Assessing preschool number sense: skills demonstrated by children prior to school entry

Components of early number sense, as identified in two Delphi studies and in the number sense literature related to mathematics difficulties, were assessed for 176 children in preschools and childcare centres across one local government area in Sydney, Australia, using tasks or modifications of tasks reported in the number sense literature. In addition, the children’s receptive vocabulary was measured using The Peabody Picture Vocabulary Test (third edition) and math reasoning was measured using Woodcock‐Johnson III Tests of Achievement. Although the children demonstrated a broad range of skills, there were no significant differences between children attending childcare and preschools for any of the measures. However, boys performed significantly better than girls in quantitative concepts and girls performed better than boys in subitising. In discussing the data, a comparison is made of the skills demonstrated by children and skills that were highlighted in the two Delphi studies and in the early number sense literature as being essential components of number sense prior to school entry. Implications for kindergarten mathematics curricula and approaches to the teaching of early number skills are discussed.     

Defining Early Number Sense: A participatory Australian study

Recent publications in Australia focus on “number sense” as an important component of mathematics instruction. The current study attempted to tap into local expert knowledge in the area of early mathematics in an effort to establish a consensus on which skills reflect the number sense typically acquired by school entry. A modified Delphi procedure was employed whereby participants were asked to indicate their level of agreement with a variety of skills as indicators of number sense in young children. The study raised questions about the efficacy of this type of participatory research when used in relation to an ill‐defined construct. It also revealed a lack of consensus among the group of academics who agreed to participate in the study.     

How do phonological processing abilities contribute to early Chinese reading and mathematics?

Abstract

The present study examined phonological processing skills (phonological memory, phonological awareness, and rapid automatised naming, RAN) in relation to early Chinese reading and early Chinese mathematics for young children. Early Chinese reading was assessed with single character reading and multi-character word reading, and early mathematics was assessed with procedural arithmetic and arithmetic story problems. Among 86 Chinese kindergarteners, phonological processing skills explained 20% of the variance in character reading and 28% of the variance in word reading; they accounted for 8% of the variance in arithmetic and 11% of the variance in story problem performance. Specifically, findings further highlight the general importance of phonological awareness in early Chinese single character reading, word reading, simple arithmetic and story problems, and the specific role of RAN in single character reading and simple arithmetic.

• Highlights

• Phonological awareness and rapid automatised naming explained unique variance in Chinese single character reading and procedural arithmetic.

• Only phonological awareness significantly accounted for unique variance in Chinese word reading and arithmetic story problems.

• The associations of phonological awareness with procedural arithmetic and arithmetic story problem were maintained even beyond other variables.

     

A participatory approach to the identification of measures of number sense in children prior to school entry

The research reported in this paper used a modified Delphi procedure in an attempt to establish a consensus on tasks proposed to assess components of number sense identified as essential for early mathematics success by a broad range of academics with expertise in the area of early mathematics. Tasks included as measures of these components were based on assessment tasks developed by early mathematics researchers. Eighteen questionnaires were returned by academics from Australia, the UK, New Zealand, The Netherlands and the USA, all with published work in the areas of early mathematics and/or number sense. Both the proposed components and tasks in the questionnaires were limited to the number domain. The study revealed considerable agreement with a number of the proposed tasks and thus provided a way forward for the development of an early number sense assessment to be trialled with young children prior to their first year of formal schooling.     

Reasoning about Representations: Effects of an Early Math Intervention

ABSTRACT

The outcomes of a longitudinal randomized number sense intervention including pre-, post- and follow-up tests are reported. The intervention was conducted in Grade 0 when children were six years old. Using Concrete-Representational-Abstract principles, a structured explicit 10-week program focusing on numbers and collective reasoning about representations was conducted by the classroom teachers. In addition to their regular mathematics teaching, a trained control group received an equally structured and explicit intervention program but without the critical mathematics component. The children in the experimental group outperformed the children in the control group on number sense growth between the pre- and the post-test. There was also a sustained effect of the intervention nine months later when children were assessed in Grade 1.     

Making abstract mathematics concrete in and out of school

We adopt a neo-Vygotskian view that a fully concrete scientific concept can only emerge from engaging in practice with systems of theoretical concepts, such as when mathematics is used to make sense of outside school or vocational practices. From this perspective, the literature on mathematics outside school tends to dichotomise in- and out-of-school practice and glamorises the latter as more authentic and situated than academic mathematics. We then examine case study ethnographies of mathematics in which this picture seemed to break down in moments of mathematical problem solving and modelling in practice: (1) when amateur or professional players decided to investigate the mathematics of darts scoring to develop their “outing” strategies and (2) when a prevocational mathematics course task challenged would-be mathematics teachers’ concept of fractions. These examples are used to develop the Vygotskian framework in relation to vocational and workplace mathematics. Finally, we propose that a unified view of mathematics, outside and inside school, on the basis of Vygotsky’s approach to everyday and scientific thought, can usefully orientate further research in vocational mathematics education.     

MyTeachingPartner-Math/Science pre-kindergarten curricula and teacher supports: Associations with children's mathematics and science learning

MyTeachingPartner-Math/Science (MTP-MS) is a system of two curricula (math and science) plus teacher supports designed to improve the quality of instructional interactions in pre-kindergarten classrooms and to scaffold children's development in mathematics and science. The program includes year-long curricula in these domains, and a teacher support system (web-based supports and in-person workshops) designed to foster high-quality curricular implementation. This study examined the impacts of the intervention on the development of mathematics and science skills of 444 children during pre-kindergarten, via school-level random assignment to two intervention conditions (Basic: MTP-M/S mathematics and science curricula, and Plus: MTP-M/S mathematics and science curricula plus related teacher support system) and a Business-As-Usual control condition (BaU). There were intervention effects for children's knowledge and skills in geometry and measurement as well as number sense and place value: Children in Plus classrooms made greater gains in geometry and measurement, compared with those in BaU classrooms. Children in Plus classrooms also performed better on the number sense and place value assessment than did those in Basic or BaU classrooms. We describe the implications of these results for supporting the development of children's knowledge and skills in early childhood and for developing and providing teachers with professional development to support these outcomes.     

The Operation of Bureaus of Educational Research–With Particular Reference to Wisconsin

ABSTRACT

Advanced mathematics and science coursetaking is critical in building the foundation for students to advance through the STEM pathway—from high school to college to career. To invigorate students’ persistence in STEM fields, high schools have been introducing applied STEM courses into the curriculum as a way to reinforce concepts learned in traditional mathematics and science classes and to motivate students’ interests in a long-term pursuit of these areas. The author examines the role of taking applied STEM courses early in high school on taking advanced mathematics and science courses later in high school. The results suggest a positive link between early applied STEM coursetaking and later advanced mathematics and science coursetaking—one that is delineated by specific type of applied STEM course and by individual-level demographic characteristics. The findings of this study thus support policymakers and practitioners’ efforts to expand the STEM curriculum beyond traditional subjects. Continuing to do so may be one way to expand the number of students persisting in STEM.     

A sense of belonging among Australian university students

ABSTRACT

This study was designed to explore what students perceive as essential factors influencing their sense of belonging. Gaining insight into what students perceive as influencing their sense of belonging enables design of interventions to foster that sense of belonging. Two hundred and nine students from a university in Sydney responded to the question: ‘What would help you to feel that you belong at Macquarie University?’ Results showed students most frequently identified people as instrumental in feeling that they belonged at university. Students also reported that places where there is respect, and where others are accepted, contributed to their feelings of belonging. Lastly, opportunities to interact with other students, such as within clubs, societies and at events, were reported by students to contribute to their feelings of belonging. Findings of the current study are discussed in relation to existing literature, to develop approaches that may enhance university students’ sense of belonging.     

Fostering a “head start” in math: observing teachers in early childhood mathematics engagement

ABSTRACT

Studies show that early engagement with mathematics leads to increased math achievement later in life. Yet, early childhood teachers do not regard mathematics as critical to young learners’ development and lack confidence with helping children learn mathematics. Early childhood teacher comfort and engagement with mathematics is a critical element to promoting intentional math instruction. Research was conducted to examine the effects of an innovative professional development program for Head Start preschool teachers with the goal of increasing pedagogical content knowledge and confidence in teaching mathematics. The findings in this article focus on classroom observations that concentrated on teacher engagement with mathematics.     

Information processing and mathematics learning difficulties

Abstract

Successful mathematics learning requires the efficient processing of the information that defines the arithmetic tasks. Information processing relates to the ways in which individuals make sense of, or interpret, the information to which they are exposed.

The present study examines four aspects of information processing and their relationship for whole number computation for third and fifth grade students. The aspects included students’ ability to (1) manipulate numerals, (2) encode number sentences , (3) recognise order among numbers and (4) perform an arithmetic procedure.

Information processing in each area correlated with computational skill. At risk students were less efficient in their information processing. As well, the complexity of the numerical information affected how well the students could use it. The more complex the numerical information was, the greater the load it placed on the learner. The implications for diagnosing low mathematics achievement are discussed.     

How does a STEM Access module prepare adult learners to succeed in undergraduate science?

ABSTRACT

This article explores the impact of a science, technology, engineering and mathematics (STEM) Access module on the progression of students to undergraduate Science. Drawing on the Widening Participation (WP) literature, this research investigated the experience of adult learners from disadvantaged backgrounds taking their first steps into higher education (HE). A mixed methods institutional case study was conducted, drawing on extensive survey data and interviews with students and tutors. Key findings included: enhanced student understanding of how to use tutor support; improvement in the skills and confidence of students in relation to maths, as a result of an embedded interdisciplinary curriculum; and an uplift in student study skills. This study was undertaken in a distance learning context, addressing issues in entry-level STEM, but the conclusions are applicable to other HE settings.     

数感、数学效能感与数学成绩的关系研究

本研究以小学生为被试,探讨小学生数感、数学效能感发展特点以及数感、数学效能感和数学成绩之间的关系。研究结果如下:数感、数学效能感与数学成绩之间的相关均达到显著水平,且数感与数学成绩的关系较之数学效能感与数学成绩的关系更紧密;数感对数学成绩的预测力较强,数学效能感的预测力弱一些;数学效能感在数感和数学成绩之间起部分中介作用。     

The Study of Number Sense: Realistic Activities Integrated into Third-Grade Math Classes in Taiwan

ABSTRACT

The authors compared the performance of students who received integration of number sense activities in instruction with students who received instruction using regular mathematics textbooks. Two classes of third-grade students (N = 60) were randomly assigned to experimental and control groups. Students in each group were given a pretest, post I test, and post II test, and were interviewed individually across 20 class periods of intervention. Results showed that the performance of the students in the experimental group was significantly higher than those in the control group. The interview data also showed that the students in the experimental group performed better than students in the control group in flexible and effective ways to use number sense.     

Calling for the development of children's number sense in primary schools in Malaysia

Although the early development of children's number sense is a strong predictor of their later mathematics achievements, it has been overlooked in primary schools in Malaysia. Mainly attributable to underdeveloped number sense of Malaysian primary and secondary school children, their inability to handle simple mathematics tasks, which require the understanding of basic mathematical concepts, numerical estimation, and mental computation, is a cause for worry. To enhance the perception of curriculum designers and mathematics teachers about why and how number sense ought to be developed, this article serves as a review of essential components, theoretical framework, and test of number sense.     

RETHINKING FOOD UTILIZED AS MATERIALS FOR ART

ABSTRACT

Teaching mathematics in an early childhood program requires mathematical content knowledge and teacher self-efficacy, yet research has shown that early childhood educators often have negative attitudes towards mathematics and feel underprepared to teach mathematical concepts. The study reported here documents the reconceptualization of a graduate, preservice teacher education program, a program designed to address teacher anxiety and increase capacity to teach mathematics in a play-based early childhood setting. The study aimed to investigate: (1) the effectiveness of the mathematics component of the course in equipping teacher candidates to teach mathematics in early childhood, and (2) whether participation in the mathematics component of the course changed teacher candidates’ self-efficacy regarding mathematics. Findings show that both self-efficacy and content knowledge improved when teacher candidates had the opportunity to engage with play-based learning experiences that embed mathematical concepts. Furthermore, the focus on a learning trajectories approach supports the identification of developmental progression points in children’s emerging mathematical understanding, assisting with teacher candidates’ fine-grained observations, assessment of children’s learning, and authentic, individualized planning for learning.     

Exploring mathematics identity: an intervention of early childhood preservice teachers

ABSTRACT

Early childhood and elementary preservice teachers often fear mathematics, find it irrelevant, have mathematics anxiety, hold negative self-perceptions, and have low mathematics achievement. This study investigates the influence of an identity exploration intervention on preservice teachers’ mathematics identities during a college Algebra course specifically designed for education majors. Results provide insight into the patterns of change in identity and motivation. Data was analyzed following a theoretical framework on role identity that highlights the interaction between self-perceptions, beliefs, goals, and action possibilities. Analysis identified patterns of change in student identities. Themes across cases highlight the differences in change amongst participants, the influence of initial identity, and the impact of perceived relevance on identity exploration.     

Improving early childhood teacher education: Preservice teachers' beliefs about inclusion

Abstract

The purpose of this study is to describe early childhood preservice teachers’ beliefs about the inclusion of children with special needs in early childhood settings. Nineteen female undergraduate early childhood education preservice teachers participated in one of five focus groups. Students were divided into three groups based on the courses they were enrolled in or had completed: Beginner (sophomore and junior courses), Intermediate (senior courses), and Advanced (student teaching). Additionally, 6 of the 19 students participated in individual interviews. Data analysis resulted in themes related to students’ beliefs and philosophies of inclusion, as well as their thoughts concerning practice in inclusive programs. This paper describes students’ beliefs within each group and compares responses across the different groups. Implications are discussed in relation to teacher education programs and directions for future research.     

The direction of the relation between oral communicative competence and social preference in early childhood classrooms,and the role of dialogic classroom talk

ObjectiveThe present study investigated the direction of the relation between oral communicative competence and social preference in early childhood classrooms. Additionally, we explored the role of dialogic classroom talk in this relation.MethodsN = 311 children (aged four to seven) participated. Oral communicative competence was measured with the Nijmegen Test for Pragmatics and social preference was assessed with a peer nomination method (both constructs measured at two timepoints).ResultsOutcomes of cross-lagged analyses demonstrated a directional link from social preference to oral communicative competence, but not the other way around. There were no differences in the relation between the two constructs between classrooms in which dialogic classroom talk was implemented and classrooms in which it was not.ConclusionThis study seems to indicate the importance of children's social preference for developing adequate communicative abilities.     

Fostering Instructor Knowledge of Student Thinking Using The Flipped Classroom

Abstract

In this article, we share a model of flipped instruction that allowed us to gain a window into our students’ mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be used to design experiences that help students make sense of mathematics during class sessions.