As we begin a new academic year, it may be interesting to consider: what makes a teacher a good teacher? The answer seems to be a strong mix of content and pedagogical content knowledge. It is not enough to know what to teach, but it is necessary to know how to teach it too.
In educational research on teaching maths and the sciences, pedagogical content knowledge has been a particular focus for the past two decades. This type of knowledge hones in on the particularities of teaching a specific subject and highlights the numerous decisions high-quality teaching involves in building learners’ knowledge. Pedagogical content knowledge is a core element of the knowledge required for teaching.
The term "pedagogical content knowledge" was coined in 1986 by Lee Shulman in his presidential address to the American Educational Research Association. Shulman defined pedagogical content knowledge as that which goes beyond knowledge of the subject matter and extends to representing and formulating that subject to make it comprehensible to others. This type of knowledge is particularly relevant for mathematics.
Communicating knowledge of “new” mathematics incorporates in-depth and fundamental knowledge of maths in addition to well-honed pedagogical skills.
Educators constantly make decisions about the most appropriate way to represent a topic and use this knowledge to build students’ understanding, often through anticipating and interpreting errors or misconceptions.
For example, consider this classroom task taken from Prof Deborah Ball (you might like to try this on a sheet of paper yourself): you are teaching students in fourth class how to multiply two-digit numbers and ask them to multiply 49 by 25. As you are observing students’ work around the classroom, you see three different incorrect answers: 1,485, 325, and 1,275.
Focusing solely on the correct answer and method will not benefit all learners in your classroom. You therefore interpret, in the moment, how each individual student came to their answer and consider the best prompt to led them to communicate, reflect on and rethink their strategy – perhaps for the benefit of the entire class.
In this situation you are drawing on your pedagogical content knowledge and, by doing so, providing the most constructive environment to build your students' understanding of mathematics.
Positive correlation
While teachers’ content knowledge is, of course, a core feature of the knowledge required for teaching, a number of research studies (for example from Heather Hill and colleagues) have also identified a positive correlation between teachers’ pedagogical content knowledge and student learning.
In pre-service teacher education programmes, such as that in the UCD College of Science, we focus on developing teachers' subject-specific content and pedagogical content knowledge. In addition, models of teacher professional development, such as the Japanese model of lesson study (a focus of my own research), builds on teachers' pedagogical content knowledge and contributes greatly to students' learning.
Shulman began his 1986 address with the infamous and insulting phrase that has plagued the profession of teaching – “He who can, does. He who cannot, teaches.”
He went on to detail and highlight the import and complexity of high-quality teaching, which looks effortless but isn’t. We have all heard the age-old adage about a teacher who was brilliant at their subject but just didn’t know how to teach it. What were they missing? Pedagogical content knowledge.
Excellent teachers make an incredibly important contribution to our society. Furthermore, as established by the SFI Science in Ireland barometer from 2015, teachers influence students’ interest in and enjoyment of mathematics and science.
High-quality teachers are integral to the strengthening of our understanding of the world around us and are vital in encouraging more young people to consider pursuing an interest in the sciences. To that end, focusing on developing, strengthening and acknowledging the content and pedagogical content knowledge of our teachers is integral to our learning of mathematics and science.
Dr Aoibhinn Ní Shúilleabháin is an assistant professor in the UCD school of mathematics and statistics