Noticing mathematical potential – A proposal for guiding teachers

International audienceIt has been shown to be problematic for teachers to use Krutetskii´s definition of mathematical abilities to recognize mathematically highly able pupils (MHAPs). Aiming to concretize what teachers can notice in pupils’ problem-solving processes, we connect a 10-year-old boy’s problem-solving process to some of the abilities defined by Krutetskii. The results give clear descriptions of what teachers can observe in pupils’ mathematical activities to notice their mathematical potential. We concretize, for example, how a pupil’s abilities to grasp a problem’s formal structure and to generalize can be observed. To be able to notice MHAPs, teachers need research-based support on how and what to observe in their pupils. Our proposed guide needs to be tested and validated to explore if it will help teachers to notice MHAPs s and subsequently support their learning

Mathematically Able but Yet Underachieving in School Mathematics

Teacher observation has shown that some pupils achieve very high on the Kangaroo Competition test (KC) but very low on the Swedish National test in Mathematics (SNM). This study will investigate the number of pupils who have high achievement scores on the KC (top 10%) but low achievement scores on the SNM (bottom 50%). Individual results on the SNM given in grade 6 (age 12) will be compared to results on the KC given in grade 7; concerning approximately 700 individuals. Results will give an example of the quantity of mathematically able pupils who underachieve in School Mathematics in Sweden. Data interpretation will connect this study to international research concerning mathematical abilities and mathematical achievement among mathematically able pupils

High achiever! Always a high achiever? : A comparison of student achievements on mathematical tests with different aims and goals

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

Med rätt att utmanas - i en skola för alla : Att utveckla verksamheten kring att inkludera elever med särskild begåvning i lärande.

Detta är en rapport av ett skolutvecklingsprojekt som pågått från och med våren 2015 till och med våren 2017, det vill säga tre år. Projektets övergripande syfte var att möta den problematik som finns i svensk skola kring att elever med särskild begåvning ofta är understimulerade och ofta lämnas utan stöd och stimulans att vidareutvecklas i kunskap genom undervisning i skolan. Ett mer konkret syfte var att på vetenskaplig grund utveckla innehåll och undervisningssituationer i matematik för elever med särskild begåvning i matematik i det svenska heterogena klassrummet. Målet var att öka kunskapen hos skolpersonal om dessa elever, deras behov, styrkor och svårigheter, samt deras rättigheter. Ett mer detaljerat mål var att definiera vilken typ av innehåll som lämpar sig för elever med särskild begåvning, både med avseende på matematiska förmågor och specifikt matematikinnehåll. Ett ytterligare mål var att identifiera några typer av undervisningssituationer som är speciellt lämpliga för dessa elever i det vanliga klassrummet. Som resultat av projektet har 14 grundskolelärare i Karlstads kommun och en i Borlänge kommun utvecklat sin kompetens att identifiera elever med särskild begåvning i sina klassrum. De har också utvecklat sin kompetens i att möta dessa elever i undervisning. Lärarna uppger vidare att de har ändrat sitt tankesätt kring hur undervisning kan gå till, vilket lett till att de nu utmanar alla elever i klassrummet mer. Genom projektet har vi analyserat, utvecklat och i tre interventioner prövat tio matematikuppgifter. Denna rapport beskriver projektet och de utvecklade uppgifterna, som finns presenterade i rapporten, är ett sätt att sprida projektet vidare till andra pedagogiska verksamheter. Vår förhoppning är att rapporten kan hjälpa andra att utveckla sina verksamheter så att fler elever med särskild begåvning får stöd och stimulans att utvecklas vidare i kunskap genom undervisning i svensk skola.Rapporten består av två delar. Del 1: Att bredda kompetensen, och Del2: Uppgifter</p

Developing the design of a role-play in a professional development

The poster shows how a role-play conducted by teachers can be developed through the methodology of educational design research. The role-play represents a classroom situation and is an instructional activity as part of a two-year long teacher professional development program. The implementation focuses on some of the features identified as important in an effective professional development. The aim of the role-play is to practice and deepen mathematics teachers’ knowledge and skills of stimulating mathematically gifted pupils higher order thinking. After the development of the role-play, the study can move forward and include; teachers’ change in instruction and pupil learning in order to study the effectiveness of the role-play as a part of a professional development program

Harnessing teachers’ perspectives : Recognizing mathematically highly able pupils and orchestrating teaching for them in a diverse ability classroom

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.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.Artikel 4 publicerad som manuskript i avhandlingen, nu publicerad.</p

The suitability of rich learning tasks from a pupil perspective

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

Teachers' Views on Teaching Highly Able Pupils in a Heterogeneous Mathematics Classroom

Aiming to bring teachers' perspectives to research, teachers' (N = 12) discussions are explored in the context of a professional development program on teaching highly able pupils (HAPs) mathematics. The findings show that the teachers perceive they have the competence to recognize HAPs, for example through continuous assessment. However, they express that collaboration with colleagues is necessary and that they would like their principals' acknowledgement for their competence. They connect and verbalize their practical expertise with theories of teaching HAPs and demonstrate several criteria for teaching that successfully meet pupils' learning needs in heterogeneous classrooms. Thus, they feel confident in how to orchestrate teaching that is inclusive of HAPs in heterogeneous mathematics classrooms.Artikeln publicerad som manuskript i Mellroths (2018) doktorsavhandling: Harnessing teachers’ perspectives: Recognizing mathematically highly able pupils and orchestrating teaching for them in a diverse ability classroom</p

Sverige och undervisning av elever med särskild begåvning i slutet av 2018

Denna artikel bygger på en historisk beskrivning hur undervisning av elever med särskild begåvade börjat ta plats i det svenska skolsystemet. Syftet med artikeln är att ge en bild av hur långt Sverige har kommit, i slutet av 2018, i utvecklingen av undervisning av elever med särskild begåvning. Det historiska perspektivet är tänkt att ge läsaren en bättre förståelse och bakgrund till lägesbeskrivningen. Artikeln avslutas med en kort summering, samt förslag på prioriterade satsningar för att lyckas med att etablera hållbara strukturer för undervisning av dessa barn och elever

Hur man kan identifiera och stimulera barns matematiska förmågor

  Syftet med denna studie är att undersöka om utvalda matematiska problem fungerar som stöd vid identifiering av barn med förmåga och fallenhet för matematik. Studien ämnar även till att visa hur förmågorna enligt Krutetskii kan visa sig på ett konkret sätt. Ytterligare ett syfte är att inspirera andra lärare och skolledare till att stödja och stimulera barn med förmåga och fallenhet för matematik. I en fallstudie följer vi en pojke under höstterminen i årskurs 4. Fallstudien visar att de utvalda problemen fungerar väl som identifikationsmedel av barn med förmåga och fallenhet för matematik. Med flera konkreta exempel visar studien hur förmågorna kan ge sig till känna i arbetet med problemlösning som matematisk aktivitet. Glädjen och tillfredsställelsen pojken visar när han lyckas lösa och förstå problem som utmanat honom matematiskt är även värt att notera.        The purpose of this study is to investigate if chosen mathematical problems work as a support for the identification of children with high abilities in mathematics. The study aims to identify the children with these abilities, according to Krutetskii, in a concrete way. Another purpose is to inspire other teachers and leading persons within the school world, to support and stimulate children with high abilities in mathematics. In a case-study, we follow a boy during the autumn term in the fourth grade. The study shows that the chosen mathematical problems work well to identify children with a high ability in mathematics. With several concrete examples, the study shows how theses mathematical abilities within the child are revealed in the work with problem solving as a mathematical activity. The joy and satisfaction the boy shows, when he succeeds in solving and understanding the mathematical problems that have challenged him, is also worth taking notice of