Three articles were published online in Journal of Mathematics Teacher Education on Monday:
- Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions, by Ji-Won Son and Sandra Crespo. Abstract: Recognizing meaning in students’ mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary and secondary teachers to a student’s non-traditional strategy for dividing fractions. Six categories of reasoning were constructed, making a distinction between deep and surface layers. The connections between the participants’ reasoning, their teaching response, and their beliefs about mathematics teaching were investigated. We found that there were not only differences but also similarities between the prospective elementary and secondary teachers’ reasoning and responses. We also found that those who unpacked the mathematical underpinning of the student’s non-traditional strategy tended to use what we call “teacher-focused” responses, whereas those doing less analysis work tended to construct “student-focused” responses. These results and their implications are discussed in relation to the influential factors the participants themselves identified to explain their approach to the given teaching-scenario task.
- Working with mathematics teachers and immigrant students: an empowerment perspective, by Núria Planas and Marta Civil. Abstract: This article centers on a professional development project with a group of high school mathematics teachers in Barcelona. The eight participating teachers taught in low-income schools with a high percentage of immigrant students. Our model of professional development is based on the involvement of the teachers as co-researchers of their local contexts and practices. In this approach, our concept of social justice is tied to the notion of empowerment, both for teachers and for their immigrant students. Our analysis of data from twelve sessions with the teachers shows the development of a shared awareness of their local situation that leads to their questioning of their practices followed by a reconstruction of those. Teachers worked together to move from talking to action. Our analysis of data from the implementation of one lesson in a classroom shows that action, and illustrates signs of empowerment in the teacher and the students, such as students’ challenging of aspects of the task and taking on a more participatory role and the teacher’s reflection on the overall experience.
- Understanding the influence of two mathematics textbooks on prospective secondary teachers’ knowledge, by Jon D. Davis. Abstract: This study examines the influence of reading and planning from two differently organized mathematics textbooks on prospective high school mathematics teachers’ pedagogical content knowledge and content knowledge of exponential functions. The teachers completed a pretest and two posttests. On the pretest, the teachers possessed an incomplete understanding of content and pedagogical content knowledge related to exponential functions. The teachers’ understanding of how to translate from table to closed-form and recursive equations grew as a result of their use of the Mathematics: Modeling Our World textbook, while the Discovering Algebra textbook appeared to be more beneficial in terms of pedagogical content knowledge. Teachers read from the student lessons in both textbooks, but read differently from the sections of both textbooks intended for the teacher. They focused more on the purpose of the Mathematics: Modeling Our World lesson and more on the places where students might experience difficulties in the margins of the Discovering Algebra lesson. The teachers’ learning was influenced by their own personal characteristics (e.g., previous textbook experiences) as well as textbook qualities (e.g., organization).