What We Know About Deepening Teachers' Content Knowledge: Considering the Use of Student Instructional Materials

Practitioner Insights

If teachers have substantial gaps in their content background, professional development programs often concentrate on deepening teachers' knowledge of the mathematics/science content they are expected to teach at the level they are expected to teach it. Some programs focus the professional development on the actual instructional materials teachers are using, teaching content within the context of those materials. In addition, engaging teachers with examining student instructional materials and tasks within these materials provides an opportunity to ground professional development in the realities that teachers experience every day; and to help teachers deepen their understanding of how specific instructional materials are intended to develop student understanding in mathematics/science.

When queried about this strategy for deepening teachers' mathematics/science disciplinary and/or pedagogical 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.

Look at it from the students' perspective—Experiencing the instructional materials as their students will use them can deepen teachers' understanding of mathematics/science content.

It seems obvious that "you can't teach what you don't know." Elementary teachers typically have had very little college coursework in mathematics and science; especially in the physical and earth sciences, they describe themselves as not very well prepared. Middle and high school level science teachers may have been prepared in a single area, e.g., biology, but assigned to teach multiple science subjects. And teachers of mathematics at all grade levels may not have had an opportunity to learn content that was added to the K–12 curriculum after many of them had completed their pre-service preparation, e.g., algebraic thinking in the lower grades, discrete mathematics in the higher grades, and probability and statistics at all grades. One MSP evaluator shared:

I would stress the importance of engaging teachers as learners of mathematics as part of any examination of instructional materials. It is a critical first step in any process of deepening content or pedagogical knowledge.

If the content that teachers are assigned to teach is unfamiliar to them, then the first priority is likely to be to help them understand the disciplinary content at least at the level their students will be expected to learn. And, program leaders suggest, it is helpful to allow teachers to concentrate their efforts on learning the targeted content before considering how to teach that content to their students. Said one:

In my experience, it works much better when there is ample time -- at least a week -- to focus on the content ourselves, rather than a short one-week shot in which content is just one of several things we are doing.

Engaging teachers with the student instructional materials to help them learn mathematics/science content also provides an opportunity to model effective use of those materials. Said one program leader:

I have found it is important to focus on units as you would want teachers to implement them with their students. In other words, don't skip around with activities during a workshop if you intend teachers to follow them in the order provided by the curriculum developer.

What's the story?—An analysis of the mathematics/science ideas in student instructional materials and how they relate to one another is helpful in deepening teachers' pedagogical content knowledge.

If the goal is to deepen teachers' pedagogical content knowledge, professional development needs to provide teachers with explicit opportunities to consider how the various activities in the student materials fit together to promote concept development. As one program leader stated:

It's not just focusing on the learning goals of the activities, but understanding how to identify the conceptual understandings (as opposed to factual information) that students need to gain from each activity and how a sequence of activities links ideas together to form more abstract concepts.

Experienced program leaders suggested that addressing instruction provides opportunities for addressing mathematics/science content as well. As one program leader noted, a discussion about, "'What might your students think [about a particular problem]' can lead to useful 'digressions' on the ideas themselves. (As in, 'A student might think X. Well, what would be wrong with that? Is it wrong?')"

Program leaders noted that they had seen both effective and ineffective attempts to use student instructional materials for deepening teachers' pedagogical content knowledge. Examples they provided of effective use of this strategy include the following:

Where this is done well, it is typically done over time and in smaller chunks where examining student learning is an intentional learning target. Teachers are engaged with the activities, often as learners themselves, where the specific learning target of the activity is clearly defined (not just the "activity"). They are asked to consider their own prior ideas, how those ideas may have changed based on the activities, and what about the activity helped them develop a new and deeper understanding...This work is linked intentionally with some learning theory - most frequently that described in How People Learn - so that teachers have a framework for talking about the learning process. In this context teachers can talk meaningfully about how people learn, what their intended learning targets are, what anticipated student responses might be, and upon analysis of student work, consider where and how the activities supported their learning target, where it didn't and why.

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I have used immersion in content work with several groups of K-3 and K-5 teachers. In that content work, we usually worked on the content ourselves first, through activities designed to be challenging for adults/teachers (but usually at about the same grade level as they taught, because of their own poor scientific knowledge background), then thought about what our learning taught us about the ease or difficulty of putting together the big ideas for that content. Then, we thought about what it might be like for children, and what paths (whether the same as the adults or different) that their learning might take, and how it might be different or the same as ours.

Ineffective use of this strategy, by contrast, was described as follows:

Teachers are simply asked to go through one activity after another. The learning goals for the activities may or may not be defined. Even if they are, the focus remains on how to do the activities in a "mechanical" fashion. Teachers basically learn how to set up the activities and "get through" the unit, but it is unclear whether they understand what the purpose of the unit or each activity really is, how the sequence of activities is intended to develop understanding, or how students might be anticipated to respond to various activities. Teachers leave knowing "what" to do, but not why they are doing it. Here teachers teach the unit on "butterflies" without realizing that the unit was intended to address the larger issue of life cycles. They may comment on affective domains - students like it, students didn't like it - but are unlikely to be able to discuss evidence of learning and correlate that with the materials or instruction.

A number of program leaders suggested providing a conceptual "frame" for examining the student instructional materials, or co-constructing one as part of the professional development, to help teachers focus on the core mathematics/science ideas and how these ideas relate to one another. One program leader noted that examining conceptual underpinnings of instructional materials without a big picture perspective on the content is "like looking through the keyhole of a door," as teachers would have a limited view of how a lesson develops mathematics/science ideas in the context of the larger conceptual territory. Understanding this conceptual frame, program leaders suggest, provides teachers with the knowledge that will allow them to maintain the mathematics/science storyline in implementation.

Others noted that having teachers analyze the "learning progression" in student materials across grades is also helpful, examining how the specific mathematics and science concepts/skills develop over time. Such an analysis helps teachers know where their students have been, and where they are going, in relation to key mathematics and science ideas; it also enables teachers to consider whether there are aspects of a concept that are not well addressed, and how those gaps can be addressed.

Analysis of student instructional materials can also focus on the level of cognitive demand of particular activities; experienced practitioners suggested that this strategy helps highlight the mathematics/science concepts being targeted, and enables teachers to consider how various modifications to problems/tasks might affect student learning. As one program leader noted, we want teachers to "understand the content well enough that when they make the pedagogical adaptations to their context, they maintain the intellectual integrity of the curriculum materials and translate them accurately to their students."

Program leaders noted that highly skilled and knowledgeable facilitators are especially important when professional development is addressing multiple goals, people who understand the mathematics/science content and can teach it well and also understand K–12 teaching considerations. For example:

It seems to be more satisfying for the teachers to have someone who knows the landscape of the content well and can relate to the pedagogical implications of the curriculum materials, the students, and the ideas, e.g., the high school teachers or scientists who are sympathetic to the real world of the classroom. This means it is not enough to be a scientist and it is not enough to be a scientist who can talk to teachers.

Keep your eye on the prize—Ensure that teacher concerns about logistics and classroom management do not get in the way of addressing mathematics/science content and pedagogical content knowledge goals.

Engaging teachers with student instructional materials provides an opportunity to ground teacher learning of mathematics/science content in problems of practice. Using this approach provides an intrinsic motivation for teachers to want to learn the content, a factor many program leaders indicate is an essential component to the success of this strategy. However, especially if they are using a set of student instructional materials for the first time, teachers may be anxious about classroom management issues that are not primarily about the teaching of particular mathematics or science concepts. Professional developers need to find ways to help teachers with the logistical management issues while emphasizing both the key concepts addressed in those materials and the strategies for teaching those concepts. Said one program leader:

Teachers need to have facilitated conversations about the conceptual flow of the science content in a unit of instruction. The professional development cannot focus only on the mechanics of teaching the unit or the materials management. Teachers need to reflect on the content of the unit as well.

Consider the source—The quality of the student instructional materials has implications for how teachers should engage with them in professional development.

Instructional materials vary in the extent to which they are conceptually coherent and provide students opportunity to learn science and mathematics concepts. Program leaders suggested that it is important to recognize this variation and consider the implications in designing professional development that incorporates student instructional materials.

When using well-designed student instructional materials as a way to deepen teachers' pedagogical content knowledge, the analysis can focus on the purpose for a particular activity or series of activities, the level of cognitive demand of each, and why they are designed to be done in a particular way. Similarly, if the instructional materials have well-designed support materials for teachers, including commentary on the targeted mathematics/science to help teachers teach the content, then content-focused analysis and discussion of the teachers' guides can help teachers learn how to capitalize on those supports.

Of course, not all student instructional materials are well-designed, and program leaders noted that materials that are not likely to be effective in developing student understanding are not likely to help teachers either. Although program leaders suggested that well-designed materials are ideal for teacher analysis, they caution that providers must be prepared to provide professional development to help teachers use whatever instructional materials they are expected to use, and do so as effectively as possible. As one MSP PI stated:

If we accept the premise that not all instructional materials are of high quality, one must recognize the need to offer professional development for teachers who must use student instructional materials that are not well-constructed and conceptually coherent. How do you provide good professional development for those teachers? Perhaps by turning lemons into lemonade. A good professional development provider can use those materials to help teachers see their flaws and to understand the teacher's responsibility to provide good instruction even if working with instructional materials that are not that good.

One program leader noted that when the student instructional materials used in professional development are poorly designed, it is helpful for teachers to consider research about how students learn the particular mathematics/science content before analyzing the instructional materials.

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 student instructional materials as a strategy for deepening their disciplinary and/or pedagogical 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 student instructional materials to deepen their 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.