REL Midwest Ask A REL Response

Math

March 2021

Baglici, S. P., Codding, R., & Tryon, G. (2010). Extending the research on tests of early numeracy: Longitudinal analyses over two school years. Assessment for Effective Intervention, 35(2), 89–102. https://eric.ed.gov/?id=EJ871472

From the ERIC abstract: “The purpose of this study was to extend the research on the ‘Tests of Early Numeracy’ (TEN) by following a cohort of 61 students from kindergarten through first grade. Specifically, this study examined the relationship between kindergarten and first-grade TEN measures built within and across school years and their predictive validity of a math curriculum-based measurement and teacher-derived measures of mathematics administered in first grade. Correlation analyses indicated significant relationships between kindergarten and first-grade TEN performance. Results from repeated-measures analyses of variance indicated that students made significant growth on all of the TEN measures from winter kindergarten to spring of first grade; however, different measures yielded significant growth within each grade. Kindergarten TEN performance also accounted for a significant amount of variance in first-grade computation skills and was moderately correlated with teacher ratings.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016–1031. https://eric.ed.gov/?id=EJ802180

From the ERIC abstract: “This study examined whether the quality of first graders’ (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children’s pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be predictive of their learning of answers to unfamiliar arithmetic problems. The relation to learning of unfamiliar problems remained after controlling for prior arithmetic knowledge, short-term memory for numbers, and math achievement test scores. Moreover, presenting randomly chosen children with accurate visual representations of the magnitudes of addends and sums improved their learning of the answers to the problems. Thus, representations of numerical magnitude are both correlationally and causally related to arithmetic learning.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Burgoyne, K., Malone, S., Lervag, A., & Hulme, C. (2019). Pattern understanding is a predictor of early reading and arithmetic skills. Early Childhood Research Quarterly, 49, 69–80. https://www.sciencedirect.com/science/article/pii/S0885200619300900

From the ERIC abstract: “There is increasing interest in the role that pattern understanding may play in the development of arithmetic and reading skills. However, longitudinal studies are rare and typically do not control for other predictors which contribute to development in these domains. This large-scale longitudinal study examined the extent to which pattern understanding is a unique predictor of reading and arithmetic, after controlling for a range of theoretically important skills. We assessed a large sample of 5-year old children (N = 569) in the first few months of school on measures of reading, arithmetic, naming speed, number knowledge, counting, non-symbolic magnitude, executive function, oral language, and non-verbal IQ. Children completed alphanumeric and non-alphanumeric pattern understanding tasks six months later. Reading and arithmetic skills were assessed again 12 months after the initial assessment. Latent variable path models showed that pattern understanding predicted significant additional variance in both reading and arithmetic after controlling for a range of other variables. Pattern understanding was in turn predicted by executive function, which indirectly predicted both reading and arithmetic. Thus, we find support for a role of domain general skills (executive function and pattern understanding) as shared predictors of both reading and arithmetic.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Conoyer, S. J., Foegen, A., & Lembke, E. S. (2016). Early numeracy indicators: Examining predictive utility across years and states. Remedial and Special Education, 37(3), 159–171. https://eric.ed.gov/?id=EJ1100478

From the ERIC abstract: “Two studies using similar methods in two states investigated the long-term predictive utility of two single-skill early numeracy Curriculum Based Measures (CBMs) and the degree to which they can adequately predict high-stakes test scores. Data were drawn from kindergarten and first-grade students. State standardized assessment data from the ‘Iowa Test of Basic Skills’ (ITBS) and ‘Missouri Assessment Program’ (MAP) were used as criterion measures to evaluate multi-year predictive utility. Logistic regression and Receiver Operating Characteristic (ROC) curves were used to examine the extent to which the measures predicted success or failure on ITBS and MAP. Correlational and logistic regression results indicated the Early Numeracy CBMs effectively predict success or failure for the ITBS and MAP. However, further analysis of the diagnostic utility of the measures suggests that practitioners need to carefully consider specificity, sensitivity, and the degree to which the predictability of common screening measures can be generalized to all state standardized assessments.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. https://eric.ed.gov/?id=EJ779938

From the ERIC abstract: “Using 6 longitudinal data sets, the authors estimate links between three key elements of school readiness—school-entry academic, attention, and socioemotional skills—and later school reading and math achievement. In an effort to isolate the effects of these school-entry skills, the authors ensured that most of their regression models control for cognitive, attention, and socioemotional skills measured prior to school entry, as well as a host of family background measures. Across all 6 studies, the strongest predictors of later achievement are school-entry math, reading, and attention skills. A meta-analysis of the results shows that early math skills have the greatest predictive power, followed by reading and then attention skills. By contrast, measures of socioemotional behaviors, including internalizing and externalizing problems and social skills, were generally insignificant predictors of later academic performance, even among children with relatively high levels of problem behavior. Patterns of association were similar for boys and girls and for children from high and low socioeconomic backgrounds.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Fyfe, E. R., Rittle-Johnson, B., & Farran, D. C. (2019). Predicting success on high-stakes math tests from preschool math measures among children from low-income homes. Journal of Educational Psychology, 111(3), 402–413. https://eric.ed.gov/?id=ED600991

From the ERIC abstract: “State-mandated tests have taken center stage for assessing student learning and for holding teachers and students accountable for achieving adequate progress. What types of early knowledge predict performance on these tests, especially among low-income children who are at risk for poor performance? We report on a longitudinal study of 519 low-income American children ages 5–12, with a focus on mathematics performance. We found that nonsymbolic quantity knowledge and repeating pattern knowledge at the end of preschool were reliable predictors of performance on standards-based high-stakes tests across three different grade levels (4th–6th grade), over and above other math and academic skills. Further, these effects of preschool math knowledge were partially mediated through symbolic mapping and calculation knowledge at the end of 1st grade. These findings suggest that nonsymbolic quantity knowledge and repeating pattern knowledge prior to formal schooling are valuable indicators of low-income children’s performance on high-stakes state math tests in the middle grades.”

Gersten, R. M., Clarke, B., Jordan, N. C., Newman-Gonchar, R., Haymond, K., & Wilkins, C. (2012). Universal screening in mathematics for the primary grades: Beginnings of a research base. Exceptional Children, 78(4), 423–445. https://eric.ed.gov/?id=ED578244

From the ERIC abstract: “This article describes key findings from contemporary research on screening for early primary grade students in the area of mathematics. Existing studies were used to illustrate the constructs most worth measuring and the diverse strategies that researchers used to study potential measures. The authors discussed the strengths and weaknesses of assessing a few key proficiencies (as is often done in early reading) versus a more full-scale battery, and described the importance of going beyond merely reporting predictive validity correlation coefficients to examining the classification accuracy, specificity, and sensitivity of screening measures.”

Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20(2), 82–88. https://eric.ed.gov/?id=EJ872586

From the ERIC abstract: “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.”

Jordan, N. C., Glutting, J., Ramineni, C., & Watkins, M. W. (2010). Validating a number sense screening tool for use in kindergarten and first grade: Prediction of mathematics proficiency in third grade. School Psychology Review, 39(2), 181–195. https://eric.ed.gov/?id=EJ891847

From the ERIC abstract: “Using a longitudinal design, children were given a brief number sense screener (NSB) screener (N = 204) over six time points, from the beginning of kindergarten to the middle of first grade. The NSB is based on research showing the importance of number competence (number, number relations, and number operations) for success in mathematics. Children’s mathematics achievement on a validated high-stakes state test was measured 3 years later, at the end of third grade. Test-retest reliability estimates were obtained for the NSB. Two criterion groups were then formed on the basis of the third-grade achievement test (children who met and who did not meet mathematics standards). Diagnostic validity analyses for the NSB were completed using repeated measures analyses of variance and receiver operator curve analyses. Results from all analyses revealed that scores on the NSB in kindergarten and first grade predicted mathematics proficiency in third grade. Areas under the receiver operator curve indicated that the NSB has high diagnostic accuracy (areas under the receiver operator curve = 0.78-0.88). Findings suggest that kindergarten and first-grade performance on the NSB is meaningful for predicting which children experience later mathematics difficulties.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Kiss, A. J., & Christ, T. J. (2019). Screening for math in early grades: Is reading enough?. Assessment for Effective Intervention, 45(1), 38–50. https://eric.ed.gov/?id=EJ1233143

From the ERIC abstract: “Difficulties in reading and math are more likely to occur simultaneously than difficulties in either area alone; however, the research on that comorbidity is relatively sparse. The purpose of this study was to examine the relation between early reading skills as predictors of math achievement. A group of 102 kindergarten and 65 first-grade students were assessed with curriculum-based measures of early reading and early math, and a measure of broad math achievement. The results of multiple regression analyses indicated that when early numeracy was controlled for, the measures of early reading did not explain unique variance in math achievement among students. Interestingly, screening with only measures of early reading skills yielded acceptable area under the curve (AUC) values but did not yield accurate identification of students at risk for math difficulties (MD) when misclassification and specificity were taken into account. Results suggest that early math measures are most accurate in identifying students at risk for MD in early grades. Findings provide further insight into the relation between math and reading skills at the start of formal schooling. Authors provide recommendations for a combination of reading and math screeners to predict broad math achievement.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Kiss, A. J., Nelson, G., & Christ, T. J. (2019). Predicting third-grade mathematics achievement: A longitudinal investigation of the role of early numeracy skills. Learning Disability Quarterly, 42(3), 161–174. https://eric.ed.gov/?id=EJ1221859

From the ERIC abstract: “Despite the vast research on the early predictors of mathematics achievement, little research has investigated the predictors of various domains of mathematics (e.g., geometry, statistics). The purpose of the present study was to examine the predictive relation between first-grade early numeracy and computation skills and third-grade mathematics achievement as measured by a state test. Furthermore, we explored the relations between these measures for students who were Below Proficient and Proficient. Findings suggest that proficiency level matters when examining the relation between mathematics skills. Also, there are different patterns of significant predictors depending on the domain of later mathematics achievement and whether or not reading achievement was considered. Findings are discussed in the context of mathematics learning for students with mathematics difficulty.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Locuniak, M. N., & Jordan, N. C. (2008). Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities, 41(5), 451–459. https://eric.ed.gov/?id=EJ806369. Full text available from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3935894/

From the abstract: “Children’s number sense in kindergarten was used to predict their calculation fluency in second grade (N = 198). Using block entry regression, usual predictors of age, reading, memory, and verbal and spatial cognition were entered in the first block and number sense measures were added in the second block. Number sense measures contributed a significant amount of variance over and above the more general predictors (26%-42%). Uniquely predictive subareas were active memory for numbers, number knowledge, and number combinations, with number combinations standing out as the strongest single predictor. Number sense screening in kindergarten, using ‘at-risk’ versus ‘not-at-risk’ criteria, successfully ruled out 84% of the children who did not go on to have calculation fluency difficulties and positively identified 52% of the children who later showed fluency difficulties. The relation of early number skills to later calculation fluency has important implications for math screening and intervention.”

Martin, R. B., Cirino, P. T., Sharp, C., & Barnes, M. (2014). Number and counting skills in kindergarten as predictors of grade 1 mathematical skills. Learning and Individual Differences, 34, 12–23. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4116688/

From the abstract: “The present study focused on the role of number skills assessed in kindergarten with regard to their ability to predict mathematical outcomes in grade 1. Number skills included those involving written symbols (symbolic number identification and symbolic number comparison) and counting (procedural and conceptual). Their contributions were contextualized against domain general (working memory, phonological awareness, and behavioral inattention) factors. Both types of kindergarten domain specific skills were strongly correlated with each math outcome in first grade. However, hierarchical regression showed that written symbolic number skills accounted for variance over and above counting predictors. In final models, domain general factors had unique effects (verbal working memory for math fluency, phonological awareness for computation, verbal working memory and phonological awareness for applied problems, and spatial working memory and phonological awareness for story problems). Results highlight the interplay among math precursors and math related domain general factors and their differential roles for different mathematical outcomes.”

Missall, K. N., Mercer, S. H., Martínez, R. S., & Casebeer, D. (2012). Concurrent and longitudinal patterns and trends in performance on early numeracy curriculum-based measures in kindergarten through third grade. Assessment for Effective Intervention, 37(2), 95–106. https://eric.ed.gov/?id=EJ955506

From the ERIC abstract: “The purpose of this study was to extend the research on the ‘Tests of Early Numeracy Curriculum-Based Measurement’ (TEN-CBM) tools by examining concurrent and predictive relations from kindergarten through third grade. Using a longitudinal sample of 535 students, this study included logistic regression, latent cluster, and latent transition analyses to examine the patterns and trends of student performance on all four TEN-CBM measures in kindergarten and first grade, math CBM (M-CBM) in first grade, and mathematics performance on a statewide high-stakes assessment in third grade. Results suggest that two of the TEN-CBM tools, Quantity Discrimination and Missing Number, are most robust at predicting later math performance. Longitudinal analysis indicated that students who are low performing in early numeracy at the beginning of kindergarten tend to be low performing in math at third grade. Low-achieving students also demonstrated a greater decrease in math skills over summer months when compared to higher-achieving peers.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Nguyen, T., Watts, T. W., Duncan, G. J., Clements, D. H., Sarama, J. S., Wolfe, C., & Spitler, M. E. (2016). Which preschool mathematics competencies are most predictive of fifth grade achievement?. Early Childhood Research Quarterly, 36(3), 550–560. https://eric.ed.gov/?id=ED566923

From the ERIC abstract: “In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children’s emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement.”

Powell, S. R., & Fluhler, S. K. (2020). A brief measure of mathematics symbols: Performance at grades 1, 3, and 5. Assessment for Effective Intervention, 45(4), 266–276. https://eric.ed.gov/?id=EJ1263979

From the ERIC abstract: “To understand mathematics, children must interpret mathematics symbols. In this study, we designed a brief assessment of mathematics symbols for children in the elementary grades. For each of 23 symbols, children identified the symbol, provided the meaning of the symbol, and used the symbol. We assessed 297 children in Grades 1, 3, and 5. Internal consistency reliability was established across grade levels. Results indicated the overall symbol knowledge of children increased across grade levels, and children demonstrated higher scores on questions related to the identification and use of the symbol rather than explaining the meaning of the symbol. Across grades, symbol knowledge was a significant predictor of mathematics computation, although the variance accounted for was greatest in first grade and least in fifth grade.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Rittle-Johnson, B., Fyfe, E. R., Hofer, K. G., & Farran, D. C. (2017). Early math trajectories: Low-income children’s mathematics knowledge from age 4 to 11. Child Development, 88(5), 1727–1742. https://eric.ed.gov/?id=ED566266

From the ERIC abstract: “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 age 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. Further, 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.”

Seethaler, P. M., & Fuchs, L. S. (2010). The predictive utility of kindergarten screening for math difficulty. Exceptional Children, 77(1), 37–59. https://eric.ed.gov/?id=EJ898540

From the ERIC abstract: “This study examined the reliability, validity, and predictive utility of kindergarten screening for risk for math difficulty (MD). Three screening measures, administered in September and May of kindergarten to 196 students, assessed number sense and computational fluency. Conceptual and procedural outcomes were measured at end of first grade, with MD operationalized as below the 16th percentile. The authors compared single- versus multiple-skill screeners, fall versus spring kindergarten screening, and conceptual versus procedural outcomes. Reliability and validity coefficients were adequate. Logistic regression and receiver operating characteristics analyses indicated that the single- and multiple-skill screeners produced good and similar classification accuracy at the fall and spring screening occasions in forecasting conceptual outcome. To forecast procedural outcome, the screeners produced similar but less accurate fits.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Seethaler, P. M., Fuchs, L. S., Fuchs, D., & Compton, D. L. (2012). Predicting first graders’ development of calculation versus word-problem performance: The role of dynamic assessment. Journal of Educational Psychology, 104(1), 224–234. https://eric.ed.gov/?id=ED529593

From the ERIC abstract: “The purpose of this study was to assess the value of dynamic assessment (DA; degree of scaffolding required to learn unfamiliar mathematics content) for predicting 1st-grade calculations (CAs) and word problems (WPs) development, while controlling for the role of traditional assessments. Among 184 1st graders, predictors (DA, Quantity Discrimination, Test of Mathematics Ability, language, and reasoning) were assessed near the start of 1st grade. CA and WP were assessed near the end of 1st grade. Planned regression and commonality analyses indicated that for forecasting CA development, Quantity Discrimination, which accounted for 8.84% of explained variance, was the single most powerful predictor, followed by Test of Mathematics Ability and DA; language and reasoning were not uniquely predictive. By contrast, for predicting WP development, DA was the single most powerful predictor, which accounted for 12.01% of explained variance, with Test of Mathematics Ability, Quantity Discrimination, and language also uniquely predictive. Results suggest that different constellations of cognitive resources are required for CA vs. WP development and that DA may be useful in predicting 1st-grade mathematics development, especially WP.”

Slusser, E., Ribner, A., & Shusterman, A. (2019). Language “counts“: Early language mediates the relationship between parent education and children’s math ability. Developmental Science, 22(3). https://eric.ed.gov/?id=EJ1212660

From the ERIC abstract: “Children’s early math skills have been hailed as a powerful predictor of academic success. Disparities in socioeconomic context, however, also have dramatic consequences on children’s learning. It is therefore critical to investigate both of these distinct contributors in order to better understand the early foundations of children’s academic outcomes. This study tests an integrated model of children’s developing math ability so as to (1) identify the specific skills and abilities most clearly linked to early math achievement and (2) measure the influence of children’s socioeconomic context on each of these skills. We first evaluated the early vocabulary, number word knowledge (knower level), and Approximate Number System (ANS) acuity of a diverse group of preschoolers. Then, approximately 1 year later as they entered Kindergarten, we administered a test of early math achievement. We find that children’s early language (general vocabulary and number word knowledge) fully mediates the relationship between parent education and math ability. Additionally, number word knowledge mediates the relationship between ANS acuity and early math. We argue that increased focus on number word knowledge, as well as general vocabulary, may help to minimize disparities in math ability as children enter kindergarten. We also highlight the role of parent education on children’s learning and note that this may be an important locus for intervention.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.