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Identity, agency, and knowing in mathematics worlds

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... Small-scale studies have found positive student perceptions towards active learningoriented mathematics programs, at least in comparison to more traditional ones, in both K-12 and collegiate settings. Students transitioning from lecture-based to active learning-oriented mathematics classrooms have reported valuing their active engagement (Boaler & Greeno, 2000;Holt et al., 2001;Love et al., 2015), which they believe keeps them focused and helps them remember course material better than in a traditional lecture course (Love et al., 2015). Students have also described appreciating a more democratic classroom environment (Holt et al., 2001) and opportunities to collaborate with peers (Boaler & Greeno, 2000;Holt et al., 2001;Love et June 2022| 77 al., 2015, which they perceive as offering access to others' reasoning and collective, conceptual understanding (Boaler & Greeno, 2000). ...
... Students transitioning from lecture-based to active learning-oriented mathematics classrooms have reported valuing their active engagement (Boaler & Greeno, 2000;Holt et al., 2001;Love et al., 2015), which they believe keeps them focused and helps them remember course material better than in a traditional lecture course (Love et al., 2015). Students have also described appreciating a more democratic classroom environment (Holt et al., 2001) and opportunities to collaborate with peers (Boaler & Greeno, 2000;Holt et al., 2001;Love et June 2022| 77 al., 2015, which they perceive as offering access to others' reasoning and collective, conceptual understanding (Boaler & Greeno, 2000). For students who had a prior history of disliking and/or feeling unsuccessful in mathematics, an active learning-oriented classroom was a welcome change (Holt et al., 2001). ...
... Students transitioning from lecture-based to active learning-oriented mathematics classrooms have reported valuing their active engagement (Boaler & Greeno, 2000;Holt et al., 2001;Love et al., 2015), which they believe keeps them focused and helps them remember course material better than in a traditional lecture course (Love et al., 2015). Students have also described appreciating a more democratic classroom environment (Holt et al., 2001) and opportunities to collaborate with peers (Boaler & Greeno, 2000;Holt et al., 2001;Love et June 2022| 77 al., 2015, which they perceive as offering access to others' reasoning and collective, conceptual understanding (Boaler & Greeno, 2000). For students who had a prior history of disliking and/or feeling unsuccessful in mathematics, an active learning-oriented classroom was a welcome change (Holt et al., 2001). ...
Article
Contents Developing Metacognition: Leveraging a Spiral Curriculum to Enhance Strategy-Learning Programming • Matthew Brooks, Educational Psychology A Thematic Analysis of Faculty Advice for Doctoral Students • Alexa Yunes-Koch, Katie Johnson, Teaching, Learning, and Teacher Education Emotional and Attentional Regulation: Impact of Trauma and Journal Writing • Jody-Ann Coore, Educational Psychology From Active Learning Trigonometry to Lecture-Oriented Calculus: Student Interactions • Kelsey Quaisley, Teaching, Learning, and Teacher Education Maximizing Student Citizenship Education • Consuelo Gallardo, Teaching, Learning, and Teacher Education Masked or Unmasked? The Impact of Hidden Facial Expressions on Interpretations of Emotion • Justin Andersson, Educational Psychology, Lauren Thayer, Special Education and Communication Disorders Bridging Metacognition and Executive Function: Enhancing Metacognition Via Development of the Dorsolateral Prefrontal Cortex • Matthew Brooks, Educational Psychology
... Small-scale studies have found positive student perceptions towards active learningoriented mathematics programs, at least in comparison to more traditional ones, in both K-12 and collegiate settings. Students transitioning from lecture-based to active learning-oriented mathematics classrooms have reported valuing their active engagement (Boaler & Greeno, 2000;Holt et al., 2001;Love et al., 2015), which they believe keeps them focused and helps them remember course material better than in a traditional lecture course (Love et al., 2015). Students have also described appreciating a more democratic classroom environment (Holt et al., 2001) and opportunities to collaborate with peers (Boaler & Greeno, 2000;Holt et al., 2001;Love et June 2022| 77 al., 2015, which they perceive as offering access to others' reasoning and collective, conceptual understanding (Boaler & Greeno, 2000). ...
... Students transitioning from lecture-based to active learning-oriented mathematics classrooms have reported valuing their active engagement (Boaler & Greeno, 2000;Holt et al., 2001;Love et al., 2015), which they believe keeps them focused and helps them remember course material better than in a traditional lecture course (Love et al., 2015). Students have also described appreciating a more democratic classroom environment (Holt et al., 2001) and opportunities to collaborate with peers (Boaler & Greeno, 2000;Holt et al., 2001;Love et June 2022| 77 al., 2015, which they perceive as offering access to others' reasoning and collective, conceptual understanding (Boaler & Greeno, 2000). For students who had a prior history of disliking and/or feeling unsuccessful in mathematics, an active learning-oriented classroom was a welcome change (Holt et al., 2001). ...
... Students transitioning from lecture-based to active learning-oriented mathematics classrooms have reported valuing their active engagement (Boaler & Greeno, 2000;Holt et al., 2001;Love et al., 2015), which they believe keeps them focused and helps them remember course material better than in a traditional lecture course (Love et al., 2015). Students have also described appreciating a more democratic classroom environment (Holt et al., 2001) and opportunities to collaborate with peers (Boaler & Greeno, 2000;Holt et al., 2001;Love et June 2022| 77 al., 2015, which they perceive as offering access to others' reasoning and collective, conceptual understanding (Boaler & Greeno, 2000). For students who had a prior history of disliking and/or feeling unsuccessful in mathematics, an active learning-oriented classroom was a welcome change (Holt et al., 2001). ...
Article
Active learning is an important component in many college mathematics classes. However, not all college mathematics classes are being taught using active learning-oriented methods. This phenomenological study examined how four undergraduate students’ reflections on their recent experiences in a lecture-based Calculus I course compared to their reflections on their previous experiences in an active learning-oriented Trigonometry course. According to participants’ reflections, certain prescribed classroom structures, such as large classroom sizes, seemed to negatively affect student interactions with both instructors and peers in Calculus I lecture, especially their ability to ask questions. Whereas feeling comfortable to ask questions in either Trigonometry or Calculus I recitation was not always a given for all participants, all participants remarked that the collaborative, group work environment, usually in addition to their instructors, in both Trigonometry and Calculus I recitation were helpful, approachable, or beneficial. Given these students’ reflections, we emphasize the importance of establishing classrooms in which students are not only provided with opportunities to contribute their perspectives but feel that their perspectives are a welcome and important part of the classroom.
... In recent decades, inquiry-based, discussion-rich instruction has gained traction and popularity as an effective form of teaching mathematics (Boaler & Greeno, 2000;Munter et al., 2015;Schoenfeld, 2014). The premises of this type of instruction lie in constructivism -the Piagetian theory of learning as a process triggered by disequilibrium, whereby the learner needs to actively assimilate new information into existing mental schemes, or when the existing schemes are inappropriate, accommodate them to account for observed phenomena in the world (Perkins, 1999;Piaget, 1976). ...
... Along the pitfalls of meta-level shifts, growing evidence in the literature is pointing to the positive effects that agency-giving practices such as launch-explore-discuss, classroom discussions and problem solving can have on students' mathematical identities and motivation (Boaler & Greeno, 2000;Chen et al., 2020). Therefore, it seems reasonable that the instructional practices seen in this episode, which are highly similar to Accountable Talk teaching practices (Resnick et al., 2018) are conducive for building and maintaining students' positive and productive mathematical identities. ...
... More generally, the fact that identities -stable, repeatedly authored subjectifications -have an impact on the mathematics that gets discussed and learned by different students, has been corroborated by multiple studies (Boaler & Greeno, 2000;Boaler & Selling, 2017;Sfard & Prusak, 2005). Yet studies of identity and affect in mathematical learning often neglect the actual mathematical content being impacted by certain identities (Graven & Heyd-Metzuyanim, 2019). ...
Article
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Situations where students encounter mathematical "impasses" – instances where their current discourse is incommensurable with the discourse demanded to solve a task – have the potential to stir emotional responses of different types. They can engender feelings of confusion and bafflement, or even embarrassment, or alternatively open students' curiosity to the ways by which more advanced mathematics can solve a problem. In this study, we closely examine the subjectifications (affective communication) of a group of graduate students encountering such an impasse in the form of a request to account for the area and perimeter of the Sierpiński triangle. We analyze these subjectifications in relation to an a priori mathematical analysis of the impasse inherent in the task. We show two major types of subjectifications, found to be communicated by distinct members of the classroom: "I'm baffled", and "this is not a problem". We show how the students subjectifying "this is not a problem" were those who avoided engagement with the impasse by attending only to the infinite process that defines the fractal, while those students who subjectified "I'm baffled" were those who engaged with the process as well as its outcome. Moreover, despite the lack of substantial contribution to the exploration of the impasse by those students who subjectified "this is not a problem", they were positioned as the "explainers", in a position of power relative to those students who expressed bafflement. We conclude by discussing the dialectical relationship between identity and engagement with mathematical impasses.
... One is that which concerns the mathematical contentoften referred to as "conceptual understanding" (Hiebert & Carpenter, 1992;Hiebert & Grouws, 2007), "cognitive demand" (Boston & Smith, 2009; and "making connections" (Hiebert & Grouws, 2007;NCTM, 2000;Stein et al., 2008). The other aspect focuses on student activity during the lesson, envisioned as student participation and engagement in mathematics discussions (Esmonde & Langer-Osuna, 2013;Henningsen & Stein, 1997), student agency and authority (Boaler & Greeno, 2000;Langer-Osuna, 2018), or student accountability to the learning community (Michaels et al., 2008). These two aspects of teachingthe mathematical content and the way by which students engage with this contentare thus the main subjects being talked by teachers, teacher educators and researchers during their communication about reform types of teaching and learning mathematics. ...
... The launch is followed by individual and group work and finalized with a WCD where representatives of the groups share their solutions. This type of lesson structure, including opportunities for students to discuss their ideas in small groups and then with the whole class, promotes student agency and authority (Boaler & Greeno, 2000;Langer-Osuna, 2017). It also affords students the opportunity to build on each other's ideas and to get acquainted with different strategies and solutions paths (Esmonde, 2009;Webb, 1991). ...
... It also affords students the opportunity to build on each other's ideas and to get acquainted with different strategies and solutions paths (Esmonde, 2009;Webb, 1991). These kind of participation frameworks can diminish the tendency of students to seek the approval of the teacher (Boaler & Greeno, 2000), as well as promote accountability for the discipline and for explaining one's thinking to each other (Bill et al., 1992;Resnick et al., 2010). ...
Thesis
In recent years, many efforts have been put into enhancing mathematics teaching towards improving student conceptual understanding and engagement. One of the complexities of this type of teaching lies in the elusive conceptualization used to describe teaching and learning processes. Terms such as “teaching for conceptual understanding” do not operationalize what needs to happen in the classroom for such "conceptual understanding" to be evident. This PhD dissertation draws upon the commognitive theory, which offers an alternative language for talking about teaching mathematics in the form of Teaching for Explorative Participation (TfEP). The main goal of this dissertation is to develop, implement and test a novel tool – The Realization Tree Assessment (RTA) as a visual mediator for communicating about TfEP. The RTA visually depicts the mathematical objects at the core of a task and the different realizations of these mathematical objects, while mapping whether narratives are authored by students, or teacher. This dissertation encompasses three studies. The first study aimed at developing the RTA as an assessment tool and examining its affordances. The second study applied the tool to a larger set of data and quantified the RTA image. The third study examined the affordances of the RTA as a pedagogical tool for adopting explorative practices. The three research questions are thus: 1. What can the RTA qualitatively exhibit regarding TfEP? 2. How can the RTA be quantified? And what can be displayed via this quantification regarding TfEP? 3. How can the RTA be used as a learning tool for pre-service teachers who get acquainted with TfEP? This research took place in the context of the TEAMS (Teaching Exploratively for All Mathematics Students) professional development project during which teachers videotaped themselves implementing in their classrooms a task describing the perimeter of a train of n hexagons. I collected 34 hexagon lessons and I coded them with the RTA. For the 1st RQ I qualitatively examined the differences between the RTA images and for the 2nd RQ I quantitatively analyzed them by statistical methods. For the 3rd RQ discourse analysis was performed on the narratives produced around RTAs by teachers. The first study qualitatively describes different RTA images that reveal different types of classroom discussions, which differ both in the level of student authority (students-centered vs. teacher-centered) and in the mathematical object students received opportunities to produce narratives about. The second study, which dealt with the quantification of the RTA images for examining large scale data, revealed through cluster analysis three types of opportunities for saming in the algebraic discourse: ritual, explorative and opportunities for saming in the informal algebraic discourse. The third study, which examined the RTA as a pedagogical tool, revealed that the RTA images enable teachers to refer both to the social aspects of teaching and to the mathematical objects at the core of the lesson. Overall, findings showed the usefulness of the RTA as a research and pedagogical tool in discussing, explicating and operationalizing the opportunities given to students for explorative participation in whole-classroom discussions.
... In contrast to the in-depth individual ethnographic studies of identity, some studies have leveraged focus groups to understand the educational contexts and their link to identity development (e.g. Boaler & Greeno, 2000;Solomon et al., 2010). For example, Boaler and Greeno (2000) relied on paired interviews with 48 secondary school students. ...
... Boaler & Greeno, 2000;Solomon et al., 2010). For example, Boaler and Greeno (2000) relied on paired interviews with 48 secondary school students. They framed reports about students' mathematical learning as 'perceptions and understandings of the figured social worlds of mathematics education' and demonstrated how students' reflections are sensibly seen as a window into their 'authoring of identities as learners and performers of mathematics' (p. ...
... So, this is what you're given."' Thus, their experience in standard calculus is aptly characterized as one of simply trying to survive and resonates with the figured world of 'received knowing' described by Boaler and Greeno (2000). ...
Article
This study explores how the goals and enactment of three tailored calculus courses, referred to as course variations (standard calculus, life sciences calculus, and physics calculus), at the same university impact students’ mathematical identity. In this mixed-methods study, we draw on the framework of figured worlds to interpret how students’ mathematical identities can be refigured by the enactment of three calculus course variations. Results demonstrate that students in life sciences calculus had opportunities to refigure their identity as capable learners and doers of mathematics yet still viewed the subject as ancillary to their disciplinary interests. Students in physics calculus sustained their mathematical identity through strong peer collaborations. Finally, students in standard calculus shifted their identity as survivors of mathematics, conveying a sense of received knowing from their instructor. The ability of any particular course variation enactment to provide opportunities for refiguring mathematical identities resides within the goals, structures, students, and instructors that help to form these figured worlds. The results presented here provide insights into course variation instructional design and instructional practices that can positively affect students’ mathematical identities, and in turn, their persistence in mathematics and science.
... According to Ma and Singer-Gabella (2011), the figured world of mathematics classrooms can shape students' sense of self as mathematics learners through constructing joint meanings for various classroom activities. As Boaler and Greeno (2000) showed, many mathematics classroom environments described by students are dominated by rote learning and ritualized practices-that is, a figured world of "received knowing"-in which students consider their knowledge as primarily dependent upon and derived from an authoritative Content courtesy of Springer Nature, terms of use apply. Rights reserved. ...
... Compensating for large class sizes and striving for efficiency, instruction focused on procedures featuring minimal student involvement (Lui & Leung, 2013). While Boaler and Greeno (2000) assert that the school context and teaching approach can significantly impact students' future participation in mathematics learning, we extend this argument to the impact on PSTs' intended future teaching practice as schoolteachers. Using figured worlds, we add to the descriptions of current school mathematics classroom practices from the perspectives of three Hong Kong PSTs and address how these PSTs come to understand their ability to "craft their future participation, or agency, in and across figured worlds" (Urrieta, 2007, p. 120) to teach school mathematics. ...
Article
Full-text available
Felix Klein’s notion of “double discontinuity” between university mathematics and secondary school mathematics has persisted in mathematics teacher education. Situating this study in Hong Kong, we investigated three prospective secondary teachers’ experiences in higher education and secondary mathematics classrooms, including their figured worlds, identities, and mathematical knowledge constructed through those experiences. Our analysis revealed their contrasting experiences in these two contexts, adding to our understanding of the phenomenon of “double discontinuity” in terms of not only how it is relevant to Hong Kong but also how it may manifest in the specific cultural context. Moreover, we found coherency and continuity during the prospective teachers’ secondary–tertiary transition; their learning experiences in both environments served as critical resources upon which they reflected to envision their future mathematics teaching. We conclude with implications and suggestions for mathematics teacher education to support prospective teachers’ (and their future students’) transitions between high school and university mathematics.
... Classroom context creates interpersonal and informational resources of participation which define student beliefs about mathematics and themselves (Hand & Gresalfi, 2015) in figured worlds of secondary mathematics (Boaler & Greeno, 2000;Horn, 2008). ...
... Identity as narrative (Sfard & Prusak, 2005) has the unique potential to challenge educational structures in which calculus becomes the metric for success in secondary mathematics. Students may not be challenged to think deeply or to justify their reasoning as they operate in mathematical worlds of didactic instruction and procedural routines that often characterize advanced mathematics classrooms (Boaler, 1997;Boaler & Greeno, 2000;Schoenfeld, 1988). Narrative analyses using three distinct yet complementary methodologies provide a critical window on identity and persistence for hyper-accelerated Algebra I students. ...
... Mathematics identity is a construct that provides a lens for better understanding student choices related to mathematics. Researchers have explored mathematics identity in different settings, such as classroom interactions (Boaler & Greeno, 2000;Esmonde, 2012;Hima et al., 2019) and outside-theclassroom experiences (Nasir, 2002;Nasir & de Royston, 2013), and they have conceptualized mathematics identity in various ways. They have, for instance, focused on figured worlds (Holland & Lave, 2001), discourse (Sfard & Prusak, 2005), and social factors, such as race (Larnell, 2016;Martin, 2000Martin, , 2006. ...
... These different settings and ways of conceptualizing the construct are not mutually exclusive, but often overlap (Bishop, 2012), as seems inevitable when investigating a complex concept in what is often a messy and dynamic environment, such as the classroom. In addition to providing a way to understand how and why students position themselves in the classroom in certain ways, the concept of mathematics identity helps us better understand why students may or may not want to pursue mathematics (Boaler & Greeno, 2000;Cribbs et al., 2016). ...
Article
Full-text available
Changes in mathematics identity over time were examined as well as beliefs regarding the nature of mathematics identity and experiences with mathematics that might be related to mathematics identity development. Survey data from 131 college students were analyzed using a Wilcoxon Signed-Rank test to assess longitudinal changes in self-perceptions about mathematics identity. In addition, open-ended responses were analyzed using a phenomenological approach to examine experiences with and beliefs about mathematics. The results indicate that mathematics identity, as reported by students, is a stable measure over time. Several overarching themes emerged from the qualitative data to indicate that participants’ reported formative experiences center around to performing in mathematics and teaching others or sharing mathematics. A majority of participants believe it is possible to become a “math person”; however, an underlying belief that mathematics is an innate ability is also evident.
... as boring and unenjoyable (Boaler & Greeno, 2000;Motala, Dieltiens, & Sayed, 2012). ...
... They are encouraged to pursue or ask questions that they find interesting as a result of this image and are accountable to the teacher and fellow learners for justifying why they chose to pursue these questions. Curiosity is an important attribute in a 21st century world and this attribute is typically overlooked in mathematics classrooms where learners often surrender their human agency to the agency of the discipline (Boaler & Greeno, 2000). Question 4 and question 5 require learners to make judgements about political decisions that were taken on the basis of mathematics and the nature of the information given to the public. ...
Article
Full-text available
The coronavirus disease 2019 (COVID-19) pandemic supported an investigation of ongoing challenges as to whether and how to make mathematics relevant to learners’ lifeworlds. Given that COVID-19 created major disruptions in all learners’ lives, we developed and taught tasks that attempted to make links between their experiences of the pandemic and disciplinary mathematical knowledge. We located our investigation in current debates about the extent to which disciplinary knowledge can be linked to learners’ out-of-school experiences. We developed and analysed two tasks about COVID-19 that could support link-making and productive disciplinary engagement, and analysed one Grade 10 teacher teaching these tasks. We found that linking mathematics to learners’ lifeworlds is both possible and extremely difficult in relation to task design and how the teacher mediates the tasks. In relation to task design, we argue that teachers cannot do it alone; they need to be supported by the curriculum and textbooks. In relation to mediation, we saw that teacher practices are difficult to shift, even in the best of circumstances. We articulate the complexities and nuances involved in bridging powerful knowledge and lived experience and thus contribute to debates on how to teach powerful knowledge in relation to learners’ lifeworlds.
... as boring and unenjoyable (Boaler & Greeno, 2000;Motala, Dieltiens, & Sayed, 2012). ...
... They are encouraged to pursue or ask questions that they find interesting as a result of this image and are accountable to the teacher and fellow learners for justifying why they chose to pursue these questions. Curiosity is an important attribute in a 21st century world and this attribute is typically overlooked in mathematics classrooms where learners often surrender their human agency to the agency of the discipline (Boaler & Greeno, 2000). Question 4 and question 5 require learners to make judgements about political decisions that were taken on the basis of mathematics and the nature of the information given to the public. ...
... As Chan and Clarke (2017) argue, open-ended CPS tasks offer affordances for student collaboration, but the realisation of such affordances is highly dependent on the students involved and their interaction. Thus, student agency has been strongly connected with the collaborative construction of mathematical arguments during CPS (Boaler & Greeno, 2000;Wagner, 2004Wagner, , 2007. Broadly, agency is demonstrated when students take initiatives and make contributions during mathematical collaboration (Gresalfi et al., 2009;Mueller et al., 2012). ...
... In recent years, there have been multiple calls for applying sociocultural frameworks to examine student agency to challenge the dominant individualistic approaches (Arnold & Clarke, 2014;Nieminen et al., 2021;Nieminen & Tuohilampi, 2020). Following these suggestions, agency in this study is understood as a situationally constructed phenomenon, not as a student attribute but as a social phenomenon constructed through language and practices; this is a widely shared understanding in the field of mathematics education (Boaler & Greeno, 2000;Gresalfi et al., 2009;Mueller et al., 2012;Wagner, 2004Wagner, , 2007. Wagner (2004) implied that language acts as an instrument that offers a way to study the concept of agency indirectly. ...
Article
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The important role of student agency in collaborative problem-solving has been acknowledged in previous mathematics education research. However, what remains unknown are the processes of agency in open-ended tasks that draw on real-life contexts and demand argumentation beyond “mathematical”. In this study, we analyse a video recording of two student groups (each consisting of four students) taking part in collaborative problem-solving. We draw on the framework for collaborative construction of mathematical arguments and its interplay with student agency by Mueller et al. (2012). This original framework is supplemented by (i) testing and revising it in the context of open-ended real-life tasks, with (ii) student groups rather than pairs working on the tasks, and by (iii) offering a strengthened methodological pathway for analysing student agency in such a context. Based on our findings, we suggest that the framework suits this new context with some extensions. First, we note that differences in student agency were not only identified in terms of the discourse students drew on, but in how students were able to shift between various discourses, such as between “mathematical” and “non-mathematical” discourses. We identify a novel discourse reflecting student agency, invalidation discourse, which refers to denying other students’ agency by framing their contribution as invalid. Finally, we discuss the need to reframe “mathematical” arguments—and indeed student agency—while the task at hand is open-ended and concerns real-life contexts.
... Second, inquiry-oriented mathematics more authentically refl ects the practices of mathematicians (Lehrer & Schauble, 2004;Schoenfeld & Hermann, 1982;Sinclair, 2006), with its emphasis on persuasion, insight, and enjoyment. Finally, because inquiry-oriented instruction focuses on children's sense-making, it fosters autonomy and agency in ways that support the development of positive mathematical dispositions (Boaler & Greeno, 2000;Gresalfi , 2007;Horn, 2008). ...
... The norms of inquiry class rooms often emphasize collaboration and communication, for example, through inviting partial answers and offering different approaches to solving problems. Research shows that classroom norms shaping what counts as competent mathematical behavior have significant implications for the kinds of relationships students are likely to develop to school mathematics (Boaler & Greeno, 2000;Boaler & Staples, 2008;Cobb, Gresalfi, & Hodge, 2009) . ...
Chapter
Cultural myths about mathematics as a set of known facts pose unique obstacles for inquiry instruction. What is there to discover if everything is already known? At the same time, decades of mathematics education research shows the potential for inquiry instruction to broaden participation in the discipline. Taking a classroom ecology perspective, this chapter uncovers common obstacles to inquiry in school mathematics and identifies three leverage points for redesigning instruction toward this goal. These include: teachers’ knowledge for inquiry mathematics, curricular connections to other contexts, and classroom norms and practices. The chapter proposes that design thinking around these leverage points holds promise for wider-spread implementation of inquiry instruction in mathematics classrooms.
... To the best of our knowledge, this is the first study of learning that combined methods of discourse analysis and eye tracking (see Strohmaier et al., 2020). Collaborative learning and group work may be helpful in terms of offering students opportunities to enact agency, thus achieving explorative participation and strengthening their identities as mathematical learners (Boaler & Greeno, 2000), yet it bears with it also the dangers of miscommunications and inequitable roles within the problem-solving group (Chan & Sfard, 2020;Heyd-Metzuyanim & Sfard, 2012). Thus, much research has already established that certain groups can be more successful than others. ...
Article
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We present the analysis of an episode of mathematical problem solving in a group, where data came from multiple advanced recorders, including multiple video cameras, Smartpen recorders, and mobile eye tracking glasses. Analysis focused on a particular group that was ineffective in their problem-solving process. Relying on the commognitive theory of learning on the one hand, and on quantitative descriptors of eye-tracking data on the other hand, we ask how do the interpretations of the discourse analysis and gaze data complement each other in understanding the obstacles to problem-solving in this episode. The setting included four Finnish 9th grade students solving a geometrical problem in the students’ authentic mathematics classroom. The commognitive analysis revealed intensive social communication (subjectifying) along with the mathematical one (mathematizing), which seemed to interfere with the problem-solving process. Specifically, it masked the differences in students’ interpretation of the tasks, and did not allow explication of meta-rules according to which students endorsed mathematical claims. Diagrams of quantified gaze data enabled a more macro-level picture of the full 15 min interaction, revealing differential loci of attention of the group members and thus triangulating the micro-analysis.
... The interaction between structure, identity, and agency has been explored to examine self-authoring through action (Boaler & Greeno, 2000;Sfard & Prusak, 2005) and how agency impacts, and is impacted by social structures (Varelas, Settlage, & Mensah, 2015). When structure or local actors impose inequitable positionings, individuals may act through critical agency to refigure those positions more favorably. ...
... In mathematics education research there is a growing body of literature utilising the concept of identity (e.g. Boaler & Greeno, 2000;Wiliam et al., 2004;Sfard & Prusak, 2005;Grootenboer, Smith, & Lowrie, 2006;Lerman, 2006;Ingram, 2008;Stentoft & Valero, 2008;Black, Mendick, & Solomon, 2009;Bishop, 2012). Like others, Grootenboer et al. (2006) advocated its use in mathematics education research as a unifying concept. ...
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School mathematics education is submerged in a discursive field of social valorisation. Being a significant part of children's lived experience, it provides an arena for children's identity work. Kalila was a ten/eleven year old girl living in Denmark. In interviews, she articulated her experiences with learning school mathematics in a way that showed how these were an integral part of her developing identity. She believed mathematics was important to fulfilling her dreams for her future. Experiences of struggling were labelled as boring. They threatened her hopes for her future. These were implications Kalila faced in her encounters with the social practices of school mathematics education.
... Research on a student's agency in mathematics education draws on Pickering's (1995) metaphor of the 'dance of agency' (Boaler & Greeno, 2000;Cobb et al., 2009;Wagner, 2007). In the 'dance of agency ', Pickering (1995) claims not to use science to explain knowledge but to explain how things are done. ...
... Ultimately, when educators adopt these practices they "share the process of mathematical problem solving with students … making mathematics more equitably accessible, and also encouraging larger numbers of students to explore mathematics as a career" (Boaler & Greeno, 2000, p.189). Unsurprisingly, positive mathematical identities flourish in these types of learning environments because students are given agency over the mathematical process, are encouraged to view themselves as mathematicians, and experience first-hand the value of mathematics in their lives (Boaler, 2002;Boaler & Greeno, 2000). ...
Article
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Mathematical identity is a socio-motivational construct known to be a predictor of mathematical achievement. Students who identify positively with mathematics are more likely to pursue advanced courses and Science, Technology, Engineering, and Mathematics (STEM)- related occupations. Although mathematical identity is shaped by a myriad of internal and external factors on both a small and large scale, educators play a significant role in the formation of their students’ mathematical identities. This paper presents an overview of research and theory regarding those pedagogical practices for teaching mathematics that can foster the formation of positive mathematical identities.
... Ultimately, when educators adopt these practices they "share the process of mathematical problem solving with students … making mathematics more equitably accessible, and also encouraging larger numbers of students to explore mathematics as a career" (Boaler & Greeno, 2000, p.189). Unsurprisingly, positive mathematical identities flourish in these types of learning environments because students are given agency over the mathematical process, are encouraged to view themselves as mathematicians, and experience first-hand the value of mathematics in their lives (Boaler, 2002;Boaler & Greeno, 2000). ...
Article
Mathematical identity is a socio-motivational construct known to be a predictor of mathematical achievement. Students who identify positively with mathematics are more likely to pursue advanced courses and Science, Technology, Engineering, and Mathematics (STEM)-related occupations. Although mathematical identity is shaped by a myriad of internal and external factors on both a small and large scale, educators play a significant role in the formation of their students’ mathematical identities. This paper presents an overview of research regarding those pedagogical practices for teaching mathematics that can foster the formation of positive mathematical identities.
... Studies of identity-oriented approaches in the context of school science and STEM education research, in particular, have shown that through engagement in 'identity work' activities, learners develop a sense of their identity as students of science with positive outcomes in terms of persistence in learning motivation, academic achievement and future sense of self in relation to science including future career decisions (Calabrese Barton et al. 2013;Carlone and Johnson 2007;Steinke 2017;Trujillo and Tanner 2014). Similar findings have emerged in intervention studies of student identity in mathematics education (Boaler and Greeno 2000;Heffernan et al. 2020;Radovic et al. 2018). ...
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Ofsted’s 2021 Curriculum Research Review outlines a language pedagogy predicated on an exclusively cognitivist approach to language learning, which relies on three ‘pillars of progression’: phonics, vocabulary and grammar. The review makes a brief acknowledgement of the importance of motivational factors, including ‘pupils’ positive views of themselves as language learners’ though these factors do not seem to inform its conclusions about what constitutes ‘high-quality languages education’. Tellingly, the authors seem to believe that motivational factors are unrelated to learners’ perceptions of the relevance of language learning in their lives. Addressing the issue of learners’ perception of ‘the relevance of languages in their lives’ is indeed an important challenge, as the literature indicates, yet it is difficult to see how an exclusively cognitivist approach to language education can do this effectively. In this paper, we point to the growing recognition in languages education research of the key role played by multilingual identity development in successful language learning. We draw also on evidence from our recent AHRC-funded interventional study of Year 9 and Year 10 pupils (ages 13-15) in schools in England to argue for an identity-oriented language pedagogy as an integral component of a transformative approach to language learning.
... As found by other researchers in how women make a place for themselves in mathematics [53], Rita must make sense of conflicting discourses about her place in the world of mathematics. Other studies of gender in mathematics have found high school girls moving away from mathematics as it became less about connected knowledges [54]. ...
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Conversations of educational equity in mathematics necessitate a more deliberate, nuanced look at the mathematical processes of learning for students of color from historically marginalized communities. This paper describes the theoretical work of a research collaborative that seeks to develop understanding of the experiences around mathematical identity of Latinas labeled with Learning Disabilities in mathematics classrooms. Expanding the theory of Complex Embodiment from Disability Studies, we explore new interdisciplinary theoretical and methodological tools to analyze the emotional, embodied experience of learning mathematics in the social worlds of mathematics classrooms, using emotional discourse. We take up theoretical and methodological practices around intersectionality through analysis of how power and positioning operate in mathematics identity development. We find that the young woman whose narratives we explore in this paper is positioned through deficit discourses around disability and multilingual learners, yet she understands herself through a positive mathematical affinity she shares with her mother. Over time, we see her narratives shift emotionally away from mathematics, as well as away from this connection with her mother. Her narratives help us develop a theoretical perspective that understands emotion in mathematics learning as both embodied and socially constructed.
... 3. How do students negotiate the convergences and divergences between these two sets of experiences and relationships? Boaler and Greeno (2000) argue that: "The mathematics classroom may be thought of as a particular social setting-that is, a figured world-in which teachers and children take on certain roles that define who they are" (p. 173). ...
... 3. How do students negotiate the convergences and divergences between these two sets of experiences and relationships? Boaler and Greeno (2000) argue that: "The mathematics classroom may be thought of as a particular social setting-that is, a figured world-in which teachers and children take on certain roles that define who they are" (p. 173). ...
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This experimental study ascertained the benefits of project VLOGI (Video Lectures on Giving Instruction) to Grade 8 learners and mathematics teachers to resolve the mathematical content issues in probability. The researcher observed that this content has a low level of proficiency in higher grade levels of all time since it falls in the last quarter of the school year. Thus, some mathematics teachers teaching in the lower grades tend to skip or fail to teach the learning competencies due to lack of time, resulting in spiral deterioration rather than having a spiral progression approach of the Philippine K to 12 Basic Education Program. To bridge the gap of the untaught learning competencies under the content of probability, the researcher utilized project VLOGI to his instructions. Explicitly, this study sought to answer the following questions; 1. What is the students' performance in the pre-test for those exposed to the traditional method and project VLOGI? 2. Is there a marked difference in students' performance in the pre- test between those disclosed in the conventional teaching and project VLOGI? 3. What is the students' performance in the post-test for those exposed to the traditional method and project VLOGI? and 4. Is there a significant difference in students' performance in the post-test between those disclosed in the conventional teaching and project VLOGI?. The researcher's intervention, named project VLOGI, was inspired by video blogging (Vlog), which is the new blogging trend for digital natives in contemporary times. Currently, Vlog has a lot to offer in an educational setting. In the current situations, Vlogs may consider as support instructional materials in blended learning modalities for instruction. This videoblogging has a richer web experience than conventional text blogging since it integrates movies, sound, still images, and text, increasing the information – and potential emotions – shared with users (Kusumaningrum and Rahkmanina, 2017). Videoblogging activities can meet today's students' needs surrounded by these highly dynamic and interactive technologies (Baran, 2007). Furthermore, in some research, using videos as a learning medium in mathematics improves students' motivation to learn, their comprehension and interpretation of the lesson, and their achievement (Lalian, 2019). The researcher used the experimental research design in his study. The researcher made VLOGs with all the learning competencies under the mathematical content of probability were anchored from the DepEd's Curriculum Guide (2016) of the Philippines. The two (2) randomly selected classes out of the six (6) heterogeneous-classes in school were the study respondents; 1. the control group or the group exposed in the Conventional Method of teaching, and 2. the group exposed in an approach where project VLOGI introduced was the experimental group. Utilizing the 20-item ready-made questioners taken from the DepEd Learners Module in Mathematics 8 (2013) served as the research instruments before and after the interventions. The invited expert panel of evaluators was there to examine the content validity of the construct. The data were obtained and tabulated for statistical treatment using the pre-test scores compared to all respondents' post-test scores. The researcher used the means, standard deviations, and the independent sample t-test using the SPSS tool to analyze and interpret the outcomes. The study results showed that both groups had started with the same performance level before the implemented intervention. Fortunately, there was a significant improvement in the learners' scores observed using project VLOGI than in Conventional Method in teaching after the conducted intervention with a medium effect size of comparison by Cohen's (1992). Thus, utilization of project VLOGI may awaken students' interest and may augment teacher's absence in the classroom. Hence, project VLOGI should use as an alternative approach in teaching mathematics, and it is highly recommended to those teachers with uncertain responsibilities because of the ancillary services in school. Moreover, the digital learners performed way better in introducing project VLOGI in their lessons. Likewise, it encouraged students' interest to learn with excitement as they engaged their learning to any social media platforms using this project VLOGI.
... Second, STEM professional and educational spaces need to become more welcoming to students from underrepresented groups (Leonard et al., 2010). Third, we want to combat the too-common imposter concerns among CLD students that perhaps STEM fields are not for them (Boaler & Greeno, 2000;McGee, 2020). Actively modeling a broader cultural and racial view of STEM -as well as dispelling stereotypes surrounding computer geeks and lab coatsprovides our kids with an equitable vision for STEM and thus a stronger "STEM Smart" foundation. ...
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STEM education researchers are well aware of the need for increased access and inclusivity in Science, Technology, Engineering, and Mathematics (STEM) education for students from culturally and linguistically diverse (CLD) backgrounds. One of the many barriers for students from underserved cultural and linguistic groups is the difficulty of connecting families to school models of STEM education. This is one reason we advocate for improvement in culturally relevant STEM curriculum and content instruction. This commentary does not focus on STEM content instruction, although we certainly believe children from CLD communities deserve high expectations and high quality, culturally sustaining, STEM pedagogy. In this article we discuss non-curricular skills that are vital to success in STEM-and the advantages of sharing with family members the importance of particular essential life skills that support STEM learning. Communicating these essential "STEM Smart skills" showcases the power and influence that families have in kids' STEM learning. In this commentary we describe a school-based family STEM night that included a demonstration that success in a STEM task is not based primarily on content knowledge but on "STEM Smart skills." Many family members found success in the activity, regardless of parents' educational level or background in STEM. Family members' rich life experiences, critical thinking skills, and cultural knowledge include these "STEM Smart skills." We argue that teachers and schools should communicate to families about these life skills. This focus can benefit students by highlighting family members' power and role in teaching and modeling, essential skills for students' STEM success. This focus also can benefit educators by challenging common stereotypes about families from underrepresented cultural and linguistic backgrounds. In this way, acknowledgement of "STEM Smart" life skills could play a small part in dismantling structural racism and inequitable power relations between schools and communities.
... Mathematical identity refers to a person's beliefs, attitudes, emotions, and dispositions about mathematics and their resulting motivation and approach to learning and using mathematics knowledge (Martin, 2000). It includes students' beliefs on whether or not they can do mathematics and that they belong in mathematics (Boaler & Greeno, 2000). However, self-perception alone is not sufficient for the development of a mathematics identityrecognition (i.e. to be recognized by others as a 'mathematics person') and interest are also paramount (Cribbs et al., 2015). ...
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We conducted a systematic review to generate a comprehensive understanding of cisgendered girls’ mathematical identity within the United States to better understand: (a) how mathematical identity is associated with girls’ participation, engagement, and achievement in mathematics; (b) the factors related to girls’ mathematical identity; and (c) strategies for developing strong mathematical identities within girls. We identified 76 articles that examined mathematical identity in young girls and women. Our review suggests that positive girls’ mathematical identity was consistently linked with increased performance, participation and persistence in mathematics. Factors and strategies affecting girls’ mathematical identity included the role of parental attitudes and beliefs; societal and cultural influences; and the intersections of sex and race. Practical implications for researchers and practitioners are also discussed.
... Scholars have long chronicled how structures like racism and White supremacy (e.g., Battey & Leyva, 2016;Martin, 2009Martin, , 2013Martin, , 2019Rubel, 2017;Shah, 2017;Spencer & Hand, 2015), capitalism (e.g., Gutstein, 2009;Stinson, 2004), heteropatriarchy (e.g., Boaler, 2002;Hottinger, 2016;Leyva, 2017;Mendick, 2005), ableism (e.g., Yeh et al., 2020), language discrimination (e.g., de Araujo, 2018), ethnocentrism (e.g., d'Ambrosio, 1985, imperialism (e.g., Bishop, 1990), and combinations thereof (e.g., R. Gutiérrez, 2018) pervade the histories, cultures, and practices of mathematics education as it is typically enacted, systematically privileging some students and disenfranchising others. Scholars have also documented how mathematics educators often adhere to narrow definitions of mathematical activity and mathematical ability (Louie, 2017; see also Boaler & Greeno, 2000;Cobb & Hodge, 2011;Horn, 2007;Nasir et al., 2008). As a result, any participation and participants who do not conform are excluded from being mathematical, regardless of whether their nonconformity can be attributed to individual differences or cultural mismatches (e.g., Parker et al., 2017;Turner et al., 2009). ...
Article
Education researchers have long wrestled with the interplay of oppressive structures and individual agency in reproducing, sustaining, and contesting marginalization. In this article, we suggest that Weis and Fine’s construct of critical bifocality may assist researchers in understanding and addressing marginalization in mathematics education. We conduct a conceptual review of existing mathematics education literature that accounts for both structure and agency in theorizing marginalization. By reading this literature alongside Weis and Fine’s 2012 article, we develop four criteria for operationalizing critical bifocality in mathematics education research. The findings from this review highlight the interconnectedness of structures and individual lives, of the material and ideological elements of marginalization, of intersectionality and within-group heterogeneity, and of histories and institutions. Additionally, they offer theoretical and methodological recommendations for researchers studying marginalization in mathematics education.
... Multiple factors contribute to this perception, such as one-way teaching due to stagnant curriculum, topdown traditional pedagogies, and large-sized classes (Engle & Faux, 2006). Teachers are required to strictly follow particular curriculum and instruction policies without any freedom (Boaler & Greeno, 2000). Also, teachers have very few chances to address their weaknesses in adapting curriculum to meet students' wide-ranging needs. ...
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Teacher agency is an important topic in educational research, but its theoretical observations have not filtered down into practical Vietnamese teaching contexts. The action research project described here showcases a training-based intervention for teacher educators in various disciplines at eight universities in Vietnam. The intervention aimed to develop teaching skills and increase knowledge for teacher educators by helping them explore their students’ learning needs and facilitate their professional development. This study occurred within the context of changing Vietnamese political, cultural, economic, and social ways of being. Eight Vietnamese teacher educators of different cultural backgrounds, and working across a variety of subjects were invited to participate in the project. Two stages of research sought to help educators in higher education reflect on their exploration and perception of their teacher agency. The first stage involved training sessions that offered educators necessary knowledge and skills to exercise agency effectively. In the second stage, educators’ promotion of their agency in classrooms was analytically observed. Data collected included observation notes, reflective journals, and recordings from semi-structured interviews. Analysis of this data suggested that educators became more knowledgeable, intercultural, and inspirational agents in their classrooms after the educational intervention. Educators exhibited that the more positive attitudes, the more active participation. Conclusions discussed the benefits of fostering teacher agency and how this can be facilitated through professional development.
... A separate line of research that has inspired learning sciences research perhaps more than this first line of research examines how learning is deeply and fundamentally tied to students' developing identities in particular subject matter areas (Boaler & Greeno, 2000;Martin, 2000;McCarthy & Moje, 2002;Nasir, 2002;Wortham, 2006). For instance, Boaler and Greeno interviewed high school mathematics students about their engagement and motivation in advanced math classes and sense of themselves as math learners. ...
... Revised studio problems position students in the role of engineers on teams where they need to identify core foundational principles as conceptual tools to progress on tasks that resemble realistic engineering work (Engle & Conant, 2002;Johri & Olds, 2011). In a previous study during this initiative, we used an activity systems framework (Boaler & Greeno, 2000;Engeström, 2001) to reveal elements that influence students' adoption of more or less productive approaches to learning. By far, exam expectations were the most common element cited by students to prompt undesired rote learning approaches (Michor & Koretsky, 2020). ...
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Background Authentic assessment and two-stage exams have recently received attention; however, they are rarely used together. We reimagine assessment by integrating an authentic, computer-based assessment into the structure of a two-stage exam in a large engineering class. Purpose We seek to identify ways that such assessment extends classroom testing to better align with engineering practice by examining the ways teams negotiate uncertainty to make engineering decisions. We also identify differing students' reactions to increased uncertainty during tests. Design/Method Using the methodical framework of design-based research, we analyze performance and reflection data for 117 student teams through two design iterations to explore four design and theoretical conjectures. Results Teams chose multiple solution paths to this authentic task, an aspect that aligns with the characteristics of engineering practice that we seek to assess. In addition, the technology tool allows the evaluation of procedural accuracy for many of the teams' chosen paths. The teams' decision-making performances correlate; however, decision-making and traditional assessments do not correlate, suggesting they measure different competencies. The computer-based second stage provides a holistic assessment that shifts the messages that students implicitly receive about valued practices in the classroom. However, not all students took up the authentic group assessment in desired ways. Conclusions Technology-based two-stage exams with authentic assessment show promise to shift testing practices in large engineering classes to include decision-making. Such assessments better align with engineering practices that are valued in the profession, but more work is needed to develop systems for widespread implementation.
... Identity development has been well documented in STEM-related disciplines, including (1) middle and high school science (e.g., Andree & Hanson, 2013;Brickhouse & Potter, 2001) and (2) undergraduate mathematics (e.g., Boaler & Greeno, 2000), technology (e.g., C. Hall et al., 2011), and (3) engineering education (e.g., Capobianco, 2006;Tonso, 2006). Similarly, engineering identity-defined as how one comes to view themselves as the kind of person who could be an engineer (Capobianco, 2006)-contributes in significant ways to a student's ability to persist in challenging STEM tasks and content courses as well as major in and complete postsecondary degrees in these fields (Capobianco et al., 2012). ...
Article
Background Limited research examines the effects of integrated science and engineering (SE) instruction emphasizing disciplinary literacy and language activities on engineering identity and content understanding. Far fewer studies target English learners (ELs). Purpose The impact of an SE intervention on the development of science, engineering, and technology knowledge as well as engineering identity was examined. To address ELs' learning needs, the curricular design was built on a validated SE model by integrating (1) developmental, (2) language scaffolds, and (3) culturally based accommodations. Design/Method Separate analysis of variance examined the effects of the intervention on science, engineering, and technology knowledge as well as engineering identity. The relationship among engineering identity and content outcomes was also examined. ELs from kindergarten to second grade classrooms were randomly assigned to the integrated SE group or control group. Results Integrated SE instruction significantly increased ELs' science, engineering, and technology knowledge as well as a substantially developed engineering identity. Overall, ELs' engineering identity is associated with an increase in science, engineering, and technology content knowledge. However, second grade girls' identity development was not associated with learning measures. These correlations suggest the context of the engineering activity may have reinforced gendered stereotypes and reduced the effects for girls' engineering attitudes. Conclusions Integrated SE instruction emphasizing disciplinary literacy and cultural accommodations increases early elementary ELs' learning and engineering identity. Future studies should examine the unique effects of language scaffolds and cultural modifications on student learning and the impact of gender stereotypes on girls' engineering attitudes.
... 3. How do students negotiate the convergences and divergences between these two sets of experiences and relationships? Boaler and Greeno (2000) argue that: "The mathematics classroom may be thought of as a particular social setting-that is, a figured world-in which teachers and children take on certain roles that define who they are" (p. 173). ...
Conference Paper
Estimation is a concept that is constantly used both in daily life and in scientific studies, and it is not a random action. It is a skill developed as a result of experiences gained in mathematics. Estimation term; It refers to find out the most appropriate approximate value that can be substituted for an exact number corresponding to a certain context alone. Reys and Bestgen (1981) defined estimation as finding the approximate outcome of an operation or problem based on mental calculation. In the literature, it has been observed that there are studies aimed at determining the estimation skills of primary and secondary school students regarding estimation skills (Aytekin&Uçar, 2014 ; Baroody&Gatzke, 1991 ; Bobis, 1991 ; Boz&Bulut, 2012; Crites, 1992; Çilingir&Türnüklü, 2009; Dowker, 1997 ; Hanson&Hogan, 2000 ; Kılıç&Olkun, 2013; Luwel&Verschaffel, 2008; Pilten&Yener, 2009 ; Star Rittle,Lynch&Perova, 2009; Tekinkır, 2008;Yazgan, Bintaş&Altun, 2002), determining the estimation skills of teacher candidates(BozveBulut, 2002; Goodman, 1991;Sulak, 2008;Özcan,2015) and determining the estimation skills of mathematics teachers(Dowker, 1992). The results of these studies revealed that the estimation skill levels of the participants were low. The low estimation skill levels of the students requires revealing their self-efficacy beliefs about the subjects that require estimation skills. This is a quantitative study to develop a valid and reliable scale in order to determine estimation skills self-efficacy of middle school students' and to investigate the estimation skill of middle school students in terms of various variables by means of the developed scale. In this context, the study was conducted on 327 middle school students. In the development process of the scale, exploratory factor analysis, confirmatory factor analysis and Cronbach Alpha internal consistency coefficient and Guttman Split Half values reliability calculations were performed. As a result of the analysis, the total variance percentage of the 29 items, which was composed of five factors, is 55.61%.The model obtained as a result of confirmatory factor analysis is acceptable. The Cronbach Alpha internal consistency coefficient for the whole scale is .91. The results of this study show that a valid and reliable scale was developed to determine the self-efficacy of middle school students' estimation skills. In addition, through the developed scale, it was obtained that self-efficacy of middle school students' estimation skills differed according to the type of gender and grade levels.It was observed that the self-efficacy of the male student regarding the prediction skill was higher than the female students, but this difference is not significant. In addition, When the self-efficacy levels of the students in estimation skills were examined according to their grade level, it is seen that the self-efficacy scores of the 5th and 6th grade students are higher than the self-efficacy scores of the 7th and 8th grade students.
... While in most studies the transition from secondary to tertiary mathematics education is framed as a problem, Hernandez-Martinez et al. and has been seen as decisive for capturing levels of participation in mathematical practices (Boaler & Greeno, 2000;Sfard & Prusak, 2005;Solomon, 2007). For the purpose of our study, we will here shortly discuss some recent research on identity in terms of student autonomy and individual learning strategies in relation to the institutional setting of university mathematics. ...
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Mathematics education at the tertiary level is a practical concern in many institutions of higher education, and efforts are being made world-wide to improve its quality. A growing number of mathematicians and mathematics educators see the need for doing research and thoughtful development work in mathematics education not only at school level, but also at tertiary level. To give momentum to the establishment of a scientific community of mathe-maticians and mathematics educators whose concern is the theoretical reflection, the re-search-based empirical investigation of mathematics education at tertiary level, and the exchange of best- practice examples, the khdm (German Centre for Higher Mathematics Education, www.khdm.de) and the Volkswagen Foundation jointly organized a conference named “Didactics of Mathematics in Higher Education as a Scientific Discipline”, which was held from 1st to 4th December 2015 in Hannover, Germany, at Schloss Herrenhausen. We are delighted that about 100 experts from 16 different countries with scientific background in mathematics or mathematics education followed our invitation to present and to discuss research and innovative efforts for improving the teaching and learning of mathematics at tertiary level, as well as experiences from teaching practice and empirical and theoretical research approaches that aim at a better understanding students’ difficulties in learning mathematics and in learning to think mathematically. The book is structured in 9 sections: Mathematics as a subject in pre-service teacher education, Mathematics for math majors, Mathematics as a service subject (in engineering and economics), Tertiary level teaching (analyses, support and innovations), Motivation, beliefs and learning strategies of students, Learning and teaching of specific mathematical concepts and methods, Curriculum design including assessment, Theories and research methods, Transition: research and innovative practice (https://kobra.uni-kassel.de/handle/123456789/2016041950121)
... Social cultural research in education has highlighted, for example, the ways by which societal and organizational structures that provide differential educational opportunities to students from different social groups frame those students' self-definitions, sense of agency, perceived competence, and goal-setting (McCaslin, 2009;McCaslin & Lavigne, 2010). Social cultural research has also demonstrated how classroom contexts and educational practices that manifest different meanings (e.g., reflected in didactic versus discussionbased instruction) shape students' conceptions of learning the subject matter, sense of what it means to be a member of the subject matter community, self-perceptions and personal sense of belonging to the community, and motivation and learning of the content (Boaler & Greeno, 2000;Nolen et al., 2011;Sfard & Prusak, 2005). Social cultural research has also described how students appropriate and negotiate their identities through different modes of participation in activities, such as engaging in full participation, legitimate peripheral participation, peripheral and marginal nonparticipation, as well as different trajectories toward or away from participation. ...
Chapter
Educational psychology is a field of inquiry that involves the application of psychological science to the investigation and improvement of educational phenomena, and reciprocally, to the enhancement of psychological science itself. Surprisingly, until relatively recently, the concept of identity has been mostly missing from the extensive educational psychological literature. Much more common has been the use of the related concept Self, reflecting diverging theoretical traditions that identity scholars and educational psychologists have drawn upon. However, during the past two decades this has been changing. In the current chapter, we provide a framework to consider the diverse ways by which educational psychologists have employed the concept of identity to conceptualize and investigate learning, motivation, and achievement in educational settings. We begin by briefly reviewing three different categories of perspectives on identity and their complementary foci: (1) social cognitive and social psychological perspectives that foreground identity content; (2) psychosocial perspectives that foreground identity structure and formation processes; and (3) social cultural perspectives that foreground the role of culture in identity and its formation. We then describe an emerging integrative perspective of identity as a complex dynamic system and its application in educational psychological scholarship. We conclude by noting several emergent areas of identity research in educational psychology and by emphasizing the potential of identity research from integrative perspectives to bridge educational psychological scholarship with educational practice and policy.
... 3. How do students negotiate the convergences and divergences between these two sets of experiences and relationships? Boaler and Greeno (2000) argue that: "The mathematics classroom may be thought of as a particular social setting-that is, a figured world-in which teachers and children take on certain roles that define who they are" (p. 173). ...
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Thinking is the process of deciding what to believe or what to do by making sense of the current situation as an action that keeps the brain functioning continuously (Cüceloğlu, 1999). Thinking, which is a mental product, realizes thanks to the interactions between elements that exist in the mind, and if adaptation, reasoning or judgment is to be made, it reaches the result by activating affective inputs in mental processes (Jones, 2019). Environmental factors, education level and social environment are important factors in the development of an individual's thinking skills (Özdemir, 2005). It is divided into many different types in terms of thinking, purpose and skills. For example; creative thinking, critical thinking, analytical thinking, metacognitive thinking, divergent thinking, convergent thinking, lateral thinking, algorithmic thinking and critical thinking (Çiftçi, 2017). According to NACE (2017), employers rated the need for critical thinking/problem solving as the most needed competency for career readiness. During the last two decades students at higher education are being more exposed to the concept of critical thinking as a way to improve not only their professional skills, but their personal competencies as members of a global community (Altuve, 2010; Crenshaw, Hale, & Harper, 2011; Facione, 2013; Moore, 2013; Villarini, 2003). Halpern (2014) warns that in our era, in which a myriad of knowledge can be easily accessed at one click, it is important to teach students to be critical and effective thinkers. Critical thinking is usually related to other skills that are considered key in the 21st century in students’ learning process, with stakeholders, and in everyone’s family life: metacognition, motivation, and creativity (Moeti, Mgawi, & Mealosi, 2017). Critical thinking is a competence student need in their personal and professional lives. Therefore, universities should do their best to include this in their teaching programs and classroom practice. Since there is no clear definition of critical thinking competence and many new methodologies need to be developed to develop this skill, it seems to be an issue that educators should focus on for many years (Bezanilla, et al., 2019). This study was conducted on the classroom teacher candidates' levels of using critical thinking skills through advertisements. This work was carried out with 14 teacher candidates in 3rd grade, the classroom education department of a university in South Anatolia region in Turkey. Before the data were collected, a questionnaire study was carried out on how to reflect their critical thinking skills to prospective teachers in the most comfortable way. This survey included topics such as social problems, covid-19 process, cultural values, our education life, personal development, individual needs, global problems, communication problems and advertisements. Since it was concluded that more than half of the students participating in the study chose the subject of advertising, this study was conducted on advertisements. The opinions and critical approaches of the advertisements given to the pre-service teachers to watch and interpret were analyzed. When the results were examined, it was concluded that the advertisements of the teacher candidates were generally gathered in the themes such as violation of ethical values, products that do not reflect the truth, subliminal messages, gender inequality, and women's body preemptive of products. In general, it can be said that pre-service teachers can look at advertisements critically, but some of them have very superficial implications. The reason for the pre-service teachers' such shallow answers may be that they have not received any thinking training throughout their education. For this, at least after high school education, it can be suggested that the courses with the content of thinking education should be included in the curriculum.
... Learning mathematics is not just about knowing definitions and theorems to recognize when they are used and applied. [7] states that learning mathematics is like doing mathematics at least in one important way. At each stage of learning mathematics, students have several concepts and methods that they already known and understood. ...
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The major objective of this study was to investigate the effectiveness of the PIPEK model in learning modern algebra. This study was to identify the effects of the use of PIPEK model on students’ engagement and students’ learning in modern algebra course at Mathematics Department in Semester 2, 2020. During this study, the students completed achievement test and questionnaire. The study revealed that, in terms of surface strategy, students tended to memorize formulas and the method for solving problems. Moreover, students still relied heavily on the lecturer’s instructions; Particularly, related to the aspects of the attitude, student participant generally found modern algebra as a boring and difficult course. Futhermore, students felt stressed and anxious; The findings related to the behavioral aspect indicated that although student’s attention were high, they were not diligent in accomplishing independent work task. The finding also demonstrated that, the level of mastery achievement of student learning outcomes has not achieved classical completeness. However, the PIPEK model has given students the opportunity to engage more in student center learning process.
Chapter
Recent studies have revealed that the existing measurement methods related to computational thinking (CT) pivot on gauging thinking skills, recommending an extended understanding of CT as disposition. Disposition reflects inclination towards learning CT and indicates the interest to think intelligently about issues confronting them. Hence, the aim of this chapter is to assess students' affection towards learning CT as problem solving tool that can transform knowledge more productively. In the context of the affective domain, attitudes and beliefs can be regarded of as generic responses to something, the core quality of an emotion, feeling, mood, or temperament, and hence as affective mental activities. The framework of the CT disposition proposed in this chapter was developed based on tripartite classification of mental activities known as of trilogy of mind: cognitive, affective, and conative. The basic tenet of this chapter is aligned with the theoretical underpinnings of thinking dispositions which is expected to suit different contexts and needs.
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There is tremendous excitement around makerspaces for deepening and enriching curricula across subjects, as well as engaging traditionally marginalized learners in new ways. To address the lack of translation of maker education projects to mathematics learning, we propose that educators aspire to create a “Mathland” when designing maker educational activities. Mathlands are environments envisioned by Seymour Papert where mathematics are learned alongside ways of doing mathematics in self-selected contexts, leading to an epistemology and natural language of mathematics that pervades all experiences. To imagine a Mathland where women’s participation in mathematics is lifelong and lifewide, we explore traditionally female-dominated fiber crafts where long-term engagement, mathematics, and heritage intersect. As part of a longitudinal embedded multi-year ethnographic study, we conducted cohort analyses as well as grounded, iterative, and thematic coding of semi-structured interview data, augmented with crafting artifacts from 65 adult fiber crafters. Using qualitative analytical techniques, we asked: How does math occur in craft? How do crafters observe the intersection between math and craft in process? Fiber crafts were found to present a “Mathland,” a lifelong context for immersive math engagement. We present crafters’ math insights in the craft, as well as multiple aspects of the crafts and surrounding communities that supported the crafters in sustaining their engagement with mathematics throughout their lifetime. This study has implications for the design of inclusive and lifelong maker educational environments for mathematics learning.
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The HELMeTO Conference aims at bringing together researchers and practitioners working in Higher Distance Education Institutions or studying Online Learning Methodologies to present and share their research in a multidisciplinary context. The conference provides a forum for the discussion of new research directions and applications in these fields, where different disciplines could effectively meet.
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Professional learning can support teachers in developing their understanding of how to position students as agentic and authoritative – a rarity in most classrooms. We analyzed teachers’ discourse during professional development focused on agency and authority in middle school mathematics classrooms. We found that teachers frequently engaged with ideas related to student agency and authority. Though less common, episodes in which teachers constructed new ideas and critiqued existing ones indicate that using activity prompts, practicing responsive facilitation, normalizing critical stances, and positioning frameworks as tentative are important for supporting deeper engagement with ideas related to student agency and authority.
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Textbooks have been the subject of research within and across disciplines, but have not yet been widely studied from a disciplinary literacy perspective. Readerly agency is also understudied in disciplinary literacy. The present paper aims to illuminate both of these areas by examining facets of agency that readers demonstrated during think-aloud interviews with a college calculus textbook, thus exploring the disciplinary literacies that are involved in reading this didactical text. Authors have drawn on the recently forwarded theory of “didactical disciplinary literacy,” as well as definitions of agency in both literacy and math fields, to reveal how agency was enacted by readers using the textbook to negotiate unknowns in calculus. Findings show participants exhibiting agency in a range of ways, but not always in direct relationship to themselves as agents within the field of mathematics. This study invites college instructors and secondary teachers to consider ways they might foster didactical disciplinary literacy skills to support student learners in mathematics, and other disciplines.
Article
The centrality of knowledge construction to student learning is well-recognised in education. In this study, we explore what it means to go beyond knowledge construction to knowledge evaluation, and how knowledge evaluation combined with direct disciplinary access improves opportunities for meaningful learning. We first review literature to advance a theoretical understanding of a) the importance of student evaluation of knowledge and b) direct disciplinary access, and then review how both of these in tandem support students’ learning with science content. We then use a single case study with a highly effective teacher to better understand the practical significance of these topics. Findings demonstrate how the teacher’s approach supported students’ opportunities to evaluate (rather than just construct) knowledge, which improved students’ meaning-making around science concepts. Her approach also supported students’ direct and unmediated access to science content, which has further implications for their scientific literacy and civic engagement. In describing the link between knowledge evaluation and direct disciplinary access in one teacher’s classroom, we further articulate what it means for students to take a central role in the evaluation and use of science knowledge.
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Zusammenfassung Identität von Mathematiklernenden beschreibt das Sprechen und Denken über das Selbst in Bezug zur Mathematik und kann das Mathematiklernen von Schülern und Schülerinnen und ihre Beziehung zum Fach maßgeblich beeinflussen. Frühere Studien zeigten für lehrerzentrierten Mathematikunterricht, dass die dem Mathematiklernen zugeschriebene Relevanz einen verkürzten und widersprüchlichen Diskurs darstellt, dass Lehrererklärungen Möglichkeiten des Verstehens monopolisieren und dass oft kaum Möglichkeiten gesehen werden, seine Persönlichkeit im Unterricht einzubringen. Diese Barrieren stehen einer Teilhabe am Mathematikunterricht für viele Schüler und Schülerinnen im Weg. Andere Studien wiesen jedoch daraufhin, dass schülerzentrierter Mathematikunterricht diese Hürden abbauen kann. In der hier berichteten Interviewstudie wurden Schüler und Schülerinnen aus zwei schülerzentriert unterrichteten Klassen der Sekundarstufe befragt, von der eine nach einem Freiarbeitskonzept arbeitete. Die Ergebnisse wurden entlang des poststrukturalistischen Konzepts der Identitätsarbeit ausgewertet. Zum einen zeigte sich selbst für die schülerzentriert unterrichteten Klassen ein verkürzter Relevanzdiskurs, der jedoch durch geeignete Nachfragen aufgebrochen werden konnte. Zum anderen bestätigten sich bezüglich der Rolle der Lehrererklärungen und der Persönlichkeitseinbringungen Vorteile für die Identitätsarbeit im schülerzentrierten Mathematikunterricht.
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