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.     

“You can go to college”: Employing a Developmental Perspective to Examine How Young Men of Color Construct a College-Going Identity

This article examines college-going identity construction for Black, Latino, and Asian American and Pacific Islander high school students. The authors use Marcia’s (J Personal Soc Psychol 3(5):551–558, 1966; in: Delson (ed) Handbook of adolescent research, Wiley, New York, 1980) ego identity statuses perspective to examine how students develop their college-going identities to consider their post-high school pathways. We draw on focus groups interviews with 153 Black, Latino, and Asian American Pacific Islanders students enrolled in 10 urban and suburban high schools in California. The findings show the importance of being somebody, not quitting before establishing a career or graduating from college, joining the military as a pathway to finance postsecondary education, and the internal pressure to pay for higher education. The significance of this paper challenges the dominant narrative of young men of color not invested or interested in higher education, but highlight how the young men of color negotiate their agency in constructing their ideas and making decisions based on how various tensions and aspirations shape their goals after high school.     

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.     

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.     

“We’re Friends,We Have to be in This Together”: Examining the Role of Culturally Relevant Peer Interactions in Urban Youth’s College Readiness and Access

This paper analyzes how and why ten Black and Latina/o youth attending an urban public high school engage culturally relevant peer interactions (Knight and Marciano in College ready: preparing Black and Latina/o youth for higher education—a culturally relevant approach. Teachers College Press, New York, 2013) in preparing for, applying to, and/or enrolling in college. The study reconsiders culturally relevant pedagogy (Ladson-Billings in The dreamkeepers: successful teachers of African American children. Jossey-Bass, San Francisco, 1994) as an analytic tool for exploring youth’s culturally relevant peer interactions as supportive of their college-going processes (Tierney and Colyar in Preparing for college: nine elements of effective outreach. SUNY Press, Albany, 2005) and new media literacy practices (Ito et al. in Living and learning with new media: summary of findings from the Digital Youth Project. The MacArthur Foundation, Chicago, 2008. http://www.macfound.org/media/article_pdfs/DML_ETHNOG_WHITEPAPER.PDF). Research findings include: new understandings of the reciprocal nature of youth’s culturally relevant peer interactions; and new enactments of youth’s college-going new media literacy practices. Recommendations for educational policy, practice, and research supportive of students’ college readiness and access are discussed.     

Supporting Students’ Learning and Socioscientific Reasoning About Climate Change—the Effect of Computer-Based Concept Mapping Scaffolds

Climate change is one of the most challenging problems facing today’s global society (e.g., IPCC 2013). While climate change is a widely covered topic in the media, and abundant information is made available through the internet, the causes and consequences of climate change in its full complexity are difficult for individuals, especially non-scientists, to grasp. Science education is a field which can play a crucial role in fostering meaningful education of students to become climate literate citizens (e.g., NOAA 2009; Schreiner et al., 41, 3–50, 2005). If students are, at some point, to participate in societal discussions about the sustainable development of our planet, their learning with respect to such issues needs to be supported. This includes the ability to think critically, to cope with complex scientific evidence, which is often subject to ongoing inquiry, and to reach informed decisions on the basis of factual information as well as values-based considerations. The study presented in this paper focused on efforts to advance students in (1) their conceptual understanding about climate change and (2) their socioscientific reasoning and decision making regarding socioscientific issues in general. Although there is evidence that “knowledge” does not guarantee pro-environmental behavior (e.g. Schreiner et al., 41, 3–50, 2005; Skamp et al., 97(2), 191–217, 2013), conceptual, interdisciplinary understanding of climate change is an important prerequisite to change individuals’ attitudes towards climate change and thus to eventually foster climate literate citizens (e.g., Clark et al. 2013). In order to foster conceptual understanding and socioscientific reasoning, a computer-based learning environment with an embedded concept mapping tool was utilized to support senior high school students’ learning about climate change and possible solution strategies. The evaluation of the effect of different concept mapping scaffolds focused on the quality of student-generated concept maps, as well as on students’ test performance with respect to conceptual knowledge as well as socioscientific reasoning and socioscientific decision making.     

Morphological awareness and reading in second and fifth grade: evidence from Hebrew

Research suggests that morphological awareness facilitates word decoding, improves lexical knowledge, and helps reading comprehension (Carlisle, 2010; Nagy et al., 2014; Verhoeven & Perfetti, 2011). The present study examined the relationship among morphological awareness, word recognition and reading comprehension in 153 second- and fifth-grade Hebrew speakers at an elementary school in Israel. Students were given morphological awareness tests and tests for word recognition and reading comprehension. Three types of morphological awareness were analyzed: inflection, derivation and construct formation. Overall, students with low morphological awareness in derivation and construct formation showed relatively poor achievement in word recognition and comprehension. All three types were found to correlate with reading comprehension in readers with high morphological awareness. These readers also exhibited good reading skills. The results are discussed with regard to the special characteristics of Hebrew morphology and reading process, which aid morphological decomposition.     

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.     

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.     

Examining the structure of vocational interests in Turkey in the context of the personal globe model

The structural validity of the Personal Globe Inventory-Short (PGI-S: Tracey in J Vocat Behavi 76:1–15, 2010) was examined in a Turkish sample of high school and university students. The PGI-S measures eight basic interest scales, Holland’s (Making vocational choice, Prentice-Hall, Englewood Cliffs, 1997) six types, Prediger’s (J Vocat Behav 21:259–287, 1981) people/things, data/ideas dimensions, and prestige. After adapting the original PGI-S items into Turkish (PGI-S-T), the inventory was administered to high school students (N = 605) and university students (N = 359). The fit of Holland’s RIASEC and the PGI eight type model were examined separately using the randomization test of hypothesized order relations. Results indicated a strong fit for both the eight type and the RIASEC model. Expected significant differences were found between PGI-S-T subscales across gender and age. The results support the structural validity of the adapted PGI-S-T in a Turkish sample.     

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.     

A Qualitative Study of the Experiences of Counseling Students Who Participate in Mindfulness-Based Activities in a Counseling Theory and Practice Course

This study explored the lived experiences of two cohorts of counselors in training (CITs) who experienced mindfulness-based activities in a counseling theory and practice course. Utilizing Merriam’s Interpretive Qualitative Approach (Merriam 1988, 2002), the data suggested that students perceived the activities to have enhanced their experiences as students and development as counselors. Implications for improving counselor preparation are considered.     

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.     

Increasing the Depth of Field: Critical Race Theory and Photovoice as Counter Storytelling Praxis

Thru the Lenz was a youth participatory action project in which a group of urban high school students explored their lives and communities through art, photography, and narrative. Drawing on data from Thru the Lenz, I deploy CRT to reimagine the research space as a place for counter storytelling. Majoritarian stories are stories that invoke and perpetuate white privilege, are based on racist ideology, are pervasive and are told by whites as well as people of color (Solórzano and Yosso in Qual Inq 8:23–44, 2002a). Counter stories are a method and a tool that enable a deeper understanding of the stories the youth co-constructed though their photos and narratives and also challenge the majoritarian stories told about them, their school, and community (Solórzano and Yosso in Qual Inq 8:23–44, 2002a). Specifically, I present the research praxis organized in the form of an emerging counter story based on two key themes: good community and successful school. When constructed using a CRT framework, the students’ stories about their educational experiences provide a strong critique of neoliberal education reform. I conclude with a discussion of the tensions and challenges of engaging in counter story as critical, emancipatory praxis that elucidates the linkages of personal experiences and macro policies (Stovall in Race Ethn Educ 9:243–259, 2006).     

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.     

Achieving excellence: Bringing effective literacy pedagogy to scale in Ontario’s publicly-funded education system

This paper offers an insiders’ perspective on the large-scale, system-wide educational change undertaken in Ontario, Canada from 2003 to the present. The authors, Ministry and school system leaders intimately involved in this change process, explore how Ontario has come to be internationally recognized as an equitable, high-achieving, and continuously improving jurisdiction (Brochu et al. in Second report from the 2009 programme for international student assessment. Council of Ministers of Education, Canada, Toronto, 2011; Mourshed et al. in How the world’s most improved school systems keep getting better. McKinsey & Company, New York, 2010; OECD in Strong performers and successful reformers in education: lessons from PISA for the United States. OECD, Paris, 2010). The narrative of improvement in Ontario presented here was developed out of systematic interviews with Ministry and School Board leaders’ experiences of the literacy improvement strategy, and informed by document and data analyses. It addresses the historical and political context of Ontario’s change efforts, the shifting understanding of teaching and learning in the province, the essential respect for the professionalism of educators, the structures that facilitated the change, and concludes with key characterizations of the present culture of education in Ontario. While the paper focuses on the elementary literacy strategy, its wider objective is to outline the collaborative approach to shifting pedagogical practice that has opened the ceiling for what a public education system is capable of achieving by fostering local ownership of change while raising the floor by setting high standards for literacy achievement for all students.     

What do second-order judgments tell us about low-performing students’ metacognitive awareness?

According to the unskilled and unaware effect (Kruger and Dunning 1999), low-performing students tend to overestimate their performance. Differentiating the assessment of metacognitive judgments into performance judgments (PJs) and second-order judgments (SOJs), PJs of low-performing students tend to be inflated, while their SOJs are usually lower than those of high-performing students (Händel and Fritzsche 2016; Miller and Geraci 2011). This suggests some level of awareness. The present study investigated whether low-performers’ lower SOJs actually indicate metacognitive awareness. We studied SOJs after adequate and inadequate PJs, and investigated whether low-performers’ lower SOJs are made by default or whether their lower SOJs differ in a similar magnitude compared to those of high-performers (indicating metacognitive awareness). We address this issue by disentangling student and item effects via generalized linear mixed models. Reanalyzing the data of Händel and Fritzsche (2016) from N?=?116 students, we found that SOJs depended on the students who provided the SOJ and on the items on which the SOJ was made. Overall, SOJs depended on the PJs and on the interaction of performance and PJs, but not on the performance itself. Separate analyses for students of different performance levels revealed that low-performing students showed less awareness, indicated by a non-significant interaction effect of performance and PJs. Thus, it takes mixed models to tell the whole story of low-performing students’ lower SOJs.     

Student perception of assessment practices: towards ‘no loser’ classrooms for all students in the ethnic minority schools in Hong Kong

As part of a wide-scale education reform, Hong Kong schools have been focusing on the creation of ‘no loser’ classrooms that support learning for all students (Education Commission 2000). This article examined both groups of ethnic minority and Chinese students’ perception of assessment practices and the extent to which classroom practice is consistent with preferred assessment practices. The 11 items of assessment practices list, developed by Brown et al. (2009a), were used to investigate the perceptions of 1,518 student respondents from 15 primary and secondary schools, in which a large number of ethnic minority students were accommodated. A confirmatory factor analysis showed that the respondents in the group from secondary schools viewed teacher-dominated assessment as the most important assessment practice in the model examined (Brown et al. Learning and Instruction, 19(2), 97–111, 2009b) whereas those in the primary group considered teacher-student interactive assessment as the most important practice. Also, three perceptions of assessment practices of ethnic minority students were confirmed: teacher-dominated, student-centred and teacher-student interactive. Amongst them, the most preferred one was the teacher-student interaction assessment practice. Finally, the implications of the creation of a no loser classroom for all students are discussed.     

Cross-Cultural Validation of Four Positive Psychology Assessments for Use with a Ghanaian Population

This study reports the evaluation of four positive psychology assessments for use in clinical, education, and research settings with individuals in Ghana, Africa. The analyses attempted to identify validity evidence for internal structure and relationships with related variables for the Satisfaction with Life Scale (SLS; Diener et al. Journal of Personality Assessment, 49, 71–75, 1985), General Mattering Scale (GMS; Marcus 1991), Short Grit Scale (GS; Duckworth and Quinn Journal of Personality Assessment, 9, 166–174, 2009), and Brief Resilience Scale (BRS; Smith et al. International Journal of Behavioral Medicine, 15, 194–200, 2008). The data yielded from 657 Ghanaian participants indicated factor structures ranging from a strong model fit (SLS and GMS) to an acceptable fit following modifications to factor structure (GS and BRS), while evidence based on relationships to related variables was convincing. Implications for use of these assessments and for future research are discussed.