The Relevance and Significance of Mathematical Knowledge in Teachers

Hill, H.C., Rowan, B., and Ball, D.L. "Effects of Teachers' Mathematical Knowledge

for Teaching on Student Achievement." American Educational Research

Journal; (Summer 2005), Vol. 42, No. 2: 371-406.

In a similar study, the importance of non-pedagogical mathematical content knowledge among teachers was evident. This study highlights the practical implications and difficulties of teacher improvement programs whose purpose is to implement the conclusions about the importance of certain aspects of mathematics competency in teaching. It also relied partially on the evidence that certain aspects of mathematics competency in teachers corresponds to better learning and achievement even in the elementary grades where mathematical concepts are insufficiently complex to allow any knowledge difference in teachers to manifest itself in learner achievement.

According to this study, the recognition of correspondence between teacher knowledge of or academic achievement in mathematics and student benefit is largely useless without a more in-depth understanding of how and why teacher knowledge or achievement in mathematics translates into positive learning outcomes for students. The authors suggest that is particularly true with respect to using that information to design professional improvement programs for teachers. For example, it is important to know how to measure mathematical knowledge in teachers in connection with improving their performance.

Among the various criteria, the authors discuss the relatively low importance of the performance of teachers on mathematical proficiency tests and of their highest level of the academic study of mathematics in their own educational histories. As in the...

Similarly, it is important to understand whether it is something specific about mathematics knowledge that corresponds to better teaching abilities or if it is simply the case that some of the same intellectual characteristics that promote better or more advanced mathematical knowledge also happen to be conducive to better natural abilities as teachers.
In principle, mathematics can be taught in a manner that significantly promotes intellectual exploration, conceptual understanding, and that reinforces the communication of ideas between learners and instructors. Alternatively, the identical subject matter can be taught in a highly process-oriented mechanical way that is largely devoid of the benefits to learners of the more intellectually enriching educational process. Furthermore, the authors suggest that teachers with more extensive academic backgrounds on mathematics might actually contribute negatively to this process in some cases, by virtue of being that much more committed to traditional mechanical methods of mathematics instruction. Ultimately, teachers with better conceptual understanding of same material than other teachers communicate mathematical concepts to learners in a manner that is highly conducive to stimulating intellectual curiosity and to mastering a conceptual understanding than teachers who teach mathematics mechanically, without a deeper understanding of their own and without the ability to recognize, reward, and encourage the growth of mathematical (and logical) reasoning in the process of teaching mathematics.