Language Use and Development in the Matematics Classroom.

LaUDiM is an intervention project where the main goal is to gain knowledge on the learning environment's significance for developing young learners' mathematical thinking and understanding, and their ability to express mathematical ideas, orally and written, alone and in collaboration. This entails the ability to discuss mathematics and justify why something is true or not. The teachers conduct lessons planned in collaboration with the researchers. Video recordings from the lessons and written pupil-work are discussed and analyzed as a collaborative enterprise. Theoretical framework for the project is Brousseau's Theory of didactical situations (TDS). TDS contributes to design teaching, to analyze what happens in the classroom and to develop teaching. The latter is another aim in the project. Language development and conceptual development are central topics. This also entails the role of language for stimulating particular ways of thinking when solving a mathematical problem. In a study, soon to be published, pupils? construing of a shape preserving enlargement as a multiplicative structure is explored. Language cues that contribute to pupils shifting from an additive to a multiplicative way of thinking are identified. How do second-graders understand the concept of "one half"? Three different interpretations are identified: as halving, as modifier, and as an independent quantity. Studies on work with polygons find conditions that indicate a need to address and clarify the concepts hjørne (vertex)and kant (edge) in Norwegian schools, in classrooms and in textbooks. A study researching how the teacher actively uses pupils? language in the phase of TDS where the mathematical knowledge is institutionalised, shows how a TDS-based design gives the teacher the opportunity to obtain insight in the pupils? language, and how she uses this insight to establish a shared, and mathematically acceptable, knowledge in the class. Another study shows that the teacher works from an overarching goal of encouraging the pupils to work like mathematicians. Three actions that stimulates such work are identified: modeling explorative work, monitoring the pupils' work and orchestrating whole-class discussions to attain agreement. Main findings from the project and a presentation of TDS are soon to be published (autumn 2020) in a book entitled Samtaleorientert matematikk ? et samspill mellom didaktiske og adidaktiske situasjoner. What stimulates and what impedes mathematical progress in pair-work? Shared goal, co-reasoning, involvement in each other?s thinking supported by different representations stimulate such progress. Lack of progress is connected to disputational talk where individual decision-making substitutes argumentation and involvement in each other?s thinking. A study of young children?s drawings in the exploration of multiplicative situations identify four different problem-solving functions: tool for exploration, holder of information, developing calculation strategies and as representation of the answer. How does one teacher communicate with the pupils in pair-work? A study shows that she lets them keep agency of the task, an important point in TDS. Building on their own thoughts, she helps them to explore, clarify and formulate these. Another study shows how the teacher draws on this knowledge when she uses pupils? work in a way that takes care of and unite the mathematics with pupil involvement in whole-class discussions. How do the participants develop their thinking and practice, and how is new knowledge created? A study shows that through preanalysis and design of teaching situations in mathematics, didacticians learn about adaptations to students? prerequisites and teachers learn about epistemological prerequisites for students? learning. TDS with its model of teaching has helped the project group to focus on the function of the target knowledge and led to changed practice for the teachers. The doctoral student has made visible underlying factors and processes in the teachers' work on facilitating, and further build on the pupils' own thinking. She explores the communication between teacher and pupils, structural considerations in the organization and the teacher's role in the span between academic mathematical discourse and the development of a mathematical classroom discourse. A subproject explores student teachers' whole-class dialogues. Use of video in post-lesson mentoring support the student teachers in developing their role as interpreter and translator of the pupils' thinking so the dialogue becomes productive for all the pupils. Findings from the project are presented at seminars, conferences and in publications for different target groups. Knowledge developed in the project will strengthen teaching and a research-based teacher education. Open access publications and references to published articles and conference presentations are found at https://ntnu.no/ilu/laudim

I løpet av prosjektperioden har både lærerutdannerne og lærerne endret og utviklet sin undervisning som følge av funn og teoretisk rammeverk. Gjennom publikasjoner har andre i utdanningssystemet hatt god tilgang til våre resultater. Erfaringer fra hvordan vi har samarbeidet i prosjektgruppa kan ha betydning for forskningsfeltet. Vi kan ikke si noe om påvirkninga. Boka fra prosjektet som kommer høsten 2020 er et viktig bidrag som har potensial til å nå lærerutdannere og mange framtidige lærere.

The main objective of LaUDiM is to develop scientific knowledge of a successful learning culture in early learning of mathematics with special emphasis on language development. This comprises the pupils' proficiency in a broad register of mathematical dis course, as well as the teachers' proficiency in preparing for and orchestrating the mathematics classroom in ways that are instrumental to pupils reaching the learning goals defined by the teacher. The project aims at creating a milieu which improves pup ils' proficiency in expressing mathematical concepts and ideas using a variety of representations, and further, improves their proficiency in mathematical reasoning and justification. To explore these questions we will conduct a four year long interventi on-based classroom study in a hermeneutic qualitative research paradigm. We have chosen a video-based design which encompasses the complexity and the diversity of voices, perspectives and issues at play. Video-recorded classroom situations will be analyse d in collaboration with the involved teachers in two schools. The recorded discussions will be analysed in comparison with analyses of pupils' written work and teachers' written responses. The project will contribute to knowledge development relevant fo r early learning and teaching, it will provide teaching materials for teacher education and mentor education, and it will introduce video as a mediating tool in field practice in GLU 1.-7. and school development projects. It meets needs in LK06 within the field of basic skills, and calls in white papers for early effort for lifelong learning and identification of "best practice" in mathematics education. The project will also strengthen the research-based learning in teacher education. We also aim to deve lop knowledge on how video can be used as a tool for fostering user involvement in classroom research. LaUDiM will be conducted in collaboration with users and fellow researchers, nationally and internationall