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Studying the process of becoming a teacher educator in technology-enhanced mathematics

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Abstract

In this paper, we explore the process of becoming a teacher educator in the pedagogical use of digital tools in mathematics teaching. The study took place in the context of an in-service program during the trainees’ engagement in their practicum fieldwork activities including the process observation–reflection–design–implementation–reflection. We explored the features of this context that facilitated the trainees’ transition from the level of trainee educator to the level of teacher educator as well as the nature of the trainees’ documentation work for teachers. The results showed that observation of other teacher educators’ teaching in conjunction with reflection during the program’s respective sessions facilitated the trainees’ transition to the professional level. The identified operational invariants underlying the trainees’ designs concerned the focus of their observation in teacher education classrooms, the importance they attributed to the constraints and opportunities provided by the wider educational context and epistemological issues regarding the teaching and learning of mathematics with technology. The analysis of trainees’ designs revealed three kinds of documents (“explanatory,” “instructive” and “facilitative”) and corresponding roles of trainees during the implementation. These documents targeted different aspects of TPACK depending on the trainees’ conceptualizations of teachers’ roles either “as students” or “of students.”

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Notes

  1. Teachers’ personal theory of knowledge and knowing (Hofer 2004).

  2. From a broader epistemological perspective, this view is closer to fallibilism that considers a mathematicians’ activity as a process including conjectures, refutations and new proofs (Lakatos 1976).

  3. Mathematics as the science of typical deduction from axioms to theorems (Davis and Hersh 1981).

  4. Scenarios are activity plans addressing critical aspects of the teaching and learning process and the corresponding materials (digital, e.g., microworlds, or non-digital, e.g., worksheets). A scenario structure was developed by the Educational Technology Lab (http://etl.ppp.uoa.gr) (National and Kapodistrian University of Athens) which participated in the design of the program and the course materials. This structure included: (1) title; (2) identity (i.e., author, subject area, topic); (3) rationale (i.e., innovations, added value by the use of technology, students’ learning problems addressed); (4) context of implementation (i.e., class year, duration, location, prerequisite knowledge, classroom social orchestration, goals); (5) phases of implementation (i.e., sequence and analysis of activities, participants’ roles, anticipated teaching/learning processes); (6) possible extension; and (7) references.

  5. The aspects involved in the observation form were: topic and aims of the lesson; trainees’ levels concerning the use of technology; resources used; classroom organization; teaching methods/processes; and classroom interactions.

  6. Templates in which trainees described aspects of their designs and their experiences from the implementation (e.g., distance between design and actual implementation, teachers’ participation/difficulties, potential changes in case of redesigning a scenario).

  7. The category ‘SI’ concerned primarily the institutional role of CTES within the national educational system (e.g., number of teachers in CTES classrooms, timetable), and it seems to be of less importance for the trainees at this phase of their training.

  8. Function Probe is a multi-representational software with three windows: Table, graph, and calculator. You can produce function graphs in a number of ways, e.g., inserting a formula for the function in the graph (“Input field”), “receiving” ordered pairs (x, y) from a table (“x” and “y” columns can be generated). Particular tools allow horizontal and vertical transformations of functions (translations, reflections and stretches) through direct actions on the graph. The graphs of the transformed functions are depicted in the same window.

  9. The stretch tool allows mouse-driven horizontal and vertical stretching of the graph. The corresponding magnitude of the stretches changes dynamically during the stretching and appears in the right corner of the “Input field.” A history window in the graph allows viewing the formulas of the transformed functions.

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Authors and Affiliations

  1. Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece

    Giorgos Psycharis

  2. Educational Technology Lab, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece

    Elissavet Kalogeria

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  1. Giorgos Psycharis
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  2. Elissavet Kalogeria
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Correspondence to Giorgos Psycharis.

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Psycharis, G., Kalogeria, E. Studying the process of becoming a teacher educator in technology-enhanced mathematics. J Math Teacher Educ 21, 631–660 (2018). https://doi.org/10.1007/s10857-017-9371-5

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