Teacher Content Knowledge & Pedagogical Content Knowledge

**Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade and how can we decide? American Educator (fall 2005), 14–22, 43–46. Retrieved from http://www.aft.org/sites/default/files/periodicals/BallF05.pdf

This article argues that there is a specialized mathematical knowledge that is unique to teaching and the work that teachers do. Specifically, the authors assert that teachers need fluency with skills such as error analysis and anticipation, modeling, representations, reasoning, example selection, and an understanding of how and when to shift between informal and technical, content-specific language. In their research, the authors assessed the “common” knowledge of mathematics (content knowledge) and “specialized” knowledge (teacher-specific knowledge) of a large sample of teachers. They found that teachers’ specialized knowledge significantly predicts student test scores, even when controlling for student socioeconomic status, student absence rate, teacher credential, teacher experience, and average length of math lessons. The researchers also found that teachers can learn these specialized skills in professional development, especially if the learning opportunities focus on proofs, analysis, exploration, communication, and representation. The article concludes that a focus on developing the specialized mathematical knowledge of teachers could raise student achievement, improve teaching for disadvantaged students, and improve the professional standing of math teachers.

Haverly, C. (n.d.) Many elementary teachers have anxiety about teaching STEM subjects. 100Kin10. Retrieved from https://grandchallenges.100kin10.org/assets/downloads/many-elementary-teachers-have-anxiety-about-teaching-stem-subjects/GrandChallengesWhitePapers_Haverly.pdf

This article describes a cycle of how young students may develop poor mathematics self-concept and grow to pay it forward to their own students when they become teachers. Recent research shows that many elementary teachers in science, technology, engineering, and mathematics (STEM) disciplines experience a lack of confidence with STEM content knowledge and pedagogy—often arising from their own early experiences with STEM education. Research demonstrates that when teachers display anxiety, their students are more likely to believe that they themselves are also bad at STEM content. In order to interrupt the cycle, the author suggests that all stakeholders work together to foster more positive STEM experiences for elementary educators through professional development and authentic learning opportunities. 

Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics (Educational Practices Series #19). Retrieved from http://www.ibe.unesco.org/fileadmin/user_upload/Publications/ Educational_Practices/EdPractices_19.pdf

Drawing on a wide range of research, the authors describe ten pedagogical approaches that engage learners and lead to desirable outcomes in mathematics. For example, one approach calls for an ethic of care, caring classroom communities that are focused on mathematical goals help develop students’ mathematical identities and proficiencies. Another approach is mathematical communication, in which effective teachers are able to facilitate classroom dialogue that is focused on mathematical argumentation. The authors emphasize that these ten principles are not stand-alone indicators of best practice. Any practice must be understood as nested within a larger network that includes the school, home, community, and wider education system.

**This document is considered a priority reading.