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Boesen, Jesper

Open this publication in new window or tab >>Mathematical reasoning requirements in Swedish upper secondary level assessments### Palm, Torulf

### Boesen, Jesper

### Lithner, Johan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2011 (English)In: Mathematical Thinking and Learning, ISSN 1098-6065, E-ISSN 1532-7833, Vol. 13, no 3, p. 221-246Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis, 2011
##### National Category

Didactics
##### Research subject

didactics of mathematics
##### Identifiers

urn:nbn:se:umu:diva-40879 (URN)10.1080/10986065.2011.564994 (DOI)
#####

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Available from: 2011-03-11 Created: 2011-03-11 Last updated: 2018-06-08Bibliographically approved

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

National Center for Mathematics Education, University of Gothenburg.

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

We investigate the mathematical reasoning required to solve the tasks in the Swedish national tests and a random selection of Swedish teacher-made tests. The results show that only a small proportion of the tasks in the teacher-made tests require the students to produce new reasoning and to consider the intrinsic mathematical properties involved in the tasks. In contrast, the national tests include a large proportion of tasks for which memorization of facts and procedures are not sufficient. The conditions and constraints under which the test development takes place indicate some of the reasons for this discrepancy and difference in alignment with the reform documents.

Open this publication in new window or tab >>Matematikutbildningens mål och undervisningens ändamålsenlighet: gymnasiet hösten 2009### Bergqvist, Ewa

### Bergqvist, Tomas

### Boesen, Jesper

### Helenius, Ola

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); ### Lithner, Johan

### Palm, Torulf

### Palmberg, Björn

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_1_j_idt188_j_idt202",{id:"formSmash:j_idt184:1:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2010 (Swedish)Report (Other academic)
##### Place, publisher, year, edition, pages

Göteborg: NCM, 2010. p. 71
##### National Category

Didactics
##### Research subject

didactics of mathematics
##### Identifiers

urn:nbn:se:umu:diva-40576 (URN)
#####

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Available from: 2011-03-01 Created: 2011-03-01 Last updated: 2018-06-08Bibliographically approved

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Social Sciences, Department of applied educational science, Interactive Media and Learning (IML).

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

Örebro universitet.

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Open this publication in new window or tab >>Mathematical competencies: A research framework### Lithner, Johan

### Bergqvist, Ewa

### Bergqvist, Tomas

### Boesen, Jesper

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); ### Palm, Torulf

### Palmberg, Björn

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_2_j_idt188_j_idt202",{id:"formSmash:j_idt184:2:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2010 (English)In: Mathematics and mathematics education: Cultural and social dimensions / [ed] Bergsten, Jablonka & Wedege, Linköping, Sweden: Svensk förening för matematikdidaktisk forskning, SMDF , 2010, p. 157-167Conference paper, Published paper (Refereed)
##### Place, publisher, year, edition, pages

Linköping, Sweden: Svensk förening för matematikdidaktisk forskning, SMDF, 2010
##### Series

Skrifter från Svensk förening för matematikdidaktisk forskning, SMDF, ISSN 1651-3274 ; 7
##### National Category

Didactics
##### Research subject

didactics of mathematics
##### Identifiers

urn:nbn:se:umu:diva-37367 (URN)91-973934-6-0 (ISBN)
##### Conference

The seventh mathematics education research seminar, Stockholm, January 26-27, 2010
#####

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Available from: 2010-10-28 Created: 2010-10-28 Last updated: 2018-06-08Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

Umeå University, Faculty of Social Sciences, Department of applied educational science. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

Open this publication in new window or tab >>The relation between types of assessment tasks and the mathematical reasoning students use### Boesen, Jesper

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).### Lithner, Johan

### Palm, Torulf

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2010 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 75, no 1, p. 89-105Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2010
##### Keywords

mathematical reasoning, task characteristics, assessment, learning difficulties
##### National Category

Didactics
##### Research subject

didactics of mathematics
##### Identifiers

urn:nbn:se:umu:diva-35796 (URN)10.1007/s10649-010-9242-9 (DOI)000292148800005 ()
#####

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Available from: 2010-09-03 Created: 2010-09-03 Last updated: 2018-06-08Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did not require conceptual understanding. In contrast, test tasks that do not share important properties with the textbook mostly elicited creative mathematically founded reasoning. In addition, most successful solutions to such tasks were based on this type of reasoning.

Open this publication in new window or tab >>Matematikutbildningens mål och undervisningens ändamålsenlighet: grundskolan våren 2009### Bergqvist, Ewa

### Bergqvist, Tomas

### Boesen, Jesper

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).### Helenius, Ola

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); ### Lithner, Johan

### Palm, Torulf

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.### Palmberg, Björn

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_4_j_idt188_j_idt202",{id:"formSmash:j_idt184:4:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2009 (Swedish)Report (Other academic)
##### Place, publisher, year, edition, pages

Göteborg: NCM, 2009. p. 65
##### National Category

Didactics
##### Research subject

didactics of mathematics
##### Identifiers

urn:nbn:se:umu:diva-40574 (URN)
#####

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Available from: 2011-03-01 Created: 2011-03-01 Last updated: 2018-06-08Bibliographically approved

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Social Sciences, Department of applied educational science, Interactive Media and Learning (IML).

Örebro universitet.

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

Open this publication in new window or tab >>Assessing mathematical creativity: comparing national and teacher-made tests, explaining differences and examining impact### Boesen, Jesper

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2006 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Matematik och matematisk statistik, Umeå universitet, 2006. p. 198
##### Series

Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 34
##### Keywords

Mathematical reasoning, creative reasoning, moderate high stake, teacher made tests, imitative reasoning, assessment, impact, influence, effect, mathematical competence, national tests
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-833 (URN)91-7264-136-3 (ISBN)
##### Public defence

2006-09-19, MA121, MIT-huset, Umeå universitet, Umeå, 13:15
##### Opponent

### Gjone, Gunnar

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##### Supervisors

### Lithner, Johan

### Palm, Torulf

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Available from: 2006-08-29 Created: 2006-08-29 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Students’ use of superficial reasoning seems to be a main reason for learning difficulties in mathematics. It is therefore important to investigate the reasons for this use and the components that may affect students’ mathematical reasoning development. Assessments have been claimed to be a component that significantly may influence students’ learning.

The purpose of the study in Paper 1 was to investigate the kind of mathematical reasoning that is required to successfully solve tasks in the written tests students encounter in their learning environment. This study showed that a majority of the tasks in teacher-made assessment could be solved successfully by using only imitative reasoning. The national tests however required creative mathematically founded reasoning to a much higher extent.

The question about what kind of reasoning the students really use, regardless of what theoretically has been claimed to be required on these tests, still remains. This question is investigated in Paper 2.

Here is also the relation between the theoretically established reasoning requirements, i.e. the kind of reasoning the students have to use in order to successfully solve included tasks, and the reasoning actually used by students studied. The results showed that the students to large extent did apply the same reasoning as were required, which means that the framework and analysis procedure can be valuable tools when developing tests. It also strengthens many of the results throughout this thesis. A consequence of this concordance is that as in the case with national tests with high demands regarding reasoning also resulted in a higher use of such reasoning, i.e. creative mathematically founded reasoning. Paper 2 can thus be seen to have validated the used framework and the analysis procedure for establishing these requirements.

Paper 3 investigates the reasons for why the teacher-made tests emphasises low-quality reasoning found in paper I. In short the study showed that the high degree of tasks solvable by imitative reasoning in teacher-made tests seems explainable by amalgamating the following

factors: (i) Limited awareness of differences in reasoning requirements, (ii) low expectations of students abilities and (iii) the desire to get students passing the tests, which was believed easier when excluding creative reasoning from the tests.

Information about these reasons is decisive for the possibilities of changing this emphasis. Results from this study can also be used heuristically to explain some of the results found in paper 4, concerning those teachers that did not seem to be influenced by the national tests.

There are many suggestions in the literature that high-stake tests affect practice in the classroom. Therefore, the national tests may influence teachers in their development of classroom tests. Findings from paper I suggests that this proposed impact seem to have had a limited effect, at least regarding the kind of reasoning required to solve included tasks. What about other competencies described in the policy documents?

Paper 4 investigates if the Swedish national tests have had such an impact on teacher-made classroom assessment. Results showed that impact in terms of similar distribution of tested competences is very limited. The study however showed the existence of impact from the national tests on teachers test development and how this impact may operate.

Institutt för laerarutdanning og skoleutvikling, Universitetet i Olso.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.