Abstract:Background and Purpose:The purpose of this virtual presentation of a study on the sustainable development of mathematics education is to contribute to research on the use of AI for examining Swedish pre-service mathematics teachers. The research question is as follows: "How can Swedish pre-service mathematics teachers be digitally examined on sustainable mathematics education using AI as a digital tool?"The course "Numeracy in Arithmetic" is offered as a distance course with a digital examination. Following the breakthrough of AI as an aid, many students use AI-based tools in their exam solutions. A current question is therefore whether this should be considered as cheating. One way to ensure that AI is used creatively is to design exam tasks as write a short essay on the sustainable development of mathematics education in arithmetic using given arithmetic concepts.

Method and Result:150 Swedish pre-service teachers were given the task to write an essay as described in the Background, using a prescribed set of mathematical concepts, chosen with respect to the level of the course in question. The exam was anonymous, so no student could be identified. The written exams were analysed in categories of the sustainable global goals (SGD). A major part of the students (78,0%) solved this task successfully. However, some students (18,9 %) did not hand in any answer due to shortage of time. 

Conclusion, and Discussion:The analysis of the result indicates that the participants used AI as a creative tool and not as a mean of cheating by uncritically accepting AI-generated texts. An important observation is that AI can generate false but linguistically convincing results, necessitating an extra critical review of students' solutions.A challenge for future teacher educators is to break new ground in the use of AI in mathematics education, due to the facts that AI was not adapted for mathematics previously, but that significant development has taken place recently.This study should be considered a pilot study on a limited and fundamental area of mathematics. To meet the future needs of pre-service teachers of mathematics in their teaching careers, they must learn to use available AI-based tools critically if they shall be able to integrate AI into teaching as a facilitating support.

Principal Topic

The empirical evidence shows that the Sustainable Development Goals (SDGs) have received significant attention for addressing global challenges like poverty, inequality, and environmental sustainability. However, there is growing interest in exploring their potential impact on improving students' competencies in core subjects like mathematics, which fosters problem-solving, critical thinking, and decision-making skills.In this context, the study aims to investigate the impact of the SDGs on students' mathematical competencies by comparing Austria and Sweden. Specifically, it seeks to answer: (1) Do SDGs enhance knowledge acquisition in mathematics? (2) How does causality influence the relationship between SDGs and numbers? (3) Are these texts in the sense of SDGs fact-based, normative, or pluralistic in terms? 

Methodology/Key Propositions

The empirical analysis is based on 250 essays. Business school students from Austria and teacher students from Sweden were given the task of writing a 100–150-word essay on natural and rational numbers, including the SDGs. Mathematical terms such as whole numbers, order, the number 0, positive, non-negative, denominator, numerator and quotient were to be part of the essay.In our methodological framework, the unit of analysis is the students' writing, which gives us insight into their perceptions of the link between mathematical literacy and the SDGs. 

Results and Implications

The main findings indicate that the SDGs have a minor influence on Austrian students' decision-making, with the number associated with each SDG being the key factor. Most Austrian students (55.9%) focused on SDG 4 'Quality education', followed by SDG 1 'No poverty' (15.8%) and SDG 12 'Responsible consumption and production' (5.9%). Swedish students also favored SDG 4 (21.4%), followed by SDG 1 (14.5%), but ranked SDG 10 'Reduced inequality' (7.5%) third. Overall, Austrian students mainly viewed the SDGs through a mathematical lens, without recognizing numbers as tools for addressing sustainability. In contrast, some Swedish students saw mathematics as a tool to allocate resources and reduce inequality, aiming for a more just society.

The purpose of this study is to shed light on how static and dynamic proportionality is treated by authors of teaching materials, on national tests and by teachers and students in the classroom, as well as how students encounter mathematics tasks where proportional reasoning is an option. The research is based on two sets of empirical data. In concrete terms, the thesis includes three studies examining three themes that relate to proportionality in classroom interaction and in texts. The first study analyses how proportionality is presented in some Swedish textbooks, in curricular texts and national course tests in mathematics for students in upper secondary school. The second study is a case study of how a teacher instructs and explains a task in a class in Grade 6, where proportional reasoning is a possible solution technique. Finally, the third study concerns how students in Grade 6 handle proportional reasoning when they encounter a patterning task involving proportional relationships. The analyses of textbooks and national course tests show that proportionality is handled differently in these two settings in the context of “Mathematics A” at the upper secondary school. About a quarter of the tasks in the textbooks and the national course tests involved proportionality tasks of one specific kind (missing value). Other types of proportionality tasks were infrequent. The results of the classroom studies show that students are able to engage in early forms of proportional reasoning before being taught about proportionality as a mathematical concept. The concept of learning trajectory is used to identify situations in the learning process during instruction where students meet obstacles and need scaffolding and teacher support. It is shown how a teacher dealing with a mathematical task involving mixtures of liquids encounters a task that has the possibility of making proportional reasoning visible for the students, and how she struggles to make the modelling required intelligible to herself and to the students. The instructional strategy of using everyday problems as a basis for learning implies that the initial modelling phase becomes crucial, and the students have to be aware of the conditions and limitations under which proportional reasoning is applicable. In conclusion, students engage in early forms of proportional reasoning well ahead of formal instruction. The difficulties they experience as they are to develop their proficiency, and where they require support from the teacher, concern how to model the familiar, everyday situations they encounter in exercises in mathematically precise and productive ways. In addition, in textbooks and national course tests proportionality is presented in a standardized, and rather simplified, form, and it is not sufficiently connected to the various areas of mathematics teaching and learning where it is applicable

This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students’ use of spontaneous concepts when first dealing with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a microgenetic analysis was performed to identify students’ learning trajectories, starting with students familiarizing themselves with pattern structure, followed by engagement in proportional reasoning, and ending with students perceiving a new technique to handle a situation where proportional reasoning did not suffice. While some student groups were able to move along the whole trajectory, most groups, when facing challenges, regressed to simpler techniques. The results provide new insights into students’ learning trajectories, which can be used to support students’ progress in the context of student-teacher interaction.

This article reports on an analysis of the process in which knowledge to be taught was transposed into knowledge actually taught, concerning a task including proportional relationships in an algebra setting in a grade 6 classroom. We identified affordances and constraints of the task by describing the mathematical praxeology of the two different types of knowledge exposed, in the task as such and in the activity of the classroom. Through the teacher’s explicit process of reasoning, modeling, revising, solving, and repeatedly explaining the task, we found that the transposition of knowl- edge was seriously affected by the contextualization of the task. Modeling word problems about everyday situations has its limitations and can, as in this case, make the problem unsolvable unless it is accepted as a Btextbook task^ disguised as real but adjusted to the norms of school mathematics. Such constraints may obscure mathe- matical ideas afforded by the task. We conclude that learning opportunities embedded in a task do not necessarily surface when a task is treated in a classroom setting

Uppgifter har en central roll inom matematikundervisning, och eftersom utbudet av yrkesrelaterade uppgifter är begränsat är det viktigt förmatematiklärarepå yrkesprogram att kunna skapa nya sådana uppgifter.

I den svenska matematikundervisningen har ett trendbrott inträffat i och med att billiga bärbara datorer, interaktiva skrivtavlor, sofistikerade mobiltelefoner och en i högre grad problembaserad undervisning blivit allt vanligare. I det övergripande syftet i ämnesplanen för matematik betonas att eleverna ska ”ges möjlighet att utveckla sin förmåga att använda digital teknik, digitala medier och även andra verktyg som kan förekomma inom karaktärsämnena” (Skolverket, 2011). Digitalaverktygfinns även med i kunskapskraven för alla betygsstegi kursen Matematik 1. Där ingår att eleven ”löser uppgifter av standardkaraktär med viss säkerhet, både utan och med digitala och andra praxisnära verktyg” (Skolverket, 2011).

• Digital teknik (t.ex.responsprogram, utbildningsplattformar, interaktiva tavlor, applikationer, bokföringsprogram, bokningsprogram, schema, kalkylprogram)
• Digitala medier (internet, mobiltelefoner, surfplattoroch dator)
• Verktyg inom karaktärsämnen(sinushylla, linjaler med skala, mätverktyg, termometer, våg mm.)

Vi fokuserar i denna text på hur digitala hjälpmedel och verktyg påverkar möjligheter till interaktion i klassrummet.