Testing the Immediate and Long-Term Efficacy of a Tier 2 Kindergarten Mathematics Intervention

ABSTRACT

This study examined the efficacy of a kindergarten mathematics intervention program, ROOTS, focused on developing whole-number understanding in the areas of counting and cardinality and operations and algebraic thinking for students at risk in mathematics. The study utilized a randomized block design with students within classrooms randomly assigned to treatment or control conditions. Measures of mathematics achievement were collected in the fall (pretest) and spring (posttest) in kindergarten and in the winter of first grade (delayed posttest). Significant differences between conditions favoring treatment students were found on four of six measures at posttest. Treatment students reduced the achievement gap with their not-at-risk peers. No effect was found on follow-up first-grade achievement scores. Implications for Tier 2 mathematics instruction in a Response to Intervention model are discussed.     

QuickSmart: a basic academic skills intervention for middle school students with learning difficulties

QuickSmart is a basic academic skills intervention designed for persistently low-achieving students in the middle years of schooling that aims to improve the automaticity of basic skills to improve higher-order processes, such as problem solving and comprehension, as measured on standardized tests. The QuickSmart instructional program consists of three structured, teacher- or teacher aide-directed, 30-minute, small-group lessons each week for approximately 26 weeks. In this study, 42 middle school students experiencing learning difficulties (LD) completed the QuickSmart reading program, and a further 42 students with LD took part in the QuickSmart mathematics program. To investigate the effects of the intervention, comparisons were made between the reading and mathematics progress of the intervention group and a group of 10 high-achieving and 10 average-achieving peers. The results indicated that although the standardized reading comprehension and mathematics scores of QuickSmart students remained below those of comparison students, they improved significantly from pretest to posttest. In contrast, the standardized scores of comparison students were not significantly different from pretest to posttest. On measures of response speed and accuracy gathered using the Cognitive Aptitude Assessment System (CAAS), QuickSmart students were able to narrow the gap between their performance and that of their high- and average-achieving peers. Implications are drawn regarding the importance of interventions that emphasize the automaticity of basic academic skills for students with learning difficulties.     

Effects of metacognitive instruction on mathematics achievement and attitude towards mathematics of low mathematics achievers

An experiment was conducted to examine the effects of metacognitive instruction on mathematics achievement and attitude towards mathematics of low mathematics achievers at a middle school in the North‐West Province of South Africa. Forty standard (std) 7 pupils were identified whose non‐verbal general ability and previous mathematics achievements were significantly lower than those of other std 7 pupils. These subjects were randomly assigned to an experimental group and a control group. Metacognitive strategies in solving mathematical problems related to four mathematics topics were individually taught to the members of the experimental group, while the pupils in the control group were taught the four mathematics topics through the conventional method of teaching mathematics. The comparisons of pretest and posttest measures of general ability, metacognitive awareness, attitude towards mathematics, and mathematics achievement revealed that the posttest scores of all the four variables for the experimental group were significantly higher than those for the control group.     

Student performance and attitudes using personalized mathematics instruction

This study investigated the effects of personalized instruction on the achievement and attitudes of Taiwanese students on two-step mathematics word problems. A total of 136 fourth-graders in a Taiwanese public school participated in the study. Subjects initially completed a Student Survey on which they chose their favorite foods, sports, stores, classmates, and other selections. The most popular items were then used to create personalized math word problems for the pretest, personalized instructional program, and posttest. Subjects were blocked by ability based on their pretest scores and were randomly assigned within ability levels to either a personalized or nonpersonalized version of the print-based instructional program. After finishing the program, subjects completed a student attitude survey and the posttest. A repeated-measures univariate analysis of variance revealed that subjects in the personalized treatment made significantly greater pretest-to-posttest gains than those in the nonpersonalized treatment. Subjects also performed significantly better on the personalized pretest and posttest problems than on the nonpersonalized problems. Personalized subjects and higher-ability students both had significantly more positive attitudes toward the instructional program than did their nonpersonalized and lower-ability counterparts. This research was conducted while he was a doctoral student at Arizona State University.     

Deaf college students' mathematical skills relative to morphological knowledge, reading level, and language proficiency

This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and meaning were all significantly correlated with both the ACT Mathematics Subtest and National Technical Institute for the Deaf (NTID) Mathematics Placement Test scores. Multiple regression analyses identified the best combination from among these potential independent predictors of students' performance on both the ACT and NTID mathematics tests. Additionally, the participating deaf students' grades in their college mathematics courses were significantly and positively associated with their reading grade level and their knowledge of morphological components of words.     

Can the Emotion Recognition Ability of Deaf Children be Enhanced? A Pilot Study

We evaluated the effectiveness of an 11-lesson psychoeducational program designed to enhance the ability of deaf children to understand the emotional experience of themselves and other people. The "Funny Faces Program" was provided to 14 children, aged 9 to 13, with moderate to profound hearing impairments. All children were enrolled in an "oral" education program at a school for the deaf. Alternate forms of the Emotion Recognition Scales (Dyck, Ferguson, & Shochet, 2001) were administered at pretest and posttest. Results indicate significant increases in emotion vocabulary and emotion comprehension but not in the speed or accuracy of emotion recognition (ER), from pretest to posttest. At posttest, children whose hearing loss was moderate to severe did not differ from hearing children in ER abilities but children with profound hearing loss continued to show substantial ability deficits.     

Effects of reading picture books on kindergartners’ mathematics performance

This article describes a field experiment with a pretest–posttest control group design which investigated the potential of reading picture books to children for supporting their mathematical understanding. The study involved 384 children from 18 kindergarten classes in 18 schools in the Netherlands. During three months, the children in the nine experimental classes were read picture books. Data analysis revealed that, when controlled for relevant covariates, the picture book reading programme had a positive effect (d = .13) on kindergartners’ mathematics performance as measured by a project test containing items on number, measurement and geometry. Compared to the increase from pretest to posttest in the control group, the increase in the experimental group was 22% larger. No significant differential intervention effects were found between subgroups based on kindergarten year, age, home language, socio-economic status and mathematics and language ability, but a significant intervention effect was found for girls and not for boys.     

Promoting social competence in deaf students: the effect of an intervention program

The aim of this study was to determine the effects of a social skills training program on the social skills and social behaviors of deaf children in a mainstream setting. The study used a pretest/posttest design. The participants consisted of 18 severely and profoundly hearing-impaired children (ages ranged from 9;1 to 13;6) who were enrolled in three elementary schools in the Canary Islands. Results indicated that the intervention succeeded in improving students' social problem-solving skills, especially in making comprehensible the steps implied in the solution of interpersonal problems; the intervention also led to significant improvement of deaf students' assertive behavior as rated by their teachers and by themselves. Significant differences in social or academic integration as judged by companions in a sociometric questionnaire were not found.     

Cochlear implanted pupils in Scottish schools: 4-year school attainment data (2000-2004)

The Achievements of Deaf Pupils in Scotland (ADPS) project has been tracking the educational attainment of deaf pupils in Scotland's schools since 2000. At the time of writing, the database contains records for 1,752 deaf pupils (2000-2005). Here 4-year aggregate educational attainment data are reported for a subset of 152 school-aged deaf pupils with cochlear implants notified to the ADPS database between June 2000 and June 2004. The data describe primary and secondary school results in reading, writing, and math for this subgroup, as well as placement and communication characteristics. The educational attainment of the group of deaf pupils with cochlear implants is clearly marked when the deaf pupil population is disaggregated for hearing loss, achieving comparatively higher average attainment in both 5-14 Curriculum National Tests (Mathematics in particular) and Standard Grades. Therefore the gap in performance relative to the national population data is reduced for those deaf pupils, although it still widens at higher levels of achievement for the National Tests. Although most pupils with cochlear implants are placed in the mainstream, there is no pattern of migration toward mainstream schools. Some deaf pupils with cochlear implants moved out of mainstream to other types of placement, and this has implications for health-economic cost-utility assessments of cochlear implantation that favor mainstream education by drawing upon the relative cost of different placement types. These findings suggest that the ADPS program of research can contribute school outcome data as valuable real-life outcome measures in wider assessments of the benefit of cochlear implants to deaf children and deaf young people.     

The effect of an historical perspective on prospective teachers’ beliefs in learning mathematics

Many learners hold traditional beliefs about mathematics that can hamper their learning in the discipline. To address this issue, a “history-based” intervention program entailing problem-solving and writing activities that instigate cognitive conflict was implemented. Data sources were pretest and posttest scores of a 12-theme questionnaire designed for this study called “Prospective teachers’ beliefs questionnaire about mathematics learning” and written reflections of prospective teachers. The survey of the prospective teachers beliefs related to the nature of mathematics and the way it is learned, taught, and practiced showed a great majority of them failed to hold progressive beliefs. Fortunately, the intervention program has helped the prospective teachers revise and correct their beliefs, thoughts, and understandings. Study of the prospective teachers’ written reflections and observations of their oral presentations during whole-class discussions strengthen the results of the quantitative study.     

Family mediation of mathematically based concepts while engaged in a problem-solving activity with their young deaf children

This qualitative study examined the relationship between young deaf children's level of mathematics ability ("high" and "low," as defined by test score on the Test of Early Mathematics Ability-3) and opportunities available for the construction of early mathematics knowledge during a problem-solving task implemented by their parents. Findings indicate that the manner in which the mathematically based concepts (number/counting, quantity, time/sequence, and categorization) were incorporated into the activity was more meaningful for children who demonstrated high levels of mathematical ability. In addition, children who demonstrated high levels of mathematical ability experienced a more purposeful use of mediation during activity implementation; however, overall use of mediated learning experience was limited for children from both ability groups.     

Investigating the Efficacy of a Core Kindergarten Mathematics Curriculum to Improve Student Mathematics Learning Outcomes

This study examined the efficacy of a core kindergarten mathematics program, Early Learning in Mathematics (ELM), a 120-lesson program with four content strands: (a) number operations, (b) geometry, (c) measurement, and (d) vocabulary. The study utilized a randomized block design, with 129 classrooms randomly assigned within schools to treatment or control conditions. Measures of achievement were collected in the fall (pretest) and spring (posttest) in kindergarten and in the winter of first grade (follow-up). Although students in ELM classrooms did not differ significantly from students in control classrooms, we expected and found that the effects of ELM depended on students’ initial achievement. Initial achievement moderated condition effects for Test of Early Mathematics Ability (TEMA) scores (p =.0039), but not the Early Numeracy–Curriculum-Based Measurement (p =.1887). We found no effects on follow-up first-grade scores from the Stanford Achievement Test Tenth Edition Problem Solving subtest (p =.9737) or Procedures subtest (p =.6336).     

The effects of educational computer game on low-performing children’s early numeracy skills – an intervention study in a preschool setting

The aim of this study was to determine the effects of an educational computer game, Lola’s World, on low-performing children’s early numeracy skills. Four preschools with 33 children from families of low socio-economic status (M _age = 5.5 years) took part in this study. Of the 33 children, 23 were split randomly into two groups: an intervention group playing a numeracy game (Lola’s World) and an active control group playing an early reading skills game (Lola’s ABC party). The remaining 10 children served as a passive control group. The intervention phase lasted three weeks, during which time the children played the games daily for about 15 min. The children’s numeracy skills were measured using the Early Numeracy Test. Those children (n = 22) who exhibited low numeracy (i.e. at risk for learning difficulties in mathematics) were included in the analyses. The three groups did not differ in terms of parental educational levels or home languages. They were comparable in terms of nonverbal reasoning and the amount of time spent playing. The Lola’s World group improved its early numeracy performance from pretest to post-test. No between-group differences were found. The results are discussed in relation to providing game-based support for low-performing preschoolers.     

Implementing a successful writing program in public schools for students who are deaf.

A 2-year project to improve the writing skills of children who are deaf included instruction for teachers in the process approach to teaching writing. The project encompassed 10 public school programs for students who are deaf and included 325 students in Grades 4-10 and 52 teachers. The project included specific training goals for teachers, a self-report procedure for the teachers, and a data-collection and analysis phase to assess short-term effects on students' writing. Teacher self-reports indicated widespread involvement in the project, and pretest and posttest results showed dramatic improvement in students' writing--particularly in grammatical skills. Scoring systems for students' papers are included.     

Effects of mathematics learning through children's literature on math achievement and dispositional outcomes

The purpose of this study was to analyze the effectiveness of using children's literature to promote mathematics learning. Fifty-seven kindergarteners were randomly assigned to either a control group or an experimental group. The experimental group received mathematics related storybook reading and discussion time and played with mathematics materials that were related to the storybook content during free play. The control group had ordinary storybook reading time and played with mathematics materials unrelated to the storybook content. The Learning Readiness Test and the Early Mathematics Achievement Test were administered. Four mathematics tasks were also given to compare the mathematics achievement of the two groups. The children's choice of favorite corners, the time spent, and the number of children who played in the mathematics corner were investigated also to measure children's disposition toward doing mathematics. The results showed that more children in the experimental group liked the mathematics comer, chose mathematics tasks, and spent more time in the mathematics corner. Furthermore, the experimental group did significantly better than the control group in the classification, number combination, and shape tasks, and there were qualitative differences in the content analysis.     

Effects of an Online Mathematics Curriculum for English Language Learners

This study measured the effects of an online supplementary mathematics curriculum designed for middle school English language learners who speak Spanish as a first language. A randomized experiment measured the achievement differences between middle school English language learners who used the Web-based HELP Math (Help with English Language Proficiency) curriculum and students who used other technology-based programs. Three hundred and ninety-six students participated. Both groups made statistically significant gains from pretest to posttest within their respective curricula, but no main effect was found between the two groups. Post hoc analyses revealed that students with higher levels of English proficiency, who participated in the comparison condition, performed significantly better than students in the HELP Math condition, while students with lower levels of English proficiency performed better in the HELP Math program (although these differences were not statistically significant). Findings are interpreted with caution due to the truncated length of the intervention.     

Evaluating Intervention Effects in a Diagnostic Classification Model Framework

The evaluation of intervention effects is an important objective of educational research. One way to evaluate the effectiveness of an intervention is to conduct an experiment that assigns individuals to control and treatment groups. In the context of pretest/posttest designed studies, this is referred to as a control‐group pretest/posttest design. The transition diagnostic classification model (TDCM) was recently developed to assess growth, defined as change in attribute mastery status over time, in a diagnostic classification model framework. The TDCM, however, does not model multiple groups, and therefore is not able to analyze data from a control‐group pretest/posttest designed experiment. In this study, we extend the TDCM to model multiple groups, thereby enabling the examination of group‐differential growth in attribute mastery and the evaluation of intervention effects. The utility of the multigroup TDCM is demonstrated in the evaluation of an innovative instructional method in mathematics education.     

USING CHILDREN'S WORK TO REFLECT ON TEACHING: ONE EARLY CHILDHOOD STUDENT TEACHER'S REFLECTIONS

Abstract

The purpose of the study was to examine the engagement of preservice teachers in the kind of authentic experiences that provided the modeling needed to make high‐quality instruction in mathematics a reality for young children. Inasmuch as these preservice teachers had not yet received any formal methods classes in mathematics, the authors theorized that classroom teachers whose practices and dispositions were congruent with the National Council of Teachers of Mathematics standards and the State of South Carolina Mathematics Standards could model effective teaching instruction for young children using the project approach. These same teachers could then provide mentoring and encouragement to preservice teachers as they became involved in this high‐quality program for 4‐year olds, deepening the knowledge base of the preservice teachers regarding developmentally appropriate ways to teach numeracy to 4‐year olds. © 2005 Elsevier Inc. All rights reserved.     

The Contributors' Column

This project investigated the effects of a standards-based mathematics methods course on the mathematics anxiety levels of preservice teachers. The qualitative portion of the study examined aspects of a math methods course that affected mathematics anxiety levels and the antecedents of mathematics anxiety. Findings revealed a significant difference (p.05) between pretest and posttest mathematics anxiety levels, indicating a decrease in mathematics anxiety from the onset of the mathematics methods course.     

Deaf children's informal knowledge of multiplicative reasoning

Multiplicative reasoning is required in different contexts in mathematics: it is necessary to understand the concept of multipart units, involved in learning place value and measurement, and also to solve multiplication and division problems. Measures of hearing children's multiplicative reasoning at school entry are reliable and specific predictors of their mathematics achievement in school. An analysis of deaf children's informal multiplicative reasoning showed that deaf children under-perform in comparison to the hearing cohorts in their first two years of school. However, a brief training study, which significantly improved their success on these problems, suggested that this may be a performance, rather than a competence difference. Thus, it is possible and desirable to promote deaf children's multiplicative reasoning when they start school so that they are provided with a more solid basis for learning mathematics.