There are only few studies on teachers’ professional development that involves
providing teachers with a research-based lens through which they can analyze and
think about their lessons. In this paper, I present a framework, adapted from research,
for analyzing the quality of mathematics lessons and illustrate its use by teachers for
assessing a lesson. The teachers’ version of the research-based framework I propose
here aim to add to this repertoire of tools for this kind of work. The development of
this framework is part of a larger research project that involves developing of a
research-informed lesson study model for mathematics teachers in Philippines. The
project is in its initial stages and its first focus is the research lesson.
In lesson study, the research lesson is the shared space and the object under
investigation of the teachers. It is considered the critical mediator of professional
learning hence the importance of having a practical but theory-based framework to
serve as lens to teachers in analyzing the research lesson particularly the quality of
the mathematics lesson.

In the study, quality of mathematics lesson is defined in the study in terms of two interrelated components: the quality of the mathematics and the quality of mathematics instruction. The word quality refers to an attribute of something (x) or a standard of x. A framework for analyzing quality mathematics lesson should therefore capture both sense. There are a number of frameworks in the field that have been used in analyzing mathematics lessons (Charalambous & Praetorius, 2018) but the framework that responds to our notion of quality mathematics lesson and at the same time aligns with the sociocultural perspective of the study is the mathematical discourse in instruction (MDI) framework (Adler & Ronda, 2015). The MDI framework consist of five interacting cultural tools of instruction namely task, examples, naming, legitimations and learner participation that together mediates the object of learning of the lesson.

Our description of quality of mathematics in the study is a function of a view of mathematics as a form of scientific knowledge (Vygotsky, 1978) which is characterized by its generality, structure, consistency and symbolic systems. The study focuses particularly to its generality attribute. This is to foreground to teachers that generality or generalizing is an important goal and means to understand mathematics. Opportunities to generalize are visible in the selection and sequencing of examples, in the problematic in the tasks, in the choice of words to refer to the mathematical aspects in the instructional talk, and the extent to which claims are substantiated mathematically. On the other hand, attributes of quality of mathematics instruction include learners’ participation, coherence of the lesson and explicit connections. Indicators of standard for each of these attributes were developed building from those in the MDI framework. In the presentation, I will discuss the framework with more detail and exemplify its use. Preliminary analysis showed aspects of mathematics and aspects of its instruction that were foregrounded including those not captured by the framework.

References Adler, J., & Ronda, E. (2015). A framework for describing mathematics discourse in instruction and interpreting differences in teaching. African Journal of Research in Mathematics, Science and Technology Education, 19(3), 237-254. doi:10.1080/10288457.2015.1089677

Charalambous, C. Y., & Praetorius, A.-K. (2018). Studying mathematics instruction through different lenses: setting the ground for understanding instructional quality more comprehensively. ZDM, 1-12.

Dr. Ronda presenting the MDI framework at the WALS Conference 2018 |

In the study, quality of mathematics lesson is defined in the study in terms of two interrelated components: the quality of the mathematics and the quality of mathematics instruction. The word quality refers to an attribute of something (x) or a standard of x. A framework for analyzing quality mathematics lesson should therefore capture both sense. There are a number of frameworks in the field that have been used in analyzing mathematics lessons (Charalambous & Praetorius, 2018) but the framework that responds to our notion of quality mathematics lesson and at the same time aligns with the sociocultural perspective of the study is the mathematical discourse in instruction (MDI) framework (Adler & Ronda, 2015). The MDI framework consist of five interacting cultural tools of instruction namely task, examples, naming, legitimations and learner participation that together mediates the object of learning of the lesson.

Our description of quality of mathematics in the study is a function of a view of mathematics as a form of scientific knowledge (Vygotsky, 1978) which is characterized by its generality, structure, consistency and symbolic systems. The study focuses particularly to its generality attribute. This is to foreground to teachers that generality or generalizing is an important goal and means to understand mathematics. Opportunities to generalize are visible in the selection and sequencing of examples, in the problematic in the tasks, in the choice of words to refer to the mathematical aspects in the instructional talk, and the extent to which claims are substantiated mathematically. On the other hand, attributes of quality of mathematics instruction include learners’ participation, coherence of the lesson and explicit connections. Indicators of standard for each of these attributes were developed building from those in the MDI framework. In the presentation, I will discuss the framework with more detail and exemplify its use. Preliminary analysis showed aspects of mathematics and aspects of its instruction that were foregrounded including those not captured by the framework.

References Adler, J., & Ronda, E. (2015). A framework for describing mathematics discourse in instruction and interpreting differences in teaching. African Journal of Research in Mathematics, Science and Technology Education, 19(3), 237-254. doi:10.1080/10288457.2015.1089677

Charalambous, C. Y., & Praetorius, A.-K. (2018). Studying mathematics instruction through different lenses: setting the ground for understanding instructional quality more comprehensively. ZDM, 1-12.

**Keywords:**Professional Development, Mathematics Instruction, Analytic Framework, Lesson Study Model, Research lesson*This paper was presented at the World Association of Lesson Studies International Conference 2018 at Beijing Normal University, Beijing, China on 23-26 November 2018.*

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