Pedagogical Content Knowledge
Teachers have always combined two bodies of knowledge. One is knowledge of the
subject(s) they teach: not only its facts, but its ways of thinking about the world, how we
know what we know. The other is knowledge about the practice of teaching: how to
communicate to students, and how students learn. From the combination of these two
comes a third area of teacher knowledge: pedagogical content knowledge, or subjectspecific knowledge about how students learn about the specific disciplines. Pedagogical
content knowledge addresses questions such as, how do children think about
maths/science/literature? What processes do they go through in moving from not
understanding an unfamiliar concept, to feeling comfortable with it? What are some common
misunderstandings, and how can teachers recognise when a student has fallen into them?
The term was popularised by Lee Shulman in a 1986 paper. He started with George Bernard
Shaw’s famous insult to teachers everywhere – “He who can, does. He who cannot,
teaches.” On the contrary, he argues, teachers have to not only know how to do, but also
know something about how people learn how to do. In fact teaching is tougher than just
doing, because it depends on this entire extra dimension of knowledge:
...the most useful forms of representation of those ideas [of the curriculum], the most
powerful analogies, illustrations, examples, explanations, and demonstrations – in a
word, the ways of representing and formulating the subject and formulating the
subject that make it comprehensible to others. Since there are no single most
powerful forms of representation, the teacher must have at hand a veritable
armamentarium of alternative forms of representation, some of which derive from
research whereas others originate in the wisdom of practice. [Shulman, 1986: 9]
Shulman’s idea has been enormously influential and the original paper has since been
referred to in thousands of articles in the research journals. Pedagogical content knowledge
has been developed in many ways, and a lot of research carried out both into what it means
in a range of school subjects, and into its usefulness in general.
What is pedagogical content knowledge?
Everyone studying a subject needs to learn two kinds of knowledge: not only ‘the facts’, what
is known within the subject, but also why these facts are thought to be true – the methods a
discipline uses to investigate its area. However, we all know the figure of the
incomprehensible professor, who may have brilliantly mastered both these aspects of their
subject, but is unable to communicate them to anybody else. What they say in classes may
be technically correct, but it does not reach many students. There is a difference between
how people who have mastered a discipline understand the subject matter, and how people
who are learning it come to understand. Pedagogical content knowledge is all about
effectively communicating a subject to people for whom it is all new. Therefore it requires
knowledge of how students think before learning the subject matter, and how they think
about it while learning.
In fact there are a number of types of subject-specific knowledge teachers make use of (Ball
et al [2008]):
1. Common content knowledge: The knowledge teachers have in common with other
people who are educated in the subject.
2. Curriculum knowledge: Knowledge of what specific parts of the subject teachers are
supposed to pass on to students at the specific grade level, what students will be
tested on (and how), etc. This includes ‘horizon knowledge’ about how the subject
matter in the current grade’s curriculum will be developed as the students progress
into higher grades, as well as what they have already learned in earlier grades.
3. Specialised content knowledge: Knowledge of subject matter that is specific to
teaching, that casual users of the subject matter – or even those highly trained in it –
will generally not need to know. For example, an accountant may be highly skilled in
arithmetic and be able to quickly find the difference between two numbers in their
head, barely consciously using a method picked up decades earlier at school. But if
asked how the method works – e.g., why do we ‘borrow’ a digit from the next
column? – might not be able to give a good answer. It helps a teacher, though, to
know in more depth about why the method works – what is going on?
4. Knowledge of content and students: Knowledge about how students think, what
tends to confuse, what they find interesting and motivating, what is easy and what is
hard. Also, this is about the ability to “hear and interpret students’ emerging and
incomplete thinking as expressed in the ways that pupils use language.” [Ball et al,
2008: 402]
5. Knowledge of content and teaching: This is related to curriculum knowledge, but
refers to the more detailed knowledge of how to teach each aspect of the curriculum:
in what order concepts should be introduced, how much time needs to be spent on
exercises or essays for absorption of the concepts and development of practical
experience, and so on.
Like content knowledge in general, knowledge about how people learn the content is highly
specific to each subject: learning maths is a very different thing from learning about
literature. Because of this, the research literature has tended to be subject-specific.
Knowledge of the best ways to introduce to students the organisation of the periodic table is
not much use in understanding what they get out of an argument about the origins of the
First World War. Let’s look at some examples of how the concept has been applied in
different subjects.
Example: Mathematics
As an example of the kind of pedagogical content knowledge a mathematics teacher needs
to have, Ball et al [2008: 396-99] discuss teaching three-digit subtraction to primary school
students. Students are taught the familiar procedure involving ‘borrowing’ from the next
column when the bottom digit is larger than the top.
The procedure itself is straightforward – but a teacher will need to understand more about
how it works. It is easy to see when a student makes a mistake with the procedure, but more
difficult to interpret why they have gone wrong. Why do so many students misapply it in the
same way, for example, coming up with the same wrong answer that 307 - 168 = 261? How
should we respond if the student gets the right answer by a different procedure? What if a
bright student asks why the procedure doesn’t work in some cases, as when the entire top
number is smaller than the bottom? What selection of examples and exercises will expose
the students to the full range of tricky issues involved in the procedure? Why does the
procedure work at all?
Most adults know how to use the subtraction procedure, even if they might need a reminder
in the age of calculators. But answering all these other questions is not easy, and requires
more specialist knowledge. Yet it is not the kind of specialised knowledge that is covered in
university mathematics courses – since university students have presumably moved well
beyond the multi-digit subtraction procedure. This is the kind of knowledge that needs to be
“uncovered, mapped, organised, and included in mathematics courses for teachers.” [Ball et
al, 2008: 398]
Example: English
English and social studies have seen much less writing on pedagogical content knowledge
than mathematics or science. This is not because they require less subject-specific teaching
knowledge, but likely because subject content varies much more between countries, states
and even between schools and classes. One early study into pedagogical content
knowledge in English studied the different approaches to teaching taken by two groups of
new teachers, one made up of teachers who had undertaken teacher training as well as
university English, and the other made up of teachers who had only graduated in English
without training to teach. The first group had explicit instruction in how to teach English,
while the second group had only content knowledge – at least until they gained teaching
experience. [Grossman, 1989]
The researchers found many differences in teaching style, from the choice of texts to
homework activities. These differences had deeper roots, in the teachers’ conceptions of the
purpose of English teaching: those without a teaching degree tended to see it as being
about textual analysis, while trained teachers focused more on writing and communication
skills. Both groups saw the need to know what students already understood and what they
found difficult, but the trained teachers were better able to actually find out and adapt their
teaching accordingly.
The biggest difference between the groups was in their ability to motivate students and get
them to identify with the texts. In teaching Hamlet, the untrained teachers tended to go
straight to the text and read through the whole thing closely, focusing entirely on the
structure and language. They did not see motivation as their problem. The trained teachers
did not neglect the text, but spent more time trying to relate it to the students’ lives and
worldviews, with one teacher, for example, introducing the play with a creative writing
exercise about how they would act in Hamlet’s shoes. Grossman’s point is not that forms
and content of literature are unimportant, but that teaching them is greatly helped by getting
students to see the point, to relate it to their lives and to be motivated to write by a desire to
communicate their experiences and ideas. Having good intentions about this does not seem
to be enough – it is a learned skill.
Can it be taught? Does it make a difference?
While there is clearly a body of knowledge associated with the teaching of any particular
subject, separate from knowledge of the field itself, is it really something that can be taught
to teachers? Or is it something teachers only gain from experience?
While every teacher accumulates content knowledge for teaching through experience, as
they learn how students learn by teaching them, there is evidence that a focus on it during
initial teacher training and professional development can be very effective. We have already
looked at Pamela Grossman’s [1989] research into English teaching, which compared
American teachers who had been through formal teacher training with other teachers who
had English degrees alone, finding that the first group was more attuned to how students
learn the content. Her early research has been joined by a large body of research finding a
link between formal study of pedagogical content knowledge and teaching skills, some going
a further step and linking it to the achievement of students taught by teachers who have
been through programs focusing on content knowledge for teaching.
A recent paper by Desimone [2009: 184] reviews many other studies into professional
development programs over the last two decades, and concludes that a focus on content
knowledge for teaching “may be the most influential feature” of effective professional
development programs, linking it to “increases in teacher knowledge and skills, and, to a
more limited extent, increases in student achievement.” The same result comes from a wide
variety of research methodologies, including case studies, correlational analyses with
nationally representative teacher data, quasi-experiments and experiments, longitudinal
studies of teacher development, and meta-analyses combining the results of many other
studies.
There is therefore plenty of evidence that pedagogical content knowledge makes a
difference in teaching, and that it can be taught in initial teacher training and professional
development programs.
Conclusion
Shulman’s [1986: 7] paper quotes Aristotle to counter George Bernard Shaw’s quip. Far from
being deficient relative to the practical person who just ‘does’, or the expert who only
‘knows’, Aristotle thought those who could teach had the superior skill:
We regard master-craftsmen as superior not merely because they have a grasp of
theory and know the reasons for acting as they do. Broadly speaking, what
distinguishes the man who knows from the ignorant man is an ability to teach, and
this is why we hold that art and not experience has the character of genuine
knowledge – namely, that artists can teach and others (i.e., those who have not
acquired an art by study but have merely picked up some skill empirically) cannot.
References
Deborah Loewenberg Ball, Mark Hoover Thames, Geoffrey Phelps [2008]: “Content
knowledge for teaching: what makes it special?”, Journal of Teacher Education, 59, pp. 389407.
Laura M. Desimone [2009]: “Improving impact studies of teachers’ professional
development: toward better conceptualisations and measures”, Educational Researcher, 38,
pp. 181-99.
Pamela Grossman [1989]: “A study in contrast: sources of pedagogical content knowledge
for secondary English”, Journal of Teacher Education, September-October, pp. 24-31.
Lee S. Shulman [1986]: “Those who understand: knowledge growth in teaching”,
Educational Researcher, 15:2, February, pp. 4-14.