Reviewed by Ginsburg, Lewis, & Clements
Big Math for Little Kids
The Big Math for Little Kids (BMLK) is a mathematics curriculum designed to facilitate mathematics learning for pre-kindergarten and kindergarten students (Greenes, Ginsburg, & Balfanz, 2004). The program includes six units (number, shape, measurement, constructing and partitioning numbers, patterns and logic, and navigation and spatial concepts) containing a sequence of enjoyable activities designed to promote both mathematical understanding and language (Greenes, et al., 2004). The program is designed to be used in whole-class and small-group settings, as well as with individual students. Early field-testing suggested that children taught using the curriculum achieved a high level of mathematical understanding, learned to count to high numbers, were able to take the perspective of others, and anticipated further events and predicted outcomes (Greenes et al., 2004).
The effectiveness of the curriculum has been examined using a two-year randomized controlled trial (RCT) that was funded by the US Department of Education Institute of Education Sciences. The study, which focused on low-income children attending subsidized child care centers in New York City for pre-kindergarten and kindergarten, compared the mathematics achievement of children whose teachers either used the BMLK curriculum or continued to teach mathematics using the Creative Curriculum (Dodge, Colker, & Heroman, 2002) or a home grown early childhood curriculum. The treatment teachers attended monthly workshops to deepen their understanding of young childrens mathematical learning, as well as to demonstrate important components of the curriculum.
Student achievement was assessed using the mathematics assessment developed for the Early Childhood Longitudinal Study, Birth Cohort (ECLS-B; National Center for Education Statistics) at the beginning and end of their pre-kindergarten year and then again in kindergarten, yielding scores at four time points. The advantage of using the ECLS-B is that it is (1) nationally normed and standardized and (2) that the assessment is not directly aligned with the content of the intervention, providing a stricter test of impact. The norming was conducted using a large stratified random sample including 14,000 children born in 2001 and the measure has high internal reliability (Rock & Pollock, 2002). The test itself is adaptive, meaning that the accuracy of responses determine whether the test taker receives easier or more difficult items, and allows for precise estimation of ability with fewer administered questions.
Preliminary results, using latent growth modeling, are currently available for this study and suggest that children in the BMLK group demonstrate a larger increase in mathematics achievement compared to children in the control group. There were no significant differences between the two groups at the beginning of the study, but by the end of kindergarten these differences emerge with a medium effect size (Cohens d=.43). It should be noted that this study was conducted by the authors of this paper (Clements, Lewis, and Ginsburg, 2008).
The Building Blocks (funded by the National Science Foundation) mathematics curriculum, designed for pre-kindergarten through 2nd grade children, is designed specifically to develop competencies detailed in the National Council of Teachers of Mathematics Principals and Standards for School Mathematics (Sarama, 2004). To this end, the curriculum focuses on developing spatial and geometric competencies, as well as numeric and quantitative concepts (Sarama & Clements, 2004). Within these two areas, three mathematical themes are integrated including patterns, data, and sorting and sequencing (Sarama, 2004). In addition to classroom activities, the curriculum relies heavily on the use of computer software, designed as part of the curriculum, to meaningfully engage children as young as 3 years of age in mathematical concepts (Sarama, 2004; Clements & Sarama, 2003). As a result, teachers are required to provide guidance within and between formats.
A randomized controlled trial (RCT) was conducted, comparing three groups of teachers, namely a group using the Building Blocks Curriculum, a second group using the Pre-Kindergarten Mathematics Curriculum (PreK Math; Klein, Starkey, & Ramirez, 2002), and a third control group that experienced whatever teaching was involved in business as usual. These groups included equal numbers of classrooms, some serving low-income students only and other classrooms serving both low-income and middle-income students.
Researchers assessed the impact of the three mathematics curricula using a measure of mathematics ability that was constructed by Clements and Sarama and includes many of the same mathematics activities that are part of the Building Blocks curriculum. The Early Mathematics Assessment (EMA) is administered individually to children during two 10-20 minute interviews, which include detailed protocol, coding, and scoring for the interviewer to follow (Clements & Sarama, 2008). In this study, the interviews were videotaped and recoded to ensure reliability. EMA is a comprehensive assessment of mathematical knowledge, is not aligned with any particular curriculum, and is has high internal reliability (Clements & Sarama, 2008).
Results showed that both the Building Blocks and PreK Math curriculum groups performed significantly better on the EMA measure than the control group and the Building Blocks group performed significantly better than the PreK Math intervention group (Clements & Sarama, 2008). Building Blocks outperformed the control group with a large effect size of 1.07 and outperformed the PreK Math curriculum with a medium effect size of .47. The Pre-Kindergarten Mathematics Curriculum outperformed the control group with a medium effect size of .64. Overall, the program effects for Building Blocks were the same regardless of program type (i.e., Head Start or a state-funded program), classroom socioeconomic (SES) composition, and child-level SES. In other words, there was no evidence that the impact of Building Blocks varied for different groups of students.
In addition to the impact of the curricula on the composite scores, subscore analyses demonstrated that some skills benefited more from Building Blocks than PreK Math (count higher without committing errors, describing counting errors, and explaining how to correct counting errors), while for other skills the Building Blocks and PreK Math students performed equally as well (object counting, verbal counting, comparing numbers, sequencing, shape identification and representation, and identifying counting errors) (Clements & Sarama, 2008).
Pre-Kindergarten Mathematics Curriculum
The Pre-Kindergarten Mathematics Curriculum (PreK Math), originally designed as part of the Berkeley Math Readiness Project has been evaluated as part of the Preschool Curriculum Evaluation Research (PCER) Program. PreK Math, was developed for children in grades [XX through XX] (Klein & Starkey, 2004). The curriculum is organized around seven units: enumeration and number sense, arithmetic reasoning, spatial sense, geometric reasoning, pattern sense and unit construction, nonstandard measurement, and logical reasoning. The small-group activities included in the curriculum use concrete materials and are designed to improve mathematical knowledge, specifically numerical and spatial-geometric thinking (Klein & Starkey, 2004).
An effectiveness study compared children in equivalent numbers of low- and middle-income classrooms using PreK Math to a comparison group (Klein & Starkey, 2004). Both income levels were included in order to test the researchers hypothesis that because the curriculum provides experiences to low-income children that middle-income children were likely to receive at home, the impact of PreK Math would be more pronounced among low-income children (Starkey, Klein, & Wakely, 2004). In addition to classroom activities, the authors of PreK Math developed a home component of the curriculum, which includes parent classes three times per year designed to teach parents how to use the activities with their children (Starkey, Klein, & Wakely, 2004).
Researchers administered the Child Math Assessment (CMA; Klein & Starkey, 2004; Starkey, Klein, & Wakely, 2004) to both groups of students in the fall and spring of their PreK year. The CMA assesses a wide variety of mathematical concepts using 16 separate tasks, which are administered in two 20-30 minute individual testing sessions. For this study, the assessments were videotaped and coded for reliability (Starkey, Klein, & Wakely, 2004). Half of the children received the first section during the first testing session and the other half received the second section of the test during the first testing session.
The results demonstrated that that mathematics ability for middle-income children in both study groups was significantly higher than that of their low-income peers, and that their mathematics ability grew at a faster rate over the course of the study (Klein & Starkey, 2004). The results also indicated that there was a significant main effect for PreK Math, with the intervention group having significantly higher CMA scores. The researchers conclude that while PreK Math was effective for both low- and middle-income children, it was particularly beneficial to the low-income students (Klein & Starkey, 2004; Starkey, Klein, & Wakely, 2004).
Researchers conducted a second study (also involving random assignment of classrooms) of PreK Math in two early childcare settings Head Start and state-funded preschools representing 40 pre-kindergarten classrooms (Klein, et al., in press). Teachers in the treatment group implemented PreK Math and the DLM Early Childhood Express Math software (Clements & Sarama, 2003), part of the Building Blocks curriculum, while the control group continued their regular curriculum, which included Creative Curriculum, High Scope, Montessori, and other local curricula (Klein, et. al., in press). As in the study described above, the children were assessed using the Child Math Assessment (CMA) and coded from videotapes. As, expected, the math scores of the PreK Math/DLM and control groups did not differ between groups in the fall, but by spring the intervention group scored significantly higher than the comparison groups with a medium effect size of .55 (Klein, et. al., in press). This study used a second mathematics outcome measure; this composite score consisted of the CMA, a Shape Compositions task, and the Woodcock Johnson Applied Problems score. Analyses using the composite score also demonstrated a significant difference between the treatment and control groups with an effect size of .62 (Klein, et. al., in press).
Childrens School Success (ISRC)
The Childrens School Success (CSS) Program is a comprehensive curriculum for preschool children implemented with at-risk children (low income families, students with disabilities, and/or ELL), which focuses on oral language and literacy, science, math, and social competence (Lieber, et. al., 2007). The program views young children as active, self-motivated learners and includes student choice, family involvement and individualization into the programs conceptual framework (Odom, et. al., 2007b). The curriculum utilizes linked learning, or activities that build upon the previous lessons content, integrates curricular domains across activities, includes a problem solving process, and capitalizes on childrens interests and experiences (Odom, et. al., 2007b). The mathematics aspect of the program was adapted from Douglas Clements Building Blocks curriculum and includes number and operations, geometry and spatial sense, measurement, pattern/algebraic thinking, and displaying and analyzing data (Odom, et. al., 2007b).
Three years of research was conducted with approximately 800 at-risk children in Head Start or state pre-k or private childcare centers, in which the majority of enrolled children were of Caucasian/Non-Hispanic dissent (Odom, et. al., 2007b). Student achievement was measured used the Woodcock Johnson Math Subtest. Although the authors did not provide information on the characteristics of the math subtest, a study conducted by the NICHD Early Child Care Research Network (2002) found that the Woodcock Johnson Applied Problems subtest has an internal consistency of .91. This assessment does not align directly with the curriculum itself and as such is less biased in favor of the curriculum.
Presentations on the research have not included analyses comparing the treatment and control groups. Instead, the focus of the presentations thus far has been on the impact of treatment fidelity on childrens assessment scores, as well as their initial ability levels. These presentations have presented analyses that show that treatment fidelity has a positive significant association with childrens post test scores (after controlling for their pretest scores) on many (but not all) of the outcome measures. The presentations have also shown that, not surprisingly, children with lower test scores at the beginning of the study learned more in high fidelity classrooms than initially low-achieving children in low-fidelity classrooms. The lack of research findings regarding the treatment and control group comparisons, combined with the focus on treatment fidelity in the majority of research conference presentations leads us to wonder whether the evaluation of the CSS curriculum model did not find a significant difference in the treatment and control children on study outcome measures.
Round the Rug Math: Adventures in Problem Solving
Round the Rug Math: Adventures in Problem Solving is a supplementary program for pre-K through 2nd grade classrooms that uses stories to teach problem-solving (Casey, 2004; Casey, Kersh, & Young, 2004). This approach teaches mathematics concepts within a language rich medium that extends over the course of many lessons (Casey, 2004). The program specifically focuses on spatial and analytical skills, which can help address learning gaps, so it is not meant to be a comprehensive curriculum (Clements & Sarama, 2008). However, the focus on developing spatial skills is also intended to achieve equity between girls and boys, who consistently show better spatial and geometry skills (Casey, 2004). The program does two things simultaneously: (1) integrates mathematical content into the theme-based approach generally used throughout early childhood curricula, and (2) teaches mathematics content systematically with sequenced lessons (Casey, Kersh, & Young, 2004). Specifically, the Round the Rug Math curriculum teachers mathematical concepts in a systematic, hierarchical progression through the use of long epic stories, which allow characters to have multiple adventures the expose students to mathematical problems or concepts (Casey, Kersh, & Young, 2004). Students must solve the problem before going on to the next part of the story, which includes progressively more difficult concepts.
In the first evaluation of the effectiveness of one story on students geometric understanding was conducted with Kindergarten students, comparing the Round the Rug Math curriculum to a control group. The initial results indicate that the students who learned the content with the storybook approach improved significantly more than students who learned the content without the storybook approach, although details what this control group received were not described (Casey, Kersh, & Young, 2004). However, no information on the outcome measure or any statistical information was provided on this study.
A second study comparing the effectiveness of the program by gender suggests that in Kindergarten girls benefit more than boys from learning the mathematical content in a storytelling format (Casey, Erkut, Cedar, & Young, 2008). In this experimental study, six kindergarten teachers were randomly assigned to either the treatment or control group, with 76 students in the treatment group and 79 students in the control group. Two measures were used for pre- and post-test, including Triangles subtest of the Kaufman Assessment Battery for Children (K-ABC) and the Tangram test (Casey, Erkut, Cedar, & Young, 2008). The overall reliability of the K-ABC using a split-half procedure is .86-.93, with the Triangles subtests factorial loading at .70 for boys and .76 for girls (Casey, Erkut, Cedar, & Young, 2008).
There were higher pretest scores for the intervention group on the Triangle test, but no differences on the Tangram test. For the Triangle test, a repeated measures ANOVA showed a significant improvement from pretest to posttest (p<.001), as well as a significant difference between the treatment and control group (p<.003), particularly for the girls (p<.001; partial eta2 =.141). A comparison of the boys by condition did not yield a significant difference (Casey, Erkut, Cedar, & Young, 2008). For the Tangram test, a repeated measures ANOVA showed a significant improvement from pretest to posttest (p<.001), but no other effects.
Mathematics Curriculum Developed by C. Sophian
Sophian (2004a) differentiates the developmentally appropriate curriculum as one that matches the cognitive abilities of the learner from what she coined the prospective developmental perspective, meaning that some mathematical skills are important for learning at a later developmental point. This is often the unspoken goal of early education: teaching students enough so that they are ready and able to learn effectively in later grades and for low-income children the hope is that this preparation closes the achievement gap (Sophian, 2004b). While the development of social competence has long been a goal of Head Start, recent trends in accountability have broadened the focus of early childhood educators generally, and Head Start specifically, to include reading and math skills needed for school success (Fantuzzo, et. al., 2007). In addition, research suggests that low-income children, such as those in Head Start, have less mathematical understanding compared to wealthier counterparts (Sophian, 2004b).
Sophian developed a mathematics curriculum specifically for 3- and 4- year old children attending Head Start centers, which focuses heavily on measurement, object properties, and geometry (Sophian, 2004b). The curriculum is meant to be integrated within the rest of the Head Start program rather than as a stand alone curriculum. The curriculum was organized into weekly project activities and parents and teachers were given specific activities to complete with the children.
There is great emphasis on combining shapes in new ways and measurement with various units (Sophian, 2004b). Specifically, Sophian (2004b) describes the program as exploring the relationships between shapes rather than identifying features of those shapes (i.e. number of sides or angles). Rather than including measurement as a separate unit within the curriculum, Sophian (2004b) used measurement throughout the curriculum with a specific focus on measuring the same objects with different units of measurement; something she claims is not present in other similar programs.
An evaluation of the program was conduced to determine whether this math program could improve the readiness of low-income young children. Specifically, three Head Start centers, two classrooms within each center, served in the treatment group. Then six Head Start centers were matched on center characteristics and served in the control group; three centers conducted a literacy intervention and three centers continued their regular curriculum (Sophian, 2004b). In this case, the treatment group was provided the mathematics curriculum while the comparison group received either a literacy curriculum or no intervention (i.e. business as usual group). Children were assessed in the fall and spring of their pre-K year using an assessment procedure intended to align closely with the curriculum: the Developing Skills Checklist (DSC) and a supplemental measure developed for the study. The mathematics portion of the DSC assesses:
naming shapes, reproducing and extending patterns, counting, identifying numerals, matching sets and numerals, joining and separating sets, identifying original positions, and logically operations (classification, conservation of number, estimation, and seriation) (Sophian, 2004b, pp. 69).
Using the DSC score, the mathematics intervention group scored significantly higher than either the literacy intervention group or the no-intervention group and there was a significant difference between conditions, using pretest scores as covariates, with an effect size (partial n2 = 0.092; Sophian, 2004b). The supplemental score also showed the mathematics group scored significantly higher and there was a significant effect for the mathematics intervention (partial n2 = 0.083).
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