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Drawing from the developmental and cognitive mathematics literature, the purpose of this study was to investigate the reliability, validity, and diagnostic utility of a widely-researched number line task in kindergarten. Specifically, the Number Line Assessment 0−100 (NLA 0−100) as compared to an established kindergarten screening measure was examined using (a) regression models and (b) classification accuracy. Five- and six-year-old students (n = 154) were assessed on numeracy measures in the fall and spring of their kindergarten year. The NLA 0−100 had lower predictive validity and lower classification accuracy compared to an early numeracy screening measure. The findings have implications for practice and future research using number line screening assessments.

A quasi-experimental design in six kindergarten classrooms ( n = 123 students) was used to study the effects of the KinderTEK iPad–based math program on the math achievement of students in general education classrooms. Student math outcomes in three treatment ( early start) classrooms were compared to math outcomes for students in three comparison ( late start) classrooms. Results suggested that relatively brief exposure to KinderTEK produced gains on distal measures of early numeracy and that, on average, timing of intervention delivery did not impact end of year math outcomes. However, exploratory analyses suggested that earlier and longer use of KinderTEK may have provided a benefit for students most at risk in math. The utility of quasi-experimental studies within an overarching research program and implications for the adoption of technology-based math programs in kindergarten classrooms are discussed.

Children's ability to discriminate nonsymbolic number (e.g., the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest that it may be due to a sharpening numerical representation or an improved ability to pay attention to number and filter out non-numerical information. We investigate this issue by studying change in children's performance (N = 65) on a nonsymbolic number comparison task, where children decide which of two dot arrays has more dots, from the middle to the end of 1st grade (mean age at time 1 = 6.85 years old). In this task, visual properties of the dot arrays such as surface area are either congruent (the more numerous array has more surface area) or incongruent. Children rely more on executive functions during incongruent trials, so improvements in each congruency condition provide information about the underlying cognitive mechanisms. We found that accuracy rates increased similarly for both conditions, indicating a sharpening sense of numerical magnitude, not simply improved attention to the numerical task dimension. Symbolic number skills predicted change in congruent trials, but executive function did not predict change in either condition. No factor predicted change in math achievement. Together, these findings suggest that nonsymbolic number processing undergoes development related to existing symbolic number skills, development that appears not to be driving math gains during this period. Children's ability to discriminate nonsymbolic number improves throughout development. Competing theories suggest improvement due to sharpening magnitude representations or changes in attention and inhibition. The current study investigates change in nonsymbolic number comparison performance during first grade and whether symbolic number skills, math skills, or executive function predict change. Children's performance increased across visual control conditions (i.e., congruent or incongruent with number) suggesting an overall sharpening of number processing. Symbolic number skills predicted change in nonsymbolic number comparison performance.

The provision of high-quality early mathematics instruction and intervention is critical to ensure that all students are on track for academic success. Given this, identifying and utilizing assessments that can enable the detection of nonresponse to mathematics instruction is a critical aspect of early intervention. To this end, the current study explored the extent to which there were distinct patterns of performance on embedded assessments for intervention participants within the context of a large-scale randomized control trial of the ROOTS intervention. This study also examined how performance on embedded assessments was associated with pretest mathematics scores and residual gains on mathematics measures, and how those associations differed based on (a) the point in the intervention when students demonstrated difficulty, and (b) intervention intensity. Findings from this study suggest that participants fell into 4 distinct performance categories and performance classifications were associated with pretest measures and gains in mathematics achievement. Study results also highlight the potential relevance of instructional intensity and timely monitoring of student performance. Implications for intervention and instructional planning in the context of tiered instructional delivery models are discussed. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Students who demonstrate mathematics difficulties (MDs) in the early grades are at risk of poor educational outcomes. Fortunately, strategic early mathematics intervention programs can improve academic outcomes for students with MDs, and instructional technology has demonstrated promise in delivering targeted and individualized mathematics instruction. However, it is unclear whether instructional technology is effective for all students, and there is a dearth of research on adaptations to technology-based interventions for students with difficulties attending to instruction. To this end, the current study investigated functional relations between the use of targeted instructional cueing and self-regulation support features in an iPad-based mathematics program and improved response accuracy for kindergarten students. Results presented here suggest a functional relation between the provision of instructional cueing and self-regulation support features and improved response accuracy for students who participated in an iPad-based mathematics intervention program. Implications for early mathematics instruction and technology-based intervention development are discussed.

Early number skills are a critical aspect of early mathematics development. However, the constructs that comprise early number skills differ across assessments, and previous studies have proposed v...

This manuscript presents the results from a study to investigate the technical characteristics of two versions of a number line assessment (NLA 0–20 and NLA 0–100). The sample consisted of 60 kindergarten and 46 first grade students. Both number line versions had sufficient alternate form and test–retest reliability. The NLA 0–20 had low and the NLA 0–100 had low to moderate correlations with math achievement. Results indicated that the NLA 0–100 explained a small, but unique portion of the variance in first grade mathematics performance when controlling for performance on the Assessing Student Proficiency in Early Number Sense (ASPENS) a set of early numeracy screening measures. We discuss study results related to the utility of adding number line assessment tasks to mathematics screening batteries and propose additional areas of research.

Early number skills, comprised of both informal and formal skills, are associated with later mathematics achievement. Thus, the development of foundational early number skills is an important aspect of early mathematics instruction. This study explored relations between early number skills gains and mathematics achievement for students at risk for mathematics difficulties in a kindergarten intervention study. Results indicated strong relationships between formal number skills gains and mathematics achievement across kindergarten and Grade 1. Intervention participants demonstrated larger informal and formal early number skills gains compared with their control peers, and relations between early number skills gains and first-grade mathematics achievement were moderated by intervention participation. Importantly, these findings suggest that formal and informal number skills gains may be critical components of later mathematics achievement for at-risk students. Implications for special education and intervention in tiered instructional systems are discussed.

Instructor facilitation is an essential element in the successful implementation of technology-based interventions in authentic school settings. This manuscript reports results from two studies conducted during the development of KinderTEK, an iPad delivered kindergarten mathematics intervention, to determine the relationship between instructor-reported technology experience and intervention implementation, as measured by student use. Study results show participating instructors had a range of pre-intervention technological experience with iPads and this range corresponded with variable student use in terms of both within class variability of student use and percentage of students meeting the duration of use target. Consistent with previous research, findings also indicate that second-order technology barriers may be most influential on intervention implementation; however, the quantity of barriers reported (regardless of type) was also associated with the percentage of students meeting target durations of use in each class. Lastly, instructors who reported moderate experience with iPads and/or no barriers to technology integration demonstrated the least desirable student use patterns. Implications for technology-based intervention implementation and professional development are discussed.

An increased level of parent involvement in education has been identified as a predictor of positive postschool outcomes for students with disabilities who have traditionally experienced lower rates of employment and postsecondary education than their peers without disabilities. The purpose of this study was to explore the factor structure of scales adapted from the Hoover-Dempsey and Sandler Model of Parent Involvement that might be used to predict parent involvement in secondary special education. An iterative adaption process included adding and revising scale items to reflect parent beliefs and involvement activities related to transition planning and secondary education for parents of high school students with disabilities. Participants were 149 parents of students with disabilities, ages 16–21. Two exploratory factor analyses (EFA) were conducted to examine the psychometric properties of the scales. Results of the EFA for involvement activities suggested a three-factor solution including: Future Planning; Home-based Involvement; and Agency/School-based Involvement. Results of the EFA for Motivators for Involvement suggested a seven-factor solution including: Parent Expectations for the Future; General School Invitations; Role Construction; Perceptions of Time and Energy; Knowledge, Skills, and Self-efficacy; Specific Child Invitations, and Specific Teacher Invitations. Implications and future research directions are discussed.

Accurately measuring and modeling academic achievement growth is critical to support educational policy and practice. Using a nationally representative longitudinal data set, this study compared various models of mathematics achievement growth on the basis of both practical utility and optimal statistical fit and explored relationships within and between early and later mathematics growth parameters. Common patterns included a summer lag in achievement between kindergarten and Grade 1 and an association between achievement at kindergarten entry and later achievement. Notably, there were no statistically significant relationships between early and later rates of growth, and there was minimal variability in achievement growth in the late elementary and middle school grades. Challenges related to assessing academic achievement in the middle grades and modeling academic skill development are discussed.

The purpose of this study was to investigate the incremental validity of a set of domain general cognitive measures added to a traditional screening battery of early numeracy measures. The sample consisted of 458 kindergarten students of whom 285 were designated as severely at-risk for mathematics difficulty. Hierarchical multiple regression results indicated that Wechsler Abbreviated Scales of Intelligence (WASI) Matrix Reasoning and Vocabulary subtests, and Digit Span Forward and Backward measures explained a small, but unique portion of the variance in kindergarten students' mathematics performance on the Test of Early Mathematics Ability-Third Edition (TEMA-3) when controlling for Early Numeracy Curriculum Based Measurement (EN-CBM) screening measures (R² change = .01). Furthermore, the incremental validity of the domain general cognitive measures was relatively stronger for the severely at-risk sample. We discuss results from the study in light of instructional decision-making and note the findings do not justify adding domain general cognitive assessments to mathematics screening batteries. (PsycINFO Database Record

Creating an educational program that results in positive science, technology, engineering, and mathematics or STEM-oriented outcomes for all students is an important education objective and federal policy directive in the United States. In addition to developing strong mathematics foundations in Grades K–8 that are closely associated with successful STEM outcomes, intrapersonal skill development is also critical to academic and postsecondary success. Using nationally representative data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 the current study applied structural equation growth modeling to examine relationships among mathematics achievement in Grades K–1 and Grades 3–8, and mathematics self-concept development across Grades 3–8. Study results revealed that students reported declining levels of mathematics self-concept across the middle grades. Importantly, third grade reports of self-concept were associated with both mathematics achievement at kindergarten entry and third grade mathematics achievement; however, mathematics achievement at kindergarten entry was also associated with the development of mathematics self-concept in third through eighth grade. In addition, after accounting for mathematics achievement in Grades K–1, mathematics achievement growth in Grades 3–8 was directly associated with mathematics self-concept development across the same time period. Implications for future research, mathematics instruction, and curriculum development are discussed.

The purpose of this chapter is to provide an overview of the critical importance of mathematics fluency. We begin by providing an overview of the role of mathematics in today’s society, current shortcomings in the teaching of mathematics, operational definitions of fluency, and the critical role fluency plays in the development of mathematics proficiency. Next, we summarize current interventions designed to promote the development of fluency and assessments designed to measure student acquisition of mathematics fluency. We conclude by noting the potential steps for both researchers and practitioners to take to move the field forward.

Fluency is a ubiquitous, but a complicated term. This chapter provides an overview of various conceptions of fluency across a range of disciplines and research contexts as well as discusses implications for research, assessment, and instruction. We include an overview of definitions and exemplars of fluency in language use, reading, and mathematics followed by an exploration of fluency concepts (e.g., automaticity, efficiency, and procedural skill) and considerations for research. The chapter concludes with recommendations for investigations of fluency including attending to measurement issues, explicitly defining and analyzing discrete components of fluency, and leveraging these precise definitions to evaluate the interactions between task and proficiency inherent to fluency exercises.