Spatial thinking in science,technology, engineering,and mathematics: Elementary teachers' beliefs,perceptions, and self-efficacy

Fostering students' spatial thinking skills holds great promise for improving Science, Technology, Engineering, and Mathematics (STEM) education. Recent efforts have focused on the development of classroom interventions to build students' spatial skills, yet these interventions will be implemented by teachers, and their beliefs and perceptions about spatial thinking influence the effectiveness of such interventions. However, our understanding of elementary school teachers' beliefs and perceptions around spatial thinking and STEM is in its infancy. Thus, we created novel measures to survey elementary teachers' anxiety in solving spatial problems, beliefs in the importance of spatial thinking skills for students' academic success, and self-efficacy in cultivating students' spatial skills during science instruction. All measures exhibited high internal consistency and showed that elementary teachers experience low anxiety when solving spatial problems and feel strongly that their skills can improve with practice. Teachers were able to identify educational problems that rely on spatial problem-solving and believed that spatial skills are more important for older compared to younger students. Despite reporting high efficacy in their general teaching and science teaching, teachers reported significantly lower efficacy in their capacities to cultivate students' spatial skills during science instruction. Results were fairly consistent across teacher characteristics (e.g., years of experience and teaching role as generalist or specialist) with the exception that only years of teaching science was related to teachers' efficacy in cultivating students' spatial thinking skills during science instruction. Results are discussed within the broader context of teacher beliefs, self-efficacy, and implications for professional development research.     

Pre-service and in-service teachers’ perceptions on the integration of children’s literature in mathematics teaching and learning in Ireland

The beneficial role that children’s literature plays in facilitating the meaningful integration and advancement of literacy and numeracy in the primary mathematics classroom has been well validated by research findings internationally. In Ireland, supporting the development of literacy and numeracy is a key educational priority. Consequently, a myriad of policy initiatives such as the Literacy and Numeracy for Learning and Life strategy have been introduced. All aim to address concerns about young people’s lack of basic literacy and numeracy skills and to consider new teaching and learning modalities to enhance same. Despite this, no official emphasis is given to incorporating literature in the Irish primary school mathematics curriculum. Therefore, it is pertinent and timely that this study seeks to ascertain pre-service and in-service teachers’ views on the use of literature to support mathematics teaching and learning and to investigate perceived barriers to and enablers for the integration of children’s literature in the mathematics classroom in Ireland. The analysis of the findings will be framed using Ajzen’s (Ajzen, Icek. 1991. “The Theory of Planned Behavior.” Organizational Behavior and Human Decision Processes 50 (2): 179–211) Theory of Planned Behavior (TPB) model. This research is part of a large international research collaboration (see www.mathsthroughstories.org), in which the beliefs of teachers with respect to children’s literature are investigated.     

Teachers' Spatial Anxiety Relates to 1st‐ and 2nd‐Graders' Spatial Learning

Teachers' anxiety about an academic domain, such as math, can impact students' learning in that domain. We asked whether this relation held in the domain of spatial skill, given the importance of spatial skill for success in math and science and its malleability at a young age. We measured 1st‐ and 2nd‐grade teachers' spatial anxiety (N = 19) and students' spatial skill (N = 132). Teachers' spatial anxiety significantly predicted students' end‐of‐year spatial skill, even after accounting for students' beginning‐of‐year spatial skill, phonological working memory, grade level, and teachers' math anxiety. Since spatial skill is not a stand‐alone part of the curriculum like math or reading, teachers with high levels of spatial anxiety may simply avoid incorporating spatial activities in the classroom. Results suggest that addressing teachers' spatial anxieties may improve spatial learning in early elementary school.     

Locating mathematics within post-16 vocational education in England

The political importance of mathematics in post-16 education is clear. Far less clear is how mathematics does and should relate to vocational education. Successive mathematics curricula (e.g. core skills, key skills) have been developed in England with vocational learners in mind. Meanwhile, general mathematics qualifications remain largely disconnected from vocational learning. Following a brief historical survey of mathematics within vocational education, the paper presents findings from a nested case study of student groups in three large Further Education colleges in England. The primary unit of analysis herein is student groups learning Functional Mathematics in two vocational areas: construction and hairdressing. We show how approaches to organising teaching, developing connected curricula and classroom pedagogy tend to isolate or integrate mathematics from/with the vocational experience. Integrated approaches are shown to impact positively on student engagement and attitudes to learning mathematics. The paper concludes by discussing the potential impact of academic qualifications displacing vocationally relevant mathematics.     

Examining the Relations Between Spatial Skills,Spatial Anxiety,and K‐12 Teacher Practice

Spatial skills are important for student success in STEM disciplines at the K‐12 educational level. Teachers' spatial skills and feelings about completing spatial tasks influence their teaching as well as their students' spatial learning. However, the relation between teachers' spatial skills and their spatial anxiety is not well understood. Here we investigated if teachers' spatial skills influence two kinds of small‐scale spatial anxiety: (a) anxiety for tasks involving visual imagery and (b) anxiety for tasks involving mental manipulations. In addition, we investigated if teachers' spatial skills in conjunction with their small‐scale spatial anxiety influence the integration of spatial practices, such as gestures and diagrams, into their teaching. Eighty‐two K‐12 teachers completed two subscales of small‐scale spatial anxiety, a measure of spatial skills, and a teaching activities questionnaire. Results indicate that teachers' spatial skills are negatively associated with their spatial anxiety for mental manipulation tasks, and positively associated with their use of spatial practices. These findings highlight the need to account for teachers' spatial skills when considering how to improve students' spatial learning.     

Depressive Symptoms in Third‐Grade Teachers: Relations to Classroom Quality and Student Achievement

This study investigated associations among third‐grade teachers' (N = 27) symptoms of depression, quality of the classroom‐learning environment (CLE), and students' (N = 523, M_age = 8.6 years) math and literacy performance. teachers' depressive symptoms in the winter negatively predicted students' spring mathematics achievement. This depended on students' fall mathematics scores; students who began the year with weaker math skills and were in classrooms where teachers reported more depressive symptoms achieved smaller gains than did peers whose teachers reported fewer symptoms. teachers' depressive symptoms were negatively associated with quality of CLE, and quality of CLE mediated the association between depressive symptoms and student achievement. The findings point to the importance of teachers' mental health, with implications for policy and practice.     

Encouraging Maternal Guidance of Preschoolers’ Spatial Thinking During Block Play

Spatial thinking, an important component of cognition, supports academic achievement and daily activities (e.g., learning science and math; using maps). Better spatial skills are correlated with more spatial play and more parental attention to spatial concepts. Tested here was whether informing mothers about spatial thinking and ways to encourage it would increase the spatial guidance they provide to their preschool children (N = 41; M = 5.23 years) during dyadic block play. Mothers given such instructions indeed produced more spatial language and spatial guidance than mothers asked to play as usual. In instructed dyads, children also used more spatial language; both mothers and children engaged in less pretend play. Findings offer support for designing interventions to encourage parents to foster their children's spatial skills.     

Children’s Home Numeracy Environment Predicts Growth of their Early Mathematical Skills in Kindergarten

This study investigated the longitudinal associations between children’s early mathematics and their home numeracy environment (HNE). Chilean children from families who varied widely in socioeconomic status were assessed at the beginning and end of prekindergarten in 2016 (N = 419, M_age = 4:7 [years:months]), and at the end of kindergarten in 2017 (N = 368, M_age = 5:10). Children whose parents provided frequent operational numeracy activities (e.g., learning simple sums) at prekindergarten showed better arithmetic performance and growth in nonsymbolic and symbolic number comparison at the end of kindergarten. Parents’ knowledge of number-related games predicted children’s arithmetic skills and growth in nonsymbolic number comparison. These findings underscore the persistent relations between the HNE and the development of children’s mathematical skills.     

Teacher depressive symptoms and children's school readiness in Ghana

This study investigated associations between kindergarten teachers' (N = 208) depressive symptoms and students' (Ghanaian nationals, N = 1490, M_age = 5.8) school-readiness skills (early literacy, early numeracy, social–emotional skills, and executive function) across 208 schools in Ghana over one school year. Teachers' depressive symptoms in the fall negatively predicted students' overall school-readiness skills in the spring, controlling for school-readiness skills in the fall. These results were primarily driven by social–emotional skills (r = .1–.3). There was evidence of heterogeneity by students' fall skill levels; teacher depressive symptoms predicted more negative spring overall school readiness for children who had higher fall school-readiness skills. Findings underscore the importance of teachers' mental health in early childhood education globally, with implications for policy and practice.     

LEBANESE STUDENTS’ CONCEPTIONS OF AND ATTITUDES TOWARDS SCIENCE AND RELATED CAREERS BASED ON THEIR GENDER AND RELIGIOUS AFFILIATIONS

The pedagogical practices of mathematics education for young children in English and Korean pre-schools were compared through analyses of interviews with practitioners, observations of classroom activities and an examination of documents related to the planning and implementation of mathematics education. Practitioners in both countries used integrated activities to teach mathematics, although they used such activities more frequently in nurseries than in reception classes in England and more frequently in state settings than in independent settings in Korea. Furthermore, mathematics education was more structured, more likely to be led by an adult and less holistic in reception classes than in nurseries in England, whereas it was more structured and didactic in independent than in state settings in Korea. However, mathematics education in England was more systematic, used a more individualised approach and incorporated a variety of hands-on materials and rigorous outdoor activities, whereas it was more group-oriented and utilised limited materials and fewer outdoor activities in Korea.     

The effects of educational computer game on low-performing children’s early numeracy skills – an intervention study in a preschool setting

The aim of this study was to determine the effects of an educational computer game, Lola’s World, on low-performing children’s early numeracy skills. Four preschools with 33 children from families of low socio-economic status (M _age = 5.5 years) took part in this study. Of the 33 children, 23 were split randomly into two groups: an intervention group playing a numeracy game (Lola’s World) and an active control group playing an early reading skills game (Lola’s ABC party). The remaining 10 children served as a passive control group. The intervention phase lasted three weeks, during which time the children played the games daily for about 15 min. The children’s numeracy skills were measured using the Early Numeracy Test. Those children (n = 22) who exhibited low numeracy (i.e. at risk for learning difficulties in mathematics) were included in the analyses. The three groups did not differ in terms of parental educational levels or home languages. They were comparable in terms of nonverbal reasoning and the amount of time spent playing. The Lola’s World group improved its early numeracy performance from pretest to post-test. No between-group differences were found. The results are discussed in relation to providing game-based support for low-performing preschoolers.     

Exploring Estimation in Young Primary School Children

There is an increasing emphasis in mathematics education on the importance of estimation abilities in children. This study investigates the role of context upon primary‐aged children's estimation skills. Children in three age groups (from aged 5 to 8 years) were asked to carry out a range of estimation tasks involving distance, area and volume measurements. The tasks varied in type and complexity and were either of a ‘real‐world’ or ‘mathematics task’ form. In addition to performance measures the children's answers to questions on how they carried out the estimates were recorded and analysed. Quantitative and qualitative analyses found significant effects for context and child strategy. Estimates in contexts perceived as mathematical were different, both in that they changed with age and in their error patterns, from contexts involving perceptual‐motor skills. The children's answers highlight the importance of imagery and classroom experience. The results are discussed within a model of estimating.     

Perceived autonomy support and autonomous motivation toward mathematics activities in educational and out-of-school contexts is related to mathematics homework behavior and attainment

We adopted a trans-contextual model of motivation to examine the processes by which school students' perceived autonomy support (defined as students' perceptions that their teachers' support their autonomous or self-determined motivation) and autonomous forms of motivation (defined as motivation to act out of a sense of choice, ownership, and personal agency) toward mathematics activities in an educational context predict autonomous motivation and intentions toward mathematics homework, and actual mathematics homework behavior and attainment, as measured by homework grades, in an out-of-school context. A three-wave prospective study design was adopted. High-school students (N = 216) completed self-report measures of perceived autonomy support and autonomous forms of motivation toward mathematics activities in school in the first wave of data collection. One-week later, participants completed measures of autonomous forms of motivation, attitudes, subjective norms, perceived behavioral control, and intentions with respect to mathematics homework outside school. Students' self-reported homework behavior and homework grades from students' class teachers were collected 5-weeks later. A structural equation model supported model hypotheses. Perceived autonomy support and autonomous forms of motivation toward mathematics activities in school were related to autonomous forms of motivation toward mathematics homework outside of school. Autonomous forms of motivation toward mathematics homework predicted intentions to do mathematics homework mediated by attitudes, subjective norms and perceived behavioral control. Intentions predicted self-reported mathematics homework behavior and mathematics homework grades. Perceived autonomy support and autonomous forms of motivation toward mathematics in school had statistically significant indirect effects on mathematics homework intentions mediated by the motivational sequence of the model. Results provide preliminary support for the model and evidence that autonomous motivation toward mathematics activities in the classroom is linked with autonomous motivation, intention, behavior and actual attainment in mathematics homework outside of school.     

The link between student-perceived teacher talk and student enjoyment,anxiety and discursive engagement in the classroom

This study seeks to understand the emotional connection of teachers' academically productive talk (APT) with student learning from the students' perspective. Using a sample of 2,225 students (N_{7th grade} = 1,146 and N_{8th grade} = 1,079) from 16 middle schools in a city of China, we investigate the relationship between students' perceptions of their teachers’ APT, student emotions (enjoyment and anxiety) and their discursive engagement with others in the mathematics classroom. Results from structural equation modelling and mediation analysis show that after controlling for gender, family resources and mathematics achievement, student-perceived teacher APT was positively associated with their discursive engagement with classmates. Furthermore, student enjoyment and anxiety in class mediated the relationship between student-perceived teacher APT and student discursive engagement with classmates. Multi-group analysis revealed that the model was invariant across genders and grades, indicating that the associations were applicable to male and female students as well as to seventh and eighth graders. These findings shed light on the emotional relationship of teacher APT with the discursive engagement of their students. Although prior research observes a positive relationship between teacher productive classroom talk and student discursive engagement primarily through classroom observations and teacher reflections, this study provides evidence from the students’ perspective and highlights the mediating role of student emotions in the relationship.     

Linguistic and Spatial Skills Predict Early Arithmetic Development via Counting Sequence Knowledge

Utilizing a longitudinal sample of Finnish children (ages 6–10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in kindergarten, predicted the level of arithmetic in first grade, and later growth through third grade. Study 2 (n = 378) further showed that these associations were mediated by counting sequence knowledge measured in first grade. These studies add to the literature by demonstrating the importance of written language for arithmetic development. The findings are consistent with the hypothesis that linguistic and spatial skills can improve arithmetic development by enhancing children's number‐related knowledge.     

The Development of Spatial Skills in Elementary School Students

Through five waves of data collection, this longitudinal study investigated the development of spatial skills in 304 elementary school children (M_age = 7.64 years) as they progressed from the second to fourth grade. The study focused on whether multiple latent classes with different developmental profiles best explain development. Spatial skills were measured by tests featuring two‐dimensional figures. Mathematics achievement was measured by the statewide end‐of‐year test and was included as a distal outcome variable. The role of covariates, including socioeconomic status, verbal working memory, and gender, was also explored. The results indicate a need to view two‐dimensional spatial skills development as multidimensional with two developmental profiles predicted by socioeconomic status, verbal working memory, and gender. The developmental profiles predicted differences in mathematics achievement.     

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.     

Subjective and Objective Intellectual Change in Older Adults

In this longitudinal study, 108 older individuals (M age = 70.58 years, SD = 6.94) estimated the extent to which their fluid and crystallized skills had changed over the previous three years. For each perceived change, individuals also estimated the extent to which numerous explanatory factors were responsible for such change. Crystallized skills were seen as unchanging, whereas fluid skills were perceived as having declined slightly. In both cases, self-initiated efforts to maintain one's skills were endorsed most frequently as explanations for the maintenance of one's skills. Variability in attributions in three-year changes in both fluid and crystallized skills was associated with individual differences in health, self perceived everyday cognitive failures, and state anxiety. The findings from this study suggest that it is important to identify factors over which older adults perceive themselves as having control as salient targets for educational interventions fostering a sense of self-efficacy, critical to feelings of enhanced competence in later life.