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The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. We conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical opportunities—what we call Mathematically Significant Pedagogical Opportunities to Build on Student Thinking. We analyze dialogue to illustrate a process for determining whether a classroom instance offers such an opportunity and to demonstrate the usefulness of the construct in examining classroom discourse. This construct contributes to research and professional development related to teachers' mathematically productive use of student thinking by providing a lens and generating a common language for recognizing and agreeing on a critical core of student mathematical thinking that researchers can attend to as they study classroom practice and that teachers can aspire to notice and build upon when it occurs in their classrooms.

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This study investigated pre-service secondary mathematics teachers' (PSTs) beliefs about teaching mathematics with technology, the experiences in which those beliefs were grounded, and the organizational structure of those beliefs. In particular, this article reports on research that was designed to investigate questions beyond that of whether technology can profitably be used before mathematical content has been mastered (the question about technology most commonly reported in the literature). Beliefs were defined as dispositions to act and were viewed through what is referred to as the sensible system framework. Through the qualitative research methodology called grounded theory, four PSTs were purposefully selected and studied. The primary dimensions of the PSTs' core beliefs with respect to technology, referred to as their beliefs about the nature of technology in the classroom, were beliefs about the availability of technology, about the purposeful use of technology, and about the importance of teacher knowledge of technology.Résumé : Cette étude porte sur les idées préconçues des futurs enseignants des mathématiques au secondaire quant à l'enseignement des mathématiques par le moyen des technologies, les expériences sur lesquelles ces idées se fondent et le système grâce auquel ces idées sont maintenues. En particulier, nous analysons les résultats de recherches réalisées dans le but d'aller au-delà des idées les plus courantes dans la littérature sur les technologies, à savoir si les technologies peuvent être utilisées de façon profitable avant que les contenus mathématiques aient été maîtrisés. Ces idées ont été définies comme une disposition à agir, et sont étudiées dans un cadre que nous appelons système sensé. Au moyen d'une méthodologie de recherche qualitative appelée théorie fondée, quatre futurs enseignants ont été choisis comme objet de notre étude. Les principales dimensions des idées fondamentales de ces futurs enseignants sur les technologies, que nous avons appelées idées sur la nature des technologies dans la salle de classe, portaient sur la disponibilité des technologies, leurs différentes utilisations pratiques ainsi que l'importance des connaissances qu'en ont les enseignants.

We present the results of 2 studies, a citation-based study and an opinion-based study, that ranked the relative quality of 20 English-language journals that exclusively or extensively publish mathematics education research. We further disaggregate the opinion-based data to provide insights into variations in judgment of journal quality based on geographic location, journal affiliations and publishing records, and experience in the field. We also report factors that survey respondents indicated were important indicators of journal quality. Finally, we compare our results to previous related rankings and conclude by discussing how our results might inform authors, editors, and evaluators in their efforts to publish and recognize quality research in mathematics education.

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