# Mathematical Knowledge for Teaching Article Review

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Mathematical Knowledge in Education

Differentiating Types of Mathematical Knowledge and Relevance to Education

Ball, D.L., Lubienski, S., and Mewborn, D. (2001). "Research on teaching mathematics:

The unsolved problem of teachers' mathematical knowledge." (In Handbook of Research on Teaching. New York: Macmillan).

Generally, mathematics proficiency among teachers corresponds to higher achievement in their students. While that conclusion has been supported by a substantial volume of empirical research, much less empirical research has been devoted to trying to understand how and why teacher achievement in mathematics benefits student outcomes, or what it is about mathematics, specifically, that generates this apparent relationship. Most importantly, there is a need to understand whether and to what extent teacher mathematics achievement in different aspects of mathematics matters with regard to the positive effect on learners.

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for only $8.97. According to the authors of this article, there is a fundamental difference between teaching mathematics and teaching through mathematics. In many ways, that distinction helps explain why, in general, mathematics proficiency among teachers tends to correspond to better learning outcomes. More particularly, understanding that distinction may help explain why the positive benefit of mathematics knowledge among teachers is much more evident in connection with their academic study of mathematical method than in connection with their academic study of advanced mathematics. Furthermore, it could explain why advanced mathematical achievement among teachers also corresponds to higher incidence of negative affects on some learners whereas that is not true in the case of teachers whose high achievement in mathematics relates more to their non-pedagogical content knowledge than to their pedagogical content knowledge.

## Article Review on

In principle, the value of teaching mathematics is much broader than the value of the substantive material, particularly in contemporary society that provides instant and accessible electronic calculation to solve the types of mathematical problems that could typically arise in everyday adult life. Study after study suggests that teachers who are more knowledgeable about mathematics tend to promote learning better than teachers who are less proficient in mathematics.

However, there is evidence that suggest that this relationship is much more complex than simply a direct transfer of pedagogical mathematical knowledge. For example, one unexpected finding is that the benefit of greater mathematics proficiency exists in the first grade. Presumably, all teachers are equally proficient at first-grade addition and subtraction; moreover, the academic study of mathematics in greater depth (i.e. post-calculus) should not have any impact on the level of teacher understanding of first-grade mathematics concepts. Similarly, there is no intuitive reason that either the mathematical proficiency of teachers or their highest level of mathematical study should translate to better teaching of elementary mathematical concepts. In that background, the correspondence between teachers having studied mathematical method and the highest identifiable benefits to learning seem to explain the basis of the phenomenon.

Specifically, mathematics (especially at the elementary level), can be taught rigidly and by rote rule or by conceptual understanding. Apparently, teachers with more extensive experience in studying mathematical method are better equipped to deliver mathematics lessons in a manner conducive to inspiring student initiative, stimulating the process of mathematical (and logical) reasoning, and more generally, to promote an intellectual inquisitiveness and resourcefulness that translate to higher student achievement. By… [END OF PREVIEW] . . . READ MORE

Differentiating Types of Mathematical Knowledge and Relevance to Education

Ball, D.L., Lubienski, S., and Mewborn, D. (2001). "Research on teaching mathematics:

The unsolved problem of teachers' mathematical knowledge." (In Handbook of Research on Teaching. New York: Macmillan).

Generally, mathematics proficiency among teachers corresponds to higher achievement in their students. While that conclusion has been supported by a substantial volume of empirical research, much less empirical research has been devoted to trying to understand how and why teacher achievement in mathematics benefits student outcomes, or what it is about mathematics, specifically, that generates this apparent relationship. Most importantly, there is a need to understand whether and to what extent teacher mathematics achievement in different aspects of mathematics matters with regard to the positive effect on learners.

Get full access

for only $8.97. According to the authors of this article, there is a fundamental difference between teaching mathematics and teaching through mathematics. In many ways, that distinction helps explain why, in general, mathematics proficiency among teachers tends to correspond to better learning outcomes. More particularly, understanding that distinction may help explain why the positive benefit of mathematics knowledge among teachers is much more evident in connection with their academic study of mathematical method than in connection with their academic study of advanced mathematics. Furthermore, it could explain why advanced mathematical achievement among teachers also corresponds to higher incidence of negative affects on some learners whereas that is not true in the case of teachers whose high achievement in mathematics relates more to their non-pedagogical content knowledge than to their pedagogical content knowledge.

## Article Review on *Mathematical Knowledge for Teaching* Assignment

In principle, the value of teaching mathematics is much broader than the value of the substantive material, particularly in contemporary society that provides instant and accessible electronic calculation to solve the types of mathematical problems that could typically arise in everyday adult life. Study after study suggests that teachers who are more knowledgeable about mathematics tend to promote learning better than teachers who are less proficient in mathematics.However, there is evidence that suggest that this relationship is much more complex than simply a direct transfer of pedagogical mathematical knowledge. For example, one unexpected finding is that the benefit of greater mathematics proficiency exists in the first grade. Presumably, all teachers are equally proficient at first-grade addition and subtraction; moreover, the academic study of mathematics in greater depth (i.e. post-calculus) should not have any impact on the level of teacher understanding of first-grade mathematics concepts. Similarly, there is no intuitive reason that either the mathematical proficiency of teachers or their highest level of mathematical study should translate to better teaching of elementary mathematical concepts. In that background, the correspondence between teachers having studied mathematical method and the highest identifiable benefits to learning seem to explain the basis of the phenomenon.

Specifically, mathematics (especially at the elementary level), can be taught rigidly and by rote rule or by conceptual understanding. Apparently, teachers with more extensive experience in studying mathematical method are better equipped to deliver mathematics lessons in a manner conducive to inspiring student initiative, stimulating the process of mathematical (and logical) reasoning, and more generally, to promote an intellectual inquisitiveness and resourcefulness that translate to higher student achievement. By… [END OF PREVIEW] . . . READ MORE

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