1 Introduction

Teachers’ subject-specific professional knowledge is a strong predictor of students’ achievement (Hattie 2009; Helmke 2009; Kunter et al. 2013; Sowder 2007). In the last decade, many studies investigated teachers’ professional knowledge, affective-motivational beliefs, instructional practice, and in-the-moment performances in the classroom (Baumert et al. 2010; Blömeke et al. 2011; Kaiser et al. 2014; Kunter et al. 2013; Schoenfeld 1998).

Based on Shulman (1986), different frameworks of mathematics teachers’ professional knowledge emerged contributing analytically distinguishable knowledge facets (Ball 2000; Ball and Bass 2000; Baumert and Kunter 2006; Kaiser et al. 2014). These approaches have pursued a cognitive perspective and emphasized the significance of teachers’ profound subject-specific knowledge base for the quality of instruction.

Other research contributions in mathematics education have rather drawn on a situated perspective on teachers’ professional knowledge. These studies adapt frameworks and methods from expertise research (Berliner 1992; Borko et al. 1992; Carter et al. 1988). Comparing novice and expert teachers’ perception and interpretations of teaching situations is characteristic of such research alignments. In contrast to purely cognitive approaches, these studies use proximal measures of teachers’ abilities such as classroom videos, video vignettes or exemplary student work (e.g. Jacobs et al. 2010; Kersting 2008; van Es and Sherin 2002).

Linking these two perspectives on teachers’ professional knowledge, can contribute to a more comprehensive understanding (Depaepe et al. 2013; Kaiser et al. 2014; Santagata and Yeh 2016). In this regard, Blömeke et al. (2015a) stated that “processes such as the perception and interpretation of a specific job situation together with decision-making may mediate between disposition and performance” (p. 7). The aim of this article is to present a systematic review of mathematics teachers’ situation-specific skills: perception, interpretation, and decision-making. The review reports the different conceptualizations and methodological approaches used in mathematics education empirical research and lists the main findings. The guiding questions are: To what theoretical frameworks does empirical research on mathematics teachers’ situation-specific skills refer? What designs and methods are used to assess perception, interpretation and decision-making of prospective and practicing mathematics teachers? What results do the studies on situation-specific skills offer, and can these findings contribute to a comprehensive understanding of the link between teachers’ dispositions and their performances?

2 Teachers’ situation-specific skills in mathematics education research

In the last 30 years, many efforts have been made to explore the connection between mathematics teachers’ professional knowledge and their instructional practices, with respect to their students’ achievement. Rowland and Ruthven (2011) raised the question “whether mathematical knowledge in teaching is located ‘in the head’ of the individual teacher, or is somehow a social asset, meaningful only in the context of its application” (p. 3). Current discussions in the field label these two perspectives on mathematics teachers’ professional knowledge as cognitive and situated (Depaepe et al. 2013). The aim of this section is first to outline essential contributions to both perspectives. Second, the role of situation-specific skills as mediating what teachers know and how they act is explored.

2.1 Perspectives on mathematics teachers’ professional knowledge

Large-scale assessments like cognitive activation in the classroom: the orchestration of learning opportunities for the enhancement of insightful learning in mathematics (COACTIV; Kunter et al. 2013; Bruckmaier et al. this issue), teacher education and development study in mathematics (TEDS-M; Blömeke et al. 2010) and the follow-up study TEDS-FU (Kaiser et al. 2014; Hoth et al. this issue) have contributed substantially to conceptualizing and measuring mathematics teachers’ professional knowledge. Based on Shulman’s (1986) seminal work, these studies analytically distinguished mathematics teachers’ knowledge and belief facets and explored diverse relations. The COACTIV study revealed positive effects of mathematics teachers’ pedagogical content knowledge (PCK), enthusiasm for teaching, and self-regulatory skills on their instructional quality and students’ outcomes (Kunter et al. 2013). Based on the notion of competence (Weinert 2001), the TEDS-M study investigated the professional knowledge as well as affective-motivational characteristics of (prospective) mathematics teachers. Summarizing the international state-of-the-art, Blömeke and Delaney (2014) emphasized that in advance of TEDS-M there has been limited systematic research on teachers’ professional knowledge.

Other research traditions have placed emphasis on revealing conditions of effective teaching practice close to real classroom situations. While also considering teaching as a “knowledge-intensive domain with different knowledge and affective-motivational resources” (Kaiser et al. 2015 p. 370), these research approaches focus on aspects of teachers’ professional knowledge in use. Schoenfeld (1998) has contributed a theory of Teaching-in-Context and modeled teaching as a function of a teacher’s knowledge, goals, and beliefs. Later, he extended his approach to a theory of goal-oriented decision-making and replaced the concepts of knowledge and beliefs by resources and orientations. Particularly, he pointed out that “the notion orientation/resource/goal clusters is a lens through which teacher activity can be examined—and studies of coherence and change along these dimensions could be very interesting and useful” (Schoenfeld 2010 p. 194). In their “provisional framework for proficiency in teaching mathematics”, Schoenfeld and Kilpatrick (2008) highlighted mathematics as a knowledge-intensive domain. For effective teaching, they considered as equally important knowledge about students’ learning, managing adequate learning environments as well as substantially supporting classroom discourses. Ball et al. (2008) also demanded a practice-based theory of mathematical knowledge for teaching “to unearth the ways in which mathematics is involved in contending with the regular day-to-day, moment-to-moment demands of teaching” (p. 395).

Another line of research, drawing on expertise research (Berliner 2001), elaborates on mathematics teachers’ professional vision to describe and analyze their teaching practice (Jacobs et al. 2007, 2010; Sherin and van Es 2005; van Es and Sherin 2008). Although the definitions and conceptualizations used partly differ, teachers’ abilities to analyze teaching are in the focus.

As presented above, mathematics teachers’ professional knowledge has been investigated differently. In their systematic review on pedagogical content knowledge, Depaepe et al. (2013) provided evidence for distinguishing a cognitive and a situated perspective:

Adherents of a cognitive perspective, in which PCK is conceived as a category of teacher’s knowledge base, typically define–in line with Shulman–a limited number of components to be part of PCK and distinguish PCK from other categories of teachers’ knowledge base, such as content knowledge and general pedagogical knowledge. By contrast, proponents of a situated perspective on PCK as knowing-to-act within a particular classroom context, typically acknowledge that the act of teaching is multi-dimensional in nature and that teachers’ choices simultaneously reflect mathematical and pedagogical deliberations. (p. 22).

Based on their findings, Depaepe et al. (2013) demand a more integrated view on conceptualizing and assessing teachers’ professional knowledge. Rowland and Ruthven (2011) already criticized that many research studies treat “mathematical knowledge for teaching as residing solely in the classroom teacher” (p. 2). Thus, the next section elaborates on the processes that link mathematics teachers’ knowing and acting.

2.2 Relevance of situation-specific skills

Depaepe et al. (2013) revealed several shortcomings for the two perspectives discussed above: Within the cognitive perspective, research on teachers’ professional knowledge is disconnected from real classroom situations. Neither the socio-historical context nor the way different accounts of teacher knowledge interact were considered. Within the situated perspective, the sample sizes are often small and the findings have only limited validity. Also, teachers’ choices during teaching and their justifications are not accessible by classroom observations only.

Blömeke et al. (2015a) emphasized the connection between teachers’ cognition and affective-motivational beliefs (dispositions) and their teaching behavior (performance). For integrating a cognitive and a situated perspective, Blömeke et al. (2015a) suggested considering competence as a continuum (cf. Fig. 1).

Fig. 1
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Competence modeled as a continuum (Blömeke et al. 2015a, p. 5)

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The frame work considers competence as a multi-dimensional construct, and resolves the dichotomy of “disposition versus performance” as follows: “[…] our notion of competence includes ‘criterion behavior’ as well as the knowledge, cognitive skills and affective-motivational dispositions that underlie that behavior” (Blömeke et al. 2015a, p. 3). Following this understanding, a key role is assigned to situation-specific skills. That is, perception, interpretation and decision-making are linking teachers’ professional knowledge to observable behavior.

So far, only a few studies have combined the two perspectives on teachers’ professional knowledge. One prominent example is TEDS-FU; the study enriches the rather cognitive alignment of TEDS-M by assessing teachers’ performances proximal to their classroom behavior (Kaiser et al. 2014). In TEDS-FU “professional experience, deliberate practice and the ability of perceiving essential details in class are included as well as aspects of performance like dealing with heterogeneity in a flexible manner” (Kaiser et al. 2015, p. 373). Drawing on the framework proposed by Blömeke et al. (2015a), Kaiser et al. (2015) elaborated on situation-specific skills relevant for teaching mathematics in their so-called PID-model: (P) Perceiving particular events in an instructional setting, (I) Interpreting the perceived activities in the classroom and (D) Decision-making, either as anticipating a response to students’ activities or as proposing alternative instructional strategies (p. 374). The PID-model can be applied to reveal specific aspects as, for instance, teachers’ diagnostic competence (Hoth et al. this issue).

Lindmeier et al. (2013) also integrated a cognitive and a situated perspective on teachers’ professional knowledge. Their aim was “to capture facets of teacher cognition that go “beyond” knowledge in the sense that the scales depend on professional knowledge but mirror further abilities to use knowledge in typical teaching tasks” (p. 439). Particularly, teachers’ abilities to address students’ cognition, to cope with student’s individual strategies and misconceptions, and to handle representations and explanations during instruction were analyzed. Although Lindmeier et al. (2013) did not refer explicitly to situation-specific skills, the aforementioned facets imply such aspects.

A situated perspective on teachers’ knowledge emphasizes teachers’ professional experiences, deliberate practice and ability to perceive and to attend to essential classroom situations (Putnam and Borko 2000). Focusing on teachers’ situation-specific skills draws attention to seminal research on teacher expertise (Berliner 1992; Chi 2011; Li and Kaiser 2011). Research on situated skills such as perception accuracy (Carter et al. 1988) reveals how expert and novice teachers differ fundamentally in what and how they perceive classroom incidents. The concept of noticing addresses diverse facets of teacher expertise relevant for acting in the classroom (König et al. 2014; van Es and Sherin 2006). Teacher noticing builds on the notion of professional vision defined by Goodwin (1994) as “socially organized ways of seeing and understanding events that are answerable to the distinctive interests of a particular social group” (p. 606). Sherin et al. (2011b) have “focused on noticing as professional vision in which teachers selectively attend to events that take place and then draw on their existing knowledge to interpret these noticed events” (p. 80). The components of “attending to particular events in an instructional setting” and “making sense of an event in an instructional setting” are commonly shared among researchers dealing with noticing (Sherin et al. 2011a). However, Sherin et al. (2011a) emphasized that research purposes vary as studies address either the diversity of what teachers notice or teachers’ subject-specific expertise in depth. “Making sense” includes teachers’ interpretations of classroom events such as classroom discussions or students’ work. However, Sherin et al. (2011a) emphasized that “it is not helpful to think of teacher noticing as simply another category of teacher knowledge. […] The word noticing names a process rather than a static category of knowledge” (p. 5). In their framework, van Es and Sherin (2002) define the concept of noticing as follows:

(a) identifying what is important or noteworthy about a classroom situation; (b) making connections between the specifics of classroom interactions and the broader principles of teaching and learning they represent; and (c) using what one knows about the context to reason about classroom interactions. (p. 573).

Although the framework of van Es and Sherin (2002) is often referred to, integrating and applying the construct vary substantially. First, although many researchers conceptualize noticing as “attending to” and “making sense” of particular events in the classrooms, there is no consensus on what making sense means. Second, there is a debate on the scope of the notion. For instance, Star and Strickland (2008) considered as teachers’ noticing “what catches their attention and what they miss […] when they view a classroom lesson” (p. 111). Jacobs et al. (2010) took a broader view on professional noticing as not only including teachers’ attention to and interpretation of classroom situations, but also teachers’ intended responding. Thus, the use of the concept of teachers’ noticing ranges from including perception solely, connecting perception with interpretation to also comprising decision-making.

2.3 Purpose of this study

Teachers’ situation-specific skills are processes linking their professional knowledge and performance. Systematically reviewing research on mathematics teachers’ situation-specific skills is the aim of the study. The following research questions are pursued:

  1. 1.

    What situation-specific skills are investigated in empirical research in mathematics education?

  2. 2.

    To what theoretical frameworks does empirical research on mathematics teachers’ situation-specific skills refer?

  3. 3.

    What designs and methods are used to assess perception, interpretation and decision-making of mathematics teachers?

  4. 4.

    What results do the studies on situation-specific skills offer?

3 Method

A systematic review (Petticrew and Roberts 2008) of the research literature was conducted in the three databases ERIC, PsycINFO and MathEduc. Since searching for the comprehensive but rather specific term “situation-specific-skills” (typeset between quotation marks to ensure that the entire term is included in the searching process) had not led to any significant results, the term was decomposed into corresponding concepts. Thus, the processes perception, interpretation and decision-making were addressed by searchingFootnote 1 for “perception*”, “attending”, “interpret*”, “decision*”, “notic*, “professional vision”, “situated”, and “video-based”. In addition, overarching concepts were included by referring to the search strings “competenc*”, “knowledge”, “skill*”, “education”, and “cognition”. Since the systematic review is restricted to (prospective) teachers in the domain of mathematics, the mandatory search terms “math*” and “teach*” were additionally considered. In addition to the mandatory terms math* and teach*, one term concerning processes and one term concerning concepts was obligatory.Footnote 2 The search was carried out across the titles, keywords, and abstracts included in the databases. The search was restricted to peer-reviewed journal articles (written in English) published between January 1st, 1995 and January 31st, 2016. Applying these initial search criteria ensures a broad spectrum of high quality international research.

In total, the search algorithm yielded 1418 results (1001 in ERIC, 437 in PsycINFO, 549 in MathEduc; among them 569 duplicates retrieved from two or all three databases). The contributions in this special issue—if matching the criteria–were also included. The articles matching the search terms were then checked for six exclusion criteria (EC):

(EC1) The article reports empirical data. Editorials, (narrative) literature reviews, discussion papers, theoretical articles or commentaries were excluded as they do not provide information on their database (in sum 304 articles).

(EC2) The focus of the study is on teacher variables. Thus, articles focusing on student achievement, student motivation or emotion, students’ gender or ethnicity, parents’ involvement, parents’ views, or parents’ socio-economic status were excluded (in sum 293 articles).

(EC3) The article’s context is teaching mathematics in pre- to secondary school or in tertiary education. Thus, studies focusing on other subjects (e.g. science, engineering, arts or social studies), on special education or mathematic education for other professions (e.g. medicine) were excluded (in sum 173 articles).

(EC4) The article investigates teachers’ cognition or practice embedded in mathematics. Therefore, articles on curriculum (reform), on policy as well as articles evaluating software, specific materials or specific lesson designs were excluded (in sum 332 articles).

(EC5) The study investigates aspects of teachers’ cognition or practice that are specific for teaching mathematics. Hence, studies dealing with general pedagogical topics such as classroom management or technical skills (even if conducted in mathematics lessons) were excluded (in sum 60 articles).

(EC6) The article is concerned with investigating situation-specific skills. Thus, articles using “perception” in the sense of an attitude or opinion, contributions that dealt with decisions on a higher level (e.g. curriculum decisions) as well as studies assessing teachers’ knowledge from a cognitive perspective only were excluded (in sum 205 articles).

Applying these criteria resulted in a final database of 60 research articles.Footnote 3 Nine of these studies are published in this special issue. Each study was read and analyzed by two authors of this systematic review. The articles were reviewed and summarized with respect to the theoretical framework, research questions; sample size and characteristics of the participants; research design and methods, and main results. With respect to investigating situation-specific skills and their relation to disposition and performance, a coding scheme was applied: Research on perception, interpretation and/or decision-making (a dichotomous coding for each aspect was applied with 0 = not investigated; 1 = investigated) and focus on research on skills per se, in relation to dispositions and/or performance (a dichotomous coding for each aspect was applied with 0 = not investigated; 1 = investigated). The percentages of agreement ranged between 75 % for decision-making and 86 % for interpretation with an agreement of 78 % for perception. For “focus of research” the coding showed substantial agreement: 78 % for situation-specific skills, 85 % for disposition and 82 % for performance. Disagreements were thoroughly discussed among the three authors until consensus was reached.

4 Results

In this section, the research questions of this systematic review are answered successively. First, situation-specific skills investigated in the studies are summarized (Sect. 4.1). Then, the theoretical frameworks referred to are analyzed (Sect. 4.2). Subsequently, the designs and methods used to assess perception, interpretation and decision-making are reported (Sect. 4.3). Finally, the main focus lies on analyzing the results the studies on situation-specific skills report (Sect. 4.4).

4.1 What situation-specific skills are investigated in empirical research in mathematics education?

Most of the studies investigated interpretation (78.3 %), the majority of studies perception (63.3 %) and about half of the articles researched decision-making (53.3 %). Research on teachers’Footnote 4 perception or interpretation varied from identifying the potential of mathematical tasks (Klymchuk and Thomas 2011) and elaborating on student errors (e.g. Pankow et al. this issue) to recognizing instructional features in a classroom video (e.g. Star and Strickland 2008). Decision-making was primarily accessed by asking teachers to respond to a classroom situation (e.g. Jacobs and Empson this issue) or by analyzing teachers’ planning and enactment of instructional decisions (e.g. Escudero and Sánchez 2007). Studies often examined teachers’ perception and interpretation (19 of 60 studies) or all three situation-specific skills (15 of 60 studies). Table 1 gives an overview of the teachers’ situation-specific skills investigated and the material used.

Table 1 Investigated aspects of teachers’ situation-specific skills
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4.2 To what theoretical frameworks does empirical research on mathematics teachers’ situation-specific skills refer?

The studies referred to a variety of concepts or constructs in their theoretical frameworks. Teachers’ noticing or teachers’ professional vision, and teachers’ (situated) professional knowledge were the most frequent frameworks. About half of the studies (31 studies) were related to teachers’ professional knowledge, and used a relevant framework. Several studies focused on PCK with respect to a specific mathematical theme such as fractions or proportional reasoning (e.g. Houssart 2000; Jakobsen et al. 2014; Son 2013; Son and Sinclair 2010). Other studies investigated multiple facets of teachers’ professional knowledge, including teachers’ situation-specific skills (Blömeke et al. 2015b; Bruckmaier et al. this issue; Dunekacke et al. 2015; Dunekacke et al. this issue; Knievel et al. 2015).

Numerous studies (26 studies) referred to teachers’ noticing or professional vision in their framework. Drawing on the noticing framework by van Es and Sherin (2002), most of these studies included perception and interpretation. Other studies considered noticing as merely being perception (Star and Strickland 2008) or as additionally including decision-making (Jacobs et al. 2010; Schack et al. 2013). Three studies took a theme-specific perspective and investigated teachers’ noticing of multiple representations (Dreher and Kuntze 2015), mathematics problem solving (Fernández et al. 2013) or the derivative (Sánchez-Matamoros et al. 2014). Further concepts or constructs referred to were lesson analysis (Amador and Weiland 2015; Santagata 2009; Santagata et al. 2007) and teachers’ resources, goals and orientations (Paterson et al. 2011; Thomas and Yoon 2014; Zimmerman 2015).

4.3 What designs and methods are used to assess perception, interpretation and decision-making of mathematics teachers?

This section reports on the samples included as well as the research designs and methods used to access teachers’ situation-specific skills. Additionally, the studies are checked for assessing teachers’ dispositions or performances in relation to situation-specific skills.

4.3.1 Sample size and characteristics of the participating teachers

Table 2 reports sample sizes (i.e. the number of participants included in the data analysis), characteristics of the participants (pre-service teachers, in-service teachers and teacher trainers/lecturers) as well as school level (defined by the grades that the participating teachers taught or for which they were certified).

Table 2 Sample and school level of participants
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The studies analyzed very different sample sizes with N = 1 being the minimum (case studies) and N = 676 being the maximum (Kersting et al. this issue). The mean sample size is 56.35 participants (SD = 106.50) and the median is 19.50 participants. About half of the studies focused on pre- or in-service teachers’ situation-specific skills (28 and 26 studies). Only five studies included pre- and in-service teachers. Of these five studies two analyzed differences between pre- and in-service teachers’ situation-specific skills (Dreher and Kuntze 2015; Jacobs et al. 2010). One study concentrated on the development of primary teachers and thus reported data ranging from the last year of teacher education to 4 years of teaching experience (Blömeke et al. 2015b). With regard to school level, about half the studies assessed elementary, middle or secondary school teachers, respectively. Only a few studies investigated pre-school teachers (Dunekacke et al. 2015, this issue) or higher education teachers or lecturers’ situation-specific skills (e.g. Paterson et al. 2011; Thomas and Yoon 2014).

4.3.2 Research design and methods

The studies differ with respect to their research design and the methods used to investigate situation-specific skills. Studies that included only one or a few teachers and reported results case-wise were categorized as case studies.

Studies investigating the effects of some form of intervention (e.g. a professional development course) were categorized as intervention studies. Studies conducted to confirm hypotheses or presumptions were categorized as confirmatory studies. The research methods used to assess situation-specific skill were tests,Footnote 5 questionnaires,Footnote 6 interviews, lesson observations, other observations (e.g. observation of discussions), and the analysis of documents (reflection papers, lesson plans or homework assignments). Table 3 gives an overview of the research designs and methods.

Table 3 Research design and methods used
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4.3.3 What is the specific situation?

The studies drew on rather different situations ranging from interpreting mathematical tasks (e.g. Galant 2013) to deciding upon teaching moves during instruction (Jacobs and Empson this issue). Studies investigating teachers’ situated PCK primarily used written documents of students’ work (e.g. Hines and McMahon 2005; Son 2013). Some studies applied videos of students solving tasks (e.g. Knievel et al. 2015; Stockero 2008) or participating in an assessment interview (Weiland et al. 2014).

Studies analyzing teachers’ noticing mostly used video of classroom situations (e.g. Colestock and Sherin 2009; Huang and Li 2012; Sherin and van Es 2009; Star and Strickland 2008; van Es and Sherin 2008). Exceptions were those studies that investigated theme-specific noticing by written documents of students’ work (Dreher and Kuntze 2015; Fernández et al. 2013; Sánchez-Matamoros et al. 2014). A few studies used a combination of both written documents of students’ work and video of classroom situations (Hoth et al. this issue; Jacobs et al. 2010; Knievel et al. 2015). Some studies took different approaches such as animations (Lande and Mesa this issue) or lessons to be observed live or taught (e.g. Amador and Weiland 2015; Jacobs and Empson this issue; Santagata and Yeh this issue). Table 1 reports the situations used to investigate teachers’ situation-specific skills.

4.3.4 Are teachers’ situation-specific-skills investigated in relation to their dispositions or teaching performance?

A study that included cognitive or affective-motivational aspects (e.g. content knowledge or beliefs) in the data analysis was considered to investigate dispositions.

For coding the studies as including performance data, a rather strict criterion was applied. Only if data of actual teaching and instruction practice had been reported, the study would have been coded accordingly. About one-third of the studies analyzed teachers’ dispositions (i.e., their knowledge or beliefs). Twelve studies were concerned with teachers’ performance. Of these studies two reported data on teachers’ dispositions and their teaching practice (Bruckmaier et al. this issue; Son and Kim 2015). Table 3 indicates whether studies included aspects of dispositions or performance in their data analysis.

4.4 What results do the studies on situation-specific skills offer?

The studies report on a variety of results due to the different aspects of situation-specific skills investigated. Thus, in order to maintain clarity and comprehensibility, the results of the studies are summarized with respect to similar constructs or concepts and aims. The findings are presented along the following research lines:

(1) teachers’ skill to notice classroom situations, (2) teachers’ skill to perceive, interpret and respond to students’ mathematical thinking, (3) teachers’ situation-specific skills embedded in practice, (4) teachers’ situation-specific skills in relation to their knowledge (or other dispositions) and (5) and teachers’ skill to perceive and interpret mathematical tasks and their educational potential. Studies reporting different aspects of situation-specific skills were allocated to several foci. The emphasis is on studies reporting quantitative results. Effect sizes are presented if reported in the studies or, if possible, were calculated based on the data reported.Footnote 7 Case studies or qualitative data are briefly summarized as well.

4.4.1 Teachers’ skill to notice classroom situations

A large part of the studies included in this systematic review address mathematics teachers’ noticing or teachers’ professional vision. Some of these studies investigated teachers’ noticing with a focus on students’ mathematical thinking, whereas other studies took a broader perspective on noticing. The findings indicate what and how teachers notice and how teachers’ noticing can be improved (Table 4).

Table 4 Results of the studies examining teachers’ skill to notice classroom situations
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Studies allocated to this research line took a rather situated approach. Several studies revealed that what teachers notice in a classroom as well as how teachers notice classroom events is related to their expertise and teaching experience. Experienced or expert teachers tended to show higher levels of noticing or noticed more events (Dreher and Kuntze 2015; Fernández et al. 2013; Huang and Li 2012; Jacobs et al. 2010). Ho and Tan (2013) found a researcher’s and a teacher’s professional vision of the same lessons to differ. Studies considering decision-making as a component of pre-service teachers’ noticing showed this skill to be the least developed (Jacobs et al. 2010; Schack et al. 2013). Ingram (2014) described how teachers notice differently when discussing teaching videos on mathematical or pedagogical situations, whereas Colestock and Sherin (2009) provided evidence that different teachers used rather similar sense-making strategies when viewing video of classroom situations.

Many studies reported on successful interventions to foster teachers’ noticing: a majority of these studies provided evidence for improving pre-service and in-service teachers’ noticing skills by video-based training tools (Alsawaie and Alghazo 2010; Osmanoglu et al. 2015; Roth McDuffie et al. 2014; Schack et al. 2013; Sherin and van Es 2005, 2009; Star and Strickland 2008; van Es and Sherin 2002, 2006, 2008; Wager 2014). Other contributions provided evidence for different formats of professional development (Amador and Weiland 2015; Sánchez-Matamoros et al. 2014).

4.4.2 Teachers’ skill to perceive, interpret and respond to students’ thinking

Twelve studies examined mathematics teachers’ perception and interpretation of students’ thinking or products of students’ thinking and their responding to students’ work. The results give insight into teachers’ ability to identify errors and to interpret students’ solutions. They provide also information on how to improve teachers’ ability to analyze students thinking. Table 5 provides an overview of the results.

Table 5 Results of the studies examining teachers’ skill to perceive, interpret and respond to students’ thinking
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There was evidence in the included studies that pre-service teachers had difficulties in perceiving and interpreting students’ errors and solutions. This applied especially for common misconceptions or student errors (Hines and McMahon 2005; Jakobsen et al. 2014; Pankow et al. this issue; Son 2013; Son and Sinclair 2010). Some studies indicated that teachers’ skills to perceive and interpret students’ solutions and mathematical thinking were related to their professional knowledge. Teachers’ own difficulties with mathematics tasks influenced their perception and interpretation (Hoth et al. this issue; Jakobsen et al. 2014; Magiera et al. 2013). Teachers’ proposed instructional strategies for dealing with students’ misconceptions or errors seemed to rather focus on “reteaching” (Cooper 2009) or showing students’ how to do it correctly (Son 2013).

Other studies reported on promising formats to improve teachers’ situation-specific skills with regard to student thinking, among them video-based approaches or contrasting case activities (Derry et al. 2007; Nickerson and Masarik 2010; Norton et al. 2011; Stockero 2008; Weiland et al. 2014).

4.4.3 Teachers’ situation-specific skills embedded in practice

Most of the studies reporting on teachers’ in-the-moment decision-making were case studies or reported mainly qualitative data. The same applies to those studies that investigated teachers’ situation-specific skills close to practice. Three studies in this review explored the effects of lesson study on teachers’ situation-specific skills. An overview on the studies that explored teachers’ situation-specific skills embedded in practice is provided in Table 6.

Table 6 Results of the studies examining situation-specific skills embedded in practice
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Studies allocated to this research line took a clear situated approach. Several studies revealed that teachers’ professional knowledge accounts for situation-specific skills embedded in practice (Gal 2011; Escudero and Sánchez 2007; Paterson et al. 2011; Santagata and Yeh this issue; Thomas and Yoon 2014). Another part of studies provided evidence for the complexity of in-the-moment decision-making and how multiple intentions have to be considered by teachers during instruction (Lande and Mesa 2016; Sleep 2012; Stockero and Van Zoest 2013; Zahner et al. 2012; Zimmerman 2015). Sherin et al. (2008) described teachers’ professional vision in action using in the moment videotaping, whereas responsive teaching and teaching moves were categorized by Dyer and Sherin (this issue) and Jacobs and Empson (this issue). Finally, three studies reported on successfully fostering pre-service and in-service teachers’ situation specific skills by lesson analysis (Amador and Weiland 2015; Santagata 2009; Santagata et al. 2007).

4.4.4 Teachers’ situation-specific skills in relation to their knowledge (or other dispositions)

Some studies assessed teachers’ perception, interpretation and decision-making by validated, standardized tests and in relation to dispositions. Most studies revealed evidence for the impact of CK, PCK or beliefs on teachers’ situation-specific skills. Table 7 gives an overview of these findings.

Table 7 Results of the studies examining teachers’ situation-specific skills in relation to dispositions
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The studies allocated to this research line took a rather cognitive approach but included situated measures of teachers’ situation-specific skills. The six studies provided evidence for linking teachers’ dispositions and situations-specific skills. Dunekacke et al. (2015, this issue) showed that MCK and MPCK are predictors of pre-school teachers’ perception of classroom situations and (mediated by perception) of their planning of actions. Similarly, Bruckmeier et al. (this issue) reported correlations between situated reaction-competency and CK, PCK and beliefs. In addition, this study reported a significant relationship between a sub-facet of situated reaction-competency and aspects of teachers’ instructional quality (Bruckmaier et al. this issue). Blömeke et al. (2015b) provided evidence for the impact of knowledge, beliefs and a school climate of trust on beginning mathematics teachers’ perception, interpretation and decision-making skills. Two studies revealed a strong interrelation of teachers’ knowledge facets and situation-specific skills (Kersting et al. this issue; Norton et al. 2011). Kersting (2008) and Knievel et al. (2015) reported evidence on the reliability and validity of their developed instruments and found teachers’ knowledge related to their situation-specific skills.

4.4.5 Teachers’ skill to perceive and interpret mathematical tasks and their educational potential

Some studies focused on the material used during instruction. Studies on mathematical tasks found teachers’ perceptions, interpretations and decision-making to differ partly from curriculum guidelines or research recommendations. Table 8 gives an overview of the results.

Table 8 Results of studies examining teachers’ skills to perceive and interpret mathematical tasks and their educational potential
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Three studies indicated that pre-service as well as in-service teachers struggled with differentiating routine from non-routine mathematics task and choosing adequate formats for fostering their students’ learning (Galant 2013; Klymchuk and Thomas 2011; Lee and Kim 2005). In addition, teachers’ interpretation of task-related features (Houssart 2000; Magiera et al. 2013) and their decision-making corresponded with their professional knowledge and beliefs about student thinking (Son and Kim 2015).

5 Conclusion and discussion

This systematic review reports on 60 empirical research studies on teachers’ situation-specific skills. These studies, published in English-speaking peer-reviewed journals, were selected based on a systematic search in the databases ERIC, PsycINFO and MathEduc as well as in this Special Issue. The systematic review was guided by the following research questions: What situation-specific skills are investigated in empirical research in mathematics education? To what theoretical frameworks does empirical research on mathematics teachers’ situation-specific skills refer? What designs and methods are used to assess perception, interpretation and decision-making of mathematics teachers? What results do the studies on situation-specific skills offer?

Regarding the first research question, most studies investigated interpretation (47 studies), followed by perception (38 studies) and decision-making (32 studies). One-third of the studies explored perception and interpretation. One quarter of the studies analyzed all three situation-specific skills.

With concern to the second research question, the studies referred to two main theoretical frameworks that are teachers’ noticing and teachers’ (situated) professional knowledge. Only a few studies combined both frameworks.

Articles included in this review were case studies, intervention studies or confirmatory studies. These studies used a variety of methods to investigate pre-service and in-service teachers’ situation-specific skills, ranging from standardized tests to observing teachers during instruction. Only a few studies combined diverse methods or compared pre- and in-service teachers’ situation-specific skills.

The last research question addressed the results obtained by the studies. The results revealed evidence for the significance of expertise or experience on teachers’ noticing. Pre-service teachers tend to have difficulties in perceiving or interpreting students’ work. These skills seemed to be influenced by their level of mathematical knowledge. A noteworthy finding is that video-based professional development programs can foster teachers’ noticing successfully.

Decision-making appeared to be most challenging for pre-service teachers. Teachers’ showed deficits in terms of proposing instructional strategies to foster students’ understanding that go beyond “showing how to do it right”. Case studies revealed the complexity of teachers’ in-the-moment decision-making. Based on these studies, factors hypothesized to influence teachers’ decisions were ranging from teachers’ knowledge, beliefs to goals. Multiple intentions influenced teachers’ decisions.

These hypotheses were confirmed in studies assessing the relations between teachers’ knowledge, beliefs and situation-specific skills by using standardized tests and large samples. The studies provided evidence for MCK, MPCK and beliefs being predictors of situation-specific skills, which in turn correlate with aspect of instructional quality.

Based on selection and restriction criteria, this review systematically searched for and included empirical studies. Due to the specific selection and restriction criteria applied, this review might be biased. First, the limitation to English-speaking empirical journal articles may have caused a possible bias. Excluding all non-English articles could have resulted in overlooking substantial research published in other languages. Second, the search terms (individually or combined) as well as the inclusion or exclusion criteria might have impacted on the sensitivity and specificity of the search. Due to the diverse terms and concepts used in mathematics education research, the search strategy–especially combining the different terms–might have led to a specific subset of studies. On the one hand, studies that analyze situation-specific skills, but use terms other than the chosen search terms, could have been missed. On the other hand, the criteria for including papers into the systematic review were rather soft. That is, articles were included that investigated situation-specific skills but did not explicitly refer to perception, interpretation, and decision-making.

The article is appearing in the ZDM Mathematics Education special issue on “Perception, interpretation and decision-making: understanding the missing link between competence and performance”. The studies of this special issue report on important and diverse topics. In case they met the review criteria, the articles were included in the review. Several studies taking a rather cognitive approach (i.e. measuring teachers’ professional knowledge) and a strongly situated approach (i.e. observing teachers’ practice) were considered. The three commentary papers by Mason, Schoenfeld and Schreiner (this issue) discuss the contributions of the special issue thoroughly and emphasize a huge variance on the two levels of theoretical considerations and methodological choices. This systematic review has a broader frame, as the last 20 years of empirical research in mathematics education were analyzed. Some striking observations were made in terms of conceptual clarity: across the studies different terms were used for the same aspect as well as the same terms were used for different aspects. The same lack of clarity can be observed in the theoretical frameworks used. For instance, the definitions of noticing and what situation-specific skills constitute noticing vary strongly. As Jacobs et al. (2010) stated, “researchers define noticing in a multitude of ways, but the connecting thread is making sense of how individuals process complex situations” (p. 171).

The different terminologies and conceptualizations of situation-specific skills also impact on how perception, interpretation and decision-making are studied empirically. In their systematic review on PCK, Depaepe et al. (2013) pointed out that measurements can be distinguished along the cognitive and situated perspective, that is:

Advocates of a cognitive perspective on PCK believe it can be measured independently from the classroom context in which it is used, most often through a test. […] Adherents of a situated perspective on PCK, on the contrary, typically assume that investigating PCK only makes sense within the context in which it is enacted. (p. 22).

In this systematic review, the distinction between a cognitive and a situated perspective on teachers’ professional knowledge is even more challenging when it comes to methodological approaches. There is a growing body of research developed from a cognitive perspective that reflects upon situation-specific skills as knowledge-based skills which are applied in contexts approximating classroom situations (Blömeke et al. 2015a; Kaiser et al. 2014). These approaches develop standardized video-based instruments displaying classroom situations closer to practice but not embedded in practice Other studies investigate teachers’ behavior near or in the classroom and consider teacher knowledge as integral part of teaching. Studies that investigate the long-term development of teachers’ situation-specific skills and include both perspectives are scarce: so far only Blömeke et al. (2015b) have conducted a longitudinal study.

This review shows that a considerable body of research contributions dealing with perception, interpretation and decision-making from either a cognitive or a situated perspective already exists. Comprehensive and integrative approaches that connect teachers’ situations-specific skills to teachers’ competence in terms of professional knowledge and performance are scarce yet. Research would highly benefit from combining both a cognitive and a situated perspective not only theoretically but methodologically as well. In this respect, Kersting (this issue) aptly emphasizes:

Understanding what mathematics teachers need to know, and what it takes to be able to apply that knowledge in the classroom, is critical for helping teachers improve their practice and their students’ learning. For years, progress toward this goal was hampered by imprecise and inconsistent use of terminology, a lack of well-developed theories, and a paucity of measures. (p. 1).

The initial aim of this systematic review was to explore teachers’ situation-specific skills, i.e., perception, interpretation and decision-making. These skills display the missing link between mathematics teachers’ dispositions (professional knowledge, affective motivational features) and their performance (observable behavior) (Blömeke et al. 2015a). Approaching teachers’ situation-specific skills from a rather cognitive or situated perspective led to substantial research findings. These two approaches could be brought closer by acknowledging the respective advantages and findings. Existing frameworks and methods might be used to develop integrative research designs that allow for dealing more effectively with the complexity of teaching.

In this systematic review, research on situation-specific skills in mathematics education research was thoroughly analyzed. Following Petticrew’s (2015) reflections, systematically reviewing research contributions concerning teachers’ situation-specific skills does not provide a comprehensive overview on “what works”, but rather describes “what happens” in this field. Having mapped this landscape, researchers can now proceed to direct research in this area on to solid ground where reliable findings can be gained essentially to advance teaching practice.