Mathématiques de la vie quotidienne au Burkina Faso: une analyse de la pratique sociale de comptage et de vente de mangues

Mathematics teaching in Burkina Faso is faced with major challenges (high illiteracy rates, students’ difficulties, and high failure rates in mathematics, which is a central topic in the curriculum). As evidenced in many of these studies, mathematics is reputed to be tough, inaccessible, and far from what students live daily. Students here look as though they are living in two seemingly distant worlds, school and everyday life. In order to better understand these difficulties and to contribute in the long run to a more adapted teaching of mathematics, we tried to document and elicit the “mathematical resources” mobilized in various daily life social practices. In this paper, we focus on one of them, the counting and selling of mangoes by unschooled peasants. An ethnographic approach draws on the observation of the situated activity of counting and selling mangoes (during harvesting) and on “eliciting interviews” of the involved actors. The analysis of results highlights a richness of structuring resources mobilized and distributed through this practice, related to what Lave (1988) call “the experienced lived-in-world” and “constitutive order.” The mathematical resources take the form of “knowledge in action” and “theorems in action” (Vergnaud, Rech Didact Math 10(23):133–170, 1990), embedded in the social, economic, and even cultural structures of actors.     

Emerging beliefs frustrate ecological literacy and meaning-making for students

In their treatise, Mitchell and Mueller extend David Orr’s notions of ecological literacy (2005) to include biophilia (Wilson 1984) and ecojustice (Mueller 2009). In his writings, David Orr claims that the US is in an “ecological crisis” and that this stems from a crisis of education. The authors outline Orr’s theory of ecological literacy as a lens to understand Earth’s ecology in view of long-term survival. In their philosophical analysis of Orr’s theory, Mitchell and Mueller argue that we move beyond the “shock doctrine” perspective of environmental crisis. By extending Orr’s concept of ecological literacy to include biophilia and ecojustice, and by recognizing the importance of experience-in-learning, the authors envision science education as a means to incorporate values and morals within a sustainable ideology of educational reform. Through this forum, I reflect on the doxastic logic and certain moral and social epistemological concepts that may subsequently impact student understanding of ecojustice, biophilia, and moral education. In addition, I assert the need to examine myriad complexities of assisting learners to become ecologically literate at the conceptual and procedural level (Bybee in Achieving scientific literacy: from purposes to practices, Heinemann Educational Books, Portsmouth, 1997), including what Kegan (In over our heads: the mental demands of modern life, Harvard University Press, Cambridge, 1994) refers to as “Third Order” and “Fourth Order” thinking: notions of meaning-construction or meaning-organizational capacity to understand good stewardship of the Earth’s environment. Learners who are still in the process of developing reflective and metacognitive skills “cannot have internal conversation about what is actual versus what is possible, because no ‘self’ is yet organized that can put these two categories together” (p. 34). Mitchell and Mueller indicate that middle school learners should undergo a transformation in order to reflect critically about the environment with a view toward determining critical truths about the world. However, if this audience lacks “selective, interpretive, executive, construing capacities” (Kegan in In over our heads: The mental demands of modern life, 1994, p. 29), assimilating the notions of ecojustice and biophia may be problematic.     

Expression of self-concept and adjustment against repeated aggressions: the case of a longitudinal study on school bullying

Bullying between students in the school setting is an increasing problem. Bullying can be defined as any form of repeated mental or physical violence carried out by one or several individuals on a person who is not capable of defending himself (Roland and Idsoe, Aggress Behav 27:446–462, 2001). The aim of this paper is to observe the expression of self-concept and adjustment strategies developed by children subject to this kind of violence. Five hundred twenty-four students between the ages of 8 and 12 (m = 9.44) participated in the longitudinal study. Two measurements were made during the same school year at an interval of 6 months. The results show that the student victims of bullying present weaker self-conceptions than the control group. Recourse to avoidance strategies would be dominant among student victims of bullying. Moreover, recourse to “avoidance” type strategies would lead to an increase in the frequency of bullying while recourse to “approach”-type strategies would lead to a reduction in it. Furthermore, it would seem that recourse to avoidance strategies at T1 lowers the student’s self-concepts at T2. The opposite effect is observed with the approach strategies. These different results emphasize the necessity to establish prevention programs which allow an intervention simultaneously on the level of the school, the family, and the student.     

Students’ Socio-Scientific Reasoning in an Astrobiological Context During Work with a Digital Learning Environment

In a European project—CoReflect—researchers in seven countries are developing, implementing and evaluating teaching sequences using a web-based platform (STOCHASMOS). The interactive web-based inquiry materials support collaborative and reflective work. The learning environments will be iteratively tested and refined, during different phases of the project. All learning environments are focusing “socio-scientific issues”. In this article we report from the pilot implementation of the Swedish learning environment which has an Astrobiology context. The socio-scientific driving questions are “Should we look for, and try to contact, extraterrestrial life?”, and “Should we transform Mars into a planet where humans can live in the future?” The students were in their last year of compulsory school (16 years old), and worked together in triads. We report from the groups’ decisions and the support used for their claims. On a group level a majority of the student groups in their final statements express reluctance towards both the search of extraterrestrial life and the terraforming of Mars. The support used by the students are reported and discussed. We also look more closely into the argumentation of one of the student groups. The results presented in this article, differ from earlier studies on students’ argumentation and decision making on socio-scientific issues (Aikenhead in Science education for everyday life. Evidence-based practice. Teachers College Press, New York, (2006) for an overview), in that they suggest that students do use science related arguments—both from “core” and “frontier” science—in their argumentation and decision making.     

Navigating Worlds of “Trouble and Woe and Worse” in Children’s Literature: An Exploration into the Double Text of Tony Kushner and Maurice Sendak’s Brundibar

In this article, the author explores the richly layered double text of Kushner and Sendak’s picturebook, Brundibar (2003)—the historical context of Brundibár as a Holocaust-era children’s operetta by Hans Krása and Adolf Hoffmeister, and the present day manifestation of Brundibar as a children’s picturebook. In order to contextualize the discussion of Kushner and Sendak’s text, Brundibar’s historical origins in Nazi-annexed Czechoslovakia and its transition to the stage in the Nazi “model” concentration camp, Terezín, is presented. An extensive semiotic analysis of Kushner and Sendak’s illustrations and text is also provided within the framework of what Kushner (The art of Maurice Sendak: 1980 to the present, 2003) terms “a world of trouble and woe and worse” (p. 210). Furthermore, the author discusses the development of Sendak’s Hitlerian Brundibar and the struggles that both Kushner and Sendak faced as they considered how to portray the story’s antagonist, given their somewhat differing conceptions of which difficult themes and topics children should be exposed to during childhood. To round out this discussion, the author explores pedagogical implications for teachers as they read difficult texts, particularly Holocaust texts, with children.     

“Street Love”: How Street Life Oriented U. S. Born African Men Frame Giving Back to One Another and the Local Community

This Participatory Action Research (PAR) project worked with four active street life oriented U. S. Born African men, to document how a community sample of street life oriented U. S. Born African men between the ages of 16–65, frame and use “street life” as a Site of Resiliency (Payne, Dissertation, 2005; Journal of Black Psychology 34(1):3–31, 2008). Qualitative data was collected in the form of 20 individual and two group interviews. These data reveal an inter-generational, conceptualization and use, of the term “street love” in street life oriented U. S. born African men. Also, these data reveal that notions of “street love” extend out a critique of community professionals (e.g., community researchers/interventionists, social workers, etc.) as being unable and unwilling to produce “real help” in the local community. Examples of street love, revealed in the study, include the men offering advice/counsel, money or “free turkeys” during Thanksgiving to one another as well as other members of the local community. Results support Payne’s (2005) three-dimension conceptualization of “street love”: (1) individual, (2) group and (3) communal level expressions of “street love”.

Street Smarts vs. Book Smarts: The Figured World of Smartness in the Lives of Marginalized, Urban Youth

How smartness is defined within schools contributes to low academic achievement by poor and racial/ethnic minority students. Using Holland et al.’s (1998) [Holland, D., Lachicotte, W., Skinner, D., & Cain, C. (Eds.) (1998). Identity and agency in cultural worlds. Cambridge, MA: Harvard University Press.] concept of “figured worlds,” this paper explores the “figuring” of smartness through the perspectives of marginalized youth. The youth made key distinctions between being book smart vs. street smart. This distinction is a direct challenge by the youth to the dominant discourse of smartness or “book smarts” as it operates in schools. To the youth, “street smarts” are more important because they are connected to being able to maneuver through structures in their lives such as poverty, the police, street culture, and abusive “others.” This distinction is key because street smarts stress agency in countering social structures whereas, for many of the youth, book smarts represented those structures, such as receiving a high school diploma. Implications for schools and pedagogy are discussed. B.A. earned from Indiana University – Bloomington, Masters and Ph.D. earned from University of North Carolina at Chapel Hill. Beth Hatt Fis an Assistant Professor of Educational Administration and Foundations at Illinois State University where she teaches research methods and social foundations of education. Her current research explores smartness as a cultural construct in schools and the media.     

Class, Identity, and Teacher Education

This paper explores the possibilities of working with White, working-class teacher education students to explore the “complex social trajectory” (Reay in Women’s Stud Int Forum 20(2):225–233, 1997a, p. 19) of class border crossing as they progress through college. Through analysis of a course that I have developed, Education and the American Dream, I explore political and pedagogical issues in teaching the thousands of teacher education students who are the first in their families to attend college about social class. Arguing that faculty in teacher education too often disregard the significance of deep class differences between themselves and many of their students, I propose that teacher education include coursework in which upwardly-mobile students (a) draw upon their distinctive perspectives as class border-crossers to elucidate their “complex social positioning as a complicated amalgam of current privilege interlaced with historic disadvantage” (Reay in Women’s Stud Int Forum 20(2):225–233, 1997a, p. 25) and (b) complicate what Adair and Dahlberg (Pedagogy 1:173–175, 2001, p. 174) have termed a cultural “impulse to frame class mobility as a narrative of moral progress”. Such coursework, I suggest, has implications for the development of teacher leaders in stratified schools. The paper draws upon the literatures on social class and educational attainment, on the construction of classed identities in spite of silence about class in public and academic discourse, and on pedagogies for teaching across class differences.     

From Another Perspective—training teachers to cope with problematic learning situations in geometry

“From Another Perspective” is a year-long course for teachers of mathematics that is designed to enhance teachers’ awareness of the way that their students think when they are experiencing difficulties in geometry. It also aims at equipping teachers with tools needed to analyze and cope with Problematic Learning Situations in geometry (Gal & Linchevski, 2000). This paper reviews the rationale, content, and approach of the course, which is characterized as “the Back and Forth model”. It then reports on a study that tracked the changes that course participants (pre- and in-service mathematics teachers) passed through. The paper describes the results of the case study of Eti, one of the participants, who taught mathematics to junior high school students. The findings suggest that Eti was helped to achieving the goals of: (1) expanding and deepening her understanding of students’ ways of thinking; (2) increasing her awareness of her students’ processes of thinking in order to identify their difficulties; (3) equipping her with appropriate tools to analyze and cope with such difficulties; and (4) enhancing her ability to retrieve and utilize this knowledge while making instructional decisions. Conclusions and open questions for further study are drawn.     

Facilitating Preschoolers’ Scientific Knowledge Construction via Computer Games Regarding Light and Shadow: The Effect of the Prediction-Observation-Explanation (POE) Strategy

Educational researchers have suggested that computer games have a profound influence on students’ motivation, knowledge construction, and learning performance, but little empirical research has targeted preschoolers. Thus, the purpose of the present study was to investigate the effects of implementing a computer game that integrates the prediction-observation-explanation (POE) strategy (White and Gunstone in Probing understanding. Routledge, New York, 1992) on facilitating preschoolers’ acquisition of scientific concepts regarding light and shadow. The children’s alternative conceptions were explored as well. Fifty participants were randomly assigned into either an experimental group that played a computer game integrating the POE model or a control group that played a non-POE computer game. By assessing the students’ conceptual understanding through interviews, this study revealed that the students in the experimental group significantly outperformed their counterparts in the concepts regarding “shadow formation in daylight” and “shadow orientation.” However, children in both groups, after playing the games, still expressed some alternative conceptions such as “Shadows always appear behind a person” and “Shadows should be on the same side as the sun.”     

On pigs and packers: Radically contextualizing a practice of science with Mexican immigrant students

This paper reports on instructional practices observed in a high school English Learner (EL) Science course serving newcomer Mexican immigrant youth. The school is located in a rural Midwestern meatpacking community in which labor at the hog plant is economically- and racially-segmented; it is the town’s Mexican residents, many of them undocumented, who comprise most of the unskilled labor force. The general purpose of the paper is to document how the economic and racial context of this community influences science instruction in the EL Science course and to describe how this presents particular challenges in achieving equitable science instruction for Mexican immigrant youth in these rural, globalizing places. Entering the data via critical discourse analysis (Fairclough, 1995) and then utilizing Barton’s (2003) “practice of science” perspective, with an eye toward achieving “radical contextuality” (Grossberg, 1997), we describe the science events, identities, and structures of the pig dissection lesson and detail how what these students could do with science, as rendered by that lesson, was limited by the roles the teacher attributed to the students, her inability to draw on their funds of knowledge as resources for learning, and the voice and position she allowed them to take up. The data reinforce conventional understandings of schools as sites of cultural reproduction (Bowels & Gintis, 1976), as well as of resistance (Giroux, 1983), but afford us a glimpse of the particularity of those mechanisms within the demographically-transitioning American Heartland, iconic of the era of global capitalism.

Why Compulsory Science Education Should <Emphasis Type="Italic">Not</Emphasis> Include Philosophy of Science

Like many readers of this journal, I have long been an advocate of having science students introduced to philosophy of science. In particular, influenced by the Philosophy for Children movement founded by Matthew Lipman, I have advocated such an introduction as early as possible and have championed early secondary school as an appropriate place. Further, mainstream science curricula in a number of countries have, for some time now, supported such introductions (albeit of a more limited sort) under the banner of introducing students to the “Nature of Science”. In this paper, I explore a case against such introductions, partly in role as “Devil’s Advocate” and partly exploring genuine qualms that have come to disturb me. Generally speaking, my judgement is that no justification is available in terms of benefit to the individual or to society of sufficient weight to outweigh the loss of freedom of choice involved in such forced learning. One possible exception is a minimalist and intellectually passive “Nature of Science” introduction to some uncontroversial philosophical views about science. An earlier version of this paper was presented to the Seventh International Conference on the History and Philosophy of Science and Science Teaching, University of Winnipeg, Winnipeg and subsequently published in its proceedings (see my 2003). I am grateful to those who engaged in discussion of the paper upon its presentation. I am also grateful to the advice of this journal’s anonymous referees.     

Reading pedagogy, “Evidence” and education policy: learning from history?

This paper examines the report of the Inquiry into the Teaching of Literacy (Department of Education, Science & Training (DEST) 2005) and explores the claims it makes about reading pedagogy and the centrality of particular “methods” or “approaches” to teaching backed by “scientific” evidence. Discourse analysis of the report shows that its logics allow only certain kinds of evidence to count in policy, and that it reduces difficult social and political issues to questions of technique. This allows the report to recommend an approach whereby qualitative insights and practitioners’ experience can be bypassed through valorising methods developed and verified by scientific researchers. The report’s claims are considered genealogically in the light of historical cases from the early nineteenth century, where educational reformers struggled with the issue of how to educate the children of the poor. In one, the monitorial system promoted by Lancaster in England, there was a focus on reading which made teachers or monitors artefacts of a standardised method. By way of contrast, in Scotland, a classroom approach developed by Stow (1854) made the teacher central to the process, as someone who sensitively interpreted and extended students’ experiences with texts. Stow’s approach would form the model for the modern classroom in compulsory state schooling, while the monitorial system would eventually be abandoned as ineffective. The historical cases demonstrate the dangers of approaches to policy that fail to account for the complex interplay between teacher, student and text in the reading lesson.     

Student Flow Between Community Colleges: Investigating Lateral Transfer

The traditional unidirectional (“linear”) postsecondary path from high school to a community college to a 4-year institution into the workforce represents accurately a decreasing proportion of the pathways actually taken by students through higher education. Instead, students increasingly exhibit patterns of enrollment that take them through multiple postsecondary institutions, both within levels of the higher education system (e.g., multiple community colleges, multiple 4-year institutions) and across levels (e.g., movement back and forth between community colleges and 4-year institutions). These “swirling” patterns of enrollment are widely recognized by scholars of higher education, but they remain poorly understood. In this study, I employ data that address 89,057 first-time students in the California community college system to answer a number of key questions concerning lateral transfer between community colleges, which, according to prior research, constitutes one sizeable component of student “swirl”. Building on the very limited work on this topic, I examine whether the reported high prevalence of lateral transfer holds true under a more stringent operational framework than that employed in prior work. I explore whether lateral transfer is primarily an artifact of students enrolling simultaneously in multiple community colleges, sometimes called “double-dipping”. I investigate the timing of lateral transfer from several different perspectives to determine how lateral transfer fits in students’ progress and development. Finally, I probe the relationship between students’ level of academic investment in their current community college and the risk of lateral transfer.     

On Being College Prep: Examining the Implementation of a “College for All” Mission in an Urban Charter School

This article reports findings from a four-year case study of an urban college preparatory charter high school. Through analyses of teacher and staff interviews, the author highlights how the school approached the idea of “college for all” under the archetypal influence of “college preparatory.” The interview data show how the charter school staff engaged in important educational questions about what defines college preparation even though those questions became more complex as the school matured. These findings are presented in three themes: (1) building a school, which reflects staff members’ views on the school’s start-up period of building renovation and growth, (2) building a curriculum, which reflects staff members’ views on teachers’ instructional practices, and (3) building a college culture, which reflects staff members’ efforts to provide students with supplemental academic and social supports for college planning and preparation.     

ENACTED TYPES OF ALGEBRAIC ACTIVITY IN DIFFERENT CLASSES TAUGHT BY THE SAME TEACHER

The aim of this study was to examine how teachers enact the same written algebra curriculum materials in different classes. The study addresses this issue by comparing the types of algebraic activity (Kieran, 2004) enacted in two 7th grade classes taught by the same teacher, using the same textbook. Data sources include lesson observations and an interview with the teacher. The findings show that students in the two classes were offered somewhat different algebraic experiences. At one school, more emphasis was placed on global/meta-level activities (activities that are not exclusive to algebra and suggest general mathematical processes), whereas at the other school, more emphasis was placed on transformational activities (“rule-based” algebraic activities). Analysis of the sources of the differences related to the ways in which the teacher used and enacted the curriculum materials in the two classes revealed that these were linked to the teacher’s attempts to be attentive to the students in the class and to the nature of the students’ work.     

Productive failure in mathematical problem solving

This paper reports on a quasi-experimental study comparing a “productive failure” instructional design (Kapur in Cognition and Instruction 26(3):379–424, 2008) with a traditional “lecture and practice” instructional design for a 2-week curricular unit on rate and speed. Seventy-five, 7th-grade mathematics students from a mainstream secondary school in Singapore participated in the study. Students experienced either a traditional lecture and practice teaching cycle or a productive failure cycle, where they solved complex problems in small groups without the provision of any support or scaffolds up until a consolidation lecture by their teacher during the last lesson for the unit. Findings suggest that students from the productive failure condition produced a diversity of linked problem representations and methods for solving the problems but were ultimately unsuccessful in their efforts, be it in groups or individually. Expectedly, they reported low confidence in their solutions. Despite seemingly failing in their collective and individual problem-solving efforts, students from the productive failure condition significantly outperformed their counterparts from the lecture and practice condition on both well-structured and higher-order application problems on the post-tests. After the post-test, they also demonstrated significantly better performance in using structured-response scaffolds to solve problems on relative speed—a higher-level concept not even covered during instruction. Findings and implications of productive failure for instructional design and future research are discussed.     

Social constructivism and the <Emphasis Type="Italic">Believing Game</Emphasis>: a mathematics teacher’s practice and its implications

The study reported here is the third in a series of research articles (Harkness, S. S., D’Ambrosio, B., & Morrone, A. S.,in Educational Studies in Mathematics 65:235–254, 2007; Morrone, A. S., Harkness, S. S., D’Ambrosio, B., & Caulfield, R. in Educational Studies in Mathematics 56:19–38, 2004) about the teaching practices of the same university professor and the mathematics course, Problem Solving, she taught for preservice elementary teachers. The preservice teachers in Problem Solving reported that they were motivated and that Sheila made learning goals salient. For the present study, additional data were collected and analyzed within a qualitative methodology and emergent conceptual framework, not within a motivation goal theory framework as in the two previous studies. This paper explores how Sheila’s “trying to believe,” rather than a focus on “doubting” (Elbow, P., Embracing contraries, Oxford University Press, New York, 1986), played out in her practice and the implications it had for both classroom conversations about mathematics and her own mathematical thinking.     

Lexical bundle analysis in mathematics classroom discourse: the significance of stance

In this article, we introduce the lexical bundle, defined by corpus linguists as a group of three or more words that frequently recur together, in a single group, in a particular register (Biber, Johansson, Leech, Conrad, & Finegan, 2006; Cortes, English for Specific Purposes 23:397–423, 2004). Attention to lexical bundles helps to explore hegemonic practices in mathematics classrooms because lexical bundles play an important role in structuring discourse and are often treated as “common sense” ways of interacting. We narrow our findings and discussion to a particular type of lexical bundle (called a “stance bundle” or bundles that relate to feelings, attitudes, value judgments, or assessments) because it was the most significant type found. Through comparing our corpus from secondary mathematics classrooms with two other corpora (one from university classrooms (not including mathematics classrooms) and one from conversations), we show that most of the stance bundles were particular to secondary mathematics classrooms. The stance bundles are interpreted through the lens of interpersonal positioning, drawing on ideas from systemic functional linguistics. We conclude by suggesting additional research that might be done, discussing limitations of this work, and pointing out that the findings warrant further attention to interpersonal positioning in mathematics classrooms.