Consecutive years of experience at the same grade level

Many studies have found that teacher experience has a positive effect on student achievement in mathematics (Rowan et al., 2002; Clotfelter et al., 2007; Kane et al., 2008); however, other research suggests that the effects of teacher experience tend to stabilise after a few years (Rockoff, 2004; Hanushek et al., 2005; Boyd et al., 2007). Evidence from this study revealed that a sublevel of teacher experience may play a

more important role in impacting student achievement than general teacher experience, and that this sublevel has distinct influences on teacher classroom practices. This newly identified sublevel of teacher experience has been entitled in this study as consecutive years of experience in teaching at the same grade level. Data analysis showed that consecutive years of experience in teaching at the same grade level had a unique and important impact upon a teacher’s classroom practices and attitudes and beliefs, which in turn was reported to influence student outcomes. This impact may have an effect over and above that of the teacher experience variable, in that a teacher could have ten years of experience teaching a senior class; however, if they began teaching a junior class in their eleventh year of teaching, a steep learning curve would be involved, where the benefits and knowledge gained through having experience at the senior level may not be entirely transferable to teaching at the junior level. Consecutive years of experience at the same grade level have not been considered by the teacher effectiveness literature regarding their impact on classroom interactions or student outcomes; however, findings from this study suggest that this may be a promising area for future research.

An unexpected finding of this study was that the three advantages of holding consecutive years of experience at the same grade level, which were reported by participants in this study, are three forms of pedagogical knowledge for teaching posited by Ball et al. (2008). This evidence indicates that experience at the same grade level positively influences a teacher’s pedagogical knowledge for teaching mathematics to that particular grade level. Pedagogical content knowledge was first defined by Schulman (1986, p9) as knowledge of “the most useful ways of formulating and representing the subject to make it comprehensible to others.” The findings from this study are exciting, as they add another dimension to the literature on pedagogical content knowledge, in providing an insight into how this knowledge

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originates and is used by teachers. This is notable, as Kersting et al. (2012) highlight the importance of understanding the kinds of knowledge that teachers draw upon and how they utilise them in their classroom teaching.

Table 5.1 summarises the sublevels of teacher effectiveness that holding consecutive years of experience at the same grade level was reported by interviewees to impact upon. Following this, the mechanisms through which holding consecutive years of experience impacts upon the three forms of pedagogical content knowledge identified by Ball et al. (2008) are described in detail.

Table 5.1 Levels of impact of consecutive years of experience at the same grade level Teacher Qualifications Teacher Classroom Practices Teacher Attitudes and Beliefs Student Outcomes Impact of consecutive years of experience at the same grade level Pedagogical knowledge of content and students

Teacher can anticipate mathematical concepts that students will find difficult and address difficult concepts by devoting more time to, and facilitating regular revision of, these concepts

Increased confidence regarding knowledge of the best teaching strategies and resources to promote student learning and achievement in mathematics Student learning and achievement on standardised tests Pedagogical knowledge of content and teaching Teacher is capable of clearer lesson delivery due to self-evaluation of previous lessons Pedagogical knowledge of content and curriculum

Teacher has practical knowledge of the best resources to complement teaching and student learning due to deep working knowledge of curriculum

Knowledge of content and students is defined by Ball et al. (2008, p401) as a “knowledge that combines knowing about students and knowing about mathematics” where, for example, teachers are able to anticipate what students may find confusing. Analysis of the data in this study showed that consecutive years of teaching

experience at the same grade level led to teachers reporting that they had a deep working knowledge of how their students responded to the mathematics curriculum for that particular grade level. This provided teachers with an awareness of mathematical concepts that students found difficult. Evidence showed that this information was then used by teachers in their planning and teaching the following year, in that they reported devoting extra time to teaching and revising more difficult concepts throughout the school year. For example, Alison (School B, Ireland) explained this effectively by noting:

I’ve had 4th

a few times … I know what they find difficult … so what I would do is I’d place more emphasis on the things they’re finding more difficult … spend more time.

If for each grade there are mathematical concepts within the curriculum that students commonly find difficult to understand, then CPD that is focused on these problem areas, and that is specific to each grade level, may be important for teachers who are new to a grade level – regardless of their years of experience teaching. In fact, Cohen and Hill (2000, p312) found that professional development that is grounded in gaining a deeper knowledge of student curriculum is more likely to impact teacher classroom practices than professional development that is more general or “peripheral to subject matter (‘using mathematics manipulatives’).”

Knowledge of content and teaching is defined by Ball et al. (2008, p401) as combining “knowing about teaching and knowing about mathematics”, where teachers evaluate the most advantageous way to represent and teach mathematical ideas. Further evidence of the positive effect of consecutive years of experience at the same grade level was revealed, with teachers reporting this variable’s impact upon their teaching and lesson delivery. Participants reported that self-evaluation of teaching mathematical concepts to a particular grade level often led to the perception of improved lesson delivery of these concepts in future teaching, especially with

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respect to ensuring that mathematical concepts were delivered clearly to students. For example, Geraldine (School C, Northern Ireland) explained that:

… every year … you learn from your own mistakes, and how to make things as simple as possible for them [the students], especially in numeracy … because you want to get the concepts really clear in their head.

This is notable, as several studies have linked clear lesson delivery to improved student achievement (Van de Grift, 2007; Stronge et al., 2011). It was also interpreted from the data that due to having experience in delivering concepts clearly, teachers who had consecutive years of experience in teaching at the same grade level were more confident in their teaching of mathematics concepts to that grade level. This is an important factor, as teacher self-confidence as mathematics teachers is positively correlated with their students’ self-confidence as mathematics learners (Stipek et al., 2001).

Knowledge of content and curriculum is not defined by Ball et al. (2008); however, Schulman (1986, p10) defines curricular knowledge as knowledge of “the full range of programs designed for the teaching of particular subjects and topics at a given level, the variety of instructional materials available in relation to those programs, and the set of characteristics that serve as both the indications and contraindications for the use of particular curriculum or program materials in particular circumstances.” Evidence from this study revealed that consecutive years of experience at the same grade level provided teachers with the opportunity to gain a deep working knowledge of the curriculum. As part of this, teachers reported that they were able to build up suitable resources for their teaching of that grade level, and these resources were linked to the needs of students and lesson delivery. For example, Majella (School A, Northern Ireland) noted that in gaining teaching experience at the same level:

… you build up the resources and you’re familiar with the curriculum, you’re familiar with what needs to be taught.

In summary, when teaching, teachers draw on a different kind of mathematics knowledge to that learned in university or second level mathematics courses (Ball et al., 2008). What the findings from this study show is that consecutive years of experience at the same grade level allows teachers to build upon three forms of pedagogical knowledge through self-evaluation and reflection upon mathematics teaching and learning. This sublevel of teacher experience affords teachers the opportunity to accumulate, evaluate and analyse data about teaching and learning for a specific grade level, which leads to teachers being more confident in their ability to deliver mathematical concepts clearly to students as well as being more confident in their ability to ensure student achievement, through effectively addressing mathematics concepts which students find difficult.