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Harnessing teachers’ perspectives: Recognizing mathematically highly able pupils and orchestrating teaching for them in a diverse ability classroom
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0001-8449-130X
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

There is a lack of research that explores teachers’ perspectives on teaching highly able pupils (HAPs) in the diverse ability classroom. Instead, pupils’ perspectives are common, such studies often concluding that teachers need more professional development or that they fail to support HAPs. Consequently, previous research does not support teachers in how to implement teaching that includes HAPs. This thesis aims to harness teachers’ perspectives of pedagogical possibilities that enable learning opportunities for mathematically highly able pupils (MHAPs). By comparing pupils’ (n=264) relative achievement on two different tests, traditional and non-traditional, the first part of this thesis explores teachers’ possibilities to recognize MHAPs. The results show that pupils who achieved highly on the non-traditional test, but not on the other, have higher problem-solving competence compared to pupils who achieved highly on the traditional test instead. The second part presents a teacher-initiated investigation of pupils’ perceptions of challenging mathematical tasks. The findings indicate that the developed tool can help teachers find suitable tasks for MHAPs. The final part uses positioning theory to analyze teachers’ (N=17) discussions and probe their perceptions on orchestrating teaching MHAPs. The findings show that the teachers have knowledge of how to recognize and support MHAPs. Specifically, the teachers express possibilities with challenging tasks and differentiated education to meet MHAPs’ learning needs. Furthermore, the teachers perceived fewer rights than duties to orchestrate teaching for MHAPs’, for example, to continuously asses them. The studies in this thesis support teachers to orchestrate teaching including MHAPs in the diverse ability classroom. Both practice and research can be guided by what the teachers in these studies perceived as possible to do to orchestrate such teaching. Thereby support is given to teachers, from teachers, through research.

Abstract [en]

This thesis harnesses teachers’ perspectives of pedagogical possibilities that enable learning opportunities for mathematically highly able pupils (MHAPs). Firstly, teachers’ possibilities to recognize MHAPs through assessment are explored. The results show that pupils with high problem-solving competence can achieve highly on a non-traditional test, whereas they do not on traditional tests. Secondly, a teacher-initiated investigation of pupils’ perceptions of challenging mathematical tasks is presented. The findings indicate that a developed tool can help teachers find suitable tasks for MHAPs. Finally, teachers’ (N=17) discussions are analysed and their perceptions on orchestrating teaching MHAPs are probed. The findings show that the teachers have knowledge of how to recognize and support MHAPs. Specifically, the teachers express possibilities with challenging tasks and differentiated education. Furthermore, the teachers perceived they have knowledge and competence to orchestrate teaching for MHAPs. The findings show that their knowledge is consistent with previous research on teaching highly able pupils (HAPs) to meet their learning needs. This thesis gives support, on orchestrating teaching that includes HAPs in learning, to teachers, from teachers, through research.

Place, publisher, year, edition, pages
Karlstad: Karlstads universitet, 2018. , p. 126
Series
Karlstad University Studies, ISSN 1403-8099 ; 2018:45
Keywords [en]
High ability, Gifted education, Professional development, Mathematics, Differentiated education, Inclusive education, Teachers, Positioning theory
National Category
Pedagogical Work
Research subject
Educational Work
Identifiers
URN: urn:nbn:se:kau:diva-69485ISBN: 978-91-7063-882-4 (print)ISBN: 978-91-7063-977-7 (electronic)OAI: oai:DiVA.org:kau-69485DiVA, id: diva2:1253540
Public defence
2018-12-10, Nyquistsalen, 9C 203, Karlstad, 10:00 (English)
Opponent
Supervisors
Available from: 2018-11-19 Created: 2018-10-05 Last updated: 2018-11-20Bibliographically approved
List of papers
1. High achiever! Always a high achiever?: A comparison of student achievements on mathematical tests with different aims and goals
Open this publication in new window or tab >>High achiever! Always a high achiever?: A comparison of student achievements on mathematical tests with different aims and goals
2014 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

This study explored changes in relative achievement over time. It also investigated differences in how two groups of students activate mathematical competencies. The aim of the study was to investigate students’ relative achievement in mathematics over time, and how mathematical competencies can be used to explore differences between groups of students on a non-curriculum based test in mathematics. The study was divided in two parts. Study 1 compared students’ (n=568) relative achievement in two national tests in mathematics (years 3 and 6). Study 1 explored changes in relative achievement between the two national tests as well as differences in relative achievement between the national test in year 6 and the mathematical kangaroo in year 7 (age 13). The study identified, from a sample (n=264) of study 1, two groups of students with high achievements in only one of the tests, the national test in year 6 or the mathematical kangaroo. Study 2 explored how differences between those students relative achievement on the mathematical kangaroo could be explained through activation of mathematical competencies. The results in study 1 show that students undergo large changes, both increases and decreases, in relative achievement between the national tests in years 3 and 6. Study 2 shows how the two identified groups activate the mathematical competencies differently on the mathematical kangaroo. 9% of the students achieve highly in the mathematical kangaroo although they do not in the national test. The study implicates the importance of using non-curriculum bounded tests to identify strength in mathematical competencies among students that not are able to show them through the national test.

Place, publisher, year, edition, pages
Karlstad: Karlstads universitet, 2014. p. 127
Series
Karlstad University Studies, ISSN 1403-8099 ; 2014:67
Series
Studies in Science and Technology Education, ISSN 1652-5051 ; 78
Keywords
achievement, alternative assessment, curriculum based assessment mathematical competency, mathematical kangaroo, mathematics tests, national tests
National Category
Mathematics Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-34516 (URN)978-91-7063-607-3 (ISBN)
Presentation
2014-12-19, 21A 342, Karlstads universitet, Karlstad, 10:15 (Swedish)
Opponent
Supervisors
Available from: 2014-11-18 Created: 2014-10-29 Last updated: 2018-10-05Bibliographically approved
2. The suitability of rich learning tasks from a pupil perspective
Open this publication in new window or tab >>The suitability of rich learning tasks from a pupil perspective
2017 (English)In: CERME 10: Proceedings of the Tenth Congress of European Society for Research in Marhematics Education, European Society for Research in Mathematics Education, 2017, p. 1162-1169Conference paper, Published paper (Refereed)
Abstract [en]

The construction of tasks is important to challenge pupils, but the exploration of pupils’ perceptions connected to their work with tasks, is rare. This paper presents the results of a study using a tool aimed at measuring pupils’ perception of joy and interest connected to ‘rich learning tasks’ by comparing the views of mathematically promising pupils and others. Two tasks were pre- and postevaluated, the first by 139 and the second by 106 pupils from grade 4-9. The results indicate that the tool is suited for the exploration of pupils’ views, especially as it can be deduced from the comparison that mathematically promising pupils perceived both tasks more positively than the other pupils, and that the non-identified pupils became more positive after working especially with one of the tasks.

Place, publisher, year, edition, pages
European Society for Research in Mathematics Education, 2017
Keywords
Mathematically gifted, mathematically promising, rich tasks, pupils’ perception
National Category
Social Sciences Educational Sciences Didactics Mathematics
Research subject
Educational Work; Mathematics
Identifiers
urn:nbn:se:kau:diva-48143 (URN)978-1-873769-73-7 (ISBN)
Conference
The Tenth Congress of the European Society for Research in Mathematics Education
Available from: 2018-02-08 Created: 2018-02-08 Last updated: 2018-10-05
3. Elementary teachers on orchestrating teaching for mathematically highly able pupils
Open this publication in new window or tab >>Elementary teachers on orchestrating teaching for mathematically highly able pupils
2019 (English)In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 16, no 1-3, article id 8Article in journal (Refereed) Published
Abstract [en]

Studies on high ability in mathematics rarely take a teacher’s perspective. The purpose of our study is to add such a perspective, which we will do by using positioning theory to analyze elementary teachers’ discussions on mathematical tasks, aiming to challenge all pupils, including the highly able. The study is conducted in the context of a two-year long teacher professional development program on high ability. Teachers expressed both their teaching and the mathematical tasks as helpful in orchestrating teaching suitable for highly able pupils. They highlight the opportunities given by some tasks as well as the importance of guiding highly able pupils to go further in such tasks. However, they expressed their own limited mathematical knowledge and time needed for pupils with learning difficulties as obstacles to orchestrate teaching for the highly able. The results show that it is important to, in close cooperation with teachers, further explore how to orchestrate teaching that challenges highly able pupils.

Place, publisher, year, edition, pages
University of Montana, 2019
Keywords
High ability, Mathematics, Positioning theory, Professional development, Teachers
National Category
Pedagogical Work Mathematics
Research subject
Educational Work; Mathematics didactics
Identifiers
urn:nbn:se:kau:diva-69486 (URN)
Available from: 2018-10-05 Created: 2018-10-05 Last updated: 2018-11-22Bibliographically approved
4. Manuscript: Teachers’ views on teaching highly able pupils in diverse ability classroom
Open this publication in new window or tab >>Manuscript: Teachers’ views on teaching highly able pupils in diverse ability classroom
(English)Manuscript (preprint) (Other academic)
Keywords
Differentiated education, Highly able pupils, Positioning theory, Teachers
National Category
Mathematics Pedagogical Work
Research subject
Mathematics didactics; Educational Work
Identifiers
urn:nbn:se:kau:diva-69488 (URN)
Available from: 2018-10-05 Created: 2018-10-05 Last updated: 2018-10-05

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Mellroth, Elisabet

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