Professional learning opportunities for teachers of mathematics and science have increasingly focused on teachers’ content knowledge, in some cases involving teachers working with the instructional materials they are or will be using with their students. This strategy may include teachers performing the activities themselves as learners, and/or analyzing the materials to discuss the intended learning goals and progression of ideas for students’ conceptual development. Advice from experienced practitioners offers guidance for efforts to use student instructional materials in deepening teachers’ mathematics/science disciplinary and pedagogical content knowledge. Insights provided by a group of expert practitioners with diverse backgrounds included the following ideas:
- 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.
- 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.
- 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.
- Consider the source—The quality of the student instructional materials has implications for how teachers should engage with them in professional development.
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?’)”
Insight in action
We used the ACHIEVE Foundations for Success document to have our teachers consider a model middle-level curriculum. They worked these problems (which often were quite challenging) and discussed what mathematics a student needed to know in order to be prepared for the type of questions in this book. This seemed to help our teachers learn some mathematics AND increase their appreciation of the fact that they needed to learn more mathematics.
MSP PI
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.”
Insight in action
Teachers brought their own geometry texts, and we brought some as well. We opened the books to a particular chapter (similarity, say), and looked at all the texts, answering the following questions: (a) What did the author think is the important mathematics in this lesson? (b) What are the author’s mathematical expectations from students? (c) How does the author think about teaching and learning?
The mathematical discussions that ensued got right to the subtleties of high school geomety… For example, we saw that texts that develop area before similarity can present a much more “honest” development of similarity, and they tend to have greater intellectual respect for students.
MSP PI
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.
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.
Research on Engaging Teachers with Student Instructional Materials
Studies of eight professional development programs that engaged teachers with student instructional materials in mathematics, as one of several strategies, were identified in a search of the published literature. Findings of the studies for all eight interventions, including two studies of one intervention, provided evidence of positive effects on teachers’ mathematics content knowledge (Basista & Mathews, 2002; Benken & Brown, 2008; Chazan, Yerushalmy, & Leikin, 2008; Clark & Schorr, 2000; Empson, 1999; Noh & Kang, 2007; Sowder, Phillip, Armstrong, & Schappelle 1998; Swafford, Jones, & Thornton, 1997; Swafford, Jones, Thornton, Stump, & Miller, 1999). These studies were concentrated in the elementary and middle grades, although teacher participants ranged from grade 3 to grade 12. Four of the eight interventions dealt with topics in algebra and number and operations; geometry and data/probability/statistics were each addressed by two studies. Although no studies investigated the unique contribution of the use of student instructional materials in teacher professional development, consistent positive results across the programs support claims regarding its effectiveness in deepening teachers’ mathematics content knowledge.
Research on Engaging Teachers with Student Instructional Materials in Mathematics
Professional learning opportunities for teachers of mathematics have increasingly focused on deepening teachers’ mathematics disciplinary and/or pedagogical content knowledge. One method of addressing teachers’ knowledge is to engage them with the materials they are using or will use with their students. This strategy may include engaging teachers with the student activities themselves as learners, or analyzing the materials to discuss the intended learning goals and progression of ideas for students’ conceptual development. Research studies of eight mathematics professional development programs using some form of this strategy were reviewed.
Findings from Research
For each of the eight professional learning experiences that included engaging teachers with student mathematics instructional materials the studies provided positive results on participating teachers’ content knowledge. Although none of these studies investigated the unique contribution of the strategy of using student instructional materials, consistent positive results across programs support claims regarding its effectiveness in deepening teachers’ mathematics content knowledge.
Teacher participants in the eight studies ranged from grades 3 through 12, with a majority of the studies focusing on the upper elementary and middle grades. Of the 8 interventions that were studied, 5 dealt with topics in number and operations and 4 with topics in algebra. In addition to topics in one or both of these strands, 2 of the interventions also included some attention to topics in geometry and data analysis and probability. One study (Benken & Brown, 2008) did not specify the focus of the mathematics content. Studies of 5 of the interventions involved teachers engaged with formal professional development experiences; the other 3 (Chazan, Yerushalmy, & Leikin, 2008; Empson, 1999; and Noh & Kang, 2007) involved no formal professional development, but rather studied teachers who were using an investigative mathematics curriculum with their students. In studies of two of the professional development interventions, the experiences were structured as summer institutes (Basista & Mathews, 2002; Swafford, Jones & Thornton, 1997; Swafford, Jones, Thornton, Stump, & Miller, 1999). Teachers in the intervention studied by Swafford and colleagues also participated in six half-day follow-up sessions during the ensuing academic year. The experiences in a third study were structured as courses with meetings over 14 to 16 weeks (Clark & Schorr, 2000), and a fourth program that was studied involved teachers in monthly meetings with university faculty over two academic years, as well as visits by university faculty to the teachers’ classrooms (Sowder, Phillip, Armstrong, & Schappelle, 1998).The final study examined impacts of bi-monthly on-site professional development sessions (Benken & Brown, 2008).
In addition to the use of the strategy of engaging teachers with student instructional materials, all eight programs also included strategies to help teachers connect the mathematics content they were learning to their classroom teaching. Although this aspect was not studied systematically, its common occurrence in these experiences suggests its potential importance with respect to the goal of deepening teachers’ disciplinary and/or pedagogical content knowledge.
Teachers participated in most of the professional development experiences on a voluntary basis, so generalizability of the findings from these studies must be considered in this light. The populations that the participating teachers represent are limited to those willing and able to commit to such extensive interventions.
Studies of five of these interventions either used a pre-post design to measure changes in teachers’ content knowledge or traced changes over multiple points in time. The remaining studies (Chazan et al., 2008; Empson, 1999; Noh & Kang, 2007) apparently examined interviews at a single point in time. None of the studies used comparison groups of teachers who did not participate in the professional development programs. It is possible that participating teachers might perform better on a measure of content knowledge on a post-test simply because they had completed it previously, in one case (Basista & Mathews, 2002) only a few weeks before. The use of multiple measures to some extent addresses the concern about testing bias. For example, in the study by Swafford and colleagues (1997, 1999) the participating teachers performed better in three different content areas, and on three separate measures of knowledge of geometry, following treatment; similarly, in the study by Sowder and colleagues (1998), different written instruments and interviews were used with teachers to triangulate findings. Only one of the studies, represented in two articles, used any externally-developed measures of teacher content knowledge (Swafford et al., 1997; Swafford et al., 1999).
Additional limitations were noted in the designs of some of these studies. In two cases the intervention with teachers were not described in sufficient detail to support interpretations linking their experience with the results (Benken & Brown, 2008; Clark & Schorr, 2000). There was also insufficient detail about the analysis procedures in one of these studies (Clark & Schorr, 2000). Studies of four interventions had potential concerns regarding investigator bias, as the researchers were responsible for designing and/or implementing at least some of the interventions (Basista & Matthews, 2002; Benken & Brown, 2008; Sowder et al., 1998; Swafford et al., 1997; Swafford et al., 1999). In one study (Empson, 1999), interview data were presented to make specific points that aligned with the researchers’ perspective about effective mathematics teaching. However, it was not clear the extent to which these examples were representative of the data collected, or if any discrepant examples had been identified that could have been presented. Finally, one study (Noh & Kang, 2007) offered little information on the groups of teachers it compared, and provided little data to substantiate its claims of change.
For the research on engaging teachers with student instructional materials in mathematics, click here. [PDF 14K]
The studies of the eight interventions described above were part of a more inclusive review of research on experiences intended to deepen teachers’ mathematics content knowledge. For more information about research on this relationship, you are invited to read a review of findings from studies of experiences intended to deepen teachers’ mathematics content knowledge click here. [PDF 99K]
The literature search surfaced 12 research studies of professional development programs that engaged teachers with student instructional materials in science. Each intervention included several strategies, and none of the studies was designed to measure the unique influence of using student instructional materials. Still, each one reported at least some evidence that teachers’ science content knowledge increased (Alonzo, 2002; Atwood, Christopher, & McNall, 2005; Basista & Mathews, 2002; Cohen & Yarden, 2009; Heller, Daehler, & Shinohara, 2003; Henze, van Driel, & Verloop, 2008; Jones, 1997; Monet & Etkina, 2008; Robardey, Allard, & Brown, 1994; Shen, Gibbons, Wiegers, & McMahon, 2007; van Driel, Verloop, & deVos, 1998; Williamson & Jose, 2008). Although teacher participants in the studies ranged from grades 3 through 12, only two of the studies included high school teachers. Physical science was the most frequently studied content area.
Research on Engaging Teachers with Student Instructional Materials in Science
Professional learning opportunities for teachers of science have increasingly focused on deepening teachers’ disciplinary and/or pedagogical science content knowledge. One method of addressing teachers’ knowledge is to engage them with instructional materials they are or will use with their students. This strategy may include engaging with the student activities themselves as learners, or analyzing the materials to discuss the intended learning goals and progression of ideas for students’ conceptual development. Twelve research studies investigated science professional development programs using this strategy.
Findings from Research
Each of the 12 studies that included the use of student science instructional materials reported at least some positive results on participating teachers’ content knowledge, though in some cases (Cohen & Yarden, 2009; Williamson & Jose, 2008) the results were weak. None of the studies was in fact designed to systematically study the effects of this particular strategy for deepening teacher content knowledge; rather, the studies examined programs comprising multiple interventions, without isolating the influence of any one strategy. In this sense, the studies are more akin to program evaluations than systematic research on interventions. Although none of the studies investigated the unique contribution of the strategy of using student instructional materials, consistent positive results across programs support claims regarding its effectiveness in deepening teachers’ science content knowledge.
Teacher participants in the 12 studies ranged from grades Kindergarten through 12, but the majority of the studies focused on the elementary grades. One study focused on life science, two focused on earth science, four of the studies addressed various science topics, and five focused only on physical science.
The experiences for teachers in the 12 studies included three courses (Alonzo, 2002; Robardey, Allard, & Brown, 1994; Shen, Gibbons, Wiegers, & McMahon, 2007), three academic year inservice workshops (Heller, Daehler, & Shinohara, 2003; Monet & Etkina, 2008; van Driel, Verloop, & de Vos, 1998); and five summer workshops lasting between two and four weeks (Atwood, Christopher, & McNall, 2005; Basista & Mathews, 2002; Hanley, 2006; Jones, 1997; Williamson & Jose, 2008). One of the summer experiences (Jones, 1997) also included follow-up during the school year in the form of inservice activities and classroom visits. In addition, one of the studies (Henze, van Driel, & Verloop, 2008) followed teachers using a new science curriculum.
Nine of the 12 studies used written pre- and post-tests to measure teachers’ gains in content knowledge (Alonzo, 2002; Atwood et al., 2005; Basista &Mathews, 2002; Jones, 1997; Heller et al., 2003; Monet & Etkina, 2008; Shen et al., 2007; Robardey et al., 1994; Williamson & Jose, 2008). Researchers in the Alonzo (2002) study also interviewed teachers and observed their classrooms after the intervention. van Driel and colleagues (1998) analyzed transcripts of teacher discussion during workshops. The Heller and colleagues (2003), Monet and Etkina (2008), and Williamson and Jose (2008) studies also included attitude surveys; in addition, Heller and colleagues (2003) interviewed teachers and Monet and Etkina (2008) used structured journals.
Teachers participated in each of these experiences on a voluntary basis, so generalizability of the findings from the studies must be considered in this light. The populations that the participating teachers represent are limited to those willing and able to commit to fairly extensive interventions. The small sample sizes of the studies also raise some questions about how appropriate it is to generalize the results.
Although all of these studies used either a pre-post design to measure changes in teachers’ content knowledge or traced changes over several points in time, none of them used comparison groups of teachers who did not participate in the professional development programs. It is possible that participating teachers might perform better on a measure of content knowledge on a post-test simply because they had completed it previously, in one case (Basista & Mathews, 2002) only a few weeks before. Two studies (Jones, 1997; Shen et al., 2007) implied that different questions were used for the pre- and post-tests; however, they provided no evidence that the tests had the same level of difficulty, raising questions about the comparability of the results. The Shen and colleagues (2007) study did not include statistical tests to verify that scores on the pre- and post-tests were significantly different.
Additional limitations were noted regarding some of these studies. Three of the studies did not describe the intervention in enough detail to support interpretations linking their teachers’ experience with the results (Alonzo, 2002; Heller et al., 2003; van Driel et al., 1998). Potential bias was also an issue for three of the studies (Basista & Mathews, 2002; Monet & Etkina, 2008; van Driel et al., 1998) in which the researchers designed and/or implemented the intervention. Concerns of potential bias were evident in the van Driel and colleagues (1998) study, in which only three transcript segments were analyzed from a workshop and multiple classroom observations, but no justification was given for choosing these particular segments. Finally, in one study (Cohen & Yarden, 2009) it was not clear when the sources of evidence were collected over the course of the intervention, so it is possible that the study confounded impacts of the professional development with factors related to teachers’ enrollment in professional development.
For the research on engaging teachers with student instructional materials in science, click here. [PDF 11K]
The 12 studies described above were part of a more inclusive review of research on experiences intended to deepen teachers’ science content knowledge. For more information about research on this relationship, you are invited to read a review of findings from studies of experiences intended to deepen teachers’ science content knowledge click here. [PDF 111K]