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  • 1.
    Jäder, Jonas
    et al.
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences. Bromangymnasiet, Hudiksvall.
    Lithner, Johan
    Institutionen för naturvetenskapernas och matematikens didaktik, Umeå universitet.
    Sidenvall, Johan
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences.
    Reasoning requirements in school mathematics textbooks: an analysis of books from 12 countriesManuscript (preprint) (Other academic)
    Abstract [en]

    A selection of secondary school textbooks from twelve countries in five continents is used as an indicator of the opportunities to learn mathematics through different forms of reasoning, in particular with respect to the distinction between rote learning and deeper learning. One aspect that is fundamental to the development of conceptual understanding as well as problem solving ability is the opportunity to learn how to construct mathematically well-founded reasoning. This study compared textbook tasks to the information provided previously in the book, determining if it is possible and reasonable to mimic available solution templates, or if a solution has to be constructed. The results show that the percentage of tasks where it is possible to mimic available templates is on average 79 %, but that this percentage varies widely within the books depending on the textbook authors own labeling of the tasks, and on the mathematical content. 13 % of the tasks can be solved mainly by mimicking provided templates but require some minor modification, and the remaining 9 % of the tasks require that the main parts of the solution are constructed without the guidance of a template. Although these distributions are relatively similar in all textbooks, the twelve countries perform differently in international tests such TIMSS and PISA.

  • 2.
    Jäder, Jonas
    et al.
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences.
    Sidenvall, Johan
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences.
    Mathematical Reasoning and Beliefs2014In: PME38 / PME-NA 36 Proceedings: Of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education / [ed] Peter Liljedahl, Cynthia Nicol, Susan Oesterle, & Darien Allan, Vancouver, 2014, Vol. 6, p. 114-114Conference paper (Refereed)
    Abstract [en]

    We present a research project on students’ mathematical reasoning and how beliefs are indicated in their arguments. Preliminary results show that students express beliefs that task solving does not include reflection or much struggle. The results underpin earlier studies stressing expectations as a theme of belief.

  • 3.
    Jäder, Jonas
    et al.
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences. School of Education, Health and Social Studies, Dalarna University, Falun, Sweden.
    Sidenvall, Johan
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences. School Administration, Municipality of Hudiksvall, Hudiksvall, Sweden.
    Sumpter, Lovisa
    Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden, Högskolan i Dalarna, Sweden.
    Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving2017In: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, Vol. 15, no 4, p. 759-776Article in journal (Refereed)
    Abstract [en]

    Students’ beliefs and problem solving are connected, and have been studied in different contexts. One of the common results of previous research is that students tend to prefer routine, algorithmic approaches to mathematical tasks. This study explores Swedish upper secondary school students’ beliefs and reasoning when solving non-routine tasks. The results regarding the beliefs indicated by the students were categorized relying on previous research and included expectations, motivational beliefs, and security. For example students expected tasks to be solvable by a known algorithm. Students also expressed an insecurity regarding their own reasoning. A variety of approaches to the tasks in terms of the reasoning used were found. Even though the tasks were designed to demand more than imitation of algorithms, students on several occasions used this method and failed to solve the tasks. Our study implies that there is more to create a problem solving learning environment than just to give students non-routine tasks.

  • 4.
    Sidenvall, Johan
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences.
    Att lära sig resonera: Om elevers möjligheter att lära sig matematiska resonemang2015Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Students only learn what they get the opportunity to learn. This means, for example, that students do not develop their reasoning- and problem solving competence unless teaching especially focuses on developing these competencies. Despite the fact that it has for the last 20 years been pointed out the need for a reform-oriented mathematics education, research still shows that in Sweden, as well as internationally, an over-emphasis are placed on rote learning and procedures, at the cost of promoting conceptual understanding. Mathematical understanding can be separated into procedural and conceptual understanding, where conceptual understanding can be connected to a reform oriented mathematics education. By developing a reasoning competence conceptual understanding can also be developed. This thesis, which deals with students’ opportunities to learn to reason mathematically, includes three studies (with data from Swedish upper secondary school, year ten and mathematics textbooks from twelve countries). These opportunities have been studied based on a textbook analysis and by studying students' work with textbook tasks during normal classroom work. Students’ opportunities to learn to reason mathematically have also been studied by examining the relationship between students' reasoning and their beliefs. An analytical framework (Lithner, 2008) has been used to categorise and analyse reasoning used in solving tasks and required to solve tasks.

    Results support previous research in that teaching and mathematics textbooks are not necessarily in harmony with reform-oriented mathematics teaching. And that students indicated beliefs of insecurity, personal- and subject expectations as well as intrinsic- and extrinsic motivation connects to not using mathematical reasoning when solving non-routine tasks. Most commonly students used other strategies than mathematical reasoning when solving textbook tasks. One common way to solve tasks was to be guided, in particular by another student. The results also showed that the students primarily worked with the simpler tasks in the textbook. These simpler tasks required mathematical reasoning more rarely than the more difficult tasks. The results also showed a negative relationship between a belief of insecurity and the use of mathematical reasoning. Furthermore, the results show that the distributions of tasks that require mathematical reasoning are relatively similar in the examined textbooks across five continents.

    Based on the results it is argued for a teaching based on sociomathematical norms that leads to an inquiry based teaching and textbooks that are more in harmony with a reform-oriented mathematics education.

    List of papers
    1. Students’ reasoning in mathematics textbook task-solving
    Open this publication in new window or tab >>Students’ reasoning in mathematics textbook task-solving
    2015 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 1464-5211, Vol. 46, no 4, p. 533-552Article in journal (Refereed) Published
    Abstract [en]

    This study reports on an analysis of students’ textbook task-solving in Swedish upper secondary school. The relation between types of mathematical reasoning required, used, and the rate of correct task solutions were studied. Rote learning and superficial reasoning were common, and 80% of all attempted tasks were correctly solved using such imitative strategies. In the few cases where mathematically founded reasoning was used, all tasks were correctly solved. The study suggests that student collaboration and dialogue does not automatically lead to mathematically founded reasoning and deeper learning. In particular, in the often common case where the student simply copies a solution from another student without receiving or asking for mathematical justification, it may even be a disadvantage for learning to collaborate. The results also show that textbooks’ worked examples and theory sections are not used as an aid by the student in task-solving.

    Place, publisher, year, edition, pages
    Taylor & Francis, 2015
    Keywords
    Mathematical reasoning; task-solving; mathematics textbook; upper
    National Category
    Educational Sciences
    Identifiers
    urn:nbn:se:liu:diva-117559 (URN)10.1080/0020739X.2014.992986 (DOI)
    Available from: 2015-05-08 Created: 2015-05-04 Last updated: 2018-03-21Bibliographically approved
    2. Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving
    Open this publication in new window or tab >>Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving
    2017 (English)In: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, Vol. 15, no 4, p. 759-776Article in journal (Refereed) Published
    Abstract [en]

    Students’ beliefs and problem solving are connected, and have been studied in different contexts. One of the common results of previous research is that students tend to prefer routine, algorithmic approaches to mathematical tasks. This study explores Swedish upper secondary school students’ beliefs and reasoning when solving non-routine tasks. The results regarding the beliefs indicated by the students were categorized relying on previous research and included expectations, motivational beliefs, and security. For example students expected tasks to be solvable by a known algorithm. Students also expressed an insecurity regarding their own reasoning. A variety of approaches to the tasks in terms of the reasoning used were found. Even though the tasks were designed to demand more than imitation of algorithms, students on several occasions used this method and failed to solve the tasks. Our study implies that there is more to create a problem solving learning environment than just to give students non-routine tasks.

    Place, publisher, year, edition, pages
    Springer Netherlands, 2017
    Keywords
    Beliefs, mathematical reasoning, non-routine tasks, problem solving, upper secondary school
    National Category
    Educational Sciences
    Identifiers
    urn:nbn:se:liu:diva-117561 (URN)10.1007/s10763-016-9712-3 (DOI)000395003700010 ()2-s2.0-84959365078 (Scopus ID)
    Available from: 2015-05-08 Created: 2015-05-04 Last updated: 2018-03-23Bibliographically approved
    3. Reasoning requirements in school mathematics textbooks: an analysis of books from 12 countries
    Open this publication in new window or tab >>Reasoning requirements in school mathematics textbooks: an analysis of books from 12 countries
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    A selection of secondary school textbooks from twelve countries in five continents is used as an indicator of the opportunities to learn mathematics through different forms of reasoning, in particular with respect to the distinction between rote learning and deeper learning. One aspect that is fundamental to the development of conceptual understanding as well as problem solving ability is the opportunity to learn how to construct mathematically well-founded reasoning. This study compared textbook tasks to the information provided previously in the book, determining if it is possible and reasonable to mimic available solution templates, or if a solution has to be constructed. The results show that the percentage of tasks where it is possible to mimic available templates is on average 79 %, but that this percentage varies widely within the books depending on the textbook authors own labeling of the tasks, and on the mathematical content. 13 % of the tasks can be solved mainly by mimicking provided templates but require some minor modification, and the remaining 9 % of the tasks require that the main parts of the solution are constructed without the guidance of a template. Although these distributions are relatively similar in all textbooks, the twelve countries perform differently in international tests such TIMSS and PISA.

    Keywords
    Mathematics Textbooks, Mathematics Tasks, Mathematical reasoning, Opportunities to learn, Secondary school
    National Category
    Educational Sciences
    Identifiers
    urn:nbn:se:liu:diva-117560 (URN)
    Available from: 2015-05-08 Created: 2015-05-04 Last updated: 2015-05-22Bibliographically approved
  • 5.
    Sidenvall, Johan
    Linköping University, Department of Social and Welfare Studies.
    Students’ Reasoning in Mathematics Textbook Task Solving2013In: FontD 10-year anniversary meeting with the Scientific Committee / [ed] K. Schönborn & L. Tibell, 2013Conference paper (Other academic)
    Abstract [en]

    To a large extent school mathematics consists of procedures to be memorized without understanding. Using procedures without understanding is one of the main causes behind the difficulties when learning mathematics. By developing mathematically founded reasoning, other mathematical competences are also developed; problem solving and conceptual understanding. The textbook is important in mathematical education. This study reports an analysis of students’ textbook task solving in Swedish upper secondary school were the relation between types of mathematical reasoning used and the success and failure to complete tasks was studied. Results show that using rote learning and superficial reasoning is common, although only about 50 % of the tasks where successfully solved using such strategies. In the case that mathematically founded reasoning was used, the tasks were successfully solved. Conclusions from the study are that students’ work with textbook tasks mainly let the students develop rote learning and superficial reasoning and students are not enhanced to develop mathematically founded reasoning in their work with textbook tasks. Students have to work with textbook tasks in other ways or be given other additional opportunities in order to develop mathematically founded reasoning.

     

  • 6.
    Sidenvall, Johan
    et al.
    Linköping University, Department of Social and Welfare Studies, Social Work. Linköping University, Faculty of Arts and Sciences.
    Jäder, Jonas
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences.
    Sumpter, Lovisa
    Dalarnas högskola.
    Mathematical reasoning and beliefs in non-routine task solving2014In: Current State of Research on Mathematical Beliefs XX: Proceedings of the MAVI-20 Conference September 29 – October 1, 2014, Falun, Sweden / [ed] L. Sumpter, 2014Conference paper (Other academic)
    Abstract [en]

    This paper explores low performing upper secondary school students’ mathematical reasoning when solving non-routine tasks in pairs. Their solutions were analysed using a theoretical framework about mathematical reasoning and a model to study beliefs as arguments for choices. The results confirm previous research and three themes of beliefs are used by the student. These themes are safety, expectations, and motivation. The results also show a connection between beliefs and imitative reasoning as a way to solve non-routine tasks.

  • 7.
    Sidenvall, Johan
    et al.
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences.
    Lithner, Johan
    Umeå Mathematics Education Research Centre, Umeå University, Sweden.
    Jäder, Jonas
    Linköping University, Department of Social and Welfare Studies. Linköping University, Faculty of Educational Sciences.
    Students’ reasoning in mathematics textbook task-solving2015In: International Journal of Mathematical Education in Science and Technology, ISSN 1464-5211, Vol. 46, no 4, p. 533-552Article in journal (Refereed)
    Abstract [en]

    This study reports on an analysis of students’ textbook task-solving in Swedish upper secondary school. The relation between types of mathematical reasoning required, used, and the rate of correct task solutions were studied. Rote learning and superficial reasoning were common, and 80% of all attempted tasks were correctly solved using such imitative strategies. In the few cases where mathematically founded reasoning was used, all tasks were correctly solved. The study suggests that student collaboration and dialogue does not automatically lead to mathematically founded reasoning and deeper learning. In particular, in the often common case where the student simply copies a solution from another student without receiving or asking for mathematical justification, it may even be a disadvantage for learning to collaborate. The results also show that textbooks’ worked examples and theory sections are not used as an aid by the student in task-solving.

1 - 7 of 7
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