Professional learning opportunities for teachers of mathematics and science have increasingly focused on teachers’ content knowledge. Programs aimed at deepening teacher content knowledge vary in their goals and the specific kinds of mathematics/science content knowledge they target (e.g., disciplinary content knowledge, pedagogical content knowledge, and/or ways of knowing/habits of mind). Designing a quality professional development program is essential, but the quality of the implementation of that design is also key to achieving a program’s goal of deepening teacher content knowledge.
Advice from experienced practitioners offers guidance about implementing programs to deepen teachers’ mathematics/science content knowledge. Insights provided by a group of expert practitioners with diverse backgrounds and experiences in working with teachers included the following ideas:
- Set the tone for learning—Create and maintain a productive, professional learning environment for teachers.
- Implement with intention—Align facilitation with the purposes of a particular professional development session.
- Be true to the discipline—Model mathematics/science “habits of mind.”
- Practice what you preach—Model the pedagogy teachers are intended to use in their instruction.
- Stop and take stock—Provide teachers opportunities to reflect on what they are learning.
Practitioner Insights
There are a number of important issues to consider in providing programs to deepen teacher mathematics/science content knowledge. Professional development can emphasize all or a subset of a number of teacher content knowledge goals: disciplinary content knowledge, content-related pedagogical issues, and what it means “to do” science or mathematics. Program leaders need to decide on their goals, choosing a set of goals that is both consistent with the needs of the participating teachers and feasible within the time and resources available. The next step is to develop a plan for achieving the particular goals, including deciding on the format, sequence, and timing of activities. However, appropriate program design is not enough; whether or not the desired goals are achieved depends in large measure on how well the program is implemented.
Experienced program leaders shared their insights about a number of important factors in implementing programs to deepen teacher content knowledge, which are described below.
After reviewing these insights, you will be provided with opportunities to share your own experiences with implementing programs to deepen teacher content knowledge. The information you provide will be analyzed along with the insights and examples from other practitioners as the website is periodically updated.
Set the tone for learning—Create and maintain a productive, professional learning environment for teachers.
Efforts to deepen teacher content knowledge require environments that are conducive to learning — intellectually challenging, but not threatening. Experienced program leaders noted that it is important for professional development providers to look for the knowledge that teachers already have and build from there, rather than approaching teachers from the perspective of a “deficit model.” One program leader emphasized that every teacher has expertise to bring to the group, and it is important for professional development facilitators to “promote teachers’ expertise as they reveal it.” Others suggested that all teachers have to feel safe in making themselves vulnerable to try something new, to work together on mathematics/science, and to share their thinking and perspectives with their peers and the facilitators.
In order to deepen their content knowledge, teachers need to be willing to confront the boundaries of what they know, and acknowledge what they do not yet understand. Professional development programs need to support teachers in taking these kinds of risks because, as one program leader advised, “it doesn’t work if they’re trying to hide the state of their understanding.” Explained another program leader,
All learners have to feel safe to reach out and make themselves vulnerable in trying something risky in front of others. The feeling that we are all helping each other, we’re all in this together, we respect your right to be confused and frustrated, we celebrate our breakthroughs, is so important. Laughter and sharing stories are so important to building a group that functions as a learning, evolving, growing being, in itself. And it’s important for teachers to see how such a learning group contributes to the personal knowledge of each of its members, as well as to the common, public knowledge that is shared among them.
An MSP PI noted that the creation of a “mathematical community” is essential to the success of their enterprise — mathematicians, teachers, graduate students, and other educators working together and supporting each other in a mathematical culture that involves working on really hard problems.
Still, program leaders caution against an environment that is “so safe that there is no risk and where the teacher never confronts what they do or do not know.” Said an MSP PI, “it is desirable to build upon the knowledge that teachers do have. At the same time, occasionally one finds themself trying to help a teacher learn who is seriously deficient as a teacher of mathematics with respect to the mathematics knowledge they have. If one ducks this reality, you do no one, not even that teacher, a favor.” Acknowledging the challenge – and therefore the vulnerability – in developing new knowledge is important. What is key is determining the right balance of safety and risk – finding the right point of cognitive dissonance to engage and motivate teachers in learning.
Implement with intention—Align facilitation with the purposes of a particular professional development session.
Professional development programs are often designed to achieve multiple goals across a series of sessions over time. The success of a particular session depends on the quality of implementation in relation to its specific purposes. Especially given multiple program goals, a professional development session can easily drift off track. When working on a given concept or set of concepts, there needs to be a premium on keeping the focus on the key ideas of content/pedagogical content knowledge during individual and group work, as well as during debriefing and sense-making discussions.
MSPs work to design activities that are consistent with what is known about learning, including involving teachers with problems and phenomena related to key mathematics/science ideas, often framing their investigations as fairly open inquiries. However, without appropriate guidance, engaging teachers (or any other learners) in inquiry-oriented investigations can sometimes obscure the mathematics/science content, and in some cases actually generate misconceptions. Similarly, experienced program leaders noted that simply “handing over the floor” to teachers in a discussion, without drawing out their thinking and challenging aspects of their thinking when appropriate, makes it unlikely that teachers would develop an understanding of the targeted concepts. Advised one experienced program leader,
Explicit discussion of the mathematics, and what teachers now know about the mathematics that they didn’t know before, is essential for the investigation to be a learning experience, and not just an “activity.” Having sufficient time for participants to debrief an investigation is absolutely essential. …The questions that the facilitators ask, and how they are able to take advantage of the opportunities presented in various participants’ solutions [are particularly important.]
If the purpose of a session is to help teachers grapple with issues of how students learn the content, then the focus needs to go beyond having the teachers discuss, for example, how they arrived at the answer, to include attention to what students might do with the problem. If examining student work is intended both to help teachers understand student thinking about key ideas and to address gaps in their own content knowledge, then facilitators need to decide when to focus on each of these purposes. A program leader provided an example of how a session where teachers are looking at student work could be used to help teachers increase their own content understanding, in this case about comparing fractions with unlike denominators:
Pieces of student work in which different methods are used to compare fractions (using benchmarks, rewriting them with common numerators) can help teachers recognize that there are many ways to do this, i.e., you don’t always have to rewrite fractions with common denominators to compare them.
It is important to recognize, however, that a typical professional development session provides far more opportunities to deepen teacher content knowledge than can be meaningfully pursued within the time available. A session designed to focus on teacher understanding of a particular mathematics or science concept at a fairly advanced level may surface teacher misconceptions; addressing those would not only be consistent with the purpose of the session, but essential for making progress. That same session may well elicit teacher questions about how to teach the concept; the facilitators are then faced with a dilemma. On the one hand, it seems appropriate to seize the “teachable moment” related to classroom instruction; on the other hand, doing so risks diverting attention from the goal of deepening teacher-level content knowledge. Experienced program leaders do not have an “answer” to this dilemma, but stress that it is important for professional development providers to recognize the tensions and trade-offs they need to consider when making implementation decisions.
Be true to the discipline—Model mathematics/science “habits of mind.”
Whether or not having teachers learn about ways of knowing in mathematics or science is an explicit program goal, program leaders emphasize that professional development needs to model the norms of the particular discipline to avoid sending mixed messages to teachers. For example, arguing from evidence is a hallmark of science, so it is essential that teachers be asked to consider evidence in drawing conclusions. Even if the data they collected might lead them to the “wrong” conclusion, it is important to focus on the evidence just as scientists would, questioning the quality of that evidence, if appropriate, again just as scientists would. Said one program leader,
If the idea is for teachers to be engaged in authentically-independent reasoning – doing science in a manner that resembles what scientists do – then the authority standing up and saying “right” about some traditional content-oriented conclusions would end that.
This same individual described how some instructors in a physics course for elementary teachers have an easier time than others in modeling scientific habits of mind:
Problems arise in this setting when the instructor is too uncomfortable to let wrong ideas be discussed or considered, or simply not comfortable enough such that the [teachers] can think openly and honestly. It needs to be very clear, to the instructor and to the [teachers], that the purpose is good scientific thinking, and that good scientific thinking is not synonymous with “correct.” … One of our instructors seems to run this course especially well. Watching the class, the discussions are often just vibrant – and, maybe more important, scientific in the sense that the [teachers] are arguing from evidence and reasoning back and forth with each other to support their claims. The instructor lets his own thoughts trickle in to the conversation in a way that doesn’t take them off their own reasoning but does help them make progress toward canonical ideas.
Practice what you preach—Model the pedagogy teachers are intended to use in their instruction.
Professional development should model the instructional strategies program leaders would like teachers to use in their classrooms. An MSP PI noted that observations of classroom instruction in the partner districts revealed “more direct teaching, rather than letting the students explore and create an understanding of the concepts,” a style of instruction that didn’t seem to motivate the students. Consequently, the MSP decided to emphasize the use of more investigative instruction in their professional development — actively engaging teachers in learning key mathematics ideas. By modeling this type of instruction, the project “hoped to show the teachers a way to motivate their students to want to learn.” Other program leaders agreed. For example,
I do think it’s critical that teachers encounter the content learning in ways that are similar to the ways we want them to facilitate students’ understanding — the personal experience of changing one’s own content knowledge, the “ah-has” and despairs, the hard-won triumphs and power of more sophisticated knowledge — all these are powerful influences on what teachers then do with students.
Several MSP PIs indicated that when their programs were initiated they found differences in the quality of professional development across the various learning experiences. Courses/sessions conducted by K–12 master teachers and education faculty were more likely to involve “active learning,” but in some cases without adequate attention to mathematics/science content. In contrast, courses and sessions conducted by disciplinary content faculty were more likely to focus on content, but in some cases delivered in ways that were not accessible to the participating teachers. To address this “disconnect,” a number of MSPs provided workshops for instructors to learn about best practices in professional development. For example, one large partnership provided 10 days of intensive training to a cadre of 100 facilitators, including STEM university faculty and master teachers, to help ensure that they would be modeling effective instruction when leading workshops.
Insight in Action
An MSP’s summer mathematics courses are designed to engage teachers as learners. Teachers are immersed over a two-week period of time with a series of tasks focused on big mathematical ideas. The courses are designed to deepen disciplinary content knowledge; each models the pedagogy that the project values and wants to see in the middle school. Pedagogy is only briefly discussed in the courses, yet from experiencing powerful pedagogy as learners, teachers report being transformed in how they think about teaching.
Stop and take stock—Provide teachers opportunities to reflect on what they are learning.
Time is always limited, but experienced program leaders advise resisting the urge to push ahead with the next topic before teachers have had an opportunity to reflect on what they have learned thus far, both individually and collectively. A program leader who has worked extensively with teachers in on-line professional development commented on the importance of reflection:
In my experience with rigorous science content courses designed for teacher professional development, reflection on their own ideas and practice is often cited by the participants as one of the most valuable learning experiences. In addition, participants report that putting these prior ideas and new understandings in writing is particularly helpful in deepening their knowledge and understanding.
Another program leader stated that “teachers need an opportunity to create an ongoing trace of where they are in their thinking (about a particular idea) so they can see their own development and see how to use tools in classrooms that help support students to see this as well.”
A particular professional development activity may have multiple goals, for example both deepening teacher disciplinary content knowledge and helping teachers consider how to teach the same concept to students. In those cases, participants will benefit from reflection on both aspects of their learning. One program leader suggested separating the debriefing into two parts in these situations, so teachers are: “experiencing the activity from the students’ perspective and thinking about it again from the teacher’s perspective, but not necessarily jumping back and forth throughout the entire activity.” Another program leader agreed: In professional development, “teachers shift between roles — as learners, but then as teachers. …Effective professional development explicitly refers to those roles, and gives participants opportunities to discuss/reflect on their experiences ‘wearing both hats.'”
If you are interested in how these practitioner insights were collected and analyzed, a summary of the methodology can be found here.
Teacher Content Knowledge Matters
Empirical evidence demonstrates that teachers’ mathematics/science content knowledge makes a difference in their instructional practice and their students’ achievement. Consistent findings across studies include:
- Teachers’ mathematics/science content knowledge influences their professional practice.
- Teachers’ mathematics/science content knowledge is related to their students’ learning.
Learn more about research on why teachers’ mathematics/science content knowledge matters.