Professional learning opportunities for teachers of mathematics and science have increasingly focused on teachers’ content knowledge. Learning opportunities aimed at deepening teachers’ content knowledge are designed to address their content needs. What factors related to the content needs of mathematics/science teachers should be considered when designing content-deepening experiences?
Advice from experienced practitioners offers guidance about understanding teachers’ mathematics/science content-related needs. Insights provided by a group of expert practitioners with diverse backgrounds and experiences in working with teachers included the following ideas:
- Knowing what they know—Consider whether you want to do a formal assessment of teacher content-related needs to help decide where to focus professional development efforts.
- Be realistic—Whatever areas you focus on, anticipate that many teachers will lack in-depth knowledge of disciplinary content.
- Differences are inevitable—Plan for the likelihood that any group of teachers will have diverse content-related needs.
- Different topics, different needs—Expect the nature and extent of teacher content-related needs to be different for different topics.
- Experience matters—Anticipate that experienced teachers will have different needs than those who are new to the classroom, or new to a particular instructional approach.
Practitioner Insights
How a project goes about deepening teacher content knowledge depends to a great extent on the needs in a particular context. When designing content-deepening experiences for a particular group of mathematics/science teachers, it is important to take into consideration their content-related needs.
When queried about understanding the content-related needs of mathematics/science teachers, experienced practitioners offered a number of insights, which are listed below. After reviewing these insights, you will be provided with opportunities to share your own experiences with understanding the content-related needs of mathematics/science teachers. The information you provide will be analyzed along with the insights and examples from other practitioners as the website is periodically updated.
Knowing what they know—Consider whether you want to do a formal assessment of teacher content-related needs to help decide where to focus professional development efforts.
One of the first challenges in planning programs to deepen teacher content knowledge is to decide where to focus professional development efforts. Given the breadth of content included in state mathematics/science standards, and the limited time available to work with teachers, choices need to be made. Program leaders caution, however, that while professional development should identify and target priority needs, spending too much effort on identifying needs leaves too few resources to spend on addressing those needs.
Using tests of teacher content knowledge to identify areas of need sounds appealing, but would require diagnostic measures that both address multiple areas of content and have norms for each; those types of measures are not widely available. The tests of teacher content knowledge program leaders administered, including assessments developed as part of MSP Research, Evaluation, and Technical Assistance projects, were used primarily to establish baseline measures of teacher content knowledge, rather than to inform decisions about areas of focus.
Some programs used the process of identifying teacher content-related needs as an opportunity to help ensure teacher ownership of the professional development. The reasoning was that if the project focused on the needs teachers themselves had identified, teachers would be more open to the efforts and more likely to apply what they were learning to their classroom instruction. Some programs administered surveys to teachers, while others brought representative groups together for discussions about their needs and those of their colleagues. But program leaders pointed out a limitation of these approaches, noting that “sometimes teachers don’t know what they don’t know.”
Other projects relied on mathematics and science supervisors in the participating districts for their impressions about teacher content needs. Some program leaders noted that in retrospect, they wished they had visited classrooms themselves before planning the professional development, not so much to decide which content to focus on, but rather to get a clearer idea of the ways in which teachers would need to draw on their content knowledge; it is one thing to know content at an adult level, and another thing entirely to be able to use that content to figure out where their students were getting tripped up and what to do about it.
Some program leaders decided not to try to assess teacher content needs directly, but rather based their decisions about where to focus professional development on student achievement data, the “bottom line” for parents and policy makers. Targeting content areas which students find particularly difficult, these program leaders reasoned, would help garner stakeholder support for their efforts, and have the potential for yielding the greatest gains in achievement data. Still, program leaders found that state and district test results were not always helpful in this regard, either because they couldn’t provide scores for individual content domains, and/or the items did not appear to be good measures of student understanding. And using “raw scores” was problematic in any event; an average of 60 percent correct on earth science items and 80 percent on life science items could mean that students had particular difficulty with earth science ideas, or simply that the items selected for the earth science test were intrinsically more difficult.
When professional development planners do not have detailed information about the needs of the particular teacher audience they plan to serve, they can get some general guidance from national data about teacher perceptions of their preparedness.
Click here for national data on teachers’ perceptions of their preparedness to teach mathematics/science.
Be realistic—Whatever areas you focus on, anticipate that many teachers will lack in-depth knowledge of disciplinary content.
Program leaders sometimes found that teacher content knowledge was much weaker than they had anticipated. Some projects had intended to focus their efforts on preparing teachers to implement specific instructional materials, making the assumption that teachers understood the mathematics/science content but needed assistance in how to teach that content using new materials. Discovering that teachers were struggling with the content, they adjusted their plans to spend more time on deepening teacher content knowledge. Said a PI of a science-focused MSP:
When we started offering professional development, we saw that the teachers did not know (for instance) what velocity and mass were. These are very basic principles that would be learned in a fundamental science course. Or worse, they were taught erroneously. So we had to start from scratch.
A PI of a mathematics MSP described a similar experience. The district elementary mathematics coordinator had alerted the university partners about weaknesses in content knowledge among elementary teachers, but at the secondary level the coordinator thought that the teachers knew enough mathematics to enable them to implement the new instructional materials. That turned out not to be the case, according to the PI, who speculated that secondary teachers tended to know content in “one right way,” but lacked the in-depth understanding of key mathematics ideas required to facilitate learning among students who approached problems in different ways.
The PI of a middle school science MSP expressed alarm at teachers’ weak content knowledge. The project had administered multiple-choice “content surveys” in several areas to teachers when they entered the program. Teachers answered only 20-30 percent of the items correctly. With four choices per item, you would expect 25 percent correct by chance, leading the PI to conclude that the teachers had very fragile knowledge about these particular science topics. Some leaders of programs that worked to prepare teachers for leadership also expressed surprise that some of the teachers identified for these roles had very weak content knowledge.
Differences are inevitable—Plan for the likelihood that any group of teachers will have diverse content-related needs.
Program leaders often found that the teachers participating in their professional development programs had very diverse content backgrounds, ranging from those who had completed only one or two college courses in science or mathematics to those with degrees in these disciplines. One MSP PI noted that having identified this range in content knowledge, project staff recognized that they had not given sufficient consideration to meeting the varied needs of participants within the courses. As a result, they have been re-designing courses to try to make them effective for everyone involved.
A number of programs initially mixed teachers across grade ranges, but found that their needs relative to the content varied so widely that some differentiation of professional development was needed. For example, one MSP PI remarked that the project leader hadn’t realized how hard it would be to teach science content to middle school and high school teachers at the same time:
The way that middle school and high school teachers tend to think about science content is different, and their backgrounds tend to be very different, with high school teachers specializing in one science, and middle school teachers having a broader but less deep knowledge of the sciences.
This project considered offering separate courses; they decided instead to keep the groups together but to differentiate within the courses. Other projects opted to address the issue by dividing the teachers into grade-level groups for some of the coursework. Still others decided to work with groups of teachers from across the entire K-12 spectrum, using the diversity of content-related needs as a springboard for discussions about addressing the needs of diverse learners.
Another PI noted that the focus for elementary and middle grades teachers in their project is “more on the traditional idea of understanding the science.” For high school teachers, it was geared “more toward content-specific pedagogy.” Both were considered important for all teachers, but the need was seen as different depending on teachers’ grade level.
A PI of the mathematics project described the importance of understanding the teachers’ needs in determining the goals of the professional development:
If one is going to provide professional development for mathematics teachers, the starting point should be to think about what the teachers need. Can you assume that they have a deep understanding of the mathematics they teach and can thus focus on helping them learn about how to use the instructional materials they have or to learn about how students think about the material being studied? Or, can you assume that the teachers have good “teaching skill” and/or a good understanding of how the students they teach think, but need help learning mathematics so that they will have a deep understanding of the mathematics they teach? (Of course, it’s reasonable to believe that teachers often need “all of the above.”)
Unfortunately, it is often the case that elementary and middle level mathematics teachers need to substantially upgrade their knowledge of mathematics. At the same time, many, perhaps most, of the experienced teachers with whom I have worked have really good ability to work with kids and successfully teach them, as long as they understand the mathematics they are teaching.
Different topics, different needs—Expect the nature and extent of teacher content-related needs to be different for different topics.
An MSP project that focused on middle grades science found that teachers needed more work in physics than in other science disciplines in order to be prepared to teach the state standards. Similarly, the PI of a mathematics MSP targeting elementary teacher leaders noted that content knowledge varied across content areas within mathematics. While teacher knowledge of number and operations was relatively strong, it was quite weak in geometry. As an example, the PI noted that the teachers typically knew that the area of a triangle is half the base times the height, but not very many knew why that is the formula for the area of a triangle.
An MSP’s summer institute for secondary mathematics teachers focused on two areas of mathematics content: algebra and geometry. In the algebra strand, they focused on certain topics that they knew (both from their previous experience working in these districts, as well as from pre-tests of the participating teachers) to be particularly problematic in terms of teacher content knowledge. These topics included identifying solutions to equations and systems of equations and understanding when you have a unique solution, no solution, or an infinite number of solutions in a solution set. The project “started with solutions to linear equations, and we looked at three types. And then we looked at their graphic representations. And then we went to systems and did the same thing, and then we did a compare and contrast.” In the algebra strand, they basically identified some very specific areas that are foundational to the teaching of algebra 1 – where they knew teachers’ knowledge is weak, and where they knew the textbooks can be quite confusing – and they taught that content. They engaged the teachers in problems that were similar to or related to problems they might use in their own classrooms, and then took that content deeper and connected it to big ideas.
The project’s approach was different in the design of their geometry strand, and intentionally so. They said they had “some really interesting” discussion among themselves about what was different between teaching algebra and geometry. They believed that teachers viewed algebra very procedurally, and therefore their focus was on getting teachers to see the concept behind the procedures. But, says the PI, “geometry isn’t procedural in the same sense. The big issue with geometry is that when kids come in to high school geometry courses, teachers think that they are ready to do deductive work. In almost every case, kids come in with a very, very poor structural understanding of the geometric figures that they are having to face.” So in contrast to the work in algebra which focused on teacher disciplinary content knowledge, in geometry the focus was on teacher pedagogical content knowledge, in particular teachers’ understanding of students’ developmental stages in geometry learning.
Experience matters—Anticipate that experienced teachers will have different needs than those who are new to the classroom, or new to a particular instructional approach.
Teachers participating in professional development programs are likely to vary in teaching experience, both in years of teaching and in their use of particular instructional materials. One experienced program leader described this variability as follows:
I had the opportunity several years ago to work with a group of teachers from three different districts who were at various stages of implementing the Connected Math Program (CMP). One group was in its first year, another had been using selected units for two years and the third group had been using the entire CMP curriculum for more than three years. The third group had also participated in User workshops.
There was a marked difference in the issues that the most experienced teachers brought to the table as compared to the first year folks. The former were concerned about what their students were coming to understand and how they could be sure about what they knew. The latter were concerned about the mechanics of implementing various components of the curriculum and how to keep pace. While the more experienced teachers were focused on learner concerns, the “novices” with CMP were focused on themselves.
Professional development programs aimed at deepening teacher content knowledge may require differentiation for teachers with different backgrounds. Depending on the extent and nature of teachers’ career experiences, different teachers may need varying levels of attention to understanding content as a learner, understanding content as a teacher, or understanding content as it is sequenced and presented in particular instructional materials.
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