Towards an understanding of early childhood mathematics education: A systematic review of the literature focusing on practicing and prospective teachers

As noted in Figure 1, studies investigating early childhood practicing and prospective teachers’ content knowledge of mathematics were the least common, accounting for 15% of the total studies in this area. Of these, 56% of the studies examined the content knowledge of prospective teachers, while 44% examined the content knowledge of practicing teachers. Yet there was an apparent difference in the types of content knowledge being investigated between the two groups, as many of the studies involving prospective teachers examined their mathematical content knowledge; on the other hand, those involving practicing teachers often investigated the domains of MKT, particularly pedagogical content knowledge.

Based on a specific mathematical concept (e.g. fractions, proportional reasoning, multiplication) and the manner in which it was assessed (e.g. course grade, standardized test, task-based assessment), the results regarding prospective teachers’ content knowledge in mathematics varied. Bates et al. (2011), for example, found the 89 early childhood participants in their study to have a strong mathematical foundation (mean: 257.44 out of 300). On the other hand, the majority of the research suggests that prospective teachers are lacking procedural and conceptual understandings in certain content areas, such as polygons (Canturk-Gunhan and Cetingoz, 2013; Erdogan and Dur, 2014), proportional reasoning (Pitta-Pantazi and Christou, 2011), variables and equations (Tanisli and Kose, 2013), and multiplication of two 3-digit numbers (Maher and Muir, 2013). Limited research suggests that no differences in mathematical performance were due to a person’s gender (Duru, 2011) or cognitive learning style (Pitta-Pantazi and Christou, 2009).

Moreover, research suggests that prospective teachers have difficulty in evaluating and understanding students’ explanations and misconceptions (Canturk-Gunhan and Cetingoz, 2013; Fernández et al., 2013; Jacobs et al., 2010; Maher and Muir, 2013; Morris, 2007; Tanisli and Kose, 2013), and responding through appropriate strategies and questions (Maher and Muir, 2013; Tanisli and Kose, 2013). But studies including practicing teachers suggest that such skills and understandings can be developed with time or years of experience (Foote, 2009; Jacobs et al., 2010; Lee, 2010; Warfield, 2001) and, as argued by Cengiz et al. (2011), it may depend on practicing teachers’ proficiency in all three domains of MKT. By way of example, Jacobs et al. (2010) noted how one’s ability to attend to, interpret, and respond to children’s mathematical thinking develops with expertise in the field. Beyond any differences based on experience, Zhou et al. (2006) concluded that teachers in the USA are significantly underdeveloped in certain areas of subject matter knowledge and pedagogical content knowledge compared with Chinese teachers.

Thirty-one or 19% of the studies examined practicing and prospective teachers’ dispositions regarding mathematics and how they influence instruction—namely, beliefs and attitudes about mathematics, mathematics teaching and learning, and developmentally appropriate mathematics for young children, and self-perceptions regarding mathematics ability and their role as a teacher of mathematics. Unlike the studies discussed in the content category, there was no clear distinction of what disposition was examined between groups and, in general, the results are inconclusive. In considering practicing and prospective teachers’ dispositions, there seem to be other factors influencing or shaping their beliefs and attitudes about mathematics and self. These include, but are not limited to, previous experiences with mathematics as a student (Hodgen and Askew, 2007; Lake and Kelly, 2014; McCulloch et al., 2013; Zacharos et al., 2007), mathematics anxiety (Isiksal et al., 2009), the student body (Lee and Ginsburg, 2007b), and “official” requirements and accountability (Gujarati, 2013; Hanley and Jones, 2007; Vernaza, 2012).

The studies suggest that, more often than not, practicing and prospective teachers have a positive outlook on their ability to teach mathematics to young children (Bates et al., 2011; Brown, 2005; Chen et al., 2014; Dunphy, 2009; Ertekin, 2010; Paparistodemou et al., 2014; Throndsen and Turmo, 2013; Yavuz et al., 2013), and view certain mathematical tools, such as virtual and physical manipulatives (Akkan, 2012), and computers or mobile learning devices (Doğan, 2012), to be beneficial instructional tools. As an example of the former, in a study with 346 preschool teachers, Chen et al. (2013) found that 86% were confident in their ability to observe what preschoolers knew about mathematics, 84% in their ability to plan activities, and 67% in their ability to make sense of preschoolers’ confusion.

Moreover, practicing teachers expressed the belief that teaching mathematics should be child-centered and implemented within a safe and playful environment free of stress (Benz, 2012; Franzén, 2014; Herron, 2010; Hunting et al., 2012; Jung and Reifel, 2011; Lee, 2005; Lee and Ginsburg, 2007b; Siraj-Blatchford and Nah, 2014). Hunting et al. (2012), for instance, found that 64 preschool teachers from rural areas of Australia discussed child-centered mathematical practices as, among other things, encouraging children to ask questions; providing a choice of activities and open-ended play experiences; building off prior knowledge; and teaching without forcing the pace. There are a few instances in which practicing and prospective teachers’ beliefs were more teacher-centered, such as considering children’s results more than their process (Dunphy, 2009; Ertekin, 2010; Throndsen and Turmo, 2013), which may be due to their experience in the field (Thiel, 2010).

For some, there was the belief that mathematics should be, and was, incorporated within the daily classroom routines, such as setting the table for lunch (Benz, 2012; Ertekin, 2010; Lee and Ginsburg, 2007a). On the other hand, a few studies noted how teachers who work with young children prior to kindergarten do not always value mathematics over other skills such as social-emotional and explicit language skills (Simpson & Linder, 2014; Blevins-Knabe et al., 2000; Kowalski et al., 2001), and view mathematics as a static body of knowledge to be learned (Zacharos et al., 2007). Also, in considering some of the literature regarding practicing and prospective teachers’ dispositions, it seems as if they are negotiating between their identity as a mathematics teacher and prior experiences versus their identity as a teacher of young children (Gujarati, 2013; Hodgen and Askew, 2007; McCulloch et al., 2013), or between beliefs in their own mathematics ability and their role in teaching mathematics (Bates et al., 2011; Chen et al., 2014; Lee, 2005: Olander and Nyberg, 2014), or between their beliefs in teaching mathematics and their approaches to mathematical instruction (Brown, 2005; Doğan, 2012; Olander and Nyberg, 2014; Throndsen and Turmo, 2013). As an example of this back-and-forth interplay, Gujarati (2013) concluded that for three early career third-grade teachers, there was an inverse relationship between their negative personal beliefs regarding their abilities in mathematics and the amount of effort they put into being a mathematics teacher so as to ensure that their students had positive mathematical experiences.

Of the 164 studies in this literature review, approximately 39% or 64 studies examined practicing teachers’ (97%) adapted practices within the classroom environment—in other words, practices as they unfolded naturally in the classroom as a result of an intervention, such as the implementation of techniques, materials, or strategies that were different or in addition to their typical instructional practice. The majority of these studies can be further categorized as investigating practicing teachers’ implementation of curricular material, mathematical content, and standards (26%); general instructional strategies and methods (32%); and classroom discourse and communication (28%). There was a relatively smaller number of studies (14%) focused on specific content practices and strategies such as counting (Guha, 2006), place value (McGuire and Kinzie, 2013), metacognition (Whitebread and Coltman, 2010), and the utilization of books (Carlsen, 2013).

The mathematical content implemented by practicing teachers in their classroom seemed to vary depending on their country. In the USA, counting was emphasized more often than measurement and telling the time (Blevins-Knabe et al., 2000; Gonzales and Paik, 2011; Hindman, 2013; Parks and Bridges-Rhoads, 2012; Rowan et al., 2004). For example, Rowan et al. (2004) noted how 509 practicing teachers across 53 schools focused on number concepts for 24% to 32% of the days over a year, and operations were taught for about 40% of the days over a year. In South Africa, geometry ranked the highest and data analysis the lowest (Botha et al., 2005). In Taiwan, teachers more often focused on shapes and, in Peru, the focus was on telling the time (Gonzales and Paik, 2011).

Additionally, in attempts to target lesson objectives and standards, as well as implement a new mathematical curriculum, research suggests that practicing teachers have difficulties in enacting and integrating lessons and the curriculum as intended (Brown et al., 2009; Moloi et al., 2008; Zacharos et al., 2014), which may be mediated by an over-reliance on textbooks (Henry and Brown, 2008), inadequate resources (Hu et al., 2014), or a lack of evidence-based strategies (Phillips and Morse, 2011). On the other hand, in a study conducted by Stein and Kaufman (2010), the findings indicated that practicing teachers’ implementation of the Investigations (textbook series) afforded them opportunities to maintain high cognitive demand, attend to students’ thinking and reasoning, and plan lessons with big mathematical ideas in mind when compared to practicing teachers’ implementation of the Everyday Mathematics (textbook series).

The implementation of mathematics content and curriculum in a classroom setting has also been studied by examining the general instructional strategies and methods employed by practicing teachers. The results from this literature review highlight the competing discourse between, and the implementation of, traditional teaching practices (e.g. teacher-centered worksheets) and non-traditional or reform-based teaching practices (e.g. child-centered, open-ended tasks). On the one hand, practicing teachers were noted as utilizing open-ended and/or meaningful tasks (Cahnmann and Remillard, 2002; Frid and Sparrow, 2009; Papademetri-Kachrimani, 2015), relevant manipulatives and technology (Frid and Sparrow, 2009; Lee, 2005), different solution paths (Frid and Sparrow, 2009; McClain and Cobb, 2001), and collaborative groups (Georges, 2009). On the other hand, practicing teachers are still prone to employ teacher-led demonstrations (Gonzales and Paik, 2011; Meijnen et al., 2003) and worksheets (Feza, 2014), which may be due to a lack of resources (Feza, 2014) or years of teaching experience (Meijnen et al., 2003). Moreover, it seemed as if some teachers were still grappling with the transition from a prospective to a practicing teacher (Towers, 2010), from reported self-perceptions to observed practices (Brown, 2005), or from the use of a student’s home language to an official school language (Kasule and Mapolelo, 2005). For example, Towers (2010) described not only a novice teacher’s struggle to enact inquiry-based teaching practices, but also his inability to articulate his understandings of inquiry-based teaching to others, which led to problems around collaboration and administrative evaluations.

The scholarship in this study regarding classroom discourse and communication includes both verbal (e.g. Boonen et al., 2011) and non-verbal communication (e.g. Flevares and Perry, 2001). Practicing teachers seem to employ various mathematical talk moves or communication strategies, such as, among others, questions and dialogue to check for student understanding (Wiebe Berry and Kim, 2008), intentional pauses (Cohrssen et al., 2014) and listening (Fleener et al., 2004), encouraging and using appropriate mathematical terms (Cooke and Buchholz, 2005; Rudd et al., 2008), and eliciting students’ mathematical thinking and justifications (Björklund and Pramling-Samuelsson, 2013; Tatsis et al., 2008; Warren and Cooper, 2005). These may be accounted for within the developmental trajectory of building a Math-Talk Learning Community, as developed by Hufferd-Ackles et al. (2004). These communicative practices seem to influence various student outcomes, such as their confidence in learning mathematics (Jung and Reifel, 2011), willingness to participate and collaborate as a mathematics student (Björklund and Pramling-Samuelsson, 2013; Cohrssen et al., 2014; Jung and Reifel, 2011; Kaartinen and Kumpulainen, 2012), and growth of mathematical knowledge over the course of a year (Klibanoff et al., 2006). Yet, as noted throughout the findings, these communicative acts may be hindered by various external factors, such as standards and the discourse of play (Jung and Reifel, 2011; Thomas et al., 2011).

Broadly speaking, professional development opportunities for educators vary in content, form, and duration. For example, Linder and colleagues (2016) established that across a south-eastern state in the USA, professional development in mathematics for early childhood educators is provided second to literacy and, regardless of content, was typically provided in one- to two-hour brief workshop settings. In addition, the focus of these professional development workshops was typically based on a content strand, as opposed to emphasizing the processes of learning and teaching mathematics. In the results of this literature review, the articles categorized as transformation studies included professional development opportunities lasting anywhere from a semester course to a three-year ongoing program, with a few studies including the influence of a particular assignment or task. This time duration is desirable because, as stated in a joint position paper in the USA by the National Association of Young Children and the National Council for Teachers of Mathematics: “Inservice professional development needs to move beyond the one-time workshop to deeper exploration of key mathematical topics as they connect with young children’s thinking and with classroom practices” (National Association for the Education of Young Children, 2002: 6). There also seems to be promise for professional development that involves co-teaching (e.g. Jao, 2013), mentorship (Wang and Paine, 2001), or coaching (Rudd et al., 2008) models. For example, Rudd et al. (2008) found that through professional development, 11 practicing teachers’ mathematics-mediated language increased by 56% during the observed sessions, but that those who took part in the coaching model increased their mathematical language by an additional 39%.

Of the 164 studies within this cluster of the overall literature review, 27% or 44 studies were categorized as transformation and examined changes in practicing and prospective teachers’ professional knowledge (20%), disposition (36%), and practice (44%) due to a professional development program, intervention, course, and/or task. The majority of these studies were conducted with practicing teachers (72%) as opposed to prospective teachers (18%). In general, across these studies, the changes examined by the researchers seem to be more positive than negative—in other words, educators exhibited improvements in a particular area of focus. For example, over a year-long program, Polly, Neale and Pugalee (2014) noticed an increase in practicing teachers’ MKT scores, implementation of student-centered pedagogies, and view of mathematics as discovery-oriented as opposed to transmission-oriented. Yet this does not apply to every study categorized as professional development. Piasta et al. (2015), for instance, did not observe an increase in the time allotted for preschool-aged children (aged three to five) to engage in mathematical learning opportunities at the conclusion of professional development. There are also studies in which the short-term impacts are examined, such as 18 months after completion of engagement in professional development (e.g. Warren, 2009). However, the longer-term impacts of these professional development opportunities are unclear, specifically with regard to sustaining changes in content knowledge, dispositions, and practices.

Improvements in practicing and prospective teachers’ content knowledge included an increase in MKT (Hart, 2009; Polly, Margerison and Piel, 2014; Tirosh et al., 2013; Warren, 2009), general mathematics content knowledge (Bailey, 2010; Hooks and Duarte, 2005; Tirosh et al., 2013), and specific content knowledge, including understanding place value (Bussi, 2011; Cady et al., 2014), patterns and algebra (Warren, 2009), and spatial ability (Kurtulus, 2013). For example, Tirosh et al. (2013) found that weekly meetings with preschool teachers around challenging mathematical tasks shifted the manner in which the teachers discussed the existence of multiple solutions to solve a problem and the impact of changing the parameters of a task. As another example, six Year One teachers, who engaged in professional development to support implementation of a “pattern and algebra” strand (i.e. patterns, equivalence and equations, and functions), self-reported an increase in both mathematics content knowledge and mathematical language specific to this strand (Warren, 2009). On the other hand, Polly, Neale and Pugalee (2014) could not claim that a year-long professional development program provided to 15 kindergarten teachers was successful in increasing teachers’ mathematical content knowledge, as there were both increases and decreases in scores from the beginning to the end of the professional development.

Additionally, there is evidence to suggest that professional development has a positive influence on practicing and prospective teachers’ beliefs about and attitudes towards mathematics (Afamasaga-Fuata’i and Sooaemalelagi, 2014; Erfjord et al., 2012; Graue et al., 2015; Palmer, 2009; Perry et al., 2007; Perry and MacDonald, 2015), and confidence in their ability to teach mathematics to young children (Afamasaga-Fuata’i and Sooaemalelagi, 2014; Arnold et al., 2002; Bintas, 2008; Palmer, 2009; Stavroula et al., 2015). For example, after a 10-week alternative mathematics course aimed at challenging prospective teachers’ gendered attitudes to mathematics, as well as their own subjectivity, Palmer (2009) noted a positive shift in students’ attitude about mathematics and an increase in approximately 50% of the 75 students in their confidence to teach mathematics. In addition, these prospective teachers recognized how the course changed their understandings of their personal mathematical subjectivity—in other words, what it means to be a “maths-person.” Through using a pair-dialogue approach to instruction, Tsamir et al. (2014) noted a positive change in practicing teachers’ self-efficacy related to students’ knowledge, which seemed to diminish the negative correlation between self-efficacy for teaching and student knowledge present at the beginning of the professional development. Moreover, at the conclusion of a mathematics methods course, Saçkes et al. (2012) noted an increase in prospective teachers’ efficacy beliefs for integrating science and mathematics, while Gresham (2007) found a decrease in prospective teachers’ mathematics anxiety.

Lastly, professional development has been shown to transform practicing and prospective teachers’ mathematical practices, such as their mathematical language (Rudd et al., 2008; Warren et al., 2011) and planning of lessons (Björklund, 2012; Muñoz-Catalán et al., 2010; Piasta et al., 2015). For instance, Muñoz-Catalán et al. (2010) gained an understanding of how an early career practicing teacher involved in professional development became more flexible in her planning to teach mathematics—namely, by considering her students’ difficulties, which appeared to be influenced through her joint reflection with others and through her personal reflections. Furthermore, studies have shown a change in practicing and prospective teachers’ mathematical practices to become more child-centered and include research-based strategies (Kretlow et al., 2012; Polly, Margerison and Piel, 2014; Polly, Neale and Pugalee, 2014; Thornton et al., 2009). As a specific example, professional development has been shown to increase early childhood educators’ questions—questions that invoke student thinking, exploration, and justification (Lin, 2006; Warren et al., 2011).