National Tests In Mathematics Research Articles

Parallel Optimal Calibration of Mixed-Format Items for Achievement Tests

When large achievement tests are conducted regularly, items need to be calibrated before being used as operational items in a test. Methods have been developed to optimally assign pretest items to examinees based on their abilities. Most of these methods, however, are intended for situations where examinees arrive sequentially to be assigned to calibration items. In several calibration tests, examinees take the test simultaneously or in parallel. In this article, we develop an optimal calibration design tailored for such parallel test setups. Our objective is both to investigate the efficiency gain of the method as well as to demonstrate that this method can be implemented in real calibration scenarios. For the latter, we have employed this method to calibrate items for the Swedish national tests in Mathematics. In this case study, like in many real test situations, items are of mixed format and the optimal design method needs to handle that. The method we propose works for mixed-format tests and accounts for varying expected response times. Our investigations show that the proposed method considerably enhances calibration efficiency.

A Bourdieusian Analysis of the Conversion Between Mathematical Achievement and Science Capital

Mathematics serves as a universal language and set of thinking tools for science. While prior research indicates associations between academic success in mathematics and science, there is a gap in the research that explores the possible relationship between mathematical achievement during early secondary school (ages 11-13) and subsequent participation in advanced science courses during senior secondary school (beyond age 16). This research is valuable because it could provide further insights into how early achievement in non-science subjects is related to senior participation in science. The analysis of national mathematics test data found that students who studied different science subjects in senior secondary school all had stronger foundational mathematical skills than those who did not. The results differed according to science subjects. The analysis indicated differences of over 7.2 months of equivalent learning at early secondary level in favour of those who studied physics, 6.1 months for those who studied chemistry and 2.5 months for biology. I apply a Bourdieusian lens as a way of explaining students’ conversion of mathematical achievement into participation as a form of science capital. These findings add empirical weight to previous research promoting mathematics as a crucial foundation for science learning. This research has implications for policies and practices that promote learning in mathematics and science pathways.

An analysis of item response theory using program R

The test is one of the instruments used to assess the extent of student understanding in learning. Multiple choice is a type of test commonly used in testing students. In addition to testing students' understanding, the quality of the tests used also needs to be tested. This study aims to determine the characteristics of the national mathematics test items in Baubau in the 2015/2016 academic year and the test information function with the item response theory approach. This research is an ex-post-facto study with a sample size of 574 students using a random sampling technique. Data was collected through documentation and analyzed using the LTM R package program. Findings indicated that there were four items (I1, I2, I4, and I8) for the 1-PL model, six items (I1, I2, I4, I7, I8, and I10) for the 2-PL model, and seven items (I1, I2, I3, I4, I7, I9, and I10) (3-PL) that fit the model (FM). The percentage of good (G) item parameters using R was 90% for (b) (1-PL), 90% (b) and 100% (a) (2-PL), and 90% (b), 10% (a), and 70% (c) (3-PL). The percentage of good quality items in each model for the 1-PL model was 40% or four items, the 2-PL model was 60% or six items, and the 3-PL model was 0%, or none was included in the good quality item category.

Differential relationships between mathematics self-efficacy and national test performance according to perceived task difficulty

ABSTRACT We explore the effect of students’ perceived task difficulty on the mathematics self-efficacy – performance relationship. Specifically, we expand on previous reciprocal effects studies through including students’ self-efficacy for different levels of task difficulty in an empirical investigation. We examined students’ self-efficacy for easy, medium difficulty, and hard tasks and performance on a national mathematics test in a longitudinal study of 95 Norwegian students from grade 8 to grade 9. We found differential relationships between self-efficacy for different levels of task difficulty and national test performance. In support of the ‘skill development’ model, grade 8 national test performance predicted grade 9 self-efficacy for medium and hard, but not easy, tasks. While mastery experiences are likely to arise more easily on easier tasks, such experiences are likely to matter more on harder tasks. Our findings highlight the importance of supporting students’ engagement with challenging tasks to strengthen both their performance and self-efficacy.

Young children’s mathematical activities at preschool and home in Japan

ABSTRACT Research indicates that mathematical understanding before formal schooling influences later attainment. This study investigated the mathematical activities of preschool-aged children in Japan, a neglected topic despite the high mathematical attainment of Japanese children. Preschool activities were investigated using surveys, observations, and staff interviews; activities at home and use of non-preschool educational providers were investigated using surveys of parents. The results showed that preschools overwhelmingly followed the government curricula, seeking to develop children’s interest in and sense of number, quantity, and shape through activities embedded in play and daily life; more directed teaching using workbooks was rare. Many children frequently engaged in informal mathematics-related activities at home. An unexpectedly high proportion of children engaged with learning materials from non-preschool educational providers. Results were broadly consistent across the two locations studied, despite the contrasting attainment of children in these areas in national mathematics tests. The results demonstrate that preschools in different parts of Japan avoid directed mathematical teaching. Further research is needed into the development of the mathematical understanding of preschool-aged children in Japan, especially in relation to non-preschool educational providers.

Maternal prenatal vitamin B12 intake is associated with speech development and mathematical abilities in childhood

Deficiencies of many nutrients in pregnancy have adverse effects on fetal brain development with consequent impaired cognitive function in childhood. However, it is unclear whether deficiencies of vitamin B12 prenatally are harmful to the developing fetus. We therefore used the Avon Longitudinal Study of Parents and Children to test the hypothesis that cognitive outcomes in childhood are reduced if their mothers consumed a diet low in vitamin B12 during pregnancy. A detailed exposome analysis was used to identify 9 factors independently associated with low vitamin B12 intake. These were taken into account in each of 26 outcome analyses. Results showed that the children of women with the lowest 10% intake of B12 were at increased risk of poor vocabulary at 24 months, reduced ability at combining words at 38 months, poor speech intelligibility at 6 years, poor mathematics comprehension at school years 4 and 6 (ages 8-9 and 10-11 years), and poor results on the national mathematics tests (age 13). There were no such significant adjusted associations for reading or spelling abilities, or for verbal or full-scale IQ (Intelligence Quotient) at 8 or at 15. Thus, we have confirmed that there are adverse effects on the child's development if the pregnant woman has a low intake of vitamin B12, and we have shown that these are specific to certain speech and mathematical abilities.

Supporting primary school teachers\u2019 classroom assessment in mathematics education: effects on student achievement

In a three-phase study, with a total of 40 third-grade teachers and their 830 students, teachers were supported to use classroom assessment techniques (CATs) to reveal their students’ knowledge of number operations. In phase I, four teachers and 66 third-grade students participated in five monthly workshops in which CATs were co-designed and their use was discussed. In phase II, the first phase was replicated with four workshops with six different teachers and 148 third-grade students. In these two exploratory phases, we evaluated student achievement on a standardized national mathematics test in a pre-/posttest design and compared changes herein to changes in the national norm sample. In phase III, a control condition was added to the design to experimentally investigate the effect on student achievement with 30 teachers and 616 third-grade students. Teachers were randomly assigned to participate in 0, 1, 2, or 3 1-hour workshops. In all three phases, we found a significant increase in students’ mathematics achievement scores on the standardized mathematics test. In phase III, the increase was significantly larger in the classes of teachers participating in three workshops than in classes with less workshops. Additionally, results from the analysis of classroom observations, feedback forms, and interviews indicate that teachers could easily integrate the CATs into their practice and could gather valuable information on their students. The results from the different phases of this study combined indicate that supporting teachers in their development and use of classroom assessment in mathematics may contribute to the improvement of students’ mathematics achievement.

Classroom bodies: affect, body language, and discourse when schoolchildren encounter national tests in mathematics

ABSTRACT The aim of this paper is to analyse how Swedish grade three children are discursively positioned as pupils when they are taking national tests in mathematics and when they reflect on the testing situation afterwards. With support from theories about affective-discursive assemblages, we explore children’s body language, emotions, and talk in light of the two overarching discourses that we believe frame the classroom: the ‘testing discourse’ and the ‘development discourse’. Through the disciplinary power of these main discourses children struggle to conduct themselves in order to become recognized as intelligible subjects and ‘ideal pupils’. The analysis, when taking into account how affects and discourses intertwine, shows that children can be in ‘untroubled’, ‘troubled’, or ambivalent subject positions.

Level, strength, and facet-specific self-efficacy in mathematics test performance

Students’ self-efficacy expectations (SEE) in mathematics are associated with their engagement and learning experiences. Going beyond previous operationalisations of SEE we propose a new instrument that takes into account not only facet-specificity (expectations related to particular competences or skills) and strength (confidence of the expectations), but also level (perceived task difficulty) of these expectations as proposed by Bandura (Self-efficacy: The exercise of control, W. H. Freeman & Co, New York, 1997; Self-efficacy beliefs of adolescents, Information Age Publishing, Greenwich, 2006). In particular, we included level-specific items referring to perceived difficulty on a subsequent national test in mathematics. In total 756 Norwegian grade 5, 8, and 9 students completed the “Self-Efficacy Gradations of Difficulty Questionnaire.” We fitted plausible multitrait-multimethod models using structural equation models. The best fitting model included three factors representing levels of perceived difficulty, and a-priori specified correlated uniquenesses representing four facets. The facets related to problem solving or students’ self-regulation skills during the test in order to accomplish the following: (1) complete a certain number of problems, (2) solve tasks of a certain challenge, (3) concentrate, and (4) not give up for a certain amount of time. The results indicated that three correlated constructs representing levels of SEE are associated with scores on national tests in mathematics, and that the strongest association is between national test scores and medium level SEE. Taking level (difficulty) into account broadens our understanding of the self-efficacy construct, and allows investigation into differential relationships between SEE and performance.

Den flerspråkiga elevens nationella provdeltagande i matematik - diskursiva förutsättningar

Multilingual students’ participation in national tests in mathematics – discursive prerequisites. This article explores discursive prerequisites in test-taking for second language learners with oth ...

Assessing mathematical competencies: an analysis of Swedish national mathematics tests

ABSTRACTInternationally, education reform has been directed towards describing educational goals that go beyond topic and content descriptions. The idea of mathematical competencies describes such goals. National tests have been seen as one way of communicating these goals and influence teaching. The present study analyses Swedish national tests in mathematics, and seeks evidence about the extent to which they represent these competencies and may play a role in reforming teaching. The results show that the national tests assess all competencies. However, the study also shows a limited focus on the competencies’ interpretation and evaluation aspects. Thus, the tests do not fully capture the complex nature of the competencies. This may cloud the reform message and restrict the possibilities for the tests to function as levers for reform.

Parental alcohol-related disorders and school performance in 16-year-olds-a Swedish national cohort study.

AimsTo study the links between parental alcohol‐related disorders and offspring school performance and, specifically, whether associations vary by gender of parent or child and whether associations are mediated by other adverse psychosocial circumstances commonly appearing together with parental alcohol problems, such as parental mental health problems or criminal behaviour.DesignRegister study in a national cohort.SettingSweden.ParticipantsA total of 740 618 individuals born in Sweden in 1990–96.MeasurementsParental hospital admissions for alcohol‐related disorders and school performance in their offspring, in the final year of compulsory school at age 15–16 years was analysed in relation to socio‐demographic confounders and psychosocial covariates, using linear and logistic regressions.FindingsBoth mothers’ and fathers’ alcohol‐related hospital admissions were associated with lower Z‐scores of grades and national mathematics tests scores. After adjustment for parental education and socio‐demographic confounders, beta‐coefficients of Z‐scores of grades were –0.42 [95% confidence interval (CI) = –0.45, –0.39] and –0.42 (95% CI = –0.43, –0.40), and beta‐coefficients of mathematics tests scores were –0.36 (95% CI = –0.39, –0.33) and –0.31 (95% CI = –0.33, –0.29), for mothers’ and fathers’ alcohol‐related disorders, respectively. Adjusted odds ratios (ORs) for not being eligible for secondary school were 1.99 (95% CI = 1.84–2.15) and 2.04 (95% CI = 1.95–2.15) for mothers’ and fathers’ alcohol‐related disorders, respectively. Adjusting the analyses for psychosocial factors in the family almost eradicated the statistical effects of parental alcohol‐related disorders on offspring school performance to beta‐coefficients of 0.03 to –0.10 and ORs of 0.89–1.15. The effect of a mother's alcohol‐related hospital admission on school performance was stronger in girls than in boys, whereas no gender differences were seen for a father's alcohol‐related hospital admission.ConclusionsIn Sweden, alcohol‐related disorders in both mothers and fathers are associated with lower school performance in their children at age 15–16 years, with most of the statistical effects being attributed to psychosocial circumstances of the family, such as parental psychiatric disorders, drug use and criminality and receipt of social or child welfare interventions.

Closing the gaps – Improving literacy and mathematics by ict-enhanced collaboration

Literacy and mathematics are necessary skills that for different reasons unfortunately not everybody acquires sufficiently. In OECD countries there is also a gender gap; boys lag behind girls in literacy but often outperform girls in mathematics (OECD., 2012). ICT (Information and communication technologies) may contribute useful tools to address both these problems but in order to effectively create better educational conditions there is yet a need to develop effective methods that combine ICT with key factors for learning. This research contributes to this by measuring effects of the “Write to Learn” (WTL) method. WTL lets children from 1st grade use several ICT tools to write texts and subsequently discuss and refine them together with classmates and teachers using digital real-time formative feedback and assessment. The central learning factor addressed, in mathematics as well as in literacy, is the written communication allowing the learners to interact with peers and teachers. WTL draws on methods from socio-cultural theory, including continuous social interaction and written real-time formative feedback among peers, using shared electronic forums for collaboration, thereby providing social meaning and increased learning of literacy and mathematics, among both boys and girls.The study uses quantitative methods and two control groups, one using traditional method (no ICT) and one using technology individually (without integrated social interaction and formative feedback), to compare results from 502 students in grade 3 national tests in mathematics and literacy. WTL yields by far best results; higher average score both in literacy and mathematics, smaller gender gap, and significantly better results for the under-achievers. The ITU method performs worst, which shows that ICT use must be well integrated into the pedagogy to be useful.

Rendimiento académico en las pruebas nacionales de matemática en colegios del área metropolitana y zonas alejadas de Costa Rica en 2013

En este artículo se describe el rendimiento académico del estudiantado de la región metropolitana y zonas alejadas, en la prueba nacional de matemática correspondiente a la conclusión de la educación media, considerando la prueba específica, según la modalidad y tipo de colegio: diurno (diurno científico, diurno humanístico), nocturno, técnico o centros integrados para la educación de jóvenes y adultos (CINDEA). El objetivo principal es describir el rendimiento académico estudiantil en las pruebas nacionales de bachillerato de matemática, correspondientes al año 2013, según las regiones educativas. Para el análisis de dicha información se utilizó como fuente primaria el Informe Nacional de Bachillerato, emitido por el Ministerio de Educación Pública para las pruebas estandarizadas del 2013. Una de las conclusiones, a partir de este estudio, es la necesidad de llevar a cabo un análisis histórico del rendimiento de las instituciones educativas que han obtenido, en los últimos años, los promedios más altos y más bajos en las pruebas de bachillerato de matemática, para poder profundizar en las causas de dichos rendimientos.

A avaliação das aprendizagens no ensino básico português e o reforço da avaliação sumativa externa

A avaliação das aprendizagens, nas últimas décadas, tem sido utilizada pelos Estados economicamente desenvolvidos como um processo de monitorização e de prestação de contas da qualidade da educação escolar promovida, naquilo que se vem designando de processos de accountability. Tal finalidade tem sido concretizada pelo aumento da avaliação sumativa externa, realizada por exames nacionais estandardizados. Os resultados obtidos pelos alunos nessas provas servem de barômetro para aferir e monitorizar essa qualidade educativa, com referência a padrões uniformes, determinados economicamente e que são visíveis em metas oficialmente estabelecidas para a educação escolar. É pela medição do cumprimento dessas metas pelos alunos nos exames nacionais que se processa a aferição e a monitorização por parte dos Estados da qualidade educativa. Não estando Portugal distante dessa influência neoliberal e neoconservadora na educação escolar, o objetivo do presente texto consiste em analisar e refletir sobre as mudanças nas orientações legais para a avaliação das aprendizagens no ensino básico que foram implementadas a partir de 2012 e que têm que ser enquadradas numa ideologia neoliberal mitigada. Esta análise e reflexão incidem sobre os documentos normativos que atualmente regulamentam a avaliação das aprendizagens no ensino básico português e que se traduziram no alargamento dos exames nacionais de português e a matemática aos três ciclos desse nível de ensino e na tendência de valorização dos resultados em detrimento dos processos de aprendizagem.

Birth by vacuum extraction delivery and school performance at 16 years of age

The aim of the present study was to investigate cognitive competence, as indicated by school performance, at 16 years of age, in children delivered by vacuum extraction. This was a register study of a national cohort of 126,032 16 year olds born as singletons, with a vertex presentation, at a gestational age of 34 weeks or older, with Swedish-born parents, delivered between 1990 and 1993 without major congenital malformations. Linear regression was used to analyze mode of delivery in relation to mean scores from national tests in mathematics (40.2; scale, 10-75; SD, 14.9) and mean average grades (223.8; scale, 10-320; SD, 52.3), with adjustment for perinatal and sociodemographic confounders. Children delivered by vacuum extraction (-0.51; 95% confidence interval [CI], -0.76 to 0.26) as well as by nonplanned cesarean section (-0.51; 95% CI, -0.82 to -0.20) had slightly lower mean mathematics test scores than children born vaginally without instruments, after adjustment for major confounders. Mean average grades in children delivered by vacuum extraction were -1.05 (95% CI, -1.87 to -0.23) and -1.20 (95% CI,-2.24 to -0.16) in children delivered by nonplanned cesarean section compared with children born vaginally. Children delivered by vacuum extraction had slightly lower grades at age 16 years compared with those born by noninstrumental vaginal delivery but very similar to those delivered by nonplanned cesarean. This suggests that vacuum extraction and nonplanned cesarean are equivalent alternatives for terminating deliveries with respect to cognitive outcomes.

Exploring differential bundle functioning in mathematics by gender: the effect of hierarchical modelling

Researchers interested in exploring substantive group differences are increasingly attending to bundles of items (or testlets): the aim is to understand how gender differences, for instance, are explained by differential performances on different types or bundles of items, hence differential bundle functioning (DBF). Some previous work has modelled hierarchies in data in this context or considered item responses within persons, but here we model the bundles themselves as explanatory variables at the item level potentially explaining significant intra-class correlation due to gender differences in item difficulty, and thus explaining variation at the second item level. In this study, we analyse DBF using single- and two-level models (the latter modelling random item effects, which models responses at Level 1 and items at Level 2) in a high-stakes National Mathematics test. The models show comparable regression coefficients but the statistical significances of the two-level models are smaller due to the larger values of the estimated standard errors. We discuss the contrasting relevance of this effect for test developers and gender researchers.

Changing our Methods and Disrupting the Power Dynamics: National Tests in Third-Grade Classrooms

This article reports on a research project relating to the newly implemented mandatory Swedish national mathematics tests for third-grade students (nine and ten years old). The project's main research concerns the students' ideas about and reactions toward these tests and how the specific test situation affects their perception of their own mathematical proficiency. Drawing on theories that suggest identities are more fluid than static, we want to understand how students with special needs are “created.” The specific aim of this article is to discuss how our research methods have been refined during the various phases of data collection and report on the resulting implications. It discusses issues surrounding child research and how methods involving video recording and video stimulated recall dialogue (VSRD) can contribute to research on children's experiences. Particular attention is given to methodological and ethical issues and how to disrupt power relations. In this article, we argue that the context of the test situation not only impacted upon the students but also affected how we changed, developed, and adapted our approaches as the project evolved.

Effects of gender and ethnicity on fourth graders’ knowledge states in mathematics

This study sheds light on the achievement gap between two culturally diverse populations in Israel by employing a diagnostic model for analysing responses of a representative sample of Jewish and Arab fourth graders on a national mathematics test. The results indicated large significant differences, in favour of the Jewish group, on most attributes underlying the test, and relatively small significant gender effects only in the Jewish group, where boys outscored girls on higher-order thinking attributes. These results were discussed in light of cultural differences between the two populations, educational resources, and prevalent instruction–learning–assessment cultures in their respective schools.

The curriculum’s view of knowledge transferred to national tests in mathematics in Sweden

This article provides a report on the testing system in Sweden. The Swedish assessment system today is goal and knowledge related. Important for this system is the view of knowledge in the curriculum. In this article the authors give an overview of the view of knowledge in the curriculum and in the syllabi in mathematics and they describe how this influences the tasks in the national tests. The change from a norm-referenced to a goal and criteria referenced grading system influences how students' solutions of different tasks will be marked and assessed. In this article the authors also describe different assessment methods e.g. the assessment matrix, which focuses on different aspects of knowledge based on the syllabi in mathematics.