The effect of first school years on mathematical skill profiles

This study investigated the effect of children’s first formal school years on mathematical skill profiles, measured by a variety of arithmetical skills and Spontaneous Focusing On Numerosity (SFON) tasks. By using person-centered approach the aim was to investigate whether the amount of formal schooling is associated with mathematical skills in the same way for all children, or, whether the associations differ according to the children’s mathematical skill profiles. Data was analyzed from 652 4–7-year-old children from four European countries with different school entrance ages. A person-centered approach with latent profile regression analyses on four-factor score variables identified six mathematical skill profiles with both qualitative and quantitative differences. The results revealed significant, but small effects of the amount of schooling on mathematical profiles when chronological age and country-specific school entrance age were controlled for. Educational implications of the findings emphasize regarding the heterogeneity in children’s mathematical skill profiles and the potentially different effects of starting formal schooling across different profiles

Focusing on numerical order in preschool predicts mathematical achievement six years later

The development of numerical ordering of number symbols, unlike numerical ordering of other stimuli, such as sets of everyday items, has recently gained growing research interest. Here, we report a nine-year follow-up study with 36 three-year-old children. We investigated how children’s focusing on numerical order develops alongside number sequence production and cardinality recognition skills. Results showed large individual and developmental differences in children’s focusing on numerical order from the ages of 3 to 6 years. Preschool focusing on numerical order and spontaneous focusing on numerosity predicted curriculum-based math achievement at 12 years of age

Spontaneous Focusing on Quantitative Relations in the Development of Children's Fraction Knowledge

While preschool-aged children display some skills with quantitative relations, later learning of related fraction concepts is difficult for many students. We present two studies that investigate young children's tendency of Spontaneous Focusing On quantitative Relations (SFOR), which may help explain individual differences in the development of fraction knowledge. In the first study, a cross-sectional sample of 84 kindergarteners to third graders completed tasks measuring their spontaneous recognition and use of quantitative relations and then completed the tasks again with explicit guidance to focus on quantitative relations. Findings suggest that SFOR is a measure of the spontaneous focusing of attention on quantitative relations and the use of these relations in reasoning. In the second (longitudinal) study, 25 first graders completed measures of SFOR tendency and a measure of fraction knowledge three years later. SFOR tendency was found to predict fraction knowledge, suggesting that it plays a role in the development of fraction knowledge.</p

Modeling the developmental trajectories of rational number concept(s)

The present study focuses on the development of two sub-concepts necessary for a complete mathematical understanding of rational numbers, a) representations of the magnitudes of rational numbers and b) the density of rational numbers. While difficulties with rational number concepts have been seen in students&#39; of all ages, including educated adults, little is known about the developmental trajectories of the separate sub-concepts. We measured 10- to 12-year-old students&#39; conceptual knowledge of rational numbers at three time points over a one-year period and estimated models of their conceptual knowledge using latent variable mixture models. Knowledge of magnitude representations is necessary, but not sufficient, for knowledge of density concepts. A Latent Transition Analysis indicated that few students displayed sustained understanding of rational numbers, particularly concepts of density. Results confirm difficulties with rational number conceptual change and suggest that latent variable mixture models can be useful in documenting these processes.</p

Suosituksia monikielisten lasten varhaisten matemaattisten taitojen tukemiseen – Temaattinen synteesi

Tämän temaattisen synteesin tavoitteena on yhdistää ja analysoida aiemmassa tutkimuskirjallisuudessa esiteltyjä suosituksia monikielisten lasten varhaisten matemaattisten  taitojen tukemiseen. Aineisto koostuu viidestä suosituksia sisältävästä artikkelista, jotka on julkaistu aikavälillä 2011–2020. Temaattisen synteesin analyysivaiheita noudattaen ensin artikkelien sisältämät suositukset koodattiin. Toisessa vaiheessa koodauksen perusteella suosituksista muodostettiin 12 deskriptiivistä teemaa, jotka ryhmiteltiin neljään kategoriaan: (1) Matemaattisen toimijuuden vahvistaminen kulttuurisesti vastuullisin menetelmin, (2) Matematiikkapuheen mahdollistaminen (3) Matemaattisen oppimisympäristön tekeminen arjessa näkyväksi sekä (4) Matemaattisen ja akateemisen kielitaidon vahvistaminen. Deskriptiivisten teemojen pohjalta luodun analyyttisen mallin mukaan varhaiskasvatuksen ammattilaiset voivat tukea monikielisten lasten matemaattisia taitoja tekemällä matemaattisesta toiminnasta kulttuurisesti merkityksellistä, tiedostamalla omat ennakkokäsityksensä matematiikan ja kielen oppimisesta ja siirtämällä näkökulman puutteista vahvuuksiin sekä mahdollistamalla monipuoliset tavat osallistua matematiikkapuheeseen säännöllisesti. Suositusten kokoaminen yhteen täydentää vielä vähäistä suomenkielistä tutkimuskirjallisuutta monikielisten lasten varhaisten matemaattisten taitojen tukemisesta. Tutkimuksessa suosituksia peilataan suomalaiseen varhaiskasvatukseen, joten sen tulokset voivat toimia myös pedagogisen toiminnan suunnittelun tukena varhaiskasvatuksen arjessa.The aim of this thematic synthesis is to synthesize and analyze recommendations presented in previous research for supporting multilingual children's early mathematical skills. A search of major databases yielded five articles published between 2011 and 2020. According to the three-stage procedure of thematic synthesis, we first coded the recommendations in the articles. Second, we formed 12 descriptive themes, which were grouped into four categories: (1) strengthening mathematical agency with culturally responsible methods, (2) enabling math talk, (3) making the mathematical learning environment visible in everyday life, and (4) strengthening mathematical and academic language skills. In the third step, we generated an analytical model based on the descriptive themes. According to the analytical model, early childhood education professionals can support early mathematical skills of multilingual children by (1) making mathematical activities culturally relevant, (2) becoming aware of their own preconceptions about learning mathematics and language, and shifting the perspective from weaknesses to strengths, and (3) enabling versatile ways to participate in math talk on a regular basis. Synthesizing the recommendations complements the limited Finnish research literature on supporting multilingual children's early mathematical skills. We reflect the recommendations to Finland’s national core curriculum for early childhood education and care. Thus, the results of this study can be used to support the planning of pedagogical activities in early childhood education

The effect of first school years on mathematical skill profiles

This study investigated the effect of children’s first formal school years on mathematical skill profiles, measured by a variety of arithmetical skills and Spontaneous Focusing On Numerosity (SFON) tasks. By using person-centered approach the aim was to investigate whether the amount of formal schooling is associated with mathematical skills in the same way for all children, or, whether the associations differ according to the children’s mathematical skill profiles. Data was analyzed from 652 4–7-year-old children from four European countries with different school entrance ages. A person-centered approach with latent profile regression analyses on four-factor score variables identified six mathematical skill profiles with both qualitative and quantitative differences. The results revealed significant, but small effects of the amount of schooling on mathematical profiles when chronological age and country-specific school entrance age were controlled for. Educational implications of the findings emphasize regarding the heterogeneity in children’s mathematical skill profiles and the potentially different effects of starting formal schooling across different profiles.</p

Spontaneous focusing on quantitative relations as a predictor of rational number and algebra knowledge

Spontaneous Focusing On quantitative Relations (SFOR) has been found to predict the development of rational number conceptual knowledge in primary students. Additionally, rational number knowledge has been shown to be related to later algebra knowledge. However, it is not yet clear: (a) the relative consistency of SFOR across multiple measurement points, (b) how SFOR tendency and rational number knowledge are inter-related across multiple time points, and (c) if SFOR tendency also predicts algebra knowledge. A sample of 140 third to fifth graders were followed over a four-year period and completed measures of SFOR tendency, rational number conceptual knowledge, and algebra knowledge. Results revealed that the SFOR was relatively consistent over a one-year period, suggesting that SFOR is not entirely context-dependent, but a more generalizable tendency. SFOR tendency was in a reciprocal relation with rational number conceptual knowledge, each being uniquely predictive of the other over a four-year period. Finally, SFOR tendency predicted algebra knowledge three-years later, even after taking into account non-verbal intelligence and rational number knowledge. The results of the present study provide further evidence that individual differences in SFOR tendency may have an important role in the development of mathematical knowledge, including rational numbers and algebra.</p

Spontaneous mathematical focusing tendencies in mathematical development

Children's own spontaneous mathematical activities are crucial for their mathematical development. Mathematical thinking and learning does not only occur in explicitly mathematical situations, such as the classroom. Those children with higher tendencies to recognize and use mathematical aspects of their everyday surroundings, both within the classroom and without, appear to have an advantage in learning formal mathematical skills and knowledge. In this introduction to the special issue, we provide an overview of the existing literature on spontaneous mathematical focusing tendencies. We then provide a brief overview of the contributions to the special issue

Young children’s recognition of quantitative relations in mathematically unspecified settings

Children have been found to be able to reason about quantitative relations, such as non- symbolic proportions, already by the age of 5 years. However, these studies utilize settings in which children were explicitly guided to notice the mathematical nature of the tasks. This study investigates children&rsquo;s spontaneous recognition of quantitative relations on mathe- matically unspecified settings. Participants were 86 Finnish-speaking children, ages 5&ndash;8. Two video-recorded tasks, in which participants were not guided to notice the mathe- matical aspects, were used. The tasks could be completed in a number of ways, including by matching quantitative relations, numerosity, or other aspects. Participants&rsquo; matching strategies were analyzed with regard to the most mathematically advanced level utilized. There were substantial differences in participants&rsquo; use of quantitative relations, numerosity and other aspects in their matching strategies. The results of this novel experimental set- ting show that investigating children&rsquo;s spontaneous recognition of quantitative relations provides novel insight into children&rsquo;s mathematical thinking and furthers the understand- ing of how children recognize and utilize mathematical aspects when not explicitly guided to do so.</p

Maternal sensitivity in responding during play and children’s pre-mathematical skills: a longitudinal study from infancy to preschool age

This longitudinal study explored how mothers’ sensitivity in responding to their child’s cognitive and emotional needs in infancy and toddlerhood predicts children’s pre-mathematical skills at early preschool age. The sample consisted of 65 mother-child dyads (N = 130 individuals) videotaped during joint play at ages 1;0 and 2;0. The children’s pre-mathematical skills were tested at age 3;0. The path analyses showed that, in infancy, mothers’ autonomy support and scaffolding are more strongly related than emotional support to children’s later performance on spatial and numerical tasks. The findings are discussed in relation to how maternal sensitivity in responding fosters children’s pre-mathematical development in an optimal way.</p