# Apply minimum core specification in literacy language numeracy and act

This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract This study of networked classroom activity proposes that a resource-rich point of view is powerful in increasing the engagement of marginalized students in mathematics classes.

Our work brings attention to the values, beliefs, and power relations that infuse numeracy practices and adds attention to mathematical dimensions of social spaces.

Findings show that the multiple modes available to communicate mathematically, to contribute, and the inquiry-oriented discussions invited students to draw on a variety of expressive modes to engage with complex mathematical concepts.

Spatial analyses illuminate the relations among reproduction and production of knowledge, as well as the social space that characterized the networked classroom activity.

Students extended notions about social space by adding attention to affective features of classroom and school activities. Introduction We hope with this study to contribute to the literature that illuminates the successful participation of marginalized students in secondary mathematics classes.

From this perspective, rather than focusing on the barriers, such youth may face, we examine classroom interactions that foster their engagement in powerful mathematics learning. We use varied terms throughout the paper to refer to youth and communities that have and continue to be subject to societal inequities as a way to trouble the use of language such as urban and at-risk languages that cover deficit assumptions about people and places.

Similar stances are evident in related literature reviewed here. We approach this analysis similarly in that it is an exercise in examining what we see when we take a social spatial theoretical position and use its central tenets to analyze classroom activity and interaction. We present findings from a study of mathematical practices of high school youth in the northeast US, building on work in New Literacy Studies or NLS [ 23 ].

In addition to literacy, this framework changes the ways that we think about other disciplines, including mathematics and science. For many, mathematical and scientific practices can no longer be separated from the larger contexts in which they occur. Their differentiation between numeracy and mathematics highlights the embedded nature of mathematics in everyday life: Numeracy, then, is taken as the broader term, including both everyday practices and educational aspects, both of which may have a mathematical dimension.

Mathematics, then, we take to be a more specialised and abstract set of practices, usually the domain of professional practitioners of both mathematicians in universities and mathematics educators in both Higher Education and schooling. These dimensions shape what kind of numeracy gets done in particular situations. Their work provides important impetus for our explorations of numeracy as social practice in relation to the creation of classroom social spaces that have mathematical and cultural dimensions as central features.

Our work contributes to the social turn in mathematics education research [ 79 ]. Exploring this social turn is informative for deepening the understanding of numeracy that is inevitably constructed as students and teachers make meaning in classrooms. The focus on social construction in mathematics has included recognition that examining both every day and schooled mathematics practices is critical to understand mathematics learning and teaching and to inform both pedagogy and policy cf.

Attention to both every day and school activity is important to mathematics education research because it broadens the contexts in which mathematics learning is considered to occur. Our contribution to this work is bringing attention to the values, beliefs, and power relations that infuse numeracy practices and adding attention to mathematical dimensions of social spaces. Further, we show the ways that numeracy practices shape and are shaped by the social space of the classroom.

Spaces as Social Constructions At first blush, space may seem static as in classroom space with its apply minimum core specification in literacy language numeracy and act desks, tables, chairs, and so forth, staying largely unchanged over decades, particularly in underresourced schools serving nondominant students.

However, following theorists apply minimum core specification in literacy language numeracy and act Soja [ 15 ], Harvey [ 16 ], and de Certeau [ 17 ], we propose that, contrary to this rigidity, social space is actually dynamic and volatile. For example, cities are made up of spaces that are constructed and differentiated based on physical, social, and historical dimensions: On another scale, youth experience school spaces as different from neighborhood spaces due to the physical arrangements of people and things, the kinds of actions and talk that are treated as legitimate, and the norms for social relations among children and adults.

Finally, in school and classroom spaces, youth are positioned in relation to both the teacher and the discipline of mathematics as, among other things, producers or, more often, receivers of knowledge. Treating space as a social construction leads us to consider the practices through which spaces are created, how people are positioned in various spaces, and the implications for agency and learning.

In this paper, we examine numeracy as a social practice that creates social space, considering in particular its productive nature, or how it is implicated in the construction of space that has social, historical, cultural, and mathematical dimensions, all of which are infused with relations of power [ 9 ].

Appropriate questions to consider when looking at practices with an eye toward spatial analysis include the following. How are numeracy and social practices changing classroom social space? We find this approach promising in its attention to agency and to the variety of ways in which people engage in numeracy practices, as well as the connections among school, home, and community practices that have mathematical activity as central features cf.

A social practice view provides a unique perspective on pedagogical issues, given the focus on practices and activities that make up everyday interactions both in and out of classrooms. Taking on a spatial theory lens extends such work i.

In this study, we explore work with a networked classroom technology described below that requires collaboration among students, fosters generative learning, and transforms both the mathematical content and student-teacher roles [ 18 ].

Examination of such practices has the potential to widen the types of practices invited into classroom mathematics activity. As shown in earlier research [ 23 ], these activities can be crucial in building on practices of students that are often undervalued or excluded from mathematics teaching and learning in school. The networked technology is Hubnet and Participatory Simulations PartSims; [ 24 ] extensive information about this networked system is available at http: The system involves graphing calculators that are connected to hubs that have a wireless connection to a computer which functions as a central server.

In PartSims, students act out the roles of individual system elements and then see how the behavior of the system as a whole can emerge from these individual behaviors.

The emergent behavior of the system and its relation to individual participant actions and strategies can then become the object of collective discussion and analysis. PartSims provide opportunities for youth to be central actors and producers of mathematical discourse and practice. This view of students is in stark contrast to the conventional classrooms that position them as recipients of norms, practices, and discourses, at the mercy of adult and institutional exercises of power.

As we show below, it is also a productive arena for examining the creation of social space because youth have ample opportunity to interact and to exercise agency as to what mathematics is explored as well as how the exploration proceeds, transforming classroom practices to those that invite participation by more students and less control by teachers. The particular PartSim that is the focus of this paper is Gridlock, which involves each student individually controlling a traffic light at a specific intersection in a traffic grid and working collectively to optimize traffic flow more extensive description of the activity is included below.

The numeracy involved includes the mathematics of variation and change, working with positive and negative numbers, graph analysis, and connections to traffic flow in the city in which the classroom is situated. Gridlock is appropriate for conducting a multidimensional exploration of the construction of social spaces.

For example, students work with multiple, linked representations i. Gridlock is also rich with mathematical discourse and practice, including representations, visualization, language, and gesture serving to mediate learning and interaction. In addition, Gridlock involves rich mathematical content and reasoning in ways that are similar to SimCalc [ 2527 ]: Important for this study are the following: The Standards for Mathematical Content are a balanced combination of procedure and understanding.

Students who lack understanding of a topic may rely on procedures too heavily.

- Our understanding of some of the mathematically rich, culturally valued practices they bring to classroom learning in has become much more tangible;
- T-level Qualifications The new T-level qualifications are due to be introduced for first teaching from September , with the first students offering T-levels applying to university in the autumn of
- Teachers are working to support student learning in this atmosphere and students are working to negotiate the context, too;
- As Roschelle et al.

Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.

As seen in the findings reported below, foundational understandings of concepts and mathematical representations were built across all the events and classrooms we studied, preparing students for rigorous mathematics learning.

Beyond mathematics classrooms, understanding the mathematics of change and variation is important for many topics in the curriculum beyond algebra and calculus. As discussed earlier, social sciences, economics, and history increasingly rely on dynamic models to understand complex phenomena.

## 1 in 10 student teachers fail this test: Can you pass?

Interactive media that simultaneously present qualitative and quantitative representations are potentially useful in many fields for helping learners bridge between experience and abstraction [ 28 ], p. Both the widely applicable mathematics involved and the grounding in personal experience production can alter classroom social spaces that are ripe with opportunities to exercise agency and learn powerful mathematics.

The transformed social space and access to rigorous mathematics are particularly salient for urban schools serving students of color, where expectations of students and provision of resources are often low [ 213031 ]. The paper is organized as follows: We present findings from our study in high school mathematics classrooms in Rochester, NY, and conclude with a discussion of implications for research and pedagogy. Theoretical Framework We work in this study to particularize examinations of social space to numeracy activity in classroom contexts involving youth from nondominant groups.

Following Street, Baker, and colleagues [ 7933 ], our starting point is the social and cultural practices involved in numeracy events; we view those practices as activities that create space that has social, political, historical, cultural, and mathematical dimensions.

From this view, such activity shapes and is shaped by discipline-specific ways of speaking, interacting, acting, and using analytical and physical tools. Numeracy practices, then, emerge from interactions involving both numeracy—language, representations, symbolic and notational systems, forms of argumentation—and the contexts in which numeracy activity is taking place e.

Integral to those contexts are the power relations that permeate them, given that participants are accorded differing status in relation to content and to each other in different contexts. We add attention to the creation of social space through practices that shape the kinds of activities and modes of participation treated as appropriate or legitimate in particular places involving particular people [ 151934 ].

Such practices also shape the kinds of interactions, social relations, and knowledge that result. In addition, the ways in which everyday activity inserts dynamism, mutability, and challenge into dominant norms are made explicit.

This complements Street et al. However, social spatial theory gives us a way to examine in some detail how those power relations and values come to be. Notions of space involving a relationship among physical, mental, and social spheres of activity are useful in studies of numeracy practices across contexts because they highlight the dynamic and multidimensional aspects of space-creating activity, that is, physical, historical, sociocultural, political, and mathematical dimensions.

These spheres exist in a mutually constitutive relationship, where each influences and is influenced by the activity in the other, while retaining distinct features that make them unique arenas for action. In particular, for our work, the networked activity we examined has design principles that guide both the architecture of the system of networked calculators and the orchestration of activities that involve physical, mental, and social space.

Students are physically connected via the calculator-hub-server system, transforming the classroom from a collection of individuals to a collective body physical, social that constructs and analyzes mathematical objects and complex systems both social and mathematical.

- All of these representations were displayed visually at the front of the class see Figure 1;
- In PartSims, students act out the roles of individual system elements and then see how the behavior of the system as a whole can emerge from these individual behaviors;
- The interviews included but were not limited to specific questions about Gridlock; other questions addressed other PartSims and more general impressions and advice students would share;
- Core Maths Qualifications The University recognises the value of the Core Maths qualification to support the development of mathematical skills.

Students build conceptual understandings to scaffold work with the more abstract and formal content involved mathematical.

The resources students brought to bear in our study include informal and formal language i. For them, urban language is a hybrid derived from a variety of sources. As we show, transformation of dominated spaces that have developed over time is a key feature political. It is the explicit recognition that social space involves multiple, overlapping spheres of activity that does important conceptual work for our research.

Engagement in them is largely unreflective. Certain paths and actions are presupposed for particular places and people e.

- As shown in earlier research [ 23 ], these activities can be crucial in building on practices of students that are often undervalued or excluded from mathematics teaching and learning in school;
- Focus on interactions, utterances, gestures, and use of artifacts e;
- Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut;
- Hence, we see the activity of Gridlock inserting dynamism and mutability into numeracy practice and challenging the dominant norms of the mathematics classroom;
- Our observations outside classrooms corroborated the notion of tension;
- The first presents our analyses of the numeracy practices found in the networked classroom activity, including the mathematics and the control of symbols, signs, and knowledge.

Spatializing practices, on the other hand, are those involved in appropriation and production of space. Spatializing practices can involve both production and reproduction, depending on the purposes people have for engaging in them.

Methods Again, the guiding questions for our study are as follows. How are numeracy practices changing classroom social space? Given our theoretical framework, ethnographic style methods are appropriate. LeCompte and Schensul [ 35 ] note that ethnography uses everyday practices as a lens for interpretation as well as exploring the sociopolitical and historical nature of phenomena.

Rather than testing hypotheses, we are seeking to understand numeracy practices involving urban youth and the meanings numeracy has for them. Setting The school Biddy Mason Academy a pseudonym is a high school in Rochester, NY, located in a large urban school district that has been designated as the most needy in the state, surpassing districts in New York City, Buffalo, and Albany in the proportion of students served who are living in poverty.

Our study was apply minimum core specification in literacy language numeracy and act during the — academic years. The State Department of Education reported that, inthe school served students from grades seven to As with most schools in the US and especially urban schools, the culture of the school is shaped by an intense focus on standardized test scores and accountability, creating an atmosphere of tight control of curriculum and pedagogy.

It is also a very large, overcrowded school that focuses on strict discipline As ofa new principal was hired who has undertaken substantial changes that have, according to news reports and statements of students, begun to change some aspects of the climate.