Purpose of the project and any changes in the purpose during the project period
The purpose of the project was to deepen the understanding of the relation between the language in mathematical test tasks and the tasks’ demand of reading ability, both when it comes to linguistic properties of the tasks (e.g., wording and grammatical structure) and when it comes to the natural language used to formulate the tasks (e.g., English or Swedish). The project examined mathematical tasks in Swedish, English and German from the international comparative Programme for International Student Assessment, PISA (www.oecd.org/pisa). Both qualitative analyses of the wording of the tasks and statistical analyses of students’ results were performed. The main research questions were:
1. To what extent are there different demands of reading ability for different natural language versions of the same mathematical tasks?            
2. What linguistic properties of tasks are associated with large differences regarding demand of reading ability between different natural language versions of the same mathematical task?
There were no essential changes of the purpose of the project during the time that the project was carried out.

The three most important results from the project and an account of these results
The three most important results from the project can be summarized as follows:
1) A framework for comparing mathematical tasks in different languages (Bergqvist, Edmonds-Wathen, & Österholm). One of the publications of the project is a framework that contributes to the methodology of research on linguistic features that affect the difficulty of (mathematics) tasks. The framework can be used to compare different language versions of the same task, and can guide planning and implementation of future research in the area. Explaining differences in difficulty between mathematics tasks in different languages also contributes to the understanding of the relationships between mathematics and language both in individual languages and in terms of differences between languages.
2) There are differences between different natural languages regarding tasks’ demand of reading ability, that seem to relate to inherent features of the languages (Bergqvist, Theens, & Österholm; and Theens, Bergqvist, & Österholm). These empirical results are based on in-depth analyses of linguistic features of PISA tasks in Swedish, English, and German. This type of analysis for three different languages has not been done before. For example, our findings show that the word length, which in general is very different in these three languages (words are longest in German and shortest in English), also have different connections to demand of reading ability for tasks versions in each language. This result contributes with more specific knowledge of how certain inherent features of languages can complicate translation processes.
3) There is a correlation between the distance between natural languages and how different the reading demands of mathematical tasks are (Österholm, Bergqvist, & Edmonds-Wathen). Translated tasks always have, to some extent, different properties than the original tasks. However, this finding shows that when a task is translated to another natural language, the risk that the reading demands change, grows with the distance between the languages. Distance between languages refers here to differences in, for example, vocabulary and grammatical structure. This result therefore contributes with new knowledge of certain potential reasons for non-equivalence of translated tasks.

New research issues that have been generated through the project
We have shown the existence of different effects, in particular the second and third point above, both addressing issues of inherent properties of languages. Based on such existence, it is relevant to analyze the magnitude of these effects, in relation to the interpretation of results from international comparative assessment such as PISA. That is, we have generated new research questions, for statistical analyses: If, and to what extent, do these effects about inherent properties of languages also influence the ranking of countries, or other types of results from international assessments?

International connections of the project
The project has had several international connections:
- The reference group. The project has had an international reference group for specific linguistic competence, in particular in relationship to educational science, to mathematics, and to the three languages in particular studied in the project. The members of the reference group are well renowned researchers in the area and two are from outside of Sweden.
- Prof. Candia Morgan, professor of education at University of London, England. As one of the members of the reference group, Prof. Morgan have contributed to the project with her advice. Thanks to the collaboration initialised through her work in the reference group, she is now connected to the research group more generally as a guest professor at Umeå University, and the collaboration continues beyond the project. Prof. Morgan is one of the most experienced researchers on language in the mathematics education research field.
- An international postdoc (Edmonds-Wathen) from Australia have spent two years as member of the research group at Umeå University. She has not been funded by Riksbankens Jubileumsfond, but has worked with studies and publications in the project together with the researchers. The collaboration continues beyond her position in Umeå and will lead to future joint publications.
- Symposium on Languages and Mathematics, SLaM, June 2016, partially financed by the project. Six internationally well known researchers from different areas were invited lecturers at the symposium: Dr. Avi Allalouf, Israel (testing and evaluation), Prof. Richard Barwell, Canada (mathematics education), Prof. Kadriye Ercikan, Canada (educational measurement), Dr. Silvia Pixner, Austria (psychology), Dr. Máire Ní Ríordáin, Ireland (mathematics education), and Prof. Guillermo Solano-Flores, USA (educational assessment). The lectures were open to anyone interested, but the project group, including prof. Candia Morgan, also spent 1,5 day discussing both general issues related to the theme and particular issues related to the research project with the invited lecturers. The meeting was very productive and further collaboration with the invited lecturers is planned.
- Talks at international conferences. The researchers have, together with the phd student and the postdoc, given lectures regarding results from the project at several international mathematics education conferences. More talks of this type are already planned.
- Talks at other international events. The phd student has presented ongoing research and results from the project at international summer schools, international courses, and visits organised by the Research school for educational sciences at Umeå University.

Research communication measures outside the academic community
So far, the project has not had any communication measures outside the academic community. However, there are plans to present results from the project at the Mathematics Biennial in January 2018, which is a large conference for mathematics teachers in Sweden, attracting around 2000 teachers.

The two most important publications from the project and an account of these publications
This project focuses on mathematics tasks, but also addresses more general issues around the language of test tasks and potential problems in the translation of test tasks. We have publications that are representative of this broader perspectives, and therefore, two such publications are the two most important publications:
- Bergqvist, E., Edmonds-Wathen, C., & Österholm, M. A framework for comparing mathematical tasks in different languages. Manuscript to be submitted to International Journal of Educational Research.
- Österholm, M., Bergqvist, E., & Edmonds-Wathen, C. Effects of language distance in the translation of PISA tasks. Manuscript to be submitted to Journal of Educational Measurement.
These publications address the first and third point in the most important results from the project.

The publication strategy of the project, with comments
The project members have collaborated with researchers with funding from other sources than RJ, which has made it possible to deepen the scope of the project. Based on this collaboration, there are publications presently under review and also manuscripts that will be submitted shortly. The project aims for broad publication in scientific journals from different research areas, for example, mathematics education, general education, and educational measurement. All journals use peer-review and are of high quality. The project has also published in several conference proceedings (with peer-review) for international conferences in mathematics education. These conference proceedings are registered as scientific publications on the so called Norwegian list (dbh.nsd.uib.no/publiseringskanaler/Forside), that is often used to measure quality within educational sciences such as mathematics education.
      Open access for all publications is ensured through parallel publishing in DiVA, a finding tool and institutional repository for research publications and student theses written at Swedish universities (http://www.diva-portal.org/). Only journals that allow such parallel publishing are considered for publication of project results.