Early Math Trajectories: Low‐Income Children's Mathematics Knowledge From Ages 4 to 11

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low‐income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low‐income American children from ages 4 to 11. This model includes a broad range of math topics, as well as potential pathways from preschool to middle grades mathematics achievement. In preschool, nonsymbolic quantity, counting, and patterning knowledge predicted fifth‐grade mathematics achievement. By the end of first grade, symbolic mapping, calculation, and patterning knowledge were the important predictors. Furthermore, the first‐grade predictors mediated the relation between preschool math knowledge and fifth‐grade mathematics achievement. Findings support the early math trajectories model among low‐income children.     

The influence of early science experience in kindergarten on children's immediate and later science achievement: Evidence from the early childhood longitudinal study

This study explores the impacts of selected early science experiences in kindergarten (frequency and duration of teachers' teaching of science, availability of sand/water table and science areas, and children's participation in cooking and science equipment activities) on children's science achievement in kindergarten and third grade using data for 8,642 children from the Early Childhood Longitudinal Study‐Kindergarten cohort (ECLS‐K). A theoretical model that depicts the relationships between the study variables was developed and tested using structural equation modeling. Results demonstrated that availability of science materials in kindergarten classrooms facilitated teachers' teaching of science and children's participation in science activities. Likewise, the frequency and the duration of kindergarten science teaching was a significant predictor of children's science activities but not of the children's end of kindergarten science achievement scores. Children's engagement with science activities that involved using science equipment also was not a significant predictor of their end of kindergarten science achievement. However, children's participation in cooking activities was. Children's prior knowledge, motivation, socio‐economic status, and gender were all statistically significant predictors of their science achievement at the end of kindergarten and end of third grade. Results of this study indicate that early science experiences provided in kindergarten are not strong predictors of children's immediate and later science achievement. Findings of the study suggest that the limited time and nature of science instruction might be related to the limited effect of the science experiences. Implications for teacher education programs and educational policy development are discussed. © 2010 Wiley Periodicals, Inc. J Res Sci Teach 48: 217–235, 2011     

Young Children's Understanding of Addition Concepts

Children's knowledge of concrete versions of additive composition, commutativity and associativity was investigated in two studies. In Study 1, 24 four- to five-year-olds and 25 five- to six-year-olds judged the equivalence of conceptually related addition problems presented using groups of objects. In Study 2, 45 five- to six-year-olds judged related problems and solved addition problems. Both studies indicated that concrete versions of principles were salient to most children although associativity was more difficult than commutativity and there were considerable individual differences in children's understanding. Study 1 results indicated that schoolchildren were more accurate at recognising additive composition than preschoolers and Study 2 results suggested that commutativity knowledge was related to using advanced counting strategies for solving addition problems. Overall, the research supports the claim that examining early knowledge of addition principles provides important insights into children's emerging part-whole knowledge and mathematical development.     

The importance of number sense to mathematics achievement in first and third grades

Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial, and memory), number sense made a unique and meaningful contribution to the variance in mathematics achievement at both first and third grades. Furthermore, the strength of the predictions did not weaken over time. Number sense was most strongly related to the ability to solve applied mathematics problems presented in various contexts. The number sense screen taps important intermediate skills that should be considered in the development of early mathematics assessments and interventions.     

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.     

Enhancing Established Counting Routines to Promote Place-Value Understanding: An Empirical Study in Early Elementary Classrooms

Understanding place value is a critical and foundational competency for elementary mathematics. Classroom teachers who endeavor to promote place-value development adopt a variety of established practices to varying degrees of effectiveness. In parallel, researchers have validated models of how young children acquire place-value understanding. Faced with competing demands, teachers may resist abrupt, disruptive, or time-intensive changes to existing practices. In this study, we explore ways of introducing changes in pedagogical supports that minimally disrupt existing classroom routines that nonetheless offer potential gains in children’s understanding of base-ten number concepts. Specifically, we examine the impact of modifying how teachers demonstrate and discuss representations of the ten-for-one structure during the familiar “Days in School” counting routine on young children’s place-value understanding. We report on a 2-year longitudinal study of a cohort of students beginning in grade one, conducted in nine classrooms across a control school and a treatment school. We describe the modifications in the counting routine and report the results of children’s development of base-ten number concepts. The percentage of children who identified base-ten number concepts was three times higher for the children in the treatment group than for the children in the control group. Moreover, nearly twice as many children in the treatment group as compared with the control group advanced beyond a concatenated single-digit conception by the end of second grade when counting two-digit quantities. We conclude with a discussion of the implications of our findings for early elementary mathematics education more generally.     

Concurrent and longitudinal predictors of calculation skills in preschoolers

Early calculation abilities in preschoolers are predictive of mathematics achievement in subsequent grades (e.g., Jordan et al. 2009). Two studies were conducted to evaluate concurrent and longitudinal predictors of early calculation skills. In the first study, 102 preschoolers (57.8 % female; mean age?=?60.57?±?8.66 months) were given vocabulary, language comprehension, and verbal working memory tasks and a test battery that evaluated components of early number competence (quantity comparison, counting, number line, size seriation, semantic knowledge of digits, visual-spatial memory). The children were also asked to complete early calculation tasks, including addition and subtraction calculations. The results of this task constituted the dependent variable. The results showed that vocabulary, size seriation, and visual-spatial memory were significant concurrent predictors of early calculation competence. In the second study, 43 children completed the early number competence battery at time 1 (53.5 % female; mean age?=?59.30?±?3.46 months) and the linguistic and early calculation tasks at time 2, about 10 months later (mean age?=?69.43?±?3.31 months). The analysis of the longitudinal predictors of early calculation showed significant effects for counting and size seriation. The implications for preschool assessment and intervention are discussed.     

Are first graders' arithmetic skills related to the quality of mathematics textbooks? A study on students’ use of arithmetic principles

A major goal of the first years of schooling is students' development from using counting strategies to using calculation strategies – or even recall – to solve addition or subtraction problems. It requires the perception and usage of arithmetic principles. Although the continued use of counting strategies is problematic for further learning progress, they are frequently used by many students beyond Grade 1. While learning resources possibly play a role in students' development in this field, our knowledge about their impact is limited. In this study we investigated the presented learning opportunities of four different textbooks regarding arithmetic principles in Grade 1, and subsequently the relation to first graders' strategy use by analyzing a one-year dataset of 1614 students from 86 classes. The analyses show differences in the textbooks' quality concerning arithmetic principles as well as a considerable connection to students' strategy use at the end of Grade 1.     

Child effortful control,teacher–student relationships,and achievement in academically at-risk children: Additive and interactive effects

The joint contributions of child effortful control (using inhibitory control and task accuracy as behavioral indices) and positive teacher–student relationships at first grade on reading and mathematics achievement at second grade were examined in 761 children who were predominantly from low-income and ethnic minority backgrounds and assessed to be academically at-risk at entry to first grade. Analyses accounted for clustering effects, covariates, baselines of effortful control measures, and prior levels of achievement. Even with such conservative statistical controls, interactive effects were found for task accuracy and positive teacher–student relationships on future achievement. Results suggest that task accuracy served as a protective factor so that children with high task accuracy performed well academically despite not having positive teacher–student relationships. Further, positive teacher–student relationships served as a compensatory factor so that children with low task accuracy performed just as well as those with high task accuracy if they were paired with a positive and supportive teacher. Importantly, results indicate that the influence of positive teacher–student relationships on future achievement was most pronounced for students with low effortful control on tasks that require fine motor skills, accuracy, and attention-related skills. Study results have implications for narrowing achievement disparities for academically at-risk children.     

CONFIDENCE AND COMPETENCE AMONG COMMUNITY COLLEGE STUDENTS: SELF-EFFICACY AND PERFORMANCE IN GRAMMAR

Proper grammar is crucial for effective communication. Two surveys of students in an introductory writing course sought to identify predictors of grammar ability. Students demonstrated a limited grasp of the language, struggling with such issues as the distinction between “it's” and “its.” Women performed better than men at the beginning of the semester, but the gap later narrowed. There was a correlation between self-efficacy (confidence in one's ability to perform a particular task) and grammar ability at the end of the semester. To the knowledge of the authors, this is the first study to empirically link grammar self-efficacy and grammar performance. High school grade point average also predicted grammar ability at the end of the semester.     

Strategy diversity in early mathematics classrooms

Strategic processes are a form of procedural knowledge in which a child knows how to enact a given strategy that improves their capability in problem solving or learning. The solution strategies children use are critical components of their learning, especially in mathematics. Children vary substantially in their knowledge and use of different strategies, and much research has focused on intraindividual strategy variability. However, we do not know if classrooms that evince a broader variety of strategies across children are related to higher mathematics achievement. We investigated the diversity of arithmetical strategies within classrooms and examined the relations between strategy diversity and mathematical achievement as children moved from preschool to kindergarten and first grade. These analyses were applied to data from a large-scale experiment involving 1305 children from 42 schools and 106 classrooms. We created and applied a new method of measuring classroom strategy diversity and related this measure to children’s concurrent and subsequent math achievement. We found that early strategy diversity was strongly related to achievement, but in subsequently, less diversity was so related. We compared these results to the predictions of three theoretical categories and found that our results mainly supported one.     

Effects of reading and spelling predictors before and after school entry: Evidence from a German longitudinal study

Previous studies indicate that the effectiveness of reading and spelling predictors in transparent orthographies is affected by the onset of literacy training at school entry. In this longitudinal study with 65 German speaking children, the effects of literacy predictors on reading and spelling abilities were compared before and after school entry. Phonological awareness, letter sound knowledge, and rapid naming were assessed before and after school entry. In addition, reading and spelling abilities were assessed at the end of first grade. Path model analyses showed that letter sound knowledge before school entry predicted reading and spelling at the end of first grade, while rapid naming after school entry predicted reading but not spelling abilities. This study shows that the onset of schooling influences the predictability of early literacy predictors and indicates that with the onset of formal literacy education, predictors representing automaticity in serial processing increase in significance for reading abilities.     

Performance‐approach goals,task‐avoidant behaviour and conceptual knowledge as predictors of first graders’ school performance

The present paper aims to examine the relationship between first grade children’s performance‐approach goal orientation, task‐avoidant behaviours, conceptual knowledge and their achievement in maths and literacy. The sample consisted of 174 first grade children and their class teachers. Children’s self reports of their performance‐approach goals and avoidant behaviours as well as teacher‐reports of children’s avoidant behaviours were used. Our results indicate that performance‐approach goal orientation positively predicts children’s self‐reported task‐avoidant behaviours which in turn have a negative effect on children’s achievement outcomes. The negative effect of teacher‐rated avoidant behaviours on children’s achievement outcomes was even greater than the positive influence of children’s conceptual knowledge. These results suggest that the relationships between goal‐orientations, achievement behaviours and achievement outcomes start to form early in children’s school career (or even before that) and that children’s self‐report of their achievement goals and behaviours provide a valuable knowledge already in this early age.     

The development of first graders' reading skill as a function of pre-school motivational orientation and phonemic awareness

This study examined the development of reading skill during the first school year. The predictors were pre-school motivational orientations, coping tendencies, knowledge of the alphabet and phonemic awareness. From 151 pre-school children (6 years of age) rated by pre-school teachers on motivational orientations, 32 non-readers were allocated according to their dominating motivational disposition to one of the following extreme groups: task orientation, social dependence, ego-defensive, and multiple non-task-oriented. Each group included 8 children. The subjects' phonemic awareness and knowledge of the alphabet were assessed. Coping strategies were observed in pre-school during a play-like construction task comprising three induced pressure episodes. At the end of the first grade the children were assessed on word reading skill and again on motivational orientation. Both group comparisons and idiographic analyses were made. Results indicated that pre-school phonemic awareness was associated with first grade word reading skill. Rated task orientation in pre-school enhanced significantly the prediction of fluent word reading. Task-oriented children showed significantly better word reading skill than ego-defensive or multiple non-task-oriented children. Ego-defensive and multiple non-task-oriented subjects showed significantly less task oriented, and more ego-defensive, coping behaviour under pressure than task-oriented subjects. This finding suggests greater vulnerability of ego-defensive and multiple non-task-oriented children which may contribute to diverging reading careers. Idiographic analyses indicated parallel developmental changes in reading skill, motivational orientations and coping patterns confirming the role of motivation in the formation of an individual's reading career.     

Light's retention scale does not predict success in first-grade retainees

Light's Retention Scale totals, along with measures of reading achievement, mathematics achievement, and self-concept taken at the time first grade nonpromotion was being considered, were used to predict nine separate outcome measures of academic, emotional, and social status at the end of the repeated first grade. In none of the stepwise regressions did the Light total add to the prediction of outcome in the children repeating the first grade. This result, added to earlier studies, suggests that Light's Retention Scale is neither reliable nor valid as a psychometric device.     

Predictive validity of the WPPSI-R: A four year follow-up study

Wechsler Preschool and Primary Scale of Intelligence-Revised (WPPSI-R) scores obtained prior to enrollment in kindergarten are used to predict academic achievement scores on the Comprehensive Testing Program III at the end of grades 1, 2, and 3. Correlations between achievement and Verbal IQ are significant at all three grade levels, with measures of vocabulary, general knowledge, and verbal concept formation (Similarities) being the most consistent verbal predictors of academic achievement. Performance IQ is a poor predictor of academic achievement, with only 3 out of 16 correlations with achievement reaching significance. The Full Scale IQ's correlations with achievement appear to be due to the contributions of the verbal scale. Results are discussed in terms of their generalizability for this middle- and upper-middle-class sample engaged in a demanding academically-oriented curriculum.     

Causal Connections Between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

The acquisition of early mathematical knowledge is critical for successful long-term academic development. Mathematical language is one of the strongest predictors of children's early mathematical success. Findings from previous studies have provided correlational evidence supporting the importance of mathematical language to the development of children's mathematics skills, but there is limited causal evidence supporting this link. To address this research gap, 47 Head Start children were randomly assigned to a mathematical language intervention group or a business-as-usual group. Over the course of eight weeks, interventionists implemented a dialogic reading intervention focused on quantitative and spatial mathematical language. At posttest, students in the intervention group significantly outperformed the students in the comparison group not only on a mathematical language assessment, but on a mathematical knowledge assessment as well. These findings indicate that increasing children's exposure to mathematical language can positively affect their general mathematics skills. This study is an important first step in providing causal evidence of the importance of early mathematical language for children's general mathematical knowledge and the potential for mathematical language interventions to increase children's overall mathematics abilities.     

Metacognitive knowledge in children at early elementary school

In metacognition research, many studies focused on metacognitive knowledge of preschoolers or children at the end of elementary school or secondary school, but investigations of children starting elementary school are quite limited. The present study, thus, took a closer look at children’s knowledge about mental processes and strategies in early elementary school aiming to extend findings on the respective age period. Therefore, at first, a new test that can be administered in group settings and that assesses a broad concept of children’s metacognitive knowledge in early elementary school was evaluated. Furthermore, analyses on the structure of metacognitive knowledge were carried out in cross-sectional as well as longitudinal analyses. In a longitudinal design, the new test instrument was administered to 870 children at the end of first grade and again one year later (N?=?720). Item Response models were used to evaluate the construct validity of the test. Test characteristics were checked based on different fit statistics, test fairness, and discriminant validity. In summary, the test exhibited good psychometric properties. Analyses on the dimensionality of the assessed metacognitive knowledge revealed that different strategies seemed to form rather distinct dimensions of metacognitive knowledge. However, these dimensions showed a rather homogeneous development from first to second grade. Impacts of the findings on theoretical considerations and on the theoretical understanding of metacognitive knowledge and further analyses with metacognitive competence data are discussed.     

Predicting Long‐Term Growth in Students' Mathematics Achievement: The Unique Contributions of Motivation and Cognitive Strategies

This research examined how motivation (perceived control, intrinsic motivation, and extrinsic motivation), cognitive learning strategies (deep and surface strategies), and intelligence jointly predict long‐term growth in students' mathematics achievement over 5 years. Using longitudinal data from six annual waves (Grades 5 through 10; M_age = 11.7 years at baseline; N = 3,530), latent growth curve modeling was employed to analyze growth in achievement. Results showed that the initial level of achievement was strongly related to intelligence, with motivation and cognitive strategies explaining additional variance. In contrast, intelligence had no relation with the growth of achievement over years, whereas motivation and learning strategies were predictors of growth. These findings highlight the importance of motivation and learning strategies in facilitating adolescents' development of mathematical competencies.     

Native language predictors of foreign language proficiency and foreign language aptitude

Fifty-four students were tested at specific time intervals over 10 years to determine best native language (NL) predictors of oral and written foreign language (FL) proficiency and FL aptitude. All participants completed two years of Spanish, French, or German. Each was administered measures of NL literacy, oral language, and cognitive ability in elementary school. A measure of FL aptitude was administered at the beginning of ninth grade and FL proficiency was evaluated at the end of the 10th grade. Among the variables, NL literacy measures were the best predictors of FL proficiency, and NL achievement and general (verbal) intelligence were strong predictors of FL aptitude. Results suggest that indices of NL literacy as early as first grade are related to FL proficiency and FL aptitude nine and 10 years later. Findings provide strong support for connections between L1 and L2 skills, and for speculation that “lower level” skills in phonological processing are important for written language development and oral proficiency in a FL.