Early algebraic thinking can be connected in significant ways to sustainability issues through algebraic wicked problems (AWP). AWP are problems that mobilize children to think algebraically while experiencing dilemmas on values at stake in sustainability. Both algebraic thinking and sustainability issues become inseparably connected. From an ongoing analysis of 10 research group meetings over a school year in a group consisting of teachers, pre-service teachers, and researchers, and based on observed lessons, we explore such dilemmas as a central characteristic of AWP. This provides details into what may be important aspects in the further design of AWPs.

The presence of digital resources in mathematics classrooms can fundamentally alter mathematics teaching, learning and curriculum, as well as how they are both studied and theorized. These shifts bring new complexities to the already complex work of teaching, requiring teachers to develop new routines, practices, skills, and competencies. They also invite the generation of new frameworks and tools for conceptualizing and studying the work of teaching. The chapters in this section, Relationships Between Mathematics Teachers’ Practices, Knowledge, and Skills and the Use of Digital Resources, take these digital evolutions as a starting place and explore their implications for interactions among teachers, resources, learners, and other stakeholders and for researchers. This chapter locates the work presented in the seven chapters that follow in existing research and frameworks related to mathematics teaching practice, teacher knowledge, professional learning, and teachers’ resource systems. Within the chapter, teaching and research are viewed as cultural and context-specific practices, influenced by local norms and culturally encoded perspectives. In order to offer a global perspective, the seven chapters in the section represent work from 15 different countries or cultural contexts. This chapter provides a brief overview of each of these chapters before identifying additional questions for consideration.

We study the connections among different “actors” — human as well as nonhuman — to document and understand an inquiry group’s movement toward designing and implementing Algebraic Wicked Problems (AWPs). AWPs combine both algebraic and environmental ideas. The inquiry group consists of Swedish teachers, teacher students and a researcher-teacher educator. Since AWPs have not been explored yet in teaching, it has taken a long process to imagine and trying to formulate them. Our focus on the network of connections among actors has helped to trace aspects of this long process. It has also helped identifying specific non-human actors that constitute the network such as diagrams and materials. Our analysis suggests that the process of imagining something that does not yet exist in itself also can becomes an actor. 

This paper aims to discuss an advance in the direction of bridging the gap between early school algebra and socially relevant issues using the idea of wicked problems. We do so by focusing on the possibilities and challenges of working with the idea of algebraic wicked in the context of planning, teaching, and reflecting on algebra lessons for young children of 7-9 years old. This endeavor is a collaboration between the researcher/teacher educator, teacher students and in-service teachers following the critical research methodology of imagining and trying to create something that does not yet exist. This paper represents partly how far we have come to formulate an algebraic wicked problem that can invite students to engage into a cultural and sociological algebraic activity and as such reports on what we have learned from trying to design and enact algebraic wicked problems.

This cross-cultural study examines how elementary mathematics teachers in Finland and the United States shifted their instructional systems during the period of Emergency Remote Teaching (ERT) in the spring of 2020. Using Ruthven's (2009) framework of Structural Features of Classroom Practice, researchers analysed 15 teachers’ descriptions of their mathematics teaching during ERT in contrast to their typical practice. Exploring how teachers in both contexts navigated challenges of ERT through a cross-cultural lens allowed researchers to identify similarities and differences in teaching practices and use of activity formats, synthesized in composite models of teachers’ instructional systems. The differences in the systems can be traced to underlying cultural assumptions about the nature of elementary mathematics education and the roles of teachers, students, and curriculum resources within each system.

Cross-cultural research covering multiple languages and cultures involves negotiating conceptual and linguistic challenges. This paper focuses on how researchers working across cultural and linguistic boundaries navigate the research process and negotiate a common understanding of the constructs under study. Working towards intersubjectivity within a cross-cultural research team is essential, as it deepens understanding of one another’s contexts and our own. We analyze our own research process, as a cross-cultural team studying elementary school teachers’ use of print and digital instructional resources in Finland, Flanders, Sweden, and the U.S. Recorded team conversations served as data to help us explore the way language and culture are intertwined and how these relationships surface when developing research instruments and conducting analysis of the interviews, in which language became a focal point. Challenges emerged particularly within three research aims, namely, naming and describing teaching practices, understanding teachers’ relationships with mathematics resources, and defining digital resources in a cross-cultural survey. Our systematic analysis of instances of conceptual and linguistic inequivalence prompted the team to make language explicit and revealed that these instances varied in several ways that had implications for how and whether they might be bridged. Thus, this paper contributes to understanding the methodological impact of using a shared language, acknowledging that researchers’ lexicons about mathematics teaching are closely linked to their own cultural knowledge and experience. Therefore, working explicitly across language and culture towards mutual understanding is a necessity and a way to reinforce the validity of research outcomes. 

Curriculum resources such as textbooks and lesson guides communicate messages about the social relations between the teacher, students, artefacts, and the mathematics. Because of their implicit nature, these messages can be hard to surface and perhaps therefore are not frequently covered in curriculum resource analysis. Tackling this shortcoming, we examine mathematics lesson guides or the daily lesson descriptions written for elementary teachers. Drawing on multimodality and activity theory, we characterize the social relations messaged in the lesson guides in terms of two constructs: authority and distance. We present and illustrate an analytical approach to uncovering these messages in lesson guides from Sweden, USA, and Flanders. Our analytical approach enabled us to distinguish configurations of social relations that vary primarily across the three educational contexts, which strengthens our argument for viewing the configuration of social relations as a cultural script. 

How can powerful algebraic ideas be understood for the combined purpose of developing students’ emergent algebraic thinking and fostering future active citizens? To address this question, we have examined two major research review books on early algebra to investigate the interpretations of “powerful algebraic ideas” that are present in the books as a whole. Skovsmose and Valero’s (2008) four interpretations of powerful mathematical ideas (which focus on the logical, psychological, cultural, and sociological power of mathematics) were used. We show that in the books and book chapters there is a dominance of the logical and psychological interpretations of the power ofalgebraic. Furthermore, the cultural and sociological interpretations appear connected to algebraic thinking as a resource or tool for action in “society”. Advancing new possibilities of expanding the ways in which early algebraic thinking is made powerful for students is a challenge to research. 

We attempt to conceptualize digital curriculum resources’ (DCRs) connectivity in the context of mathematics education by relying on the frameworks of boundary crossing/boundary objects and multimodality. We exemplify our framework on three example DCRs from Flanders (Belgium) and the USA and consider impact of connectivity on social relations and issues of control and empowerment.