Professional learning opportunities for teachers of mathematics and science have increasingly focused on teachers’ content knowledge. Programs aimed at deepening teachers’ mathematics/science content knowledge vary in the specific kind of content knowledge they target (e.g., disciplinary content knowledge, pedagogical content knowledge, or ways of knowing/habits of mind). Similarly, programs vary in the strategies they use to achieve their particular content goals.
Advice from experienced practitioners offers guidance about designing 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:
- You can’t do it all—When addressing multiple goals for deepening teacher content knowledge, consider how deeply to pursue each goal.
- If the strategy fits—Select professional development strategies based on their fit with the content, the audience, and the intended goals.
- It takes time—Provide teachers multiple opportunities to explore new and difficult ideas.
- Meet teachers where they are—Design activities that are both accessible and challenging to teachers with a range of mathematics/science content understanding.
- Think big picture—Consider how the various professional development experiences will work together in deepening teacher knowledge and skills.
Practitioner Insights
There is general agreement that teachers, like all professionals, need opportunities for continuing education to stay current in their fields. Although one can argue that teachers would benefit from any of a large number of activities to deepen their disciplinary content knowledge, their pedagogical content knowledge, and/or their understanding of mathematics/science as a way of knowing, there is never enough time or resources to do it all. Attempting to do too much may result in doing none of it well, so it is essential that people designing a professional development program be clear about their goals for deepening teacher content knowledge, and plan accordingly.
Professional development programs aimed at deepening teachers’ mathematics/science content knowledge vary considerably in their goals, with some programs putting all or nearly all of their emphasis on disciplinary content, and others addressing both disciplinary content and content-related pedagogical issues, and still others focusing on teacher understanding of what it means “to do” science or mathematics. Although program developers may not detail the reasons underlying their plans, the variations in professional development designs appear to reflect different views on what knowledge teachers need for effective classroom instruction, and different views about the most efficient way to go about developing that knowledge.
There are a number of important issues to consider in designing a program to deepen teacher mathematics/science content knowledge. When queried about designing programs to deepen teacher content knowledge of mathematics/science, experienced practitioners offered a number of insights, which are described below. After reviewing these insights, you will be provided with opportunities to share your own experiences with designing programs to deepen teachers’ mathematics/science content knowledge. The information you provide will be analyzed along with the insights and examples from other practitioners as the website is periodically updated.
You can’t do it all—When addressing multiple goals for deepening teacher content knowledge, consider how deeply to pursue each goal.
Whatever goals are chosen, program designers need to make difficult decisions about how far they can go in pursuing those goals. One program leader explained the constraints as follows:
I subscribe to the following building contractors’ adage: You can get only two out of the three — cheap, fast, and good. (If it’s cheap and fast, it won’t be good; if it’s fast and good, it won’t be cheap; if it’s cheap and good, it won’t be fast).
As applied to learning, it means the following: You can only get two out of three — many concepts, short time, and deep understanding. If you address many concepts in a short time, you won’t get deep understanding. If you have a short time and go for deep understanding, you can’t address many concepts. If you want many concepts with deep understanding, you can’t do it in a short time.
And even if you choose depth over breadth, you still need to decide how deep you can go. Program leaders consistently note that it takes a great deal of time—time for teachers to grapple with the mathematics/science content and to discuss as a group what their investigations yielded—in order to develop deep understanding. One MSP PI described a teacher who, after lengthy work on a particular concept, said, “It’s coming in, it’s fading out, I just can’t hold onto it.” Still more work would be needed for that teacher to have a solid understanding of the idea.
Another MSP PI argued that particularly in the physical sciences, learners’ initial ideas are extremely resistant to change, and it therefore makes sense to strive to help teachers understand a few dimensions of science deeply to ensure that they will take hold.
We know that our ideas are resistant to change, yet we are surprised, again and again, when somebody’s ideas don’t change with intervention. And it’s not just children but all of us who have tenacious ideas that don’t change easily. If you can go deeply, and teachers can come to understand some dimension of science very well, then that in itself is a huge accomplishment. Then, when a teacher says something like, “You know, I’m thinking about light all the time…every time I look out the window, look at how the light is reflecting off of that, and I wonder how much light is being absorbed there,” it has become part of their thinking, a wonderful indicator of learning, and transfer, taking hold.
If the strategy fits—Select professional development strategies based on their fit with the content, the audience, and the intended goals.
In any endeavor, people move toward those things that are comfortable and familiar, and education is no different. Program leaders run the risk of limiting their professional development designs to familiar activities, whether or not they are the best “fit” for achieving the goals in a particular context. Experienced program leaders stress that a particular professional development strategy is unlikely to be universally helpful, but “rather may fit a particular configuration of task/learner/goals well or not.” And, in fact, MSP designs incorporate a number of different program formats, including courses on college/university campuses, courses offered via distance-learning, workshops/institutes at a variety of locations, and district and school-based study groups.
One MSP reports great success in using school-based mathematics study groups. A mathematician is paired with a middle or high school and works with a group of teachers to investigate a particular mathematics topic. The mathematics content is at an adult level, with teachers engaged with challenging problems, some of which might be directly related to a mathematical topic for students (e.g., one middle school group focused on fractions). However, the PI emphasized that the primary purpose was to give the teachers the experience of engaging with mathematics and deepening their own mathematical understanding.
Professional development in the form of teacher study groups, where teachers suggest their own agendas based on problems they’ve encountered in their classrooms, can be effective for deepening teacher content knowledge when supported and facilitated by skilled and knowledgeable study group leaders. Said one program leader,
I’ve been involved with one teacher study group that continued work enthusiastically for several years. Participation was voluntary. The teachers attended because they really wanted to learn more about math and math teaching. The group was rather small (many of the teachers’ peers came once or twice but didn’t return — perhaps due to other commitments, but also perhaps due to lack of interest). The facilitator was flexible and knowledgeable. I’m convinced [that teachers’] understanding of math content that they previously had understood only superficially was deepened significantly.
Quite a few MSP projects have incorporated online courses or other distance-learning activities into their efforts to deepen teacher content knowledge. For example, teachers in one MSP accessed online sessions that related to particular science investigations. Sometimes they did the investigation at home and posted reports of their work; at other times they did the work as teams at school. In these courses, project staff were trying to mirror the process of scientific inquiry by asking teachers to make predictions, voice ideas, and consider how their ideas may have changed based on the information they gathered. When teachers posted their reports, they could also look at the work of their colleagues online, and sometimes they went back and redid their own work to reconcile differences. In addition, all of the teachers were expected to put forth their ideas, unlike in a traditional course where some learners might dominate and others might stay quiet. And in monitoring the on-line conversations, facilitators could see what the teachers understood, and what they failed to understand, and intervene as needed.
It takes time—Provide teachers multiple opportunities to explore new and difficult ideas.
Although a single well-designed session can increase teachers’ understanding of mathematics/science concepts when they have sufficient prerequisite knowledge, teachers need to encounter new or particularly complex ideas in multiple contexts in order to develop a deep understanding. As one experienced program leader noted:
Understanding does not occur in a linear one-time sitting. This does not mean teachers do not learn in one sitting, but that our focus is on developing deep understandings that we need to come back to time after time so they can become connected to new and other mathematical ideas.
Of course, the more learning contexts provided for a single idea, the fewer ideas that can be addressed in a given period of time. Some MSP PIs noted that the fact it was taking longer than anticipated to deepen teacher content knowledge resulted in mid-course adjustments to their professional development plans. For example, one partnership that involved a subset of schools in their first cohort engaged teachers in an intensive experience in one summer, provided support during the academic year, and brought them back for another week in the second summer. The original plan was to move forward and involve future cohorts of teachers. However, even though they had seen gains in both teacher content knowledge and student achievement, project staff recognized that the teachers in the first cohort still “had a long way to go,” and decided to work with them more extensively to solidify their understandings. Another MSP PI offered the example of an equal arm balance. “If you have an equal arm balance with a huge weight on one side, and you keep adding pennies to the other side, the first penny isn’t going to make much of a difference, but if you keep adding pennies, eventually it will even out.” Oftentimes, she suggests, we don’t realize that we are adding to the collection of experiences that makes [teacher content knowledge] change happen.
Meet teachers where they are—Design activities that are both accessible and challenging to teachers with a range of mathematics/science content understanding.
In designing efforts to deepen teacher mathematics/science content knowledge, it is important to meet teachers where they are, and provide opportunities for them to move forward in their understanding. For example, in a program to help teachers understand student thinking about a particular concept, teachers who already have a grasp of the concept can move quickly to analyzing student work; those who have more limited knowledge of the concept may need more time to grapple with their own understanding prior to considering student thinking.
Program design needs to accommodate the fact that any group of teachers is likely to include individuals with a range of understanding. One MSP leader noted that they try to identify tasks for teachers to work on in their mathematics learning community that have “a low threshold and a high ceiling” so that all teachers find the work both accessible and challenging.
One program leader described on-line science courses that accommodated teachers with diverse content backgrounds.
In one course, Physics of Energy, a teacher posed a question about the Olympic luge event and whether a weighted vest was actually helpful. The instructor recognized this as a rich question for investigation and discussion at multiple levels, and the investigations and discussion attempting to answer the question continued throughout the 10-week course. All participants reported that the course deepened their content knowledge.
Another program leader suggested that when there is considerable variation in teachers’ prior knowledge, collaborative learning activities are particularly effective.
I think if you are working in heterogeneous groups in professional development like we would advocate in the classroom with students, the content may be challenging to some but not others and that could be good in terms of collaborative learning and the development of a learning community among adults.
In some cases, different experiences in how teachers have previously learned disciplinary content have implications for program design. For example, a program leader noted that although it is important to elicit learners’ prior ideas before moving ahead with instruction, teachers who have internalized a learning cycle approach will do this automatically, so the program design does not have to provide a structure for this purpose.
For some groups of teachers (I hope for this!) the professional development doesn’t have to provide opportunities for them to consider their prior ideas, because they do that for themselves all the time on their own. For sophisticated learners, sitting in a lecture is an occasion for inquiry… in their own minds, with the person sitting next to them – they make their own opportunities and don’t need us to do it for them.
Think big picture—Consider how the various professional development experiences will work together in deepening teacher knowledge and skills.
Decisions on program timing need to be made in conjunction with decisions about program formats. MSPs have found that extensive engagement with mathematics/science content during the summer is highly rewarding for some teachers, but that other teachers are either not interested in, or not able to participate in, lengthy summer experiences. Program leaders have found that initial immersion in the content is helpful, especially if the content is challenging to teachers, enabling the project to develop a culture of serious work. One MSP project realized that they could not reach all of the teachers with two-week summer institutes as they had intended, both because of the distances involved and because teachers are reluctant to commit that amount of time during the summer. They are exploring the possibility of shortening the institutes to a single week, and incorporating distance education as a more sustainable alternative.
Whether teachers are focusing primarily on their own content learning, or also addressing the application of what they are learning to classroom practice, spaced learning seems helpful in allowing teachers to reflect on what they are learning, deepening their content understanding over time. For example, after an immersion experience having teachers try out their emerging knowledge in their instruction may help them see the boundaries of their understanding, so opportunities to revisit the content in on-line dialogue or face-to-face professional development settings seem helpful.
MSP PIs highlighted the importance of an academic-year component in any on-going efforts to deepen teacher content knowledge. In fact, one MSP project that initially did much of its professional development in the summer, now does most of its work during the academic year. According to the PI, project partners have found that teachers who attend courses in their districts during the academic year are able to learn the content, then go to the classroom right away to try out what they learned, and then return to the district course with examples of student work. Said the PI, the quick turnaround means “there is pressure to see how kids make sense around it” and for teachers to get a better sense of what they themselves know and need to learn.
According to several MSP PIs, summer courses focused on specific mathematics/science content, coupled with school-year professional development, are optimal for enhancing teacher content knowledge for teaching. However, finding time during the academic year for serious efforts at deepening teacher content knowledge is difficult. Providing professional development after school is problematic because teachers are tired. Released time is problematic, especially if well-qualified substitute teachers are not available. And while teacher workdays seem ideal, especially for elementary teachers there is likely to be strong competition with other disciplines for the use of those times. Program leaders should be aware of these various constraints and work with teachers to find the most favorable times for sessions that will take place during the academic year.
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