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This is followed by an outline of South African evidence on mathematics teaching and learning related to mathematical practices that led to the choice to orient our primary mathematics knowledge for teaching course in particular ways.
It could be argued that there is not really a distinction here between the more separate integrative (CCSM) and more fundamental (Watson and Barton) views; rather, the issues and gaps seen in mathematics teaching and learning lead to the need to make visible the mathematical practices that seem to 'fall out' of enactments of mathematics in classrooms.
The proposed definition of academic literacy in mathematics includes three integrated components: mathematical proficiency, mathematical practices, and mathematical discourse.
Within our work in the Johannesburg-based Wits Maths Connect-Primary (WMC-P) research and development project, we developed a 'primary mathematics knowledge for teaching' course that incorporated attention to mathematical practices within a structure that was delineated on the basis of broad content areas.
Attention to mathematical practices continues to get wide attention in the international mathematics education literature.
The current 'common core standards for mathematics' (CCSM) (Common Core State Standards Initiative 2010) include a set of 'Standards for Mathematical Practices'.
In exploring mathematics teacher learning for teaching, Watson and Barton (2011) suggest a 'fundamental' view of mathematical practices in which 'mathematical modes of enquiry' are central: 'Knowing mathematics means being able to use mathematical concepts mathematically: the two cannot be separated'.
The study of problem-solving methods in the domain of mathematics education has been frequently undertaken by researchers and has especially influenced mathematical practices during the past 30 years (Santos-Trigo 2007).
This goal of Simon is in agreement with the contention of Artigue et al. (2007) that learning at this level is often seen as enculturation into advanced mathematical practices and of Ben-Zvi and Arcavi (2001) that making meaning in mathematics is about doing mathematics, which also involves socialization into its culture and values.
C.C.S.S. Practices Mathematical Practices 1. Make sense of problems and persevere in solving them.
We discuss and illustrate our use of Toulmin's model of argumentation to develop an analytical technique for documenting the emergence and stability of classroom mathematical practices.
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