This study investigated the effects of a fraction concept understanding intervention with six fifth-grade students with special educational needs in mathematics. Explicit instruction and CRA were cornerstones in the intervention program, with a specific focus of fraction as measurement. A single case study with a multiple baseline across student design was used. The results revealed a functional relation between intervention and fraction concept knowledge in four cases. However, all six students maintained their scores on the fraction magnitude understanding measure at a 6-week follow-up. Additionally, all participating students improved their scores on a generalization measure of fraction concept knowledge, assessed both before and after the intervention. The findings reveal that a series of nine lessons fraction intervention supports fraction learning for students with diverse characteristics, but with similar mathematical struggles and special educational needs in mathematics.

The core assumptions of the integrated theory of numerical development were tested using a cross-sectional sample of 379 fifth-grade students, who were assessed on their understanding of whole numbers and fractions, including arithmetic skills. An additional factor of part-whole knowledge was also assessed and analyzed in four structural equation models. All models showed non-significant chi-square values and good fit indices according to common modelling benchmarks. As hypothesized, whole number magnitude knowledge predicts fraction magnitude knowledge and arithmetic proficiency. Additionally, part-whole knowledge mediates numerical magnitude understanding but does not predict arithmetic outcomes. These findings are in line with the integrated theory of numerical development, suggesting that numerical magnitude knowledge is crucial for both numerical development and arithmetic learning. Our findings also reveal that part-whole knowledge may serve as a bridge to more advanced magnitude understanding. Theoretical and practical implications are discussed.

The intention of the study was to examine the effects of a fraction intervention in a whole-class environment. The intervention aimed to enhance students conceptual fraction knowledge, with a major focus on fraction magnitude understanding. This study included 120 fifth-grade students in standard classroom settings. Utilizing a cluster randomized controlled trial design, students were divided into either an intervention group (n = 64) or a control group (n = 56). Students in the intervention condition received a series of seven 35-minute lessons. Students in the control condition received "treatment as usual". Both post-test and delayed post-test results revealed that students in the intervention group performed significantly better than those in the control group on fraction concepts, with a stronger effect in measurement aspects compared to part-whole aspects. The intervention group also outperformed the control group on fraction arithmetic on both post-tests, while no significant difference was observed on fraction word problems.

Vi har studerat forskning som handlar om elevassistenters arbete för elever i behov av särskilt stöd. Syftet med studien är att undersöka elevassistenters arbete i en allmän och friare roll som resurs i skolan och om det finns forskningsstöd för den typen av insats. Genom sökningar identifierades 16 artiklar och resultaten i artiklarna användes för att genomföra en tematisk analys. Resultaten visar att elevassistenter i en fri roll agerar som (1) Undervisare av elever i behov av särskilt stöd, (2) Experter på elever i behov av särskilt stöd, (3)Stödfunktion till lärare och (4) Upprätthållare av en särskild elevsuppmärksamhet. Temana diskuteras, i ett relationellt perspektiv, utifrån riskeroch möjligheter med elevassistenters arbete med elever i behov av särskiltstöd. En slutsats vi drar av den granskade forskningen är att det är tveksamtom elevassistenter ska användas som primära undervisare för dessa elever.

I skolan ökar användningen av resurspersonal för elever i behov av särskilt stöd. ”Resurserna” innefattar främst elevassistenter, lärarassistenter och fritidshemspersonal, men även andra personalkategorier. Det gemensamma för personalgruppen är att den generellt sett har liten eller ingen utbildning för att möta elever i svårigheter. Trots det är det vanligt att resurspersonal, särskilt elevassistenter, anställs för att arbeta med elever i behov av särskilt stöd, men arbetsuppgifterna är sällan tydligt formulerade.

Mastering traditional algorithms has formed mathematics teaching in primary education. Educational reforms have emphasized variation and creativity in teaching and using computational strategies. These changes have recently been criticized for lack of empirical support. This research examines the effect of teaching two differently structured written calculation methods on teaching arithmetic skills (addition) in grade 2 in Sweden with respect to students procedural, conceptual and factual knowledge. A total of 390 students (188 females, 179 males, gender not indicated for 23) were included. The students attended 20 classes in grade 2 and were randomly assigned to one of two methods. During the intervention, students who were taught and had practiced traditional algorithms developed their arithmetic skills significantly more than students who worked with the decomposition method with respect to procedural knowledge and factual knowledge. These results provided no evidence that the development of students conceptual knowledge would benefit more from learning the decomposition method compared to traditional algorithm.

A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills.

This study set out to examine the effects of repeated testing of students’ declarative knowledge in mathematics in grade 7 (13-14 years old) and to what extent feedback moderates the effect of continually testing students’ declarative knowledge. Students who have automated the 400 basic arithmetical combinations (200 addition combinations and 200 subtraction combinations) have gained declarative knowledge. Mastering these combinations gives students an advantage where doing various calculations and performing different mathematical procedures are concerned (Dowker, 2012). If a student has automated the basic combinations, their attention will not be diverted from the procedure when solving calculation tasks, and there is thereby less risk of incorrect answers (Dowker, 2012). Previous studies have also shown that declarative knowledge in mathematics predict future results in more advanced mathematics (Hassel Bring, Goin, & Bransford, 1988; Gersten, Jordan, & Flojo, 2005; Rathmell & Gabriele, 2011).

An organizing structure that in recent years has had a major impact on how to work with students who don’t respond to regular instruction is Response to Intervention (RTI). Efforts in RTI are divided into three different tiers of instruction: primary, secondary and tertiary. In our study, we investigate the impact of intensive secondary-tier instruction on students’ knowledge of basic combinations of digits in addition. We also focus on how the students develop their use of more advanced calculations in addition during the intervention.

The results showed that students became faster at performing simple addition tasks, which indicates that their fluency – declarative knowledge – developed during the intervention phase. Our results thereby strengthen suggestions that a secondary-tier intervention level should take place in a small group of students 20-40 minutes four to five times a week. Meanwhile, the students developed their ability to solve two-digit arithmetic tasks in addition and subtraction, which could be explained by the fact that students had automated simple number combinations and thus could focus on the calculation procedure.

Context: The aim was to further understand the heterogeneity of  developmental dyscalculia (DD). Utilizing four children (8-9 year-old) performance was contrasted against predominant hypotheses of DD.

Case report: Despite showing similar mathematical deficits, these children showed remarkable interindividual variability regarding cognitive profile and deficits. Two cases were consistent with the approximate number system deficit account, and the general magnitude-processing deficit account. One case had an access deficit in combination with a general cognitive deficit. One cases suffered from general cognitive deficits only.

Conclusions: The results showed that DD cannot be attributed to a single explanatory factor. These findings support a multiple deficits account of DD and suggest that some cases have multiple deficits, whereas other cases have a single deficit. We discuss a previously proposed distinction between primary DD and secondary DD, and suggest hypotheses of dysfunctional neurocognitive correlates responsible for the displayed deficits.