What We Know About Deepening Teachers' Content Knowledge: Considering Student Thinking about Mathematics and Science
Research on Engaging Teachers in Considering Student Thinking about Mathematics
Professional learning opportunities for teachers of mathematics often include attention to student thinking as a part of deepening teachers' mathematics disciplinary and/or pedagogical content knowledge. Several different approaches to engaging teachers in considering student thinking were found in research studies investigating the effects of interventions on teachers' mathematics content knowledge. Twelve research studies investigated professional development programs that included this strategy. (See Table 1.)
Research Studies of Interventions that Included the Strategy of
Engaging Teachers in Considering Student Thinking about Mathematics
†These articles/reports are from the same study.
What Research Says
Each of the 12 studies of professional learning experiences that included engaging teachers in considering student thinking about mathematics provided positive results on participating teachers' content knowledge. Although none of these studies investigated the unique contribution of the strategy of engaging teachers with attending to student thinking, consistent positive results across programs support claims regarding its effectiveness in deepening teachers' mathematics content knowledge.
The 12 studies were spread across grades Kindergarten through 12, with more studies in the elementary and middle grades than the high school grades. Across the studies, topics in number and operations, algebra, geometry, measurement, and data/probability/statistics were addressed, as well as mathematical processes of communication, representation, and problem solving. The experiences for teachers in these 12 studies were quite varied. Eight of the studies examined the impacts of formal professional development experiences on teachers' mathematics content knowledge. Two were structured as four-week summer institutes (Basista & Mathews, 2002), one of which also provided six half-day follow-up sessions during the ensuing academic year (Swafford, Jones, & Thornton, 1997; Swafford, Jones, Thornton, Stump, & Miller, 1999). One was a ten-day workshop (Ellington, Whitenack, Inge, Murray, & Schneider, 2009), one was structured as a semester-long course (Clark & Schorr, 2000), and one took the form of 12 three-hour sessions (Goldsmith & Seago, 2007). Another study involved teachers in regular meetings with university faculty on a monthly basis (Sowder, Phillip, Armstrong, & Schappelle, 1998) over several academic years, as well as visits by university faculty to the teachers' classrooms. One study included professional learning groups throughout the school year, during professional development days and afternoon workshops (Dole, Clark, Wright, Hilton, & Roche, 2008). Three of the studies investigated teaching practice as a context for teachers to deepen their content knowledge, although it is important to note that the teacher participants in each of these three studies had also engaged in related professional development (Empson, 1999; Featherstone, Smith, Beasley, Corbin, & Shank 1995; Miller, 1991). One other study researched impacts on teachers' content knowledge related to both a professional development experience and subsequent teaching practice (Franke, Carpenter, Fennema, Ansell, & Behrend, 1998).
The means of engaging teachers in considering student thinking also varied across the interventions that were studied. Ten of the programs included activities to engage teachers directly in analysis of student thinking. Five of these ten engaged teachers with written student work, including one in which teachers learned about scoring prepared samples of written student work using rubrics (Stecher & Mitchell, 1995) and four in which teachers were provided with prepared samples of student work (Dole et al., 2008; Ellington et al., 2009; Franke et al., 1998; Goldsmith & Seago, 2007). One of these studies also included work from participating teachers' own students (Franke et al., 1998). Two additional initiatives had teachers interview students about a mathematical topic or their thinking about problems (Sowder et al., 1998; Swafford et al., 1997; Swafford et al., 1999). Another program had its teacher participants implement problems in their own classrooms and subsequently reflect on their students' mathematical thinking about those problems (Clark & Schorr, 2000). Similarly, one study of teacher learning from practice involved teachers in reflecting on what their students wrote in response to specific mathematics writing prompts (Miller, 1991). The other program that engaged teachers with analyzing student thinking was also included in a study of teacher learning from practice, but its strategies were somewhat variable from teacher to teacher, including watching videos of instruction and examining written work from other teachers' classrooms, and implementing problems in teachers' own classrooms and reflecting on how the students' thought about them (Featherstone et al., 1995).
Strategies for engaging teachers in considering student thinking other than direct analysis of student work were included in four interventions that were studied. Two of the interventions provided experiences in which teachers learned about research studies and their findings on student thinking in mathematics (Franke et al., 1998; Sowder et al., 1998). One of the programs had a focus on pedagogical issues that included strategies for assessing students' prior understandings in mathematics (Basista & Mathews, 2002). Finally, one study examined teacher learning from practice as they implemented a new mathematics curriculum material that provided activities to focus their instructional practice on their students' thinking (Empson, 1999).
In addition to the use of at least one strategy for engaging teachers in considering student thinking, some other potentially important commonalities are evident among the experiences studied within subsets of the 12 studies. First, across all 12 studies, the strategies for engaging teachers in considering student thinking were designed specifically to help teachers connect what they were learning about mathematics content and student thinking to their classroom teaching. Second, 10 of the 12 programs (Basista & Mathews, 2002; Clark & Schorr, 2000; Dole et al., 2008; Ellington et al., 2009; Featherstone et al., 1995; Franke et al., 1998; Goldsmith & Seago, 2007; Miller, 1991; Sowder et al., 1998; Swafford et al., 1997; Swafford et al., 1999) engaged teachers in a fairly lengthy and intensive program focused on mathematics content and mathematics teaching. Third, the same 10 experiences included facilitation or partnership roles involving university faculty from mathematics or mathematics education departments. None of these features was studied systematically for its contribution to the outcomes, but their common occurrence in these experiences suggests some potential importance with respect to the goal of deepening teachers' content knowledge through attending to student thinking.
All 12 of the experiences investigated in these studies included goals for developing aspects of teachers' knowledge of mathematics-specific pedagogy. Eight of the experiences also aimed at deepening teachers' disciplinary mathematics content knowledge (Basista & Mathews, 2002; Clark & Schorr, 2000; Dole et al., 2008; Featherstone et al., 1995; Franke et al., 1998; Miller, 1991; Sowder et al., 1998; Swafford et al., 1997; Swafford et al., 1999). However, measures for these targeted areas of teacher knowledge were not used in all of the studies. Specifically, only four of the studies used measures of disciplinary content knowledge (Basista & Mathews, 2002; Clark & Schorr, 2000; Sowder et al., 1998; Swafford et al., 1997; Swafford et al., 1999).
With the exception of one study (Stecher & Mitchell, 1995), teachers participated in each of these 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 the interventions, which, as noted above, were typically extensive in duration.
Seven of the studies used either a pre-post design to measure changes in teachers' content knowledge or traced changes over time (Basista & Mathews, 2002; Clark & Schorr, 2000; Dole et al., 2008; Ellington et al., 2009; Goldsmith & Seago, 2007; Sowder et al., 1998; Swafford et al., 1997; Swafford et al., 1999), while the other five presented only post-experience data. Given the experience levels of many of the participating teachers, the extent of professional development provided, and the nature of the measured changes, it is certainly reasonable to argue that changes resulted from the interventions, but without comparisons to other teachers, or over time, these claims are not solidly grounded in empirical evidence.
Only one of the studies used comparison groups of teachers who did not participate in the professional development programs or teaching experiences that were being investigated (Goldsmith & Seago, 2007). Consequently, 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 addresses this concern to some extent. In the Swafford and colleagues (1997, 1999) study, participating teachers performed better on written assessments in three different content areas, and on three separate measures of knowledge of geometry, following treatment. A number of studies used measures drawing on different data collection strategies to triangulate findings. Two studies used written assessments, interviews, and observations as measures of content-related knowledge (Clark & Schorr, 2000; Sowder et al., 1998). Others used two of these three strategies: written assessments and observations (Basista & Mathews, 2002); interviews and observations (Featherstone et al., 1995; Franke et al., 1998; Miller, 1991); or written assessments and interviews (Sowder et al., 1998). Only 2 of the 12 research efforts (Goldsmith & Seago, 2007; Swafford et al., 1997; Swafford et al., 1999) used any externally developed measures of teacher content knowledge.
Additional limitations were noted regarding some of these studies. In three studies, the intervention being investigated was described in very little detail, limiting the strength of interpretations linking teachers' experiences with the results (Clark & Schorr, 2000; Dole et al., 2008; Empson, 1999). Description of analysis procedures in three studies was not adequate, either providing insufficient evidence to link the results to the teachers' experiences (Clark & Schorr, 2000), or not describing how qualitative examples were selected from the full range of available data (Empson, 1999; Miller, 1991). In one study (Ellington et al., 2009), substantial differences in the administration of the pre- and post-tests raise questions about validity of the results.
For the research on engaging teachers in considering student thinking about mathematics bibliography, click here. [PDF 10K]
The 12 studies described above were part of a more inclusive review of research on experiences intended to deepen teachers' mathematics content knowledge. For more information, you are invited to read a summary of research on experiences intended to deepen teachers' mathematics content knowledge click here. [PDF 120K]
