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.     

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.     

Alternate Reality Games as an Informal Learning Tool for Generating STEM Engagement among Underrepresented Youth: a Qualitative Evaluation of the Source

This project developed and studied The Source, an alternate reality game (ARG) designed to foster interest and knowledge related to science, technology, engineering, and math (STEM) among youth from populations underrepresented in STEM fields. ARGs are multiplayer games that engage participants across several media such as shared websites, social media, personal communications, and real-world settings to complete activities and collaborate with team members. The Source was a five-week summer program with 144 participants from Chicago aged 13 to 18 years. The Source incorporated six socio-contextual factors derived from three frameworks: Chang’s (ERIC Digest, 2002) recommendations for engaging underrepresented populations in STEM careers, Lave and Wenger’s (Cambridge University Press, 1991) situated learning model, and Barron’s (Human Development, 49(4); 193-224, 2006) learning ecology perspective. These factors aligned with the program’s aims of promoting (1) social community and peer support, (2) collaboration and teamwork, (3) real-world relevance and investigative learning, (4) mentoring and exposure to STEM professionals, (5) hands-on activities to foster transferable skill building, and (6) interface with technology. This paper presents results from 10 focus groups and 10 individual interviews conducted with a subset of the 144 youth participants who completed the game. It describes how these six factors were realized through The Source and uses them as a lens for considering how The Source functioned pedagogically. Qualitative findings describe youth’s perception of The Source’s potential influence on STEM interest, engagement, and identity formation. Despite limitations, study results indicate that underrepresented youth can engage in an immersive, narrative, and game-based experience as a potential mechanism for piquing and developing STEM interest and skills, particularly among underrepresented youth.     

Teaching: in light of Noel Gough’s and Ajay Sharma’s articles

In their articles, Ajay Sharma (Cult Stud Sci Educ, doi: 10.1007/s11422-017-9835-z, 2017) and Noel Gough (Cult Stud Sci Educ, doi: 10.1007/s11422-017-9834-0, 2017) shed light on the impact neoliberalism has on the teaching of science and suggest ways to ensure that science education remains critical and socially equitable. In this paper, I illustrate how their proposals influenced my instructional choices during the fall of 2016 in a course entitled Epistemology and Education.     

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.     

The Use of Journal Clubs in Science Teacher Education

This qualitative study explored how in a 7-month-long journal club pre- and inservice science teachers engaged with education research literature relevant to their practice to reduce the theory–practice gap. In the journal club they had the opportunity to critique and analyze peer-reviewed science education articles in the context of their classroom practice. Data sources included audio recordings of the meetings; semi-structured pre- and post-interviews of the teachers; focus groups; and artifacts (e.g., journal articles, reflective paper, email exchanges, and researcher’s field notes). Data were analyzed using the techniques of grounded theory (Corbin & Strauss in Basics of qualitative research, 3rd ed. Sage, Thousand Oaks, 2008). In addition we used some preconceived categories that we created from existing literature on journal clubs and communities of practice (Newswander & Borrego in European Journal of Engineering Education 34(6): 561–571, 2009; Wenger in Communities of practice: learning, meaning, and identity. Cambridge University Press, Cambridge, 1998) and from our previous research (Tallman & Feldman, 2012). We found that the journal club incorporated the three characteristics of a community of practice (Wenger in Communities of practice: learning, meaning, and identity. Cambridge University Press, Cambridge, 1998) into its functioning (mutual engagement, joint enterprise, and shared repertoire). The teachers mutually engaged around the joint enterprise of reading, critiquing, and understanding the research studies with the goal of improving practice. The teachers also asked each other analytical questions, which became a shared repertoire of the journal club. They reflected on their practice by presenting, reading, and discussing the articles, which helped them to determine whether and how the findings from the articles could be incorporated into their teaching practice. In doing so, they learned the skills needed to critique the research literature in relation to their practice as classroom teachers.     

The Piagetian <Emphasis Type="Italic">Schème</Emphasis>: a Framework to Study Professional Learning Through Conceptualization

Different theories of learning have been used in vocational education studies and Piaget is a common source of reference. Our intent is to present a specific and original way in which the Piagetian theory of schèmes has been developed since the 1990s in studies called “vocational didactics”. Developed in French-speaking countries and mostly unknown to an international audience, this approach offers a specific use of Jean Piaget’s theory of learning, which has been applied to adult learning and vocational education. We will first develop the theoretical foundation of the theory of schèmes as developed by Vergnaud (1989, Recherches en didactique des mathématiques, 10(2–3), 133–170, 1990, 1996, 2001) and others after Piaget (1947). Then, we will present the methodological perspective of this approach. We will finally present significant research results to illustrate outcomes and practical implications for vocational training.     

A bit of both science and economics: a non-traditional STEM identity narrative

Black males, as one non-dominant population, remain underrepresented and less successful in science, technology, engineering, and mathematics (STEM). Researchers focused on non-dominant populations are advised against generalizations and to examine cultural intersections (i.e. race, ethnicity, gender, and more) and also to explore cases of success, in addition to cases of under-achievement and underrepresentation. This study has focused on one African American male, Randy, who expressed high-achieving STEM career goals in computer science and engineering. Furthermore, recognizing that culture and identity development underlie STEM engagement and persistence, this long-term case study focused on how Randy developed a STEM identity during the course of the study and the implications of that process for his STEM career exploration. Étienne Wenger’s (1999) communities-of-practice (CoP) was employed as a theoretical framework and, in doing so, (1) the informal STEM program in which Randy participated was characterized as a STEM-for-social-justice CoP and (2) Randy participated in ways that consistently utilized an “economics” lens from beyond the boundaries of the CoP. In doing so, Randy functioned as a broker within the CoP and developed a non-traditional STEM identity-in-practice which integrated STEM, “economics”, and community engagement. Randy’s STEM identity-in-practice is discussed in terms of the contextual factors that support scientific identity development (Hazari et al. in J Res Sci Teach 47:978–1003, 2010), the importance of recognizing and supporting the development of holistic and non-traditional STEM identities, especially for diverse populations in STEM, and the implications of this new understanding of Randy’s STEM identity for his long-term STEM career exploration.     

“But The Soldier’s Remains Were Gone”: Thought Experiments in Children’s Literature

In this article thought experiments are uncovered as key stimuli of philosophical potential in children’s literature and their presentation and function is examined in a selection of focal texts, including: Lewis Carroll’s Alice’s Adventures in Wonderland (1865) and Through the Looking-Glass (1871); Even the Parrot by Dorothy Sayers (1944); Nina Bawden’s Carrie’s War (1974); and A Game of Soldiers (1985) by Jan Needle. The thought experiment is a device common to science and philosophy and has been recognised as an heuristic tool in literature generally, but here children’s literature is drawn into the conversation, revealing that—as a dynamic mechanism of children’s narrative—thought experiments have a long-standing and particular role to play in books for young people. This paper connects with a recent turn in children’s literature discourse toward the conditions of power in books for young readers; it moves on the debate by demonstrating that the apparatus of thought experimentation places the implied child reader in a position of philosophical responsibility and forward thinking. Presenting thought experiments in different ways, formal properties of the thought experiment—such as conversational mode, double engagement and modal positioning—are identified and shown to open up a philosophical space of subsequence in children’s texts.     

Enhancing Clients’ Perspectives and the Therapeutic Process by Expanding Our View of Cultural Wealth

This article addresses the use of cultural capital to influence therapeutic practices with culturally diverse clients. Using cultural wealth from a Critical Race Theory perspective (Yosso in Race Ethnicity and Education, 8(1), 69–91, 2005) highlights unacknowledged forms of cultural capital of diverse groups. Utilizing this perspective impacts counsellors’ positioning within the therapeutic relationship, shapes the discourse within therapy, and can enhance clients’ autonomous motivation within the therapeutic process. This article builds upon Yosso’s (Race Ethnicity and Education, 8(1), 69–91, 2005) forms of cultural wealth by situating them within a therapeutic context.     

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.     

The reintegration of Tongan postgraduate scholars after study abroad: knowledge utilisation and resituation

Higher education has seen increasing educational mobility as students finance themselves or get financial support from their families to study abroad (Shields Comp Educ Rev 57(4):609–636, 2013; Verbik and Lazanowski in World education news and reviews. http://www.wes.org/educators/pdf/StudentMobility.pdf, 2007). Another significant source of support, particularly for students in developing countries, is that from international aid scholarships. This research presents the reported experiences of 15 Tongan postgraduate scholars who successfully completed overseas postgraduate studies. The study focuses on the perceptions of qualifications and of scholars, as well as knowledge utilisation and knowledge resituation in and beyond the workplace. Knowledge utilisation, sometimes referred to as knowledge management, is how others support returnees’ to share and make use of their knowledge; while knowledge resituation is a personal and individual process in which knowledge gained in one context is tuned to and made use of in a new context (Eraut in Expertise development: the transition between school and work. Open Universiteit, Heerlen, pp 52–73, 2004a, Pedagogy and practice. Culture and identities. Sage, London, 2008; Franken 2012). Given the challenges the scholars faced, we advocate for a more explicit recognition of what knowledge and skills returning scholars bring home, and a more proactive and strategic use of these by their workplaces in particular.     

Individual and Institutional Productivity in Educational Psychology Journals from 2009 to 2014

This article examines the productivity of both individuals and institutions, indexed through an examination of five educational psychology journals (Cognition and Instruction, Contemporary Educational Psychology, Educational Psychologist, Educational Psychology Review, and Journal of Educational Psychology) from 2009 to 2014. These results are discussed relative to four previous studies (Hsieh et al. Contemporary Educational Psychology, 29, 333–343, 2004; Jones et al. Contemporary Educational Psychology, 35, 11–16, 2010; Smith et al. Contemporary Educational Psychology, 23, 173–181, 1998; Contemporary Educational Psychology, 28, 422–430, 2003). Vanderbilt University and Fred Paas replaced the University of Maryland and Richard E. Mayer as the top research institution and author, respectively. Sixteen of the top 19 researchers’ institutions were outside the USA, compared to only 10 of the top 32 during 2003–2008 and three of the top 20 during 1991–1996. Educational psychology research continues the trend of becoming more international.     

Secondary-to-tertiary comparison through the lens of ways of doing mathematics in relation to functions: a study in collaboration with teachers

This article addresses the issue of transition from secondary to post-secondary education through collaborative research with teachers from both levels. It takes into account implicit elements in this transition. Research on the transition in mathematics education tends to focus more on the tertiary level, studying difficulties encountered by students or comparing curricula, tasks, and textbooks highlighting disruptions or cultural shifts. However, according to Hall (1959), and Artigue (2004) in a mathematical context, it is the implicit “ways of doing” that lead to the greatest cultural differences. In this article, attention is paid to the particular ways in which teachers’ ways of doing mathematics impact the transition. Ethnomethodology (Garfinkel, 1967) and its central concept of ethnomethods are used as the theoretical framework to conceptualize these ways of doing mathematics. A breaching situation presented to a group of secondary- and tertiary-level teachers engaged in collaborative research (Desgagné et al., 2001) brings to light familiar ways of doing mathematics. Our analysis focuses specifically on a comparison of the ways of doing mathematics related to functions at each level.     

Vehicles of Logics: The role of policy documents and instructional materials in reform

To understand the complexities of education policy implementation, it is necessary to consider how artifacts associated with reform are imbued with ideas, meanings, and values. This empirical paper draws on neo-institutional theory to reveal how artifacts carried particular logics (D’Adderio in J Inst Econ 7(2):197–230, 2011; Feldman and Pentland in Adm Sci Q 48:94–118, 2003; Pentland & Feldman in Ind Corporate Change 14(5):793–815, 2005; in: Scott, Institutions and organizations, Sage Publications, Thousand Oaks, 2001). This paper argues that two types of artifacts, policy documents, and instructional materials, carried logics of reading instruction, thereby playing a role in the implementation of this reform. This paper draws on qualitative data collected over a 13-month period in order to advance our understanding of the relationship between institutional logics, policy, and practice. The findings from this paper have implications for district and school reform, as well as for policymakers and non-system actors.     

Female Participation as Top-Producing Authors,Editors, and Editorial Board Members in Educational Psychology Journals from 2009 to 2016

This article examines top-producing female authors, editors, and editorial board members in five educational psychology journals (i.e., Cognition and Instruction, Contemporary Educational Psychology, Educational Psychologist, Educational Psychology Review, and Journal of Educational Psychology) from 2009 to 2016. Results extend data from four previous studies (Evans et al. Educational Psychology Review, 17(3), 263–271, 2005; Fong et al. Educational Psychology Review, 21(3), 267–277, 2009; Greenbaum et al. Educational Psychology Review, 28, 215–223, 2016; Robinson et al. Contemporary Educational Psychology, 23, 331–343, 1998) and also compare top female authors to the top male authors. The top-producing women in the field have, on average, less seniority in the field than do top male authors. Male authors have more publications, on average, and more sole authorships and first authorships, as compared to female authors. No discernible progress has been made by women in terms of editorial board memberships or editorships since 2004.     

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.     

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.