Early home learning support and home mathematics environment as predictors of children's mathematical skills between age 4 and 6: A longitudinal analysis using video observations and survey data

This large-scale and longitudinal study examines early home support for learning, formal/informal home mathematics activities, and their associations with children's mathematical development between age two and six. Data were collected in Germany between 2012 and 2018, N = 1184 (49% girls, 51% boys), and 15% of children had parents with a migration history. Linguistically and mathematically stimulating, attentive, and responsive parent–child engagement at age two predicted children's mathematical skills at age four and six (small-to-medium effect size). Both formal and informal home mathematical activities at age five predicted children's mathematical skills at age six (small effect size), and were associated with children's prior mathematics attainment. This study also provides indicators where individual differences and social circumstances are relevant to understanding different early mathematics outcomes.     

Do home numeracy and literacy practices of Greek and Canadian parents predict the numeracy skills of kindergarten children?

Children’s experiences with early numeracy and literacy activities are a likely source of individual differences in their preparation for academic learning in school. What factors predict differences in children’s experiences? We hypothesised that relations between parents’ practices and children’s numeracy skills would mediate the relations between numeracy skills and parents’ education, attitudes and expectations. Parents of Greek (N = 100) and Canadian (N = 104) five‐year‐old children completed a survey about parents’ home practices, academic expectations and attitudes; their children were tested on two numeracy measures (i.e., KeyMath‐Revised Numeration and next number generation). Greek parents reported numeracy and literacy activities less frequently than Canadian parents; however, the frequency of home numeracy activities that involved direct experiences with numbers or mathematical content (e.g., learning simple sums, mental math) was related to children’s numeracy skills in both countries. For Greek children, home literacy experiences (i.e., storybook exposure) also predicted numeracy outcomes. The mediation model was supported for Greek children, but for Canadian children, the parent factors had both direct and mediated relations with home practices.     

Design‐based research on the use of a tangible user interface for geometry teaching in an inclusive classroom

This design‐based research study was conducted to identify what importance of a tangible user interface (TUI) can add to teaching and learning. Over a 2‐year period, teachers (n = 39) and students (n = 145) participated in the study. The identified problem for investigation was how students, including those with low fine motor skills and those with learning difficulties, develop geometry concepts combining cognitive and physical activity. A didactical application was designed during the first iteration and implemented in inclusive classrooms during the second and third iterations. Qualitative research methods were applied. A relationship between diverse students’ needs and geometry concept learning in relation to computer‐supported learning by TUI was discovered. Two dimensions were identified: (1) TUIs support concept development, with physical and virtual representations based on dynamic geometry assisted by TUI; (2) TUI manipulative properties support students who have low motor skills and difficulties in their geometry learning as well as in their inclusion in classroom activities. The study outcomes contributed to the design process of the TUI didactical application and its implementation in inclusive classrooms, and to the body of knowledge in teaching and learning geometry concepts applied for computer‐assisted learning environments supported by TUI.     

Metacognitive skills in Belgian third grade children (age 8 to 9) with and without mathematical learning disabilities

This paper presents a study on mathematical problem solving in third-grade pupils. The relationship between mathematics, metacognition and intelligence was investigated in children with (n = 191) and without mathematical learning disabilities (n = 268). A significant relationship was found between prediction, evaluation, intelligence, procedural and mathematical fact retrieval skills in children without mathematical learning disabilities. In the children with mathematical learning disabilities a relationship was found between metacognitive and procedural skills. No such relationship was found between intelligence and metacognition or between metacognition and mathematical fact retrieval skills. In addition it was investigated if children with mathematical learning disabilities had less adequate metacognitive skills than peers without learning problems. At group level significant differences were found between both groups. However on analyzing these results further, it was found that four out of five children with combined mathematical learning disabilities, half of the children with procedural disabilities and only 5% of the children with a retrieval deficiency had low metacognitive skills. Furthermore, metacognitive problems were found in one out of five children without learning disabilities. Moreover, a majority of the children with mathematical learning disabilities and inadequate metacognitive skills had problems with prediction and evaluation skills. Most third graders with low metacognitive skills only appeared to have problems predicting the level of difficulty of tasks. Inaccurate evaluations were found on a more regular basis in children with mathematical learning disabilities and inadequate metacognitive skills as opposed to the sample of children with inadequate metacognitive skills but without learning difficulties, where their occurrence was rather a one off. The implications of this study for diagnosis and treatment will be discussed later in this paper.     

Quantitative skills as a graduate learning outcome: exploring students’ evaluative expertise

In the biosciences, quantitative skills are an essential graduate learning outcome. Efforts to evidence student attainment at the whole of degree programme level are rare and making sense of such data is complex. We draw on assessment theories from Sadler (evaluative expertise) and Boud (sustainable assessment) to interpret final-year bioscience students’ responses to an assessment task comprised of quantitative reasoning questions across 10 mathematical and statistical topics. The question guiding the study was: do final year science students graduate knowing the quantitative skills that they have, and knowing the quantitative skills that they do not have? Confidence indicators for the 10 topics gathered students’ perceptions of their quantitative skills. Students were assigned to one of four categories: high performance-high confidence; low performance-low confidence; high performance-low confidence; or low performance-high confidence – with those in the first two categories demonstrating evaluative expertise. Results showed the majority of students effectively evaluated their quantitative skills as low performance-low confidence. We argue that the application of evaluative expertise to make sense of this graduate learning outcome can further the debate on how assuring graduate learning outcomes can enhance student learning.     

Examining the Enactment of Web GIS on Students' Geospatial Thinking and Reasoning and Tectonics Understandings

Geospatially enabled learning technologies may enhance Earth science learning by placing emphasis on geographic space, visualization, scale, representation, and geospatial thinking and reasoning (GTR) skills. This study examined if and how a series of Web geographic information system investigations that the researchers developed improved urban middle-school learners’ GTR skills and their understanding of tectonics concepts. Paired-sample t tests for analyses of tectonics content knowledge and GTR achievement measures revealed statistically significant gains from pretest to posttest (p <.001) with large effect sizes. The findings provide support that GTR related to tectonics can be learned with appropriately designed learning activities using Web-based geographic information systems.     

Early Educators’ Collective Workplace Stress as a Predictor of Professional Development’s Impacts on Children’s Development

Although professional development is widely used to improve the impacts of early childhood education, little is known about the conditions under which such interventions promote child outcomes. This study applies newly developed methods for quantifying intervention impact heterogeneity to understand whether educators’ collective workplace stress moderates professional development’s impacts on children’s language and literacy skills, executive functioning, and learning behaviors. Within a sample of 406 children from the National Center for Research on Early Childhood Education Professional Development Study (M_age = 4.17; 50% female; 50% Black, 32% Latinx, 11% White), professional development positively impacted child outcomes in centers where educators collectively reported high workplace stress but negatively impacted child outcomes in centers where educators collectively reported low workplace stress.     

Proofreading as an index of crystallised intelligence

This paper reports on four studies that were all concerned with cognitive and non‐cognitive correlates of proofreading (PR) ability. A new, five‐minute PR test was devised and piloted. In the first pilot study (N = 191) it was correlated with a verbal reasoning test. In the second study (N = 103) PR scores were regressed onto measures of personality: approach to learning, general and fluid intelligence (verbal reasoning) as well as a test of general knowledge. All three cognitive ability measures were significant predictors of PR but when entered together, general knowledge alone remained significant and accounted for a third of the variance. The third study (N = 95) was similar, except it also included a measure of typical intellectual engagement. Fluid intelligence (verbal reasoning) and openness were the only significant predictors of PR. In the fourth study (N = 249) participants completed four tests: PR, fluid intelligence (verbal reasoning), vocabulary and spelling. PR was consistently correlated with verbal reasoning but more strongly correlated with measures of crystallised intelligence, namely general knowledge and vocabulary. Implications and limitations are considered.     

Rethinking Intensive Quantities via Guided Mediated Abduction

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses a/b analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students' sensation of an intensive quantity could serve as a powerful resource for grounding its formal expression, accepting the mathematical form requires students to align the sensation with a new way of reasoning about the phenomenon. I offer a case analysis of a middle school student who successfully came to understand the intensive quantity of likelihood. The analysis highlights a form of reasoning called abduction and suggests that sociocognitive processes can guide and mediate students' abductive reasoning. Interpreting the child's and tutor's multimodal action through the lens of abductive inference, I demonstrate the emergence of a proportional concept as guided mediated objectification of tacit perception. This “gestalt first” process is contrasted with traditional “elements first” approaches to building proportional concepts, and I speculate on epistemic and cognitive implications of this contrast for the design and instruction of these important concepts. In particular, my approach highlights an important source of epistemic difficulty for students as they learn intensive quantities: the difficulty in shifting from intuitive perceptual conviction to mediated disciplinary analysis. My proposed conceptualization of learning can serve as an effective synthesis of traditional and reform-based mathematics instruction.     

Differential effects of home and preschool learning environments on early language development

The present study is based on longitudinal data from a German early childhood education and care (ECEC) governmental initiative assessing children's grammatical and vocabulary development between 2;6 and 4;0 years (N = 1,331), quality of the home learning environment and quality of the preschool setting. Results showed that the quality of the home learning environment predicted development in grammatical skills, but not in receptive vocabulary at age 4, while the effects of preschool process quality showed similar relative impacts on both language outcomes. Further analyses revealed effects of accumulated advantages of preschool quality for children from medium‐ and high‐quality home learning environments in their vocabulary development. The results are compared with previous findings from the German ECEC context and discussed with respect to implications for policy efforts to improve ECEC quality and ways in which both learning environments act together on children's development.     

Learning analytics application to examine validity and generalizability of game-based assessment for spatial reasoning

Game-based assessment (GBA), a specific application of games for learning, has been recognized as an alternative form of assessment. While there is a substantive body of literature that supports the educational benefits of GBA, limited work investigates the validity and generalizability of such systems. In this paper, we describe applications of learning analytics methods to provide evidence for psychometric qualities of a digital GBA called Shadowspect, particularly to what extent Shadowspect is a robust assessment tool for middle school students' spatial reasoning skills. Our findings indicate that Shadowspect is a valid assessment for spatial reasoning skills, and it has comparable precision for both male and female students. In addition, students' enjoyment of the game is positively related to their overall competency as measured by the game regardless of the level of their existing spatial reasoning skills.

Practitioner notes

What is already known about this topic:

• Digital games can be a powerful context to support and assess student learning.
• Games as assessments need to meet certain psychometric qualities such as validity and generalizability.
• Learning analytics provide useful ways to establish assessment models for educational games, as well as to investigate their psychometric qualities.

What this paper adds:

• How a digital game can be coupled with learning analytics practices to assess spatial reasoning skills.
• How to evaluate psychometric qualities of game-based assessment using learning analytics techniques.
• Investigation of validity and generalizability of game-based assessment for spatial reasoning skills and the interplay of the game-based assessment with enjoyment.

Implications for practice and/or policy:

• Game-based assessments that incorporate learning analytics can be used as an alternative to pencil-and-paper tests to measure cognitive skills such as spatial reasoning.
• More training and assessment of spatial reasoning embedded in games can motivate students who might not be on the STEM tracks, thus broadening participation in STEM.
• Game-based learning and assessment researchers should consider possible factors that affect how certain populations of students enjoy educational games, so it does not further marginalize specific student populations.

     

Hands-On: Investigating the role of physical manipulatives in spatial training

Studies show that spatial interventions lead to improvements in mathematics. However, outcomes vary based on whether physical manipulatives (embodied action) are used during training. This study compares the effects of embodied and non-embodied spatial interventions on spatial and mathematics outcomes. The study has a randomized, controlled, pre-post, follow-up, training design (N = 182; mean age 8 years; 49% female; 83.5% White). We show that both embodied and non-embodied spatial training approaches improve spatial skills compared to control. However, we conclude that embodied spatial training using physical manipulatives leads to larger, more consistent gains in mathematics and greater depth of spatial processing than non-embodied training. These findings highlight the potential of spatial activities, particularly those that use physical materials, for improving children's mathematics skills.     

Sources of Individual Differences in Children's Understanding of Fractions

Longitudinal associations of domain‐general and numerical competencies with individual differences in children's understanding of fractions were investigated. Children (n = 163) were assessed at 6 years of age on domain‐general (nonverbal reasoning, language, attentive behavior, executive control, visual‐spatial memory) and numerical (number knowledge) competencies; at 7 years on whole‐number arithmetic computations and number line estimation; and at 10 years on fraction concepts. Mediation analyses controlling for general mathematics ability and general academic ability revealed that numerical and mathematical competencies were direct predictors of fraction concepts, whereas domain‐general competencies supported the acquisition of fraction concepts via whole‐number arithmetic computations or number line estimation. Results indicate multiple pathways to fraction competence.     

Curriculum development for quantitative skills in degree programs: a cross-institutional study situated in the life sciences

Higher education policies are increasingly focused on graduate learning outcomes, which infer an emphasis on, and deep understanding of, curriculum development across degree programs. As disciplinary influences are known to shape teaching and learning activities, research situated in disciplinary contexts is useful to further an understanding of curriculum development. In the life sciences, several graduate learning outcomes are underpinned by quantitative skills or an ability to apply mathematical and statistical thinking and reasoning. Drawing on data from a national teaching project in Australia that explored quantitative skills in the implemented curricula of 13 life sciences degree programs, this article presents four program-level curricular models that emerged from the analysis. The findings are interpreted through the lens of discipline-specific research and general curriculum design theories to further our understanding of curriculum development for graduate learning outcomes. Implications for future research and to guide curriculum development practices in higher education are discussed.     

Proportional Reasoning Ability and Concepts of Scale: Surface area to volume relationships in science

The National Science Education Standards emphasise teaching unifying concepts and processes such as basic functions of living organisms, the living environment, and scale. Scale influences science processes and phenomena across the domains. One of the big ideas of scale is that of surface area to volume. This study explored whether or not there is a correlation between proportional reasoning ability and a student's ability to understand surface area to volume relationships. Students' knowledge of surface area to volume relationships was assessed pre and post to a one‐week instructional intervention involving investigations about surface area to volume as a limiting factor in biological and physical systems. Results showed that proportional reasoning scores of middle school students were correlated to pre‐test and post‐test assessment scores, and a paired‐sample t‐test found significant differences from pre‐test to post‐test for the surface area to volume assessment. Relationships between proportional reasoning, visualisation abilities and success in solving surface to volume problems are discussed. The implications of the results of this study for learning concepts such as magnitudes of things, limits to size, and properties of systems that change depending on volume and surface are explored.     

Finding Out How They Find It Out: An empirical analysis of inquiry learners’ need for support

Inquiry learning environments increasingly incorporate modelling facilities for students to articulate their research hypotheses and (acquired) domain knowledge. This study compared performance success and scientific reasoning of university students with high prior knowledge (n = 11), students from senior high‐school (n = 10), and junior high‐school (n = 10) with intermediate and low prior knowledge, respectively, in order to reveal domain novices’ need for support in such environments. Results indicated that the scientific reasoning of both groups of high‐school students was comparable to that of the experts. As high‐school students achieved significantly lower performance success scores, their expert‐like behaviour was rather ineffective; qualitative analyses substantiated this conclusion. Based on these findings, implications for supporting domain novices in inquiry learning environments are advanced.     

Genetics Reasoning with Multiple External Representations

This paper explores a case study of a class of Year 10 students (n=24) whose learning of genetics involved activities of BioLogica, a computer program that features multiple external representations (MERs). MERs can be verbal/textual, visual-graphical, or in other formats. Researchers claim that the functions of MERs in supporting student learning are to complement information or processes, to constrain the interpretation of abstract concepts, and to construct new viable conceptions. Over decades, research has shown that genetics remains linguistically and conceptually difficult for high school students. This case study using data from multiple sources enabled students' development of genetics reasoning to be interpreted from an epistemological perspective. Pretest-posttest comparison after six weeks showed that most of the students (n=20) had improved their genetics reasoning but only for easier reasoning types. Findings indicated that the MERs in BioLogica contributed to students' development of genetics reasoning by engendering their motivation and interest but only when students were mindful in their learning. Based on triangulation of data from multiple sources, MERs in BioLogica appeared to support learning largely by constraining students' interpretation of phenomena of genetics.