Matematiikan parhaaksi osaajaksi kehittyminen perusopetuksen aikana

Abstract

Tutkimus perustuu Opetushallituksen ja Kansallisen koulutuksen arviointikeskuksen hankkeessa tuotettuun pitkittäisaineistoon, jossa samaan ikäluokkaan kuuluvien oppilaiden matematiikan osaamisen kehitystä on seurattu vuosien 2005–2015 aikana perusopetuksen kolmannelta vuosiluokalta toisen asteen koulutuksen loppuun. Tutkimus kohdistuu matematiikan parhaisiin osaajiin ja siihen, miten heidän osaamisensa on kehittynyt perusopetuksen aikana ja mikä erottaa parhaat osaajat muista. Tutkimusaineisto käsittää yhteensä 2051 oppilasta, jotka ovat osallistuneet kolmannella, kuudennella ja yhdeksännellä vuosiluokalla pidettyihin matematiikan osaamista kartoittaviin kokeisiin. Näistä yhdeksännen vuosiluokan kokeessa menestymisen perusteella parhaiden osaajien joukkoon luokiteltuja oppilaita on 256 (12,5 %). Tutkimustulosten mukaan suurin osa parhaista osaajista erottuu muusta tutkimusjoukosta jo kolmannella vuosiluokalla, ja ero muihin oppilaisiin näkyy selkeästi kuudennella luokalla. Oppilaan aikaisempi osaaminen, käsitys omasta osaamisesta ja vanhempien koulutustaso olivat selkeitä parempaa osaamista selittäviä tekijöitä. Tutkimuksessa havaittiin, että parhaiden osaajien tasolle voi yltää myös keskitasoa heikommasta lähtötasosta.
 
 Evolving into a mathematically high-achieving student during basic education
 Abstract
 The study is based on the national evaluation of mathematics carried out by the Finnish National Agency for Education (EDUFI) and the Finnish Education Evaluation Centre (FINEEC). The development of mathematical competence of students of the same age group has been investigated during 2005–2012 from the third year of basic education to the ninth year. The study focuses on mathematically high-achieving students and how their skills have evolved during basic education and what kind of factors distinguish them from others. The longitudinal data consists of 2051 students who have taken part in mathematics examinations in the third, sixth and ninth grades. Definition of high-achieving students is based on success in the examination of ninth grade. Total number of high-achieving students is 256 (12,5 %). The results indicated that high-achieving students are distinguished from others in the third grade and the difference between them and other students is clearly visible in the sixth grade. Students’ previous mathematical performance, self-competence and the level of parents’ education were explanatory factors for better competence in ninth grade. The study found that the level of a high-achieving student can be attained also from a lower than average starting level.
 Keywords: basic education, learning outcomes in mathematics, high-achieving students, longitudinal research, national evaluation in mathematics

Top Achievers in Mathematics in the End of Upper Secondary School

“…Individual factors include, for example, the individual's previous math skills, attitudes toward mathematics, and gender. A student's previous math skills in elementary school have been found to be a significant predictor for whether the student is among highachieving students in 9th grade [13]. Strong mathematical skills in basic education predict that the student will do well in mathematics also at the upper secondary level [14,35].…”

“…The data consist of students who were followed from 3rd grade of primary school to the end of upper secondary school between 2005 and 2015. The data were collected for the needs of national evaluations, and several reports have been made about mathematics national learning outcomes [8][9][10][11].…”

“…In Finland, research of mathematically gifted students has been limited. Niemi and colleagues [13][14][15] examined high-achieving 9th graders from the same longitudinal data without the data of matriculation examination. In [13], they investigated how high achievers' mathematical competence developed during basic education and what kinds of factors predicted a student's development into a high-achieving student.…”

“…Niemi and colleagues [13][14][15] examined high-achieving 9th graders from the same longitudinal data without the data of matriculation examination. In [13], they investigated how high achievers' mathematical competence developed during basic education and what kinds of factors predicted a student's development into a high-achieving student. In [14], they examined high achievers' choices when transitioning to upper secondary school and how their mathematical competence developed there.…”

Rudimentary stages of the mathematical thinking and proficiency

“…Several individual factors have been shown to affect the development in general and in mathematics in specific. Some of these are sex (see, e.g., Metsämuuronen 2017a; Niemi et al, 2020Niemi et al, , 2021, and language background including medium of instruction being the mother tongue (first language, L1) or the second language (L2) (see, e.g., Kuukka and Metsämuuronen, 2016). Other important factors found to explain the competence are relative age of starting the school (see, e.g., Dhuey et al, 2019;Kivinen, 2018;Ukkola et al 2020), attitudes toward school and self-efficacy (see, e.g., Aunola, Leskinen, & Nurmi, 2006;Bandura, 2012;Lerkkanen et al, 2010Lerkkanen et al, , 2012Tuohilampi and Hannula, 2013; see in-depth in Ukkola et al, 2020).…”