Pedagogies of practice and opportunities to learn about classroom mathematics discussions

In this paper, we argue that to prepare pre-service teachers for doing complex work of teaching like leading classroom mathematics discussions requires an implementation of different pedagogies of teacher education in deliberate ways. In supporting our argument, we use two frameworks: one curricular and one pedagogical. The curricular framework is based on the work of Hammerness et al. (Preparing teachers for a changing world. What teachers should learn and be able to do. San Francisco, Jossey-Bass Educational Series, pp 358–388, 2005) outlining four main goals of teacher learning: a vision of practice, knowledge of students and content, dispositions for using this knowledge, and a repertoire of practices and tools. The pedagogical framework is based on the work of Grossman et al. (Teach Teach Theory Pract 15(2):273–289, 2009a; Teach Coll Record 111(9):2055–2100, 2009b) outlining three pedagogies of practice: representations, decompositions, and approximations of practice. We use the curricular framework to examine the opportunities for teacher learning that were afforded by these three different pedagogies of practice in a unit on leading classroom mathematics discussion in a secondary mathematics methods course. We use evidence from our analysis to show how the coordination of those pedagogies of practice is better than any one of them in addressing important goals for teacher learning about classroom discussions.     

Intensification and isolation: Alienated teaching and collaborative professional relationships in the accountability context

The global educational landscape continues to change in response to three forces: a new paradigm of curriculum approaches that has shifted from teaching to learning; public demand for evidence of this learning; and decentralization of public schools (Sahlberg in Journal of Educational Change, 12(2):173–185, 2011). These changes have had what many researchers identify as a negative effect on the work of teachers (Cochran-Smith and Lytle in Harvard Educational Review, 76(4):668–697, 2006; Griffin and Scharmann in Journal of Elementary Science Education, 20(3):35–48, 2008; Hargreaves and Shirley in Phi Delta Kappan, 90(2):135–143, 2008; Hill in Educational Evaluation and Policy Analysis, 29(2):95–114, 2007; Jennings and Rentner in Phi Delta Kappan, 88(2):110–113, 2006; McNeil in Contradictions of school reform: Educational costs of standardized testing. Routledge, New York, 2000). One effect is alienation, which may take many forms including disengagement from work, isolation and neglect (Brooks et al. in Educ Policy 22(1):45–62, 2008; Macdonald and Shirley in The mindful teacher. Teachers College Press, New York, 2009; Zielinski and Hoy in Educ Adm Q 19(2):27–45, 1983). In this article, I use data gathered from interviews with teachers and school counselors in a suburban district outside a Rust Belt city to demonstrate that the reach of alienated teaching in the accountability context extends beyond teachers’ own work to impact the entire school community. In particular, I show that alienated teaching further isolates school counselors and teachers, whose work has long been organizationally separate, from collaborative professional relationships and ultimately prevents students from receiving the types of support services they need for postsecondary success.     

The teacher leadership process: Attempting change within embedded systems

This embedded case study examines the leadership practices of eleven teacher leaders in three urban schools to identify how these teacher leaders attempt to change the teaching practice of their colleagues while working as professional learning community leaders and as mentors for new teachers. Using a theoretical framework integrating complex systems theory with Kotter’s (Leading change. Harvard University Press, Cambridge, 1996) eight steps for leading organizational change, we analyze the work and perspectives of individual teacher leaders, and we examine how teams of teacher leaders and principals function collectively in their efforts to lead instructional change. Our findings have implications for schools seeking to utilize teacher leadership as a reform strategy for authentic instructional improvement.     

Re-inhabiting place in contemporary rural communities: Moving toward a critical pedagogy of place

Heather Zimmerman and Jennifer Weible’s (Cult Stud Sci Educ, 2016) use of place-based pedagogy in high school science education honors their participants’ lived experiences and the rural communities from which they come. They raise an unresolved tension in their findings: Why did the youth in their study, who clearly learned a lot about the local watershed, not feel empowered or knowledgeable enough to propose collective, action-oriented strategies to address the poor quality of the water? We use this tension as a focus point of our response, drawing on one author’s (Huffling’s) biography and David Gruenewald’s (Educ Res 32:3–12, 2003. doi: 10.3102/0013189X032004003) critical pedagogy of place to re-imagine the curriculum that Zimmerman and Weible describe. We provide strategies that align with Gruenewald’s (2003) constructs of decolonization and reinhabitation that could promote youths’ collective empowerment.     

Science initial teacher education and superdiversity: educating science teachers for a multi-religious and globalised science classroom

Steven Vertovec (2006, 2007) has recently offered a re-interpretation of population diversity in large urban centres due to a considerable increase in immigration patterns in the UK. This complex scenario called superdiversity has been conceptualised to help illuminate significant interactions of variables such as religion, language, gender, age, nationality, labour market and population distribution on a larger scale. The interrelationships of these themes have fundamental implications in a variety of community environments, but especially within our schools. Today, London schools have over 300 languages being spoken by students, all of whom have diverse backgrounds, bringing with them a wealth of experience and, most critically, their own set of religious beliefs. At the same time, Science is a compulsory subject in England’s national curriculum, where it requires teachers to deal with important scientific frameworks about the world; teaching about the origins of the universe, life on Earth, human evolution and other topics, which are often in conflict with students’ religious views. In order to cope with this dynamic and thought-provoking environment, science initial teacher education (SITE)—especially those catering large urban centres—must evolve to equip science teachers with a meaningful understanding of how to handle a superdiverse science classroom, taking the discourse of inclusion beyond its formal boundaries. Thus, this original position paper addresses how the role of SITE may be re-conceptualised and re-framed in light of the immense challenges of superdiversity as well as how science teachers, as enactors of the science curriculum, must adapt to cater to these changes. This is also the first in a series of papers emerging from an empirical research project trying to capture science teacher educators’ own views on religio-scientific issues and their positions on the place of these issues within science teacher education and the science classroom.     

Increasing Completion of Classroom Routines Through the Use of Picture Activity Schedules

Teachers spend the first few days of school teaching routines to children that will help transitions in the classroom between different activities. When children have difficulty, they move more slowly and/or require teacher prompting. A picture activity schedule intervention (Breitfelder in Teach Except Child Plus 4(5):2–15, 2008; Bryan and Gast in J Autism Dev Disord 30(6):553–567, 2000) was used to assist a 5-year-old boy in completing three routines within the kindergarten classroom. Results indicated that the picture activity schedule increased the child’s independent completion of each of the three routines, while also decreasing the need for teacher prompting.     

Reconceptualizing the Nature of Science for Science Education

Two fundamental questions about science are relevant for science educators: (a) What is the nature of science? and (b) what aspects of nature of science should be taught and learned? They are fundamental because they pertain to how science gets to be framed as a school subject and determines what aspects of it are worthy of inclusion in school science. This conceptual article re-examines extant notions of nature of science and proposes an expanded version of the Family Resemblance Approach (FRA), originally developed by Irzik and Nola (International handbook of research in history, philosophy and science teaching. Springer, Dordrecht, pp 999–1021, 2014) in which they view science as a cognitive-epistemic and as an institutional-social system. The conceptual basis of the expanded FRA is described and justified in this article based on a detailed account published elsewhere (Erduran and Dagher in Reconceptualizing the nature of science for science education: scientific knowledge, practices and other family categories. Springer, Dordrecht, 2014a). The expanded FRA provides a useful framework for organizing science curriculum and instruction and gives rise to generative visual tools that support the implementation of a richer understanding of and about science. The practical implications for this approach have been incorporated into analysis of curriculum policy documents, curriculum implementation resources, textbook analysis and teacher education settings.     

Why use learning outcomes in higher education? Exploring the grounds for academic resistance and reclaiming the value of unexpected learning

Learning outcomes are now mandated in higher education courses across Europe. However, their impact on teaching and student learning is both uncertain and an issue for debate. In this paper, we explore (1) what is meant by learning outcomes in diverse contexts and (2) whether policy and practice governing learning outcomes accord with developments in learning theories, especially regarding sociocultural approaches that have drawn significant interest since the 1990s (Engeström 1987; Lave and Wenger 1991). Shepard’s (Educational Researcher, 29(7), 4–14, 2000) publication is particularly salient to our examination due to her identification of an emerging paradigm to assist in the understanding of the relationships among teaching, learning and assessment. Employing recent work on conceptualisations of learning outcomes and a four-quadrant taxonomy (Prøitz in Educational Assessment, Evaluation and Accountability, 22(2), 119–137, 2010, 2014), we discuss relevant learning theory approaches. This article is a conceptual investigation exploring the grounds for the assumption that learning can be predefined in terms of (expected) outcomes. Specifically, we discuss this assumption from the perspective of recent developments in learning theories. We argue that introducing learning outcomes predominantly for policy and management purposes may actually weaken the learning outcomes’ potential to direct teaching and learning and to improve the quality of both.     

Investigating a case of hidden misinterpretations of an additive word problem: structural substitution

According to numerous studies (Barrouillet & Camos 2002; Brousseau 1988; Chevallard 1988; Riley et al. 1984; Schubauer-Leoni & Ntamakiliro, Revue Des Sciences de L’éducation, 20(1): 87–113, 1994; Vergnaud 1982; Xin, The Journal of Educational Research, 100(6):347–360, 2007), a combination of many factors, including curriculum, didactic contract and task design, can potentially lead to students experiencing difficulties in developing of a full understanding of addition and subtraction and their relationship in problem solving. Few studies (Conne, Recheche En Didactique Des Mathématiques, 5, 269–332, 1985; DeBlois, Éducation et Francophonie, 25(1), 102–120, 1997; Giroux & Ste-Marie, European Jornal of Psychology of Education, 16(2), 141–161, 2001) describe the misinterpretations of problems as a factor related to learning difficulties. We have studied how and why elementary school students misinterpret the mathematical structure of a simple additive word problem and what kind of possible (hidden) misinterpretation may occur. We analysed possible mechanisms of misinterpretations in word problem solving, discussing various examples of correct and incorrect solutions resulting from the misinterpretation of a problem. We gave the elementary school students a word problem, which could potentially be misinterpreted, and observed their solving strategies. Our results show how the particular form of mathematical misinterpretation—structure substitution—may help students obtain a correct answer and thereby hinder the development of their mathematical reasoning. We further discuss different ways of addressing this phenomenon in teaching practice.     

Editorial

Secondary-tertiary transition issues are explored from the perspective of ways of doing mathematics that are constituted in the implicit aspects of teachers’ action. Theories of culture (Hall, 1959) and ethnomethodology (Garfinkel, 1967) provide us with a basis for describing and explicating the ways of doing mathematics specific to each teaching level, according to the “accounts” provided by the teachers involved in this research project. To borrow from Hall (1959), the “informal” mode of mathematical culture specific to each teaching level plays a key role in attempts to better grasp transition issues.     

We’re Creative on a Friday Afternoon: Investigating Children’s Perceptions of their Experience of Design &; Technology in Relation to Creativity

In the last 15 years there has been an increased emphasis in both educational research and curriculum development upon investigating children’s perspectives of their experience of learning. Children naturally have very particular and important insights to offer in helping us to develop our understanding of teaching and learning. However, research into children’s perceptions in the field of primary Design &; Technology education is still at a very early stage (Lunt in International handbook of research and development in technology education, Sense Publishers, Utrecht, 2009a). For example, in three reviews of educational research in Design &; Technology (Kimbell in A guide to educational research, The Woburn Publishers, London, 1996; Eggleston in Teaching and learning design and technology: a guide to recent research and its applications, Continuum, London, 2000; Harris and Wilson in Designs on the curriculum? A review of the literature on the impact of design and technology in schools, Department for Education and Skills, London, 2003) there are only passing references made to eliciting and considering pupils’ views and, in the studies where it does occur, it is used as a supplementary method of data collection rather than as a focus of research. The work which exists is small-scale and the majority of studies relate to secondary-aged pupils. The research that we have recently undertaken has tried to redress this gap. It has focused on primary children’s (aged 9–11 years) perceptions of Design &; Technology in general (Benson and Lunt in PATT 18 international conference on design and technology educational research: teaching and learning technological literacy in the classroom, University of Glasgow, Glasgow, 2007) and latterly creativity in Design &; Technology. It has been claimed by many that Design &; Technology is a ‘creative’ subject which develops children’s creative abilities. This is a bold claim and one that needs careful consideration. This paper sets out a framework for thinking about creativity drawn from a review of the literature and uses evidence of children’s perceptions of their experience of Design &; Technology to compare practice with theory in an attempt to raise questions and issues relevant to both policy and practice.     

TEACHERS’ KNOWLEDGE OF THE CONCEPT OF A FUNCTION: A THEORETICAL FRAMEWORK

In order to teach mathematics effectively, mathematics teachers need to have a sound mathematical knowledge, but what constitutes sound mathematical knowledge for teaching is subject to debate. This paper is an attempt to unpack what constitutes teacher knowledge of the concept of a function which is a unifying idea in the mathematics curriculum. The central components of the framework, which will be elaborated on in this paper, are: teachers’ subject matter knowledge, teachers’ pedagogical content knowledge, teachers’ technological pedagogical knowledge, technological content knowledge, and technological pedagogical content knowledge in relation to the concept of a function. The framework is informed by Shulman’s (Educational Researcher 15:4–14, 1986) Types of Teachers Knowledge Framework, Ball, Bass & Hill 29:14–17, 20–22, 43–46 (2005) Mathematical Knowledge for Teaching Framework, and Mishra & Koehler’s (Teachers College Record 108:1017–1054, 2006) Technological Pedagogical Content Knowledge (TPACK) framework.     

Investigating the learning challenges presented by digital technologies to the College of Education in Kuwait University

There is now widespread recognition that digital technologies, particularly portable hand held devices capable of Internet connection, present opportunities and challenges to the way in which student learning is organized in schools, colleges and institutions of higher education in the 21st Century. Traxler, Journal of the Research Centre for Educational Technology, 6(1), 3–15 (2010) suggests such devices are pervasive and ubiquitous, conspicuous and unobtrusive, noteworthy and taken-for-granted with everyone typically owning one, using one and often having more than one. As a consequence it has been argued that the availability of such devices, controlled mainly by the student and not the teacher, has the potential to change the traditional dynamics and pedagogical patterns of the learning environment (Burden et al. 2012). Education institutions, however, typically remain organized around spatial and temporal considerations such as buildings, timetables, calendars and internal structures which are designed to classify and manage students. In the case study reported here students and faculty teaching staff from the College of Education in the Kuwait University were surveyed in order to assess their access to such technologies, their capability to use them effectively in support of achieving planned learning outcomes and the implications for change that could emanate from such findings.     

Toward re-thinking science education in terms of affective practices: reflections from the field

Rational and operationalized views of science and what it means for teachers and students to know and enact legitimate science practices have dominated science education research for many decades (Fusco and Barton in J Res Sci Teach 38(3):337–354, 2001. doi: 10.1002/1098-2736(200103)38:3<337::AID-TEA1009>3.0.CO;2-0). Michalinos Zembylas challenges historically prevalent dichotomies of mind/body, reason/emotion, and emotion/affect, calling researchers and educators to move beyond the Cartesian dualisms, which have perpetuated a myth of scientific objectivity devoid of bias, subjectivity and emotions. Zembylas (Crit Stud Teach Learn 1(1):1–21, 2013. doi: 10.14426/cristal.v1i1.2) contends that the role of emotions and affect are best understood as relational and entangled in epistemological, cultural, and historical contexts of education, which represent contested sites of control and resistance. We argue that Zembylas’ work is pivotal since “theoretical frames of reference for doing research in science education…[and] what constitutes knowledge and being within a particular frame” carry material bearings over the enactments of science teaching and learning (Kyle in J Res Sci Teach 31:695–696, 1994, p. 321. doi: 10.1002/tea.3660310703). In this paper, we hold cogen dialogue about how re-thinking notions of emotion and affect affords us, both science educators and researchers, to re-envision science education beyond cognitive and social frames. The framing of our dialogue as cogen builds on Wolff-Michael Roth and Kenneth Tobin’s (At the elbows of another: learning to teach through coteaching. Peter Lang Publishing, New York, 2002) notion of cogenerative dialogue. Holding cogen is an invitation to an openly dialogic and safe area, which serves as a space for a dialogic inquiry that includes radical listening of situated knowledges and learning from similarities as well as differences of experiences (Tobin in Cult Stud Sci Educ, in review, 2015). From our situated experiences reforms, colleges of education, schools, and curriculum place not enough emphasis on affective and bodily dimensions of teaching and learning. Instead, the privilege seems to be given to reason, evidence, and rationalities, which continue to reinforce dominant ways of knowing and experiencing. The separation of mind and body, reason and emotion, effect and affect in teaching and research might bear unintended and negative consequences for many children and teachers who are engaged in bodily and affective forms of learning science. In this forum we wish to expand on the discussion to consider the interdependent nature of learning, experience, and affect by drawing on our work with science teachers and culturally and linguistically diverse students, juxtaposed alongside Zembylas’ reflections, to further theorize the affective turn in science education.     

Planning for Reform-Based Science: Case Studies of Two Urban Elementary Teachers

The intent of national efforts to frame science education standards is to promote students’ development of scientific practices and conceptual understanding for their future role as scientifically literate citizens (NRC 2012). A guiding principle of science education reform is that all students receive equitable opportunities to engage in rigorous science learning. Yet, implementation of science education reform depends on teachers’ instructional decisions. In urban schools serving students primarily from poor, diverse communities, teachers typically face obstacles in providing reform-based science due to limited resources and accountability pressures, as well as a culture of teacher-directed pedagogy, and deficit views of students. The purpose of this qualitative research was to study two white, fourth grade teachers from high-poverty urban schools, who were identified as transforming their science teaching and to investigate how their beliefs, knowledge bases, and resources shaped their planning for reform-based science. Using the Shavelson and Stern’s decision model for teacher planning to analyze evidence gathered from interviews, documents, planning meetings, and lesson observations, the findings indicated their planning for scientific practices was influenced by the type and extent of professional development each received, each teacher’s beliefs about their students and their background, and the mission and learning environment each teacher envisioned for the reform to serve their students. The results provided specific insights into factors that impacted their planning in high-poverty urban schools and indicated considerations for those in similar contexts to promote teachers’ planning for equitable science learning opportunities by all students.     

Scholarly Learning as Vocation: A Study of Community and Broad Access Liberal Arts College Faculty

In this study we extended Neumann’s scholarly learning theory (2009)?and Hansen’s theory on vocation (1994, 1995) to explore the scholarly learning of faculty members employed at institutional types not typically recognized for faculty work beyond teaching. Through interviews with 22 participants, we studied the content of and reasons for faculty engagement in scholarly learning. Our analysis found that the content of participants’ scholarly learning focused on expanding and constructing disciplinary knowledge whereas their reasons connected to a sense of obligation and personal fulfillment. Such findings confirmed Neumann’s suggestion that administrators should conceptualize the academic profession as a learning enterprise.     

Rural science education as social justice

What part can science education play in the dismantling of obstacles to social justice in rural places? In this Forum contribution, I use “Learning in and about Rural Places: Connections and Tensions Between Students’ Everyday Experiences and Environmental Quality Issues in their Community”(Zimmerman and Weible 2016) to explicitly position rural education as a project of social justice that seeks full participatory parity for rural citizens. Fraser’s (2009) conceptualization of social justice in rural education requires attention to the just distribution of resources, the recognition of the inherent capacities of rural people, and the right to equal participation in democratic processes that lead to opportunities to make decisions affecting local, regional, and global lives. This Forum piece considers the potential of place-based science education to contribute to this project.     

Transforming an education system through professional learning: developing educational change at scale in Ontario

There has been increased attention to the importance of teachers and teacher quality in developing and sustaining successful education systems for some time now (Barber and Mourshed in How the world’s best performing school systems come out on top, McKinsey & Company, New York, 2007; Darling-Hammond et al. in Empowered educators: how high-performing systems shape teaching quality around the world, Jossey Bass, San Francisco, 2017). Germaine to the issue of teacher quality, however, is an acknowledgement of the value of supporting educator’s ongoing professional learning (PL). Drawing on findings from a large-scale case study of Ontario, Canada, this paper attempts to shed light on the question of how systems of PL can be developed and scaled? The research was conducted in several phases, including an extensive document analysis, followed by interviews with key respondents across the sector. The paper is framed within the notion of large-scale system change, with a focus on the importance of inter-professional relationships and joint work in establishing shared goals for educational improvement. As we noted in the larger study, a theory of action linked to knowledge of educational change and professional capacity building has informed the mindset, values, and strategies developed and implemented. This paper specifically illustrates Ontario’s whole-system’s focus on professional learning as part of this wider theory of action.     

Toward the sociopolitical in science education

In this paper, we explore how Jacques Rancière’s (The ignorant schoolmaster: five lessons in intellectual emancipation. Stanford University Press, Stanford, 1991) notions of radical equality and dissensus reveal horizons for activism and sociopolitical engagement in science education theory, research, and practice. Drawing on Rochelle Gutiérrez’ (J Res Math Educ 44(1):37–68, 2013a. doi: 10.5951/jresematheduc.44.1.0037; J Urban Math Educ 6(2):7–19, b) “sociopolitical turn” for mathematics education, we identify how the field of science education can/is turning from more traditional notions of equity, achievement and access toward issues of systemic oppression, identity and power. Building on the conversation initiated by Lorraine Otoide who draws from French philosopher Jacques Rancière to experiment with a pedagogy of radical equality, we posit that a sociopolitical turn in science education is not only imminent, but necessary to meet twenty-first century crises.