Recently there has been a trend to include Computer Programming and Environmental Education in national syllabuses due to the accelerated technological development and the climate crisis. This study aims to investigate how notions of Action Competence, Computer Programming and Environmental Education converge or not in Discourses in educational policy documents in Colombia and Sweden. Action Competence is the capacity to play an active role and act intentionally in addressing issues that matter to students. The Discourses that we identified are: (1) Qualification is what counts, (2) Programming has little to do with environmental education, and (3) Students are not decision makers.

This recently started action research project is a collaboration between mathematicsactivists and researchers. The aim is to generate knowledge about how out-of schoolactivities can promote mathematics foregrounds that empower youth with migrationalbackgrounds with confidence in their mathematics skills, and thereby open gatewaysto social and economic mobility. As we see it, school of today has much to learn fromsuch non-formal contexts. The overarching question is; How may activism generatemathematics activities for social justice in migrational contexts?Youth being deprived of education may result in despair, ruined prospects andagony. Mathematics education plays a crucial role in this because mathematicsfunctions as a gatekeeper for advancement in the educational systems. This is whata group of volunteers in Malmö in the south of Sweden from a mathematicshomework support NGO, Mattecentrum, experienced and responded to when theydecided to move from being homework supporters to become activists who act forchange.

Matematisk litteracitet kan definieras på många olika sätt. Varje definition försöker fånga vad det innebär att kunna ta sig fram i världen med matematik. Genom att definiera matematiskt litteracitet på ett visst sätt främjas, implicit eller explicit, ett visst slags matematiskt kunnande och därmed vissa slags sociala praktiker medan andra tonas ned eller rent av exkluderas. Det väcker frågor om hur elever inkluderas och exkluderas i relation till matematisk litteracitet i skolan. Utifrån ett kritiskt perspektiv belyser vi tre olika fall som relaterar till matematik, kroppen och tingen, matematik och flerspråkighet, samt matematik och social klass, för att visa hur vissa sociala praktiker och därmed vissa elever begränsas eller rent av exkluderas när uppmaningen ”Förklara hur du tänkte” genomsyrar matematikundervisning. Genom att anlägga ett kritiskt perspektiv vill vi uppmärksamma frågor om social rättvisa och bidra till att utmana och vidga synen på matematisk litteracitet.

We interviewed groups of students in a language diverse school, where the prevailing language norm was Swedish only, to answer the question; What do students say about relocating school academic mathematics in transitions between home and school? The students mentioned relocating school academic mathematical concepts, problem solving and arithmetical methods from home to school and vice versa. The relocating work provided resources for mathematics learning and feelings of being smart and mathematically knowledgeable and the opposite. We conclude that pedagogical designs that enhance students' first languages and home cultures as resources may benefit from considering students' work with relocating school academic mathematics to enhance opportunities for mathematics learning.

This study investigates how grade five students in a multilingual mathematics classroom where the language of instruction (Swedish) is the only shared language act to inhabit the learning space in solidarity as they encounter epistemological difference. The study contributes with empirical knowledge on students’ solidarity acts when they engage in explanatory conversations in whole class or small group discussions. Theoretically, the study contributes with coordination of Levinasian conceptions of solidarity and inferentialism to capture solidarity in epistemological dimensions of explanatory conversations among students. The study provides 4 different events that illuminate students’ solidarity acts in encounters with epistemological difference. The events include willingness to accept otherness, substituting oneself for the other, disruption and idiolect bridging, and endurance in giving reasons when being asked nonnormatively appropriate questions.

Språk, kultur och matematik är ett nationellt lärar- och forskarnätverk som bildades 2021. Här beskrivs villkoren för dagens matematikundervisning och det arbete som görs av forskare och lärare för att bättre förstå och utveckla matematikundervisningen i mångkulturella, flerspråkiga matematikklassrum. Avslutningsvis bjuds intresserade in att delta i nätverket.

Public media both refects and shapes societal perceptions and attitudes. Teachers and others around students in mathematics classrooms have expectations for the students, projected with what appears in these media. We are most concerned about the expectationsplaced on students who are identifed with minoritized groups—particularly students whoare Indigenous or migrated to Norway. We investigate how minoritized group contexts andmathematics education appear together in Norwegian news media texts. Our analysis usesthe notion of storylines to describe the expectations about minoritized groups that newsmedia project. We found seven entangled storylines: “the majority language and cultureare keys to learning and knowing mathematics,” “mathematics is language- and cultureneutral,” “minoritized groups’ mathematics achievements are linked to culture and gender,”“extraordinary measures are needed to teach students from minoritized groups mathematics,” “students from minoritized groups underachieve,” “students from minoritized groupsput in extraordinary efort and time to learn mathematics,” and “minoritized mathematicsstudents are motivated by gratitude.”

Bokens kapitel utgör viktiga bidrag i en kritisk granskning av svenskmatematikutbildning utifrån sociopolitiska samhällsperspektiv. Motbakgrund av bokens olika kapitel belyser vi upplevelser och konsekvenser av att konstrueras som den andre i svensk matematikutbildning.Med hjälp av begreppet andrafiering synliggör vi författare till dettakapitel tillsammans ’dom andra’ och deras erfarenheter i relation tillmigration och matematikutbildning. Vi som författat detta kapitel, tvånyutexaminerade lärare och två forskare, har därför ingått en så kalladallians. Vårt kapitel visar hur matematikutbildning bidrar till processerav andrafiering och skapandet av den andra och hur dessa processerpåverkar flerspråkiga elevers och lärarstudenters identitetsskapandeoch därmed även deras möjligheter att lära matematik. Flerspråkighetbehöver synliggöras och normaliseras. Alla elevers och lärarstudentersspråk och kulturer måste få ta plats, inte som exotiska inslag av kulturella uttryck utan som en del av den ordinarie matematikutbildningen. 

In this epilogue we elaborate on and synthesise what we have learnt from reading thisbook. We start by considering what the word “apply” in Applying Critical MathematicsEducation might mean. Apply connotes to put into action, but it is also related to thefollowing ideas: to work hard at, to pay close attention to, to have relevance for andto request something. In the context of our readings we think of being relational anddedicated as a matter of enhancing situated critical awareness, addressing relevantissues as a matter of highlighting complex global and local challenges and makingdemands as a matter of agency and power. To us, these themes together synthesisethe insights on critical mathematics education in action that the authors of this bookoffer; namely, propositions on how to illuminate and execute social justice and heterogenous subjectification by critically entangling local and global knowledges in contextually situated educational enactments that hold the potential to address complexchallenges. We close by sharing our ideas on how the contribution of this book gives ushope for the future in these times of crises and complex challenges

In a small on-going participatory research project, we collaborate with mathematics teachers. The project has reached a point where we, both the researchers and the teachers, have come to recognize the need to involve students in the design of their mathematics learning spaces because their knowledges and experiences may provide a crucial contribution. Therefore, we investigate in what way the students, teachers and researchers may collaborate to design mathematics learning spaces to facilitate multilingual students’ mathematics learning. Involving the students in designing socially just mathematics learning spaces necessitates particular methodological decisions and identifies challenges in need of careful attention.

In this, paper we attend to epistemological potentials of multilingual language use and mathematics in connection to the ‘language-as-resource’ idea and how the idea is actualised in Swedish mathematics education contexts. In this paper we develop and propose a framework for considering different epistemological potentials for multilingual mathematics activities that are embedded in the ‘language-as-resource’ idea.

In this chapter, we report on a small-scale critical mathematics education project in a Swedish classroom with students of varied language backgrounds. The project departed from the student Arvid’s statement “Mathematics is bad for society.” Our research interest was twofold. On the one hand, we wanted to explore what knowledge is being (re)produced by students as they try to connect and reason with a statement like “Mathematics is bad for society.” And on the other hand, we were also interested in how the students in this classroom, in which they do not have shared mother tongues, can express and (dis)acknowledge knowledge when reasoning about mathematics in society. We found that when the students (and their teacher) grappled with unpacking critical aspects such as “mathematics in society,” their reciprocal assessment of claims was based on their individual ways of knowing and talking, and tended to shape both their actions and the outcome of their efforts. We show that the discussion around critical aspects of mathematics in society that came to the fore was intertwined with both students’ and the teacher’s (lack of) meta-understanding of language diversity.

In his plenary paper, Tony Essien wrote that “The importance of mathematical examples […] cannot be overemphasised”. Tony’s paper opened my eyes to the significance of examples and of the complex practice of exemplifying in multilingual mathematics education in general, and in teacher education in particular. The triadic framework that Tony proposed captures exemplifying as illustrating concepts from the perspectives of (a) grasping the illustrated concept by discernment; (b) communicating about the illustration as a fundamental idea of teaching and learning; and (c) attending to the multilingual context (of pre-service teachers) in which the illustration is submerged.

In this paper we unpack epistemological aspects of language and mathematicspotentials embedded in the ”language as resource” discourse. We use researchliterature, policy, and interviews with a mathematics teacher and a multilingualstudent to illustrate the potentials and how they are realised in the material. Weidentified a ”lever potential” and ”one new whole” potential. To consider thepotentials in a nuanced way, we propose an analytical model which contributeswith theoretical conceptualizations that allows for grasping a relation betweenepistemologies of language and mathematics from the perspective of thelanguage as resource discourse

This paper discusses the place of precision in mathematics education by exploring its role in curricular guidelines and in classroom life. By means of a joke on precision delivered by a school student in South Sweden, our study focuses on student participation in mathematical tasks that require precision in processes of measuring and reasoning. The paper uses theories on humour and inferentialism to revisit the normative place of “precision” in mathematics classroom discourse.

Recently the prevailing language-as-resource metaphor has been problematised and theorised. Using the philosophical theory of inferentialism, we trace an epistemological dimension of multilingualism in mathematics education and add it to the current language-as-resource discussions. With data from two different settings—a mathematics classroom in Sweden and a workshop in an indigenous settlement in Colombia—we show that in encounters between language practices and plural mathematics, the semantic and the epistemological are two sides of the same coin. Inferentialism captures such encounters without dichotomising either languages or mathematics. We contend that epistemological issues move beyond the scope of language-asresource approaches, but they are not paths to improving school achievement. Neither are they matters of distinguishing between formal and informal language use. Rather, an epistemological dimension is about shaping meta-understandings of language diversity that are liberated from mathematics as fixed and prestablished knowledge.

In this article, I examine how a focus on preciseness in the mathematics classroom could affect group activity. The preciseness relates to the ways mathematical concepts, in this case angles are described in discourse between students. In this context, I consider how ‘micro-invalidations’, can limit students’ opportunities to learn in a social and language diverse classroom. I suggest that students and teachers do not merely navigate language diversity they also navigate epistemological aspects of mathematics. Learning to meet the knowledge of the Other, to avoid epistemological sanctions calls for meta understanding of language diversity which embrace epistemological aspects of mathematics

This thesis is an expedition into and beyond students’ mathematics talk in classrooms framed by migration as a matter of dichotomization betweennamed languages and (in)formal aspects of one fixed mathematics. It is an attempt to make sense of how students grapple with and move about thedivides that those dichotomizations shapes. I ask; How do students in a Grade 5 classroom framed by migration navigate language andepistemological divides when talking about mathematics? and What theoretical conceptualization of epistemological dimensions of languagediversity can be used to frame the students’ navigation of the divides?‘Navigation’ and ‘navigate’ are the metaphors I use for finding one’s way in spaces that do not have established paths to follow. In this thesisepistemological divides articulate difference when individuals and/or cultures take and treat something as mathematical knowledge. They emergewhen people do and talk about mathematics. My focus is not primarily on how students learn mathematics through their navigation, but rather onhow the students inhabit the learn-ing space together—how they relate to each other—as they navigate.To grapple with the research questionsabove, to learn about multiple relational aspects of how students navigate language and epistemological divides when they talk about schoolmathematics, I have used a flexible research design in a multilingual, yet ‘Swedish-only’ Grade 5 (students aged 11) classroom in the south ofSweden. Theoretically I bring together a) linguistic inferentialism as an alternative to the representation paradigm, b) social interaction andecological approaches on knowledge to frame the relationship between language and c) mathematics in students’ talk in a classroom with a complexdiversity of languages and socio-economic backgrounds.Results show that when students in the Grade 5 class navigated language and epistemological divides they demonstrated solidarity andsometimes perform aggressive actions towards each other in their encounters with mathematical knowledge and language diversity. Theseperformances were theoretically conceptualized as meta-understanding of multilingualism (MULD) or lack of MULD. The performances areunderstood as connected to the mathematics based discursive spaces (MBDS) that emerged when the students discoursed.The present thesis contributes to the field by taking an ecology-based relational approach towards language and epistemology in order to providetools for considering students’ responsive translanguaging in multilingual classrooms with no shared languages (except the language of instruction).In addition, this thesis is the first to use inferentialism for ecology-based approaches on social epistemological issues of multilingualism inmathematics education research.

The endeavour of this report is to provide findings on how the normative appreciation of preciseness in mathematical concepts evoke micro-aggressions when students in a linguistically and socially diverse classroom reason about angles in a group activity. Results show that Samir, an emergent Swedish speaker, becomes deprived of reliability and hence loses his chances to make claims of knowledge partly due to the rigidity of (Western) mathematics. The analysed interaction begins with Samir confidently saying “How good I am” when solving a task with his peer Darko. However, it ends with Samir´s ways of talking about himself being completely changed from confidence to insecurity and subordinance, begging Darko to rely on his mathematical knowledge saying “Forgive me…please trust me.”.

I denna del kommer ni att få läsa om, reflektera över och diskutera hur ni kan organisera och använda klassrummets resurser, såsom verktyg, material och placering av elever. Med hjälp av tekniska verktyg, till exempel dokumentkamera, kan man visa elevers lösningar för hela klassen och på så sätt underlätta, fokusera och stimulera klassens resonemang kring en gemensam problemlösningsuppgift.

I denna del kommer ni att få läsa om, reflektera över och diskutera hur användandet av digitala verktyg kan stödja dynamiska representationer i matematikundervisningen. Dessa verktyg kan hjälpa elever att jämföra och kombinera tolkningar som stöds av olika representationer.

I Del 6 kommer ni att få läsa om, reflektera över och diskutera undersökande arbetssätt med hjälp av digitala hjälpmedel.

Digitala medier är idag en naturlig del av barn och ungdomars vardag. I denna del ges exempel på hur matematikundervisning kan ta utgångspunkt i barns och ungdomars medieanvändning. Att utgå ifrån elevernas digitala värld kan vara ett sätt att koppla matematikundervisningen till samhällelig, social och teknisk utveckling ur ett elevperspektiv. Dessutom genomför ni en lektion där lösningen på en problemsituation kommer att presenteras med en film.

I denna del ska du och dina kollegor att arbeta med att utveckla elevers förmåga att kommunicera kring en statistisk undersökning. Ni kommer att få ta del av några olika aspekter av hur yngre elever kan kommunicera kring ett statistiskt material.