An Approach to the Teacher Educator’s Pedagogical Content Knowledge for the Development of Professional Noticing in Pre-Service Teacher Education
Abstract
:1. Introduction
2. Theoretical Framework
2.1. Professional Knowledge of Mathematics Teacher Educators in Pre-Service Teacher Education
2.2. Development of Professional Noticing in Initial Teacher Education
2.3. The Semiotic Registers of Representation and Their Importance in the Teaching/Learning of Mathematics
- The presence of an identifiable representation;
- The treatment of a representation consists of transforming the representation within the same register where it was formulated. For example, transforming 2(x + 1) = 3 into 2x = 1, as both are symbolic representations of the same equation (object);
- The conversion of a representation consists of transforming the representation into another one in another register while preserving part or all of the initial meaning. For example, converting the verbal representation “an odd number” to the symbolic expression 2n + 1.
3. Methodology
3.1. Study Design and Participants
3.2. Instrument
- Identify and describe the strategy or strategies used by the student to solve the task (what has been performed);
- Characterize the ideas or meanings about the asymptote that you believe the student possesses. What information do you rely on as a teacher? (What the teacher understands and where they observe it).
3.3. Data Analysis
- Knowledge of the first threshold problem [26]: This variable takes the values yes or no. Yes, if the PST demonstrates an awareness of how the semiotic register of the task conditions the strategy used by the student; no, otherwise. Reasoning like “since the function is given by a graph, Juan David couldn’t use the algebraic expression of the function to find the limit as it approaches infinity. Therefore, he analyzes the behavior graphically by observing if the graph seems to stabilize around a specific value”, which would be evidence of knowledge of the first threshold problem;
- Treatments: As previously mentioned, we aim to describe the transformations identified by the PSTs in the dialogue within the same register. To do so, the PST must indicate which registers of representation they believe Juan David uses during the fragment. Possible evidence of treatment can be found when Juan David says: “As seen in the image, it seems that it is not defined for negative values of x, so I will focus on the positive values. I would say that it looks like some kind of sine or cosine, and those functions are oscillating.” As we noted before, the student is using a graphical representation of the limit all the time;
- Conversions: This variable considers the transformations identified by the PST in Juan David’s reasoning between different registers. To do so, the PST must indicate which registers of representation they believe Juan David uses during the fragment. Possible evidence of conversion can be found when Juan David says: “the maxima (marked with dots) are becoming more negative each time, so if the larger values are getting smaller and smaller, the function tends to negative infinity.” Now, Juan David changes from a graphical idea of maxima (dots) to a numerical representation (their numerical y coordinates).
4. Results
- Initial level
- Intermediate level
- Advanced Level
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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Level of Development | Semiosis Activities | Categories | Perc. of PSTs (Per Level) | Perc. of PSTs (Total) |
---|---|---|---|---|
Initial | Knowledge of the first threshold problem | Yes | 6 (26.1%) | |
No | 17 (73.9%) | 23 (60.5%) | ||
Treatments | HA | 0 (0%) | ||
SA | 1 (4.3%) | |||
No asymptote type specified | 8 (34.8%) | |||
Conversions | HA | 1 (4.3%) | ||
SA | 1 (4.3%) | |||
No asymptote type specified | 0 (0%) | |||
Intermediate | Knowledge of the first threshold problem | Yes | 4 (50%) | 8 (21.1%) |
No | 4 (50%) | |||
Treatments | HA | 3 (37.5%) | ||
SA | 6 (75%) | |||
No asymptote type specified | 3 (37.5%) | |||
Conversions | HA | 0 (0%) | ||
SA | 2 (25%) | |||
No asymptote type specified | 2 (25%) | |||
Advanced | Knowledge of the first threshold problem | Yes | 3 (42.9%) | 7 (18.4%) |
No | 4 (57.1%) | |||
Treatments | HA | 6 (85.7%) | ||
SA | 6 (85.7%) | |||
No asymptote type specified | 1 (14.3%) | |||
Conversions | HA | 4 (57.1%) | ||
SA | 3 (42.9%) | |||
No asymptote type specified | 1 (14.3%) |
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Pérez-Montilla, A.; Arnal-Palacián, M. An Approach to the Teacher Educator’s Pedagogical Content Knowledge for the Development of Professional Noticing in Pre-Service Teacher Education. Educ. Sci. 2023, 13, 544. https://doi.org/10.3390/educsci13060544
Pérez-Montilla A, Arnal-Palacián M. An Approach to the Teacher Educator’s Pedagogical Content Knowledge for the Development of Professional Noticing in Pre-Service Teacher Education. Education Sciences. 2023; 13(6):544. https://doi.org/10.3390/educsci13060544
Chicago/Turabian StylePérez-Montilla, Andrés, and Mónica Arnal-Palacián. 2023. "An Approach to the Teacher Educator’s Pedagogical Content Knowledge for the Development of Professional Noticing in Pre-Service Teacher Education" Education Sciences 13, no. 6: 544. https://doi.org/10.3390/educsci13060544