What We Know About Deepening Teachers' Content Knowledge: Engaging Teachers with Challenging Mathematics and Science to Deepen their Content Knowledge

Practitioner Insights

Professional development often engages teachers with content that is more advanced or sophisticated than how the topics appear at the grade level that they teach. Engaging teachers with more advanced content recognizes the fact that teachers are adult learners; it is based on the expectation that teachers will be better able to guide their students' learning if teachers have a sense of where they are heading in the development of concepts. As one MSP program leader shared:

In order to teach mathematics concepts successfully, to help students clarify misconceptions and correct misunderstandings, to give students the ability to make connections and communicate mathematics, to reason about mathematics and to solve problems, the teacher must have a significantly deeper understanding than the level of mathematics that the students learn.

Given that the levels of content understanding of any group of teachers are likely to be highly variable, professional development providers may find it difficult to have challenging content for all without being below the understanding of some and/or over the heads of others. One reason for engaging teachers with content that is more advanced than what their students encounter is not simply to pose difficult problems to teachers, but rather to use tasks that are challenging at many levels.

When queried about this strategy for deepening teachers' content knowledge, experienced practitioners offered some insights, which are described below. After reviewing these insights, you will be provided with opportunities to share your own experiences with using this strategy for deepening 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.

Embrace rigor—Teachers generally respond positively to opportunities to delve into mathematics/science content.

Although there was sometimes initial resistance to challenging, content-focused professional development, MSP PIs and other program leaders noted that teachers responded very positively to opportunities to delve into the content. For example, PIs noted that their courses were demanding, and that the expectations for participants were high. Teachers responded by doing high-quality work, far beyond what project leaders had seen in other professional development efforts. One program leader reported that in evaluations of online graduate science courses, teachers often indicated that a course that was especially rigorous was also the course that was most beneficial to both their content knowledge and their teaching practice.

A PI of a mathematics MSP reported that when school-based study groups focused on pedagogy-which is what the administration requested they do-teacher attendance was low. Once these same study groups started getting into the mathematics, participation increased:

When the mathematicians go into the schools and start talking to the teachers about mathematics, the reaction is pretty uniformly that teachers really get into it. They like it, they know it's important. It's what they really want, it's what they know they need.

Similarly, a PI of another mathematics MSP shared:

I have taught (or co-taught) two of our courses for middle school teachers (Algebra & Mathematics of Change, i.e., calculus), and will be co-teaching a third this summer - Counting the Possibility, i.e., Discrete Math). These are college-level mathematics courses that are quite far removed from the Colorado Middle School mathematics frameworks, and without exception (alright, maybe one or two exceptions) the teachers "love" the material, and express a huge increase in their mathematical maturity and sophistication, giving them the confidence to explore different things/techniques/ instructional styles in their classes.

An MSP that is using school-based mathematics study groups to help teachers develop advanced content knowledge is finding them to be a very effective strategy. A mathematician is paired with a middle or high school and works with a group of teachers to investigate a particular mathematical topic. The mathematics is at an adult level, with teachers engaged with problems that are quite challenging for them. Problems might be directly related to a mathematical topic for students, e.g., one middle school group focused on fractions. But the PI emphasized that the purpose of working on these problems was to give the teachers the experience of engaging with mathematics and deepening their own mathematical understanding.

One size doesn't fit all—Plan for the likelihood that teachers with different course backgrounds in mathematics/science will have very different content-related needs.

Professional development providers often found that teacher participants came to content-focused experiences with a wide range of backgrounds, from those who had completed one or two college courses in science or mathematics to those with degrees in those fields. One MSP PI noted that having identified this range of backgrounds, the partnership staff recognized that they had not given sufficient consideration to differentiation for participants within the courses they designed for deepening teachers' content knowledge. As a result, they have been re-designing courses to try to make them effective for everyone involved.

Another MSP used a study group format to team teachers with mathematicians, based on a design developed in a previous project for high school teachers. However, that design wasn't working as anticipated with a group that included teachers from the middle grades along with high school teachers. The PI noted that the mathematicians who worked with the high school teachers found that some of the teachers had "pretty good backgrounds" in mathematics, so the study group could function as a joint learning enterprise. The middle school teachers, by contrast, had many specific questions about pieces of content, and looked to the mathematicians to lead the group.

Insight in Action
An MSP which offers a Master's degree program in elementary mathematics determined that a review of K-6 mathematics concepts was needed early in the course. Concerned that a review would be perceived as not useful by some teachers who had stronger mathematics backgrounds, the designers decided to begin with a topic that would likely be unfamiliar to all of the teachers, the Euclidean Algorithm. Through the investigation of the algorithm, the facilitators were able to review the details of fundamental arithmetic in a new context which engaged teachers with a range of prior mathematics knowledge.

Insight in Action
In order to address the range of content expertise in a mathematics content course, one MSP started with a task that could be presented at a lower grade level but then pursued the connections to more and more sophisticated ideas which would be encountered in higher grades. For example, one could start with a third grade arithmetic task but ultimately connect it to the ideas of group theory.

Insight in Action
A finite mathematics course offered by one MSP involved weekly class meetings where students worked in small groups to answer mathematics problems. To help meet teachers where they were, which varied a great deal, the project created a warm-up which was quite easy, followed by a problem which was more difficult, and finally, a challenge which was open-ended and difficult. Facilitators found that the warm-up helped teachers think about some things that they already knew and gently guided them to explore the more difficult problem and challenge.

Bridge the gap—Teachers with substantial gaps in their mathematics/science content knowledge need the same kind and depth of content coverage as is provided in content-focused graduate courses.

"I believe that teachers should be challenged to learn mathematics deeply, to explain complicated ideas, etc. Only by going much further than learning the mathematics taught in their classroom can the teacher truly be prepared to challenge students and help them learn," said one MSP PI. Some PIs believe that graduate coursework is really what is needed to deepen content knowledge of teachers who lack a mathematics/science background-especially for teachers who will serve in content-focused leadership positions. One PI equated the common approach of simply having teachers complete numerous, unrelated mathematics problems in preparation for serving as leaders to himself trying to practice law after watching 100 episodes of the TV show "Law and Order." Simply engaging with more mathematics content does not necessarily result in a deep and rigorous understanding of that content.

Another PI found that teacher leaders struggled to serve as intellectual leaders in their schools, not because of their own content knowledge, but because their colleagues' content understanding was so shallow. This observation led to the decision for the MSP to offer professional development for teachers over many of the same key concepts that are covered in graduate courses. They do not try to cover all the graduate program content, but rather identify a set of key concepts and adapt those to a teacher professional development program.

Learning is learning—Apply what is known about how people learn to experiences for teachers to deepen their content knowledge.

Research on how people learn mathematics/science concepts applies to both children and adults. Experienced program leaders note that activities intended to deepen teachers' understanding of advanced concepts need to build on their prior knowledge, providing instructional experiences that are challenging but at the same time appropriately scaffolded.

A number of MSPs utilized the elements of how people learn as a framework for the content-focused experiences they provided to teachers. Content sessions included eliciting of teachers' initial ideas, engaging activities to confront or build on teachers' initial ideas, and having teachers consider how their emerging understanding related to their initial thinking. As two program leaders stated about the importance of applying learning theory to content experiences for teachers:

Immersing the [teachers] in meaningful experiences enables them to integrate and test their preconceptions while establishing conceptual frameworks that merge new information into a useful, retrievable body of knowledge.

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Experiencing the discomfort of not knowing something, followed by systematically working through the difficult task of learning gives teachers powerful insight into what learning looks and feels like and greater empathy for their students' daily experience. Learning science content in a setting that models effective instruction gives teachers a vision of what is not only possible, but necessary, to develop student learning.

Connect the dots—It is often helpful to show teachers how the content they are encountering relates to the content they will be teaching to students.

Some program leaders emphasized that even when the content being addressed with teachers is beyond the students' level, it should be tied to the content that they will be teaching to students. From their perspective, providing clear links to the student-level content not only motivates teachers to want to learn more advanced concepts (avoiding the "this doesn't apply to me" attitude), it also increases the likelihood that teachers will draw on this knowledge appropriately in their practice.

Another program leader noted that these ties to student-level content must be explicit, as teachers will vary in their ability to be able to make these jumps on their own: "In other words, you can teach high-level content, but you need to bring it into alignment with the appropriate level for students or you are making the assumption that teachers can do this. Some will be able to and others may not, given the newness of the content for them."

Other program leaders highlighted the times when it is appropriate for teachers to focus on content knowledge that is quite distant from the classroom applications of those ideas. For example, one program leader suggested that professional development focus on core ideas in the discipline even if they are not central to the curriculum in a particular grade.

I think the topics must be central to the discipline or to the field of science that the teachers are studying in the professional development but may not necessarily be central to what the teachers teach. For example, Kindergarten teachers learning about weather should understand the role that air pressure plays in generating/sustaining weather systems, but they do not use the idea of air pressure in their teaching other than to (maybe) introduce Kindergarteners to the barometer as a scientific instrument. If air pressure is the topic, then it is not central to what the teachers teach, but it is central to the discipline (meteorology) that they are studying.

Another program leader also noted that these connections are not always needed. As one stated:

Our program explicitly does not "deliver" content within the context of grade-level relevance. While some of the content courses include opportunities for participants to think about how they would use knowledge gleaned from these courses in their middle grades classrooms, our assumption is that the participants need to experience what we offer as adult learners of science. In sum, we hope to enable the teachers to develop good habits of mind about science in general. While they may not see how this is helping their teaching while in the midst of a rigorous degree program, results from the first cohort of graduates (and their students) suggests that enhanced content knowledge may result in improved teaching and learning.

In any event, program leaders emphasized that professional development providers need to make it clear when the teachers are encountering content at a deeper level than what they are expected to teach. In the absence of clarity about the developmental appropriateness of the various learning goals, teachers may assume that the goal is for them to replicate the professional development learning activities in their classrooms.

Now It's Your Turn...

Would you like to comment on or provide an example of any of the insights listed above based on your own experiences engaging teachers with challenging mathematics or science content as a strategy for deepening their content knowledge? If so, you are invited to click here to share comments or provide an example from your own practice.

Would you like to share any insights (in addition to the list above) from your own experiences in engaging teachers with challenging mathematics or science content to deepen teacher content knowledge? If so, we invite you to add your insights here.

If you are interested in how these practitioner insights were collected and analyzed, a summary of the methodology can be found here.