# Author I. Jones

Biography: Ian Jones is a lecturer in the Mathematics Education Centre at Loughborough University. Prior to this he was a Royal Society Shuttleworth Education Research Fellow and has taught in various schools around the world. Ian is widely published in the discipline of mathematics education, with a particular interest in the assessment of mathematical understanding and the cognitive processes of learning to think mathematically.

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 http://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 http://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. Fulltext at http://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 http://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.

Jones I. (2015) Building Bridges that are Functional and Structural. Constructivist Foundations 10(3): 332–333. Fulltext at http://cepa.info/2143

Jones I.
(

2015)

Building Bridges that are Functional and Structural.
Constructivist Foundations 10(3): 332–333.
Fulltext at http://cepa.info/2143
Open peer commentary on the article “Building Bridges to Algebra through a Constructionist Learning Environment” by Eirini Geraniou & Manolis Mavrikis. Upshot: In their article, Geraniou and Mavrikis describe an environment to help children explore algebraic relationships through pattern building. They report on transfer of learning from the computer to paper, but also implicit is transfer from concrete to abstract contexts. I make the case that transfer from abstract to concrete contexts should complement such approaches.

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