Abstract
In this chapter we reflect on how the characteristics of the online environment that coordinated knowing and doing influenced the development of prospective mathematics teachers’ noticing. The formal online environment designed is part of a traineeship period included in a mathematics teaching degree program at the Universidad Estatal a Distancia de Costa Rica (UNED). Five prospective teachers wrote five narratives about their own teaching and shared and discussed them with their classmates and the university tutor in the online forums. To describe how noticing developed as a knowing and doing process online, we analyzed the presence of Mathematically Significant Pedagogical Opportunities to Build on Student Thinking (MOSTs) in prospective teachers’ narratives (knowing); we also examined whether prospective teachers took advantage of them during the lesson (doing). We then compared the narratives by examining the changes identified in the MOSTs and how prospective teachers took advantage of them. Characteristics of PT noticing development were evidenced in the changes one can observe in their narratives. These changes were based on how PTs took advantage of the MOSTs and whether PTs took advantage of different MOSTs by relating or not relating them. We exemplified these changes with the narratives of two prospective teachers. Furthermore, results showed that the development of prospective teachers’ noticing was linked to changes in their practices: changes in class management and changes in lesson planning. This link can be explained by the characteristics of the formal online environment: the cycles of writing narratives, sharing and discussing them in online forums, receiving feedback, and then writing another narrative.
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Acknowledgments
This research was supported by the project EDU2017-87411-R from Ministerio de Economia, Industria y Competitividad (Spain), and by the project PROMETEO2017-135 from Conselleria de Educación, Investigación, Cultura y Deporte de la Generalitat Valenciana (Spain).
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Appendices
Appendix 1: Summary of the instruction to write the narratives and the guided questions provided
From the lessons given during the week, choose a situation in which students are developing some aspects of the mathematical competence that you considered relevant, and describe this situation (you can use the guided questions provided). During the next week, you have to share the narrative with your fellows and give feedback to other narratives. To write the new narrative, you have to consider the suggestions given by your fellows and the tutor.
Guided questions:
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Describe the situation (identifying): Provide a detailed description of the activity (curricula contents, materials, resources, etc.), what students do (students’ answers to the activity, difficulties, etc.), and what the teacher does (methodology, interactions, etc.).
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Interpret the situation (interpreting): Indicate the activity’s mathematical objectives and provide evidence from students’ answers that they have achieved the objectives (students’ understanding of the mathematical content and difficulties).
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Complete the situation (taking decisions): Complete the situation indicating how you will proceed in order to help students progress in their learning of the mathematical content.
Appendix 2: Instruction provided in each online forum
In this forum, you can upload your narrative and provide and see feedback to/from other fellows’ narratives.
To provide feedback to your fellows, you can consider the guided questions, for example, you can observe whether in the narrative:
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The situation is described in detail providing a description of the activity (with materials, resources, etc.), what students did (writing some interactions) and what the teacher did.
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The situation is interpreted with regard to whether students’ have achieved the learning objectives, providing evidence from students’ thinking.
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The situation is completed indicating how the teacher would proceed in order to help students progress in their mathematical understanding.
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Fernández, C., Llinares, S., Rojas, Y. (2021). The Impact of an Online Teacher Education Program on the Development of Prospective Secondary Mathematics Teachers’ Noticing. In: Hollebrands, K., Anderson, R., Oliver, K. (eds) Online Learning in Mathematics Education. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-80230-1_10
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