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As PTs were learning how to be effective teachers, the students they were tutoring deepened their mathematical content knowledge and their confidence in mathematics increased as well.
They also had to complete a knowledge test from which two main outcome scores were derived: a mathematical content knowledge score (MCK) and a mathematics pedagogy content knowledge score (MPCK).
This evidence on teachers' mathematical content knowledge, much of it focused on primary level mathematics, suggests gaps at or close to the level at which they are teaching (Carnoy et al. 2008; Taylor 2011).
Specialized content knowledge (SCK) is a type of mathematical content knowledge specifically needed for teaching.
Mathematics education programs should support preservice elementary teachers' (PTs) learning of specialized content knowledge (SCK), which is a type of mathematical content knowledge specifically needed for teaching (Ball et al. 2008).
These are the richness (depth, breadth, and connectivity) of their mathematical content knowledge (MCK), the extent of their pedagogical knowledge (PK), and the quality of the synergistic relationship between the two.
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I propose a model of pedagogical mathematical biological content knowledge as a feasible starting point for connecting biology and mathematics in schools and universities.
Most often, quantitative literacy is assessed with a focus solely on mathematical and statistical content knowledge using tasks that contextualize the mathematics in real-world or problem-based situations (e.g., TIMSS [see Orpwood and Garden 1998; Mullis et al. 1998], and Programme for International Student Assessment [PISA, Organisation for Economic Cooperation and Development OECD 2000]).
"Mathematics practices," she goes on, "focus on the mathematical know-how, beyond content knowledge, that constitutes expertise in learning and using mathematics [such as] justifying claims, using symbolic notation efficiently, defining terms precisely, and making generalisations are examples of mathematical practices".
I noted in the introductory sections that gains at the level of content knowledge and mathematical practices were seen in our assessments across three cycles of the course (2012-14).
Mathematical cognition further extends beyond content knowledge to include a person's ability to reason and think mathematically to evaluate and synthesize information, make conjectures and draw logical conclusions, and apply knowledge to real-world problems and situations (Steen 2001; Wilkins 2000; National Council of Teachers of Mathematics 2000 , 1989.
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