# Content Knowledge for Teaching in Teacher Education

**DOI:**https://doi.org/10.1007/978-981-13-1179-6_175-1

## Introduction

Content knowledge for teaching (CKT) is a theoretical construct developed by researchers at the University of Michigan (Ball et al. 2008) that describes the knowledge that teachers need to carry out their work as teachers of particular subject matter. They argued that there is a body of knowledge that goes beyond simply knowing subject-matter content and is unique to teaching. The theory of CKT has led to research targeted at understanding and assessing teachers’ use of such knowledge.

Over the last century, there have been changing conceptions about the nature of knowledge that teachers need to have in order to support student learning and development. Earlier in the twentieth century, policies and assessments focused on ensuring that teachers had broad general knowledge as educated professionals. Beginning in the 1980s, there was a major focus on ensuring that teachers knew the content they were to teach. This led to changes in how teachers were prepared and assessed for licensure. For example, for many states and teacher preparation institutions, prospective teachers were expected to major in specific academic disciplines prior to or simultaneous with engaging the teacher education curriculum. In order to obtain a teaching license, prospective teachers needed to take and pass one or more assessments of content knowledge (Gitomer and Zisk 2015).

With this increased focus on content knowledge, researchers and teacher educators began to study how teachers carried out instructional tasks and the knowledge they used in doing so. Consequently, research on teacher knowledge broadened considerably, influenced by the larger emergence of the cognitive sciences and a focus on situated cognition.

### Pedagogical Content Knowledge (PCK)

The foundation of this focus is *pedagogical content knowledge* (PCK), introduced by Lee Shulman (1986). In his 1985 American Educational Research Association (AERA) address, Shulman described the ever-changing movements in classifying teacher knowledge from general knowledge to content knowledge. He acknowledged that these movements identified important aspects of teaching such as classroom organization and knowledge of the content one is teaching; however, he pointed out that they miss an important aspect of knowledge – how teachers transform their content knowledge into lessons and how they are able to teach the content that they know to those who do not yet understand it. According to Shulman, this knowledge answers the question, “How do teachers decide what to teach, how to represent it, how to question students about it, and how to deal with problems of misunderstanding?” (p. 8). In essence, this knowledge is the knowledge that enables teachers to conduct the actions necessary to teach a particular subject.

Since Shulman first developed the notion of PCK, many attempts have been made to elaborate the construct across different domains, with the majority of work being done in mathematics and science but also in English language arts (ELA), history, and technology education.For the most regularly taught topics in one’s subject area, the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstrations—in a word, the most that make it comprehensible to others … Pedagogical content knowledge also includes an understanding of what makes the learning of specific topics easy or difficult: the conceptions and preconceptions that students of different ages and backgrounds bring with them to the learning of those most frequently taught topics and lessons. (Shulman 1986, p. 9)

Though definitions of PCK have varied across research efforts, there are several principles that characterize the range of PCK definitions (van Driel et al. 1998). First, PCK is centered on specific topics and domains. Well-developed PCK in mathematics does not imply well-developed PCK in other content areas. Second, while PCK relies heavily on content knowledge, it is specifically concerned with the teaching of a subject. A mathematician, for example, who has never taught may have a large subject-matter knowledge base but may not have well-developed PCK. Finally, all definitions of PCK are made in terms of practices that characterize the work of teaching.

### Content Knowledge for Teaching (CKT)

More recently, Ball et al. (2008) sought to clarify what constitutes teaching specific content knowledge and developed the construct of *content knowledge for teaching* (CKT). While they acknowledged that the work of Shulman and others in developing the concept of PCK was critical to advancing the study of teacher knowledge, they pointed out that PCK was still inadequately understood and that the domain as a whole was underdeveloped. They pointed to the many differing definitions of PCK as hindering the development of a precise meaning of the construct. Possibly as a consequence of the lack of definition, they argued that few studies had attempted to measure teachers’ PCK in an effort to validate the construct.

*Mathematics Knowledge for Teaching*(MKT) project, which sought to better understand the knowledge teachers need to have and what they need to be able to do to effectively carry out the work of teaching mathematics. In this study, the authors looked specifically at the work of teaching and tried to first identify what a teacher needs to do in the classroom when teaching a specific subject. Then they identified the knowledge needed to carry out the tasks of teaching. Through this work, they distinguished among six types of content knowledge used in teaching a subject divided into two major categories. They divided the category of subject-matter knowledge into common content knowledge, horizon content knowledge (i.e., knowledge of content that students would encounter in the future), and specialized content knowledge. Specialized content knowledge is knowledge of the content beyond that of what a well-educated adult should know. It is the knowledge that enables teachers to carry out everyday tasks of teaching such as presenting ideas, responding to “why” questions, linking representations to underlying ideas, and modifying tasks to make them easier or harder. For example, teachers need to understand the underlying structure of a mathematical algorithm for teaching purposes (e.g., why division of fractions can be carried out with an invert and multiply algorithm), whereas the typical user of the algorithm need not have such knowledge (Fig. 1).

Overall, Ball et al. (2008) defined CKT as the knowledge that directly links the work of teaching and the content knowledge that is required to do that work. Other groups of researchers have developed frameworks for organizing CKT that include some variations from Bell et al., but, in the main, these frameworks significantly overlap with each other.

### Assessing CKT

The most significant work in the field has involved developing and validating assessments of CKT. A number of different approaches in the development of such assessments have been taken. The most common model involves identifying teaching scenarios that call for the use of teachers’ CKT and building assessment items that capture such knowledge. For example, Gitomer et al. (2014) developed CKT assessments in mathematics and ELA for the *Measures of Effective Teaching* (MET) project.

While the vast majority of elementary teachers knows the common content knowledge involved in evaluating a simple expression with exponents, this task requires teachers to understand common student misunderstandings and what student responses to particular questions can reveal about their understanding. In this case, Option C is correct because a student can answer “4” if they understand how to evaluate expressions with exponents, but they can also respond “4” if they add the base and the exponent or if they multiply the base and the exponent. Therefore, Option C would not reveal to the teacher whether a student truly understood how to evaluate such expressions.

Ms. Hupman is teaching an introductory lesson on exponents. She wants to give her students a quick problem at the end of class to check their proficiency in evaluating simple exponential expressions. Of the following expressions, which would be least useful in assessing student proficiency in evaluating simple exponential expressions?

A. 3^{3}

B. 2^{3}

C. 2^{2}

D. All of these are equally useful in assessing student proficiency in evaluating simple exponential expressions.

Another assessment approach, taken by Kersting et al. (2010), introduced the concept of usable knowledge by designing classroom video analysis tasks to which teachers needed to respond. They divided the domain of CKT into four subdomains: mathematical content, student thinking, suggestions for improvement, and depth of interpretation. In these assessments, examinees are presented with a classroom video segment and asked to analyze, in writing, how the teacher and the student(s) interacted around the mathematical content.

Tasks of teaching framework to support CKT assessments (Gitomer et al. 2014)

Task of teaching | Mathematics examples | ELA examples |
---|---|---|

1. Anticipating student challenges, misconceptions, partial misconceptions, alternate conceptions, strengths, interests, capabilities, and background knowledge | Anticipating student challenges in reasoning about and doing mathematics due to the interplay of content demands and students’ understanding | Anticipating the impact of limited English language proficiency on students’ comprehension of text and speech and on their written and spoken expression |

Anticipating likely misconceptions, partial conceptions, and alternate conceptions about particular mathematics content and practices | Anticipating how students’ background knowledge, life experiences, and cultural background can interact with new ELA concepts, texts, resources, and processes | |

2. Evaluating student ideas evident in work, talk, actions, and interactions | Evaluating student work, talk, or actions in order to identify conceptions in mathematics, including incorrect or partial conceptions | Evaluating student work, talk, or actions for evidence of strengths and weaknesses in reading, writing, speaking, and listening |

Evaluating nonstandard responses for evidence of mathematical understanding and in terms of efficiency, validity, and generalizability | Evaluating discussion among groups of students for evidence of understanding ELA concepts, texts, and processes | |

3. Explaining concepts, procedures, representations, models, examples, definitions, and hypotheses | Explaining mathematical concepts or why a mathematical idea is “true” | Explaining literary or language concepts, using definitions, examples, and analogies when appropriate |

Interpreting a particular representation in multiple ways to further understanding | Explaining processes of reading, including why certain processes are appropriate for particular texts and/or tasks | |

4. Creating and adapting resources for instruction (examples, models, representations, explanations, definitions, hypotheses, procedures) | Creating and adapting examples that support particular mathematical strategies or to address particular student questions, misconceptions, or challenges with content | Creating and adapting examples or model texts to introduce a concept or to demonstrate a literary technique or a reading, writing, or speaking strategy |

Adapting student-generated conjectures to support instructional purposes | Creating and adapting analogies to support student understanding of ELA concepts, texts, and processes | |

5. Evaluating and selecting resources for instruction (examples, models, representations, explanations, definitions, hypotheses, procedures) | Evaluating and selecting representations or models that support multiple interpretations | Evaluating and selecting examples to develop understanding of a concept, literary technique, or literacy strategy or to address particular student questions, misconceptions, or challenges with content |

Evaluating and selecting explanations of mathematical concepts for potential to support mathematical learning or in terms of validity, generalizability, or explanatory power | Evaluating and selecting procedures for writing or working with text | |

6. Developing questions, activities, tasks, and problems to elicit student thinking | Creating or adapting questions, activities, tasks, or problems that demonstrate desired mathematical characteristics | Creating or adapting prompts or questions with the potential to elicit productive student writing |

Creating or adapting classes of problems that address the same mathematical concept or that systematically vary in difficulty and complexity | Developing questions, activities, or tasks to elicit evidence that students have a particular literary understanding or skill | |

7. Evaluating and selecting student tasks (questions, problems) to elicit student thinking | Evaluating and selecting questions, activities, or tasks to elicit evidence that students have a particular mathematical understanding or skill | Evaluating and selecting questions, activities, or tasks to elicit discussion about a specific text or literary concept |

Evaluating and selecting problems that support particular mathematical strategies and practices | Evaluating and selecting questions, activities, or tasks to support the development of a particular literary understanding or skill | |

8. Doing the work of the student curriculum | Doing the work that will be demanded of the students as part of the intended curriculum | Doing the work that will be demanded of the students as part of the intended curriculum |

### Research Findings

Research studies have followed several directions. First, a number of studies have shown that it is possible to develop reliable assessments of CKT that are psychometrically defensible. Other studies have examined the relationship of scores on measures of content knowledge to scores on CKT measures. Correlations between these measures are typically very strong, though there is some evidence that these measures are capturing distinct types of knowledge. Further research is needed to validate CKT as a unique construct with empirical support.

Many studies have examined the relationship of scores on CKT measures to other measures of teaching quality including classroom observations and value-added measures of student achievement. For the most part, though the correlations between these measures have been relatively small, there is relatively consistent evidence that teachers with higher CKT scores do have higher scores on these measures.

A number of studies have compared groups with known characteristics that would be expected to show different levels of competence on CKT assessments. Several studies have shown that teachers with greater academic preparation perform better on the CKT measures. Others have also found different patterns of performance and reasoning on CKT items among those with different teaching and subject-matter backgrounds. For example, teachers with backgrounds in science perform more poorly on mathematics CKT assessments than do mathematics teachers.

As is true for other measures of content knowledge, teachers with higher CKT tend to teach in classrooms that have fewer minority and poor students and that have higher levels of prior achievement. Teachers of students with higher proportions of low-SES and minority students have lower scores on measures of CKT.

Finally, there has been research that has examined the effect of professional development on improving CKT scores. Improvement on CKT scores has been demonstrated, though effects tend to dissipate with time.

### CKT and Teacher Education

Concepts of CKT as well as exemplars of assessment tasks have been integrated into many teacher education methods classes. There has been little study of the impact of such teacher preparation curriculum changes. One of the key questions that needs to be addressed is the extent to which CKT can develop prior to immersion in classroom practice.

In order to best support how CKT should be integrated into the teacher education curriculum, further work is also needed to understand the development of CKT and how it is related to how teachers carry out instruction. Research is also needed to best determine the kinds of teaching experiences that help to develop CKT. Finally, the field needs to develop strong theories that go beyond establishing correlational relationships between measures. Work needs to establish how having CKT about particular academic content influences how teachers teach that content and how students learn this same content.

## References

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