The ultimate goal
of professional development is improving students’ learning, through the
mechanism of improving instruction. This brief review of research on
mathematics professional development summarizes what we know about the goals
and characteristics of effective mathematics professional development for
teachers. We intend this review to guide educators as they plan professional
Over the past three
decades, evidence about the nature and impact of professional development in
mathematics has accumulated both from large-scale empirical studies (e.g.,
Desimone, Smith, & Phillips, 2007; Garet et al., 2001; Heck et al., 2008;
Supovitz, Mayer, & Kahle, 2000) and from small-scale qualitative studies of
planned or emergent innovations (e.g., Borko et al., 2008; Collopy, 2003; Franke
et al., 1998; Sowder et al., 1998;
van Es & Sherin, 2008; Warfield, Wood, &
Lehman, 2005). Conceptual analyses of the mathematics knowledge for
teaching and how it develops (e.g. Ball & Cohen, 1999; Borko, 2004; Hawley
& Valli, 1999; Putnam & Borko, 2000; Thompson & Zeuli, 1999; Wilson
& Berne, 1999) have also influenced the design of mathematics professional
development. Collectively, these three bodies of research provide evidence for
the following goals and features of mathematics professional development.
Goals of Mathematics Professional Development
In service to the
long-term goal of improving students’ learning through better instruction,
research evidence to date suggests that mathematics professional development
should promote the growth of mathematics teachers in four major areas.
1. Build teachers’ mathematical knowledge and their
capacity to use it in practice.
mathematical knowledge matters and significantly predicts gains in students’
achievement (Hill, Rowan & Ball, 2005; Jacobs et al., 2007). In order to enact
instruction that supports students’ learning, teachers need mathematical
knowledge that extends beyond an understanding of mathematical procedures and
concepts (Kilpatrick, Swafford & Findell, 2001). Teachers must be able to choose
appropriate mathematical tasks, judge the advantages of particular representations
of a mathematical concept, help students make connections among mathematical
ideas, and grasp and respond to students’ mathematical arguments and solutions.
A lack of mathematical content knowledge can impede teachers’ abilities to notice
and analyze students’ mathematical thinking (Doerr & English, 2006), design
actions that respond to students’ understanding (Hunting & Doig, 1997), or
engage in productive professional conversations (Britt, Irwin, & Ritchie, 2001;
Polettini, 2000). Research has found that professional development that attends
to dimensions of teachers’ mathematical knowledge is more effective than
professional development that focuses only on pedagogy or generic teaching
skills (Garet et al., 2001; Heck et al., 2008).
indicates that teachers can develop their mathematical content knowledge in a
number of different ways, including solving and discussing mathematics
problems, studying students’ mathematical thinking, collaborating with other
teachers to plan or discuss instruction, analyzing instances of classroom
practice, and using new curricular materials (Chazan, Ben-Chaim, & Gormas,
1998; Fernandez, 2005; Hill & Ball, 2004; Horn, 2005; Lewis, Perry, &
Hurd, 2009; Remillard & Bryans, 2004). When teachers solve mathematical
problems together and share solution methods, it can affect their understanding
of the mathematical content and introduce new perspectives on a problem
(Lachance & Confrey, 2003). Teachers can also strengthen their mathematical
understanding in the process of trying to make sense of students’ work or
analyzing instances of classroom practice (Borko et al., 2008; Doerr &
English, 2006; Grandau, 2005; Jacobs et al., 2007; Lewis, Perry, & Hurd, 2009; Peressini & Knuth, 1998; Sowder
et al., 1998; Ticha & Hospesova, 2006). For example, Ticha and Hospesova
(2006) report on a teacher who expanded her ability to think flexibly about
subtraction by exploring a student’s unexpected argument that 63 – 8 = 60 – 5
because the difference remains the same if both 63 and 8 are reduced by 3. Improved
mathematical knowledge can also help teachers connect mathematics to classroom
practice as they analyze and use new curriculum materials (Cohen & Hill,
2000), investigate mathematical lessons or tasks (Lewis, Perry, & Murata,
2006) and analyze of students’ mathematical thinking (Borko et al., 2008; van
Es & Sherin, 2008). Finally, professional development that focuses on
improving teachers’ mathematical knowledge can help them develop the confidence
to teach mathematical topics that they previously avoided (Chapin, 1994).
2. Build teachers’ capacity to notice, analyze, and
respond to students’ thinking.
A number of
studies provide evidence that professional development can help teachers learn
to notice, value, and analyze students’ mathematical thinking. Professional
development that helps teachers attend to students’ thinking can shift
teachers’ focus from simply evaluating students’ work as correct or incorrect
to analyzing the particulars of students’ thinking (Borko et al., 2008;
Goldsmith & Seago, 2010; Swafford, Jones, & Thornton, 1999; van Es
& Sherin, 2008). For example, elementary school teachers participating in
Cognitively Guided Instruction (CGI) professional development learned to
recognize increasingly sophisticated strategies among students who correctly
solved addition and subtraction problems. They also learned to make principled
decisions about choosing mathematics problems that would engage and extend each
student’s current level of reasoning (Fennema et al., 1996). Similarly, teachers
participating in professional development based on CGI principles learned to
recognize a variety of students’ algebraic reasoning strategies and notice
strengths in students’ mathematical thinking that could be built on, even when
students’ solutions were not entirely correct (Jacobs et al., 2007).
development that supports close attention to students’ thinking may also help
teachers recognize that they have tended either to overestimate (Schorr &
Koellner-Clark, 2003) or underestimate their students’ understanding (Chazan,
Ben-Chaim, & Gormas, 1998; Kazemi & Franke, 2004; Lin, 2001; Warfield,
Wood, & Lehman, 2005). As teachers learn to notice and analyze students’
thinking, they gain a more accurate picture of the strengths and weaknesses in
students’ mathematical understandings (Borko et al., 2008; Jacobs et al., 2007;
Kersaint & Chappell, 2001; van Es & Sherin, 2008). Teachers can then use their analyses of students’ thinking
to refine instruction and to respond to students’ needs (Doerr & English,
2006; Kazemi & Franke, 2004; Seymour & Lehrer 2006; Sherin & Han, 2004).
3. Build teachers’ productive habits of mind.
improve one’s teaching practice is challenging, effortful work. An important
goal of professional development is to help teachers develop the beliefs,
habits, and dispositions needed to improve practice on an ongoing basis. For
example, teachers’ beliefs about mathematics (Borko, 2004; Drake, Spillane,
& Hufferd-Ackles, 2001), curriculum (Collopy, 2003: Remillard & Bryans,
2004), and students’ capacity for learning (Smylie, 1988; Warfield, Wood, &
Leman, 2005) all influence what teachers learn from professional development
opportunities. Likewise, teachers’ dispositions and habits of mind, including
habits of inquiry, curiosity, self-monitoring, attention to students’ thinking,
and experimentation influence teachers’ learning from professional development
opportunities (Allinder et al., 2000; Chazan, Ben-Chaim, & Gormas, 1998;
Clarke & Hollingsworth, 2002; Edwards & Hensien, 1999; Spillane, 2000).
development programs themselves shape teachers’ beliefs and habits of mind in
ways that influence teachers’ subsequent learning from practice (Britt, Irwin,
& Richie, 2001; Chapin, 1994; Chazan, Ben-Chaim, & Gormas, 1998;
Jaworski, 1998; Senger, 1999; Ticha & Hospesova, 2006; van Es & Sherin,
2008; Zech et al., 2000). Hence, an important criterion for selecting a
professional development program is whether it nurtures beliefs and
dispositions,that result in continued learning in daily practice. For example,
professional development experiences in which teachers analyze instruction,
live or on videotape, may help teachers shift from a descriptive or evaluative stance
toward an inquiry stance toward
practice (Perry & Lewis, 2010; van Es &
Sherin, 2008) and build teachers’ confidence that changes in their
instructional methods can improve students’ learning (Perry et al., 2009).
Professional learning experiences that involve learning mathematics related to
teaching can build teachers’ desire to learn more mathematics, perhaps by
building the sense of efficacy, identity as a mathematics learner, or collegial
support for learning (Polettini, 2000; Hodgen & Askew, 2007; Lewis, Perry,
& Hurd, 2009). Given that professional development does not automatically
build productive habits of mind, those responsible for professional development
may want to directly address whether efficacious beliefs and habits of
mind—such as inquiry into students’ thinking, confidence that all students can
make sense of mathematics, and interest in deepening one’s own mathematical
4. Build collegial relationships and structures that
support continued learning.
One way that professional development
can support teachers’ ongoing learning is by catalyzing changes in collegial
relationships and structures for collegial work. Recent research has pointed to
the value of collaboration for the learning of teachers. Collaboration with
colleagues can spark the need for teachers to explain their practices and to
articulate rationales for instructional decisions, helping teachers make tacit
ideas visible and subject to shared scrutiny and develop deeper, more widely
shared understandings of students’ learning (Chazan, Ben-Chaim, & Gormas,
1998; Horn, 2005; Kazemi & Franke, 2004). Professional conversations can
also provide teachers with the encouragement and support that is needed to
begin to experiment with new approaches to teaching (Britt et al., 2001).
Teachers value the kinds of professional relationships that can be built
through shared inquiry into practice; such interactions with colleagues can
support teachers’ sense of competence as they engage in the work of changing
practice (Arbaugh, 2003; Edwards & Hensien, 1999; Jaworski, 1998; Smylie,
However, collegial interactions do not
always lead to professional learning. The emotional support that can come from
sharing stories or observing in each other’s classrooms does not necessarily
lead to a focus on improving aspects of teaching (Cwikla, 2007; Manouchehri,
2001). When collegial interactions do focus on classroom instruction, teachers
may experience a tension between colleagues’ suggestions and their own sense of
autonomy to decide whether and how to use ideas (Puchner & Taylor, 2006).
Several studies suggest that of the effectiveness of collegial learning
structures can be built over time (Kazemi & Franke, 2004; Lewis, Perry,
& Hurd, 2009). For example, teachers in the study group that Kazemi and
Franke (2004) followed were initially unaware of the details of students’
problem-solving strategies and saw posing questions to understand students’
ideas as unimportant, despite the facilitators’ efforts to focus on students’
thinking. Over time, as teachers found ways to interact with students about
their strategies, and they began to share their efforts to understand students’
ideas in their study group meetings. Likewise, teachers at a school-wide lesson
study site showed a substantial increase in the proportion of discussion
devoted to students’ thinking from year one to year three of the school’s
adoption of lesson study (Perry & Lewis, 2010). Research reviewed in the
next section illuminates why collegial structures to support learning may
develop gradually over time, rather than emerge fully developed as an immediate
consequence of a professional development intervention.
What professional development features support these four goals?
1. Substantial Time Investment
large-scale studies suggest that the duration of professional development is
significantly associated with impact on teachers (Boyle, Lamprianou, & Boyle, 2005; Garet et al., 2001;
Heck et al., 2008; Hill & Ball, 2004). For example, a study of summer
professional development workshops ranging from 40 to 120 hours in length
associated longer workshops with teachers’ greater knowledge gain, although
some programs were exceptions to this trend (Hill & Ball, 2004). In their
evaluation of the NSF-funded Local Systemic Change initiatives, Heck and his colleagues
documented a significant relationship between hours of participation and
teachers’ self-reported increases in investigative classroom practices, with
most of the gains occurring during the first 100 hours of professional
development (Heck et al., 2008). With respect
to the use of instructional materials, much of the gain occurred with the first
80 hours of professional development, with an additional increase after about
180 hours. Ohio teachers participating in the State Systemic Initiative showed
substantial increase in the use of inquiry-based instructional practices over
the first year, after six weeks of summer professional development. These
changes leveled off and were sustained over the next two years (Supovitz, Mayer, & Kahle, 2000).
Qualitative studies illuminate some of
the reasons that professional learning takes time. Changes in
teachers’ mathematical knowledge, beliefs, dispositions, and in the
collaborative structures that support learning often occur in small increments,
with advances in any one of them depending on advances in the others (Kazemi
& Franke, 2004). Teachers’ growth is often incremental, nonlinear, and
iterative, proceeding through repeated cycles of inquiry outside the classroom
and experimentation inside the classroom (Clarke & Hollingsworth, 2002;
Fennema et al., 1996; Jaberg,
Lubinski, & Yazujian, 2002). For example, Jaberg, Lubinski, and Yazujian (2002)
reported on a teacher who
responded to professional development by changing her practice to elicit and
respond to students’ thinking more often. After making this change, she found
she needed to better understand her students’ thinking, which in turn convinced
her that she needed to increase her own mathematical content knowledge.
Similarly, studies of teachers’ collaborative work suggest that
increases in practice-focused collaboration and content knowledge can build
incrementally on each other, as teachers’ explanations of their practice lead
to questions about the mathematical content (Peng, 2007). First-year results of
a large-scale, randomized control study of middle school mathematics
professional development indicated that professional development linked to an
initial increase in teachers’ activities to elicit students’ thinking, but no
corresponding increase occurred during the first year in either teachers’
mathematical knowledge or students’ achievement. These data further suggest the
incremental and complex nature of changes in teachers’ knowledge and practice (Garet
et al., 2010).
example of iterative, incremental change in knowledge, beliefs, and practices
comes from the CGI program, which found that using challenging mathematical tasks led teachers to expand their
ideas about students’ capacity to think mathematically. This expanded set of
beliefs then led teachers to change classroom practices in ways that enabled
teachers to increase their knowledge of students’ thinking. Over time, these
experiences led teachers to develop a disposition to inquire into students’
thinking that, in turn, supported further development of both their classroom
practices and their knowledge about students’ thinking (Franke et al.,
1998). In summary, these studies suggest that teaching practice is an apt term, given the repeated cycles of
experimentation, reflection, and revision required to change elements of
instruction. Effective professional development is more likely to look like a
series of incremental changes in knowledge, beliefs, dispositions, and
classroom practices that eventually lead to students’ improved outcomes than a
direct line from professional development to practice to students’ outcomes.
2. Systemic Support
Systemic support influences the impact
of professional development programs. A number of studies have reported that
the nature and degree of principal support for a particular professional
development program influences its impact (Desimone, Smith, & Phillips,
2007; Heck et al., 2008, Woodbury & Gess-Newsome, 2002). For example,
Jaberg, Lubinski, and Aeschleman (2004) describe a number of different ways
that one principal supported and encouraged the work her teachers were
undertaking through their professional development, including building support
among parents and other community members, making time during faculty and
grade-level meetings for teachers to discuss mathematics instruction, and being
flexible about assessments of student learning.
Other system factors can also make a
difference. Garet et al. (2001) found that professional development was more
effective when teachers perceived it to be consistent with their own goals and
with state and district standards; other studies have reported that the nature
and consistency between professional development and system messages about
mathematics teaching and learning affect teachers’ learning (Cwikla, 2007;
Polettini, 2000; Scribner, 1999; Woodbury & Gess-Newsome, 2002), as does
the nature of parental and community support (Tschannen-Moran & Hoy, 2007).
Presumably, then, those responsible for professional development should attend
to building coherent support for participating teachers. This support should
come from a variety of sources, including principals, district and state
officials, and parents.
3. Opportunities for active learning
For more than a decade, the
literature on promising practices in mathematical professional development has
advocated active involvement of teachers in inquiry and problem solving with
respect to both mathematics and instruction (e.g., Putnam & Borko, 1997;
Wilson & Berne, 1999). Large-scale research studies support these
recommendations. For example, Garet et al. (2001) reported that professional
development that offered opportunities for active learning—for example,
planning lessons; observing other teachers and being observed; reviewing
students’ work; and making presentations, writing papers, or leading
discussions—were associated with teachers’ reports of increased knowledge and
The vast majority of studies about teachers’ professional
learning follow teachers’ post-professional development for a year or less, so
evidence regarding the long-term impact of mathematics professional development
on teachers’ knowledge or instructional practices is limited. In fact, even in
the short term, the impact of professional development may be less than is
suggested by the large-scale studies, which rely on self-report. Research that
includes classroom observations typically shows less use of key “reform”
instructional strategies, such as eliciting students’ thinking, than teachers’
self-reports would lead us to expect (Fisler & Firestone, 2006). These
studies reveal a tendency to adopt superficial features of reforms rather than
more fundamental features (Cohen, 1990).
limitations of current research, substantial support exists for focusing
mathematics professional development on the four broad goals of developing:
- teachers’ mathematical knowledge and capacity to
connect it to practice;
- teachers’ capacity to notice, analyze and
respond to student thinking;
- the beliefs and dispositions that foster
teachers’ continued learning; and
- collegial relationships and learning structures
that can support and sustain teachers’ learning.
In addition, three
features of professional development design appear to be important for
supporting progress toward these goals:
- systemic support for teachers’ learning; and
- opportunities for teachers’ active learning
Although research on
professional development is still emerging, the goals and features that this
review has identified emerge from a substantial number of studies and offer the
best current guidance for practitioners.
This material is based upon work supported by the National
Science Foundation under Grants DRL 0723340, DRL 0719627
DRL-0722295. Any opinions, findings, and
conclusions or recommendations expressed in this material are those of the
authors and do not necessarily reflect the views of the National Science
By Helen M. Doerr, Lynn T. Goldsmith, and Catherine C. Lewis
Sarah DeLeeuw, Series Editor
We wish to acknowledge
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The development of this brief was supported by the National Science Foundation under Grant No. 0946875
opinions, findings and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the
views of the National Science Foundation (NSF).