Cognitive and Attitudinal Predictors Related to Line Graphing Achievement among Elementary Pre-service Teachers

The purpose of this study was to determine the extent to which six cognitive and attitudinal variables predicted pre-service elementary teachers’ (N = 87) performance on line graphing. Predictors included reading comprehension and mathematics scores, logical thinking performance scores, as well as measures of attitudes toward science, mathematics and graphing. Results indicated that mathematical and logical thinking ability were the most significant predictors of line graph performance among the other variables, accounting for 41% of the total variability. Findings from this study suggest that elementary science education programs augment instruction to include aspects of mathematics and logical thinking.     

Measuring the Language Demands of Mathematics Tests: The case of the statutory tests for 11-year-olds in England and Wales

The study reported here investigates various methods for measuring the readability of the language of mathematics test questions used in the national testing programme for 11-year-olds in England and Wales. It is argued that the language used in the questions has a direct influence on test validity. It explores the use of Kane's Formula II and other selected formulae: Dale-Chall, Flesch, FOG and Fry's adaptation of his 1977 formula. These outcomes are compared with an assessment of the reading difficulty of the questions as judged by experienced primary mathematics teachers. The results indicate high levels of agreement between all the formal measures used, but very little agreement between the formal measures and the judgements of teachers. Individual questions are analysed to highlight some of the discrepancies. The conclusion is that there is currently no satisfactory way of measuring the ease or difficulty of the language of mathematics test questions and that further research is urgently needed.     

Assessing mathematics within advanced school science qualifications

Following sustained discussion regarding the relationship between advanced mathematics and science learning in England, the government has pursued a reform agenda in which mathematics is embedded in national, high stakes A-level science qualifications and their assessments for 18-year-olds. For example, A-level Chemistry must incorporate the assessment of relevant mathematics for at least 20% of the qualification. Other sciences have different mandated percentages. This embedding policy is running in parallel with an adding policy that is encouraging all young people to include the study of mathematics to 18. In this paper, we present a detailed scrutiny of the published sample assessment materials in the new A-level Physics, Chemistry and Biology qualifications in order to consider what the impact of this policy move might be for the teaching and learning of mathematics, its applications in upper secondary school advanced science studies and the implications in the transition to mathematically-demanding undergraduate studies.     

An Examination of the Relationship between Computation,Problem Solving,and Reading

The purpose of this study is to evaluate the relationship of mathematics calculation rate (curriculum-based measurement of mathematics; CBM-M), reading rate (curriculum-based measurement of reading; CBM-R), and mathematics application and problem solving skills (mathematics screener) among students at four levels of proficiency on a statewide test. It was hypothesized that CBM-M provides insufficient information to make good screening decisions and that other measures with content more similar to that of large-scale tests of mathematics would function to improve screening. One hundred and seventy students in third grade from a rural elementary school in the Midwestern United States participated. Structural equation modeling was used to evaluate direct, mediator, and latent growth models. In general, CBM-R mediated the relationship between the mathematics ability screener and passing the state assessment, while CBM-M did not have any significant paths within these models. Results are discussed in terms of the utility of CBM-M and CBM-R procedures in screening for success on state test performance in mathematics.     

DO INTERVENTION‐EMBEDDED ASSESSMENT PROCEDURES SUCCESSFULLY MEASURE STUDENT GROWTH IN READING?

Effective intervention delivery requires ongoing assessment to determine whether students are learning at the desired rate. Intervention programs with embedded assessment procedures (i.e., assessment that occurs naturally during the process of delivering intervention) can potentially enhance instructional decisions. However, there is almost no psychometric research on this type of assessment procedure. This study was designed to examine the psychometric characteristics of three types of progress measures that are embedded within a commonly used reading intervention program. Results indicated that generalized gains across different oral reading fluency passages predict concurrent gains on common and comprehensive tests of reading fluency, and that immediate instructional gains measured during instruction were significantly different from zero and thus sensitive to intervention effects. Overall findings suggest that at least some embedded assessment procedures demonstrate predictive validity and that these types of procedures have the potential to assist educators with data‐driven instructional decisions about students’ responsiveness to intervention.     

Investigating the Unique Predictors of Word-Problem Solving Using Meta-Analytic Structural Equation Modeling

The purpose of the present study is to clarify the contributions of cognitive skills (nonverbal reasoning, language comprehension, working memory, attention, processing speed) and academic skills (mathematics facts retrieval, mathematics computation, mathematics vocabulary, reading comprehension) in performing mathematics word problems among elementary school students. With the two-stage meta-analytic structural equation modeling approach, I synthesized 112 correlation matrices from 98 empirical studies (N?=?111,346) and fitted the hypothesized partial mediation model. Overall, path analysis indicated that language comprehension, working memory, attention, mathematics vocabulary, and mathematics computation were unique predictors of word-problem solving. Subgroup analysis demonstrated different unique predictors for younger and older students to perform word problems (K-2nd grades versus 3rd–5th grades). Implications, limitations, and future directions are discussed.

     

Oral Language and Reading in Bilingual Children

This article examines the question: Do lexical, syntactic, fluency, and discourse measures of oral language collected under narrative conditions predict reading achievement both within and across languages for bilingual children? More than 1,500 Spanish–English bilingual children attending kindergarten–third grade participated. Oral narratives were collected in each language along with measures of Passage Comprehension and Word Reading Efficiency. Results indicate that measures of oral language in Spanish predict reading scores in Spanish and that measures of oral language skill in English predict reading scores in English. Cross‐language comparisons revealed that English oral language measures predicted Spanish reading scores and Spanish oral language measures predicted English reading scores beyond the variance accounted for by grade. Results indicate that Spanish and English oral language skills contribute to reading within and across languages.     

A Longitudinal Investigation of Conflict and Delay Inhibitory Control in Toddlers and Preschoolers

Research Findings: A total of 81 children participated in a longitudinal investigation of inhibitory control (IC) from 2 to 4 years of age. Child IC was measured via maternal report and laboratory measures under conditions of conflict and delay. Performance on delay IC tasks at 3 years was related to performance on these same tasks at 2 and 4 years, but performance on conflict IC tasks was not related over time. Delay IC task performance was concurrently related to conflict IC task performance in 3- and 4-year-olds but was not related in 2-year-olds. Measures of IC varied in their associations with measures of verbal ability and maternal-report IC. Such findings highlight important similarities and distinctions between conflict and delay IC abilities in their relation to one another and to temperament and language over time. Practice or Policy: Studies of IC and related concepts reveal that children who are regulated enjoy school more and have higher school competence, particularly in mathematics and reading achievement. Because conflict IC and delay IC show unique patterns of development over time, educators can expect classroom behaviors drawing on the state-like conflict IC to show more fluctuation over time than those drawing on the trait-like delay IC.     

SELF-REPORT PREDICTORS: A REMINDER1

How do tests and self-reports compare as predictors of academic performance? Do tests add to the predictability from self-reports? College seniors in eight sections of an evaluation course were administered the Quantitative Evaluative Device, the Cooperative English Test: Reading Comprehension, the Concept Mastery Test, and two questionnaires concerning past academic performance, student-estimated abilities, and reading habits. The criteria were composite test scores and letter grades. The best predictors were two self-reported variables, GPA and grade in an educational psychology course, and a test variable, the QED. Multiple Rs using questionnaire data for the predictors were increased slightly by adding the test scores, but on cross-validation the rs for the two predictor sets were essentially identical. The utility of the tests, then, was not supported either by zero-order correlations or by cross-validated increments. Therefore an investigator is reminded at least to include self-report measures in his set of predictors.     

Predicting response to early reading intervention from verbal IQ, reading-related language abilities, attention ratings, and verbal IQ-word reading discrepancy: failure to validate discrepancy method

Additional analyses of a previously published study addressed three questions about growth in word reading during early reading intervention: (1) How well do Verbal IQ, reading-related language abilities (phonological, rapid naming, and orthographic), and attention ratings predict reading growth? (2) How well do language deficits predict reading growth? and (3) How well does Verbal IQ-word reading discrepancy predict reading growth? Univariate analyses showed that Verbal IQ, phonological skills, orthographic skills, rapid automatized naming (RAN), and attention ratings predicted the response to early intervention, but multivariate analyses based on a combination of predictors for real-word reading and pseudoword reading showed that Verbal IQ was not the best unique predictor. Students with double or triple deficits in language skills (RAN, phonological, and orthographic processing) responded more slowly to early intervention than students without language deficits. Verbal IQ-word reading discrepancy did not predict the response to early intervention in reading. Overall results supported the use of reading-related language and attention measures rather than IQ-achievement discrepancy in identifying candidates for early reading intervention.     

What Can Mathematics Educators in England Learn from TIMSS?

In most of the countries taking part in TIMSS, students scored at similar levels for mathematics and science. England was one of the few countries where the results did not conform to this pattern. The key question for mathematics educators in England is: why did students in England perform relatively well in science but relatively badly in mathematics? The results for 9-year-olds were particularly intriguing since the majority of students at this age in England were taught mathematics and science by their class teacher. In order to seek answers to the question posed above, this article compares the responses to the TIMSS context questionnaires made by 9-year-olds and their teachers in the 13 European countries taking part in the TIMSS survey of that age group (Population 1). Issues examined include: curriculum content; lesson time; homework; class size; use of calculators in mathematics; practical activities in science; classroom organisation and students’ attitudes.     

The Relationship of Effective Schools Indicators and Changes in the Social Distribution of Achievement

ABSTRACT

This study focused on school effectiveness in terms of changes in the distribution of achievement across socio‐economic status (SES) for a cohort of 9700 students as they progressed from grade 1 to grade 3. The achievement/SES link was operationalized as the standardized mean difference in achievement (EFFSIZE) between samples of high and low SES students for 165 schools. EFFSIZE measures in reading and mathematics were analyzed in an hierarchical linear model which allowed an assessment of the impact of 13 school characteristics on initial (grade 1) status and, more importantly, on trends over time. The results indicate that, on the average, low SES students are at an initial disadvantage relative to their high SES peers in both subjects and that the difference widens across the first three grades. True school variance in slopes was found in mathematics but not reading, a result consistent with previous research. The school characteristics, which included six indicators based on the effective schools literature, were found to be ineffective predictors of these growth parameters.     

WIDENING AND INCREASING POST-16 MATHEMATICS PARTICIPATION: PATHWAYS, PEDAGOGIES AND POLITICS

This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification pathway—Use of Mathematics—sits in parallel with long-established, traditional advanced level qualifications, what we call ‘traditional Mathematics’ herein. Traditional Mathematics is typically required for entry to mathematically demanding undergraduate programmes. The structure, pedagogy and assessment of Use of Mathematics is designed to better prepare students in the application of mathematics, and its development has surfaced some of the tensions between academic/pure and vocational/applied mathematics. Here, we explore what Use of Mathematics offers, but we also consider some of the objections to its introduction in order to explore aspects of the knowledge politics of mathematics education. Our evaluation of this curriculum innovation raises important issues for the mathematics education community as countries seek to increase the numbers of people that are well prepared to apply mathematics in science and technology-based higher education courses and work places.     

Differences in the Mathematics‐Vocabulary Knowledge of Fifth‐Grade Students With and Without Learning Difficulties

The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics‐vocabulary understanding of fifth‐grade students. Students (n = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and general vocabulary measures, students were categorized with no learning difficulty (i.e., typical), mathematics difficulty without reading difficulty (MD‐only), reading difficulty without mathematics difficulty (RD‐only), and combined mathematics and reading difficulties (MDRD). On the mathematics‐vocabulary measure, students with MD‐only or RD‐only scored significantly lower than typical students, and students with MDRD demonstrated significantly lower performance than students with MD‐only or RD‐only.     

Reading fluency from grade 2–6: a longitudinal examination

The goal of this study was to examine oral word reading fluency from a developmental perspective in a longitudinal study of students from second grade to sixth grade. The sample was consisted of native English speaking students that took part in a large longitudinal study. Participants were assessed on cognitive and literacy measures such as working memory, phonological awareness, rapid automatized naming and syntactic awareness—oral cloze. Two main research questions were examined: first, what relationships will be found between the cognitive, literacy and linguistic measures, and which of them simultaneously predict oral reading fluency, in each age group? And second, which cognitive and literacy measures in second grade predict word reading fluency in sixth grade? Results show that cognitive and literacy measures contribute differently to word reading fluency skill across the different grades, while the only strong predictor across all age groups, was the phonological awareness. Finally, taking together past and previous findings, a proposed definition of fluency from a developmental perspective is suggested, based on the results of the study that show in a clear manner, that reading fluency, its contributors and its predictors, change respectively to the reading phase obtained in each grade.     

Assessing comprehension during reading with the Reading Strategy Assessment Tool (RSAT)

Comprehension emerges as the results of inference and strategic processes that support the construction of a coherent mental model for a text. However, the vast majority of comprehension skills tests adopt a format that does not afford an assessment of these processes as they operate during reading. This study assessed the viability of the Reading Strategy Assessment Tool (RSAT), which is an automated computer-based reading assessment designed to measure readers’ comprehension and spontaneous use of reading strategies while reading texts. In the tool, readers comprehend passages one sentence at a time, and are asked either an indirect (“What are your thoughts regarding your understanding of the sentence in the context of the passage?”) or direct (e.g., why X?) question after reading each pre-selected target sentence. The answers to the indirect questions are analyzed on the extent that they contain words associated with comprehension processes. The answers to direct questions are coded for the number of content words in common with an ideal answer, which is intended to be an assessment of emerging comprehension. In the study, the RSAT approach was shown to predict measures of comprehension comparable to standardized tests. The RSAT variables were also shown to correlate with human ratings. The results of this study constitute a “proof of concept” and demonstrate that it is possible to develop a comprehension skills assessment tool that assesses both comprehension and comprehension strategies.     

Predicting word reading ability: a quantile regression study

Predictors of early word reading are well established. However, it is unclear if these predictors hold for readers across a range of word reading abilities. This study used quantile regression to investigate predictive relationships at different points in the distribution of word reading. Quantile regression analyses used preschool and kindergarten measures of letter knowledge, phonological awareness, rapid automatised naming, sentence repetition, vocabulary and mother's education to predict first‐grade word reading. Predictors generally varied in significance across levels of word reading. Notably, rapid automatised naming was a significant unique predictor for average and good readers but not poor readers. Letter knowledge was generally a stronger unique predictor for poor and average readers than good readers. Well‐known word reading predictors varied in significance at different points along the word reading distribution. Results have implications for early identification and statistical analyses of reading‐related outcomes. What is already known about this topic

• Early predictors of word reading are well established, with letter knowledge, phonological awareness and rapid automatised naming identified as key predictors.
• These relationships are primarily investigated in average readers, or in groups of good and poor readers separated by an arbitrary cut‐off score.

What this paper adds

• In this study, we used quantile regression to determine significant predictors of word reading across a range of word reading abilities.
• The quantile regression approach avoids the loss of power that can arise when creating subgroups and has none of the issues associated with the use of a single, arbitrary cut-off score to separate good and poor readers.
• Letter knowledge and phonological awareness were significantly predictive of word reading across the distribution of word reading abilities, whereas rapid automatised naming was significant only for good readers, and sentence recall was significant only for poor readers.

Implications for theory, policy and practice

• Results reinforce the usefulness of measures such as letter knowledge, phonological awareness and sentence repetition in the early identification of children at risk for reading disabilities.
• Results also suggest that measures of rapid naming may add little unique information in differentiating between children who subsequently read in the below‐average range.

     

Kindergarten Predictors of Math Learning Disability

The aim of the present study was to address how to effectively predict mathematics learning disability (MLD). Specifically, we addressed whether cognitive data obtained during kindergarten can effectively predict which children will have MLD in third grade, whether an abbreviated test battery could be as effective as a standard psychoeducational assessment at predicting MLD, and whether the abbreviated battery corresponded to the literature on MLD characteristics. Participants were 226 children who enrolled in a 4‐year prospective longitudinal study during kindergarten. We administered measures of mathematics achievement, formal and informal mathematics ability, visual‐spatial reasoning, and rapid automatized naming and examined which test scores and test items from kindergarten best predicted MLD at grades 2 and 3. Statistical models using standardized scores from the entire test battery correctly classified ～80–83 percent of the participants as having, or not having, MLD. Regression models using scores from only individual test items were less predictive than models containing the standard scores, except for models using a specific subset of test items that dealt with reading numerals, number constancy, magnitude judgments of one‐digit numbers, or mental addition of one‐digit numbers. These models were as accurate in predicting MLD as was the model including the entire set of standard scores from the battery of tests examined. Our findings indicate that it is possible to effectively predict which kindergartners are at risk for MLD, and thus the findings have implications for early screening of MLD.