paper we draw upon examples of the research traditions in Germany and in the US—where the discussion regarding quality of mathematics teaching has been particularly intensive—to provide a short overview about empirical key findings. We then describe open questions in this research field and conclude by proposing a conceptualization of high quality mathematics teaching that foregrounds the relationship between generic and topic-specific and also considers different possibilities for the measurement of the quality.
Journal Article
Comparing how college mathematics instructors and high-school teachers recognize professional obligations of mathematics teaching when making instructional decisions
This paper investigates how mathematics instructors' recognition of the professional obligations of mathematics teaching varies based on their institutional environment, specifically whether they teach high school or college mathematics. Using an instrument that measures instructors’ recognition of four hypothesized professional obligations, we surveyed 471 US high school mathematics teachers and 239 university mathematics instructors to measure the extent to which they recognized professional obligations when evaluating the appropriateness of certain instructional actions. After testing measurement invariance of four item sets, each of which measures one of the four hypothesized professional obligations—disciplinary, institutional, interpersonal, and individual obligations-, we compared the instructors’ recognition of each of the four obligations between the two groups. We found that university instructors recognized the institutional obligation more than high school teachers, while recognizing the individual and interpersonal obligations significantly less. This investigation provides insight into the variation in the nature of mathematics teaching practice across different levels of schooling.
Journal Article
