# Author P. Borg

Biography: Philip Borg has taught mathematics in secondary and postsecondary schools in Malta for twenty years. At the moment he teaches advanced level pure mathematics at De La Salle College (Malta). He is also a visiting lecturer at the University of Malta, where he teaches mathematics content and pedagogy to prospective mathematics and technology teachers, a post which he has held since 2003. Borg’s research interests are in mathematics education, with particular focus on algebra, educational technology, and radical constructivism.

Borg P. (2016) The University Lecture Room and the School Classroom: Does the Stage Affect the Acting? Constructivist Foundations 12(1): 107–108. https://cepa.info/3824

Borg P.
(

2016)

The University Lecture Room and the School Classroom: Does the Stage Affect the Acting?
Constructivist Foundations 12(1): 107–108.
Fulltext at https://cepa.info/3824
Open peer commentary on the article “A Cybernetic Approach to Contextual Teaching and Learning” by Philip Baron. Upshot: I establish similarities between the author’s teaching approach and my perspective toward teaching and learning. I also highlight some important differences between the didactic situation of a university lecturer and that of a schoolteacher that may be pertinent to the principal issues we discuss in our articles.

Borg P., Hewitt D. & Jones I. (2016) Authors’ Response: The M-N-L Framework: Bringing Radical Constructivist Theories to Daily Teaching Practices. Constructivist Foundations 12(1): 83–90. https://cepa.info/3818

Borg P., Hewitt D. & Jones I.
(

2016)

Authors’ Response: The M-N-L Framework: Bringing Radical Constructivist Theories to Daily Teaching Practices.
Constructivist Foundations 12(1): 83–90.
Fulltext at https://cepa.info/3818
Upshot: We seek to address several questions and statements made in the commentaries by elaborating on the four main aspects of the M-N-L framework. Before doing so, we discuss the issue of constructivist teaching in the context of schools. We conclude by hypothesizing on what would be lost in the M-N-L framework by taking constructivism out of the picture.

Borg P., Hewitt D. & Jones I. (2016) Negotiating Between Learner and Mathematics: A Conceptual Framework to Analyze Teacher Sensitivity Toward Constructivism in a Mathematics Classroom. Constructivist Foundations 12(1): 59–69. https://cepa.info/3810

Borg P., Hewitt D. & Jones I.
(

2016)

Negotiating Between Learner and Mathematics: A Conceptual Framework to Analyze Teacher Sensitivity Toward Constructivism in a Mathematics Classroom.
Constructivist Foundations 12(1): 59–69.
Fulltext at https://cepa.info/3810
Context: Constructivist teachers who find themselves working within an educational system that adopts a realist epistemology, may find themselves at odds with their own beliefs when they catch themselves paying closer attention to the knowledge authorities intend them to teach rather than the knowledge being constructed by their learners. Method: In the preliminary analysis of the mathematical learning of six low-performing Year 7 boys in a Maltese secondary school, whom one of us taught during the scholastic year 2014-15, we constructed a conceptual framework which would help us analyze the extent to which he managed to be sensitive to constructivism in a typical classroom setting. We describe the development of the framework M-N-L (Mathematics-Negotiation-Learner) as a viable analytical tool to search for significant moments in the lessons in which the teacher appeared to engage in what we define as “constructivist teaching” (CT) during mathematics lessons. The development of M-N-L is part of a research program investigating the way low-performing students make mathematical sense of new notation with the help of the software Grid Algebra. Results: M-N-L was found to be an effective instrument which helped to determine the extent to which the teacher was sensitive to his own constructivist beliefs while trying to negotiate a balance between the mathematical concepts he was expected to teach and the conceptual constructions of his students. Implications: One major implication is that it is indeed possible for mathematics teachers to be sensitive to the individual constructions of their learners without losing sight of the concepts that society, represented by curriculum planners, deems necessary for students to learn. The other is that researchers in the field of education may find M-N-L a helpful tool to analyze CT during typical didactical situations established in classroom settings.

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