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Building Blocks for early childhood mathematics
Abstract and Figures
Building Blocks is a National Science Foundation-funded project designed to enable all young children to build a solid foundation for mathematics. To ensure this, we used a design and development model that drew from theory and research in each phase. Our design process is based on the assumption that curriculum and software design can and should have an explicit theoretical and empirical foundation, beyond its genesis in someone’s intuitive grasp of children’s learning. It also should interact with the ongoing development of theory and research-reaching toward the ideal of testing a theory by testing the software and curriculum in which it is embedded. Our model includes specification of mathematical ideas (computer objects or manipulatives) and processes/skills (software “tools” or actions) and extensive field-testing from the first inception through to large summative evaluation studies. The initial field test results indicate that such an approach can result in significant assessed learning gains consistent with the new Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics.
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... Iterating (Lehrer et al.,2003;Sarama & Clements, 2004) The given length be measured with repeated unit 1. ...
... Children have mathematical skills that they acquire informally at a substantial rate before they start formal education (Ginsburg et al., 2008;Litkowski et al., 2020;Sarama & Clements, 2004. Strengthening these skills by supporting them with meaningful and entertaining activities can potentially prepare them for the future. ...
This study contributes to the existing research on early childhood teachers’ perceptions of technology and its integration into mathematics-related activities. In this qualitative study, the analysis draws on focus group discussions with 20 teachers. The findings suggest that although early childhood teachers held a positive attitude towards technology and acknowledged its role in young children’s lives and learning, its integration remains limited in these classrooms. The participant teachers mentioned barriers that hinder technology integration, including inadequate classroom equipment, limited teacher competence, and insufficient professional development opportunities. Also, most participants reported only using songs, videos, and images to teach mathematical concepts through drills and practice within a controlled instructional setting. Therefore, education authorities should re-consider early childhood teacher education programs and professional development opportunities to enable pre- and in-service teachers to teach mathematical concepts to young children with technology. Implications for future studies and limitations of the study are provided.
... 6 Space constraints prohibit describing the many relevant research-based projects from the fields of mathematics education (e.g., Clements, 2002b;Confrey, Castro-Filho, & Wilhelm, 2000;Confrey & Lachance, 2000;Hoyles & Noss, 1992;Hoyles, Noss, & Sutherland, 1989;Lehrer & Chazan, 1998;Lewis & Tsuchida, 1998;Stigler & Hiebert, 1999;Yerushalmy, 1997) and cognitive science (e.g., Anderson, Corbett, Koedinger, & Pelletier, 1995;Brown, 1992;Griffin & Case, 1997;Lehrer et al., 1998a;Lehrer, Jenkins, & Osana, 1998b), as well as different conceptions such as didactical engineering (Artigue, 1994). twice the originally funded 4-year period; Clements & Sarama, 2004a;Sarama, 2004;. The first summative research: small scale evaluation of the Building Blocks curriculum resulted in effect sizes of 1.71 for number and 2.12 for geometry (Cohen's d; Clements & Sarama, in press). ...
Government agencies and members of the educational research community have petitioned for research-based curricula. The ambiguity of the phrase "research-based," however, undermines attempts to create a shared research foundation for the development of, and informed choices about, classroom curricula. This article presents a framework for the construct of research-based curricula. One implication is that traditional strategies such as market research and research-to-practice models are insufficient ; more adequate is the use of multiple phases of the proffered Curriculum Research Framework.
... [LT] 2 's high-tech activities for children have been empirically validated over two decades (Clements et al., 2011(Clements et al., , 2013Clements & Sarama, 2007Sarama et al., 2008Sarama et al., , 2012Sarama & Clements, 2004), providing significant, complementary, and unique high-tech learning experiences (Clements, 1985;Foster et al., 2018;Sarama & Clements, 2020a, see also the previous section, "Educational Technology and Early Childhood Mathematics Education"). They all develop along the LTs, of course. ...
Mathematics is a core component of cognition. Unfortunately, most young children and teachers cannot access research-based early childhood mathematics resources. Building on a quarter-century of research, we are developing and evaluating an innovative, integrated, intelligent, and interactive system of technologies based on empirically validated learning trajectories that provide the best personal and digital tools for assessing and supporting children's mathematics learning. This article reviews the research that guided us, then describes the design principles of the new project, justifying their selection using theory and research, and shares how the design principles helped address challenges in development. The goal is to provide teachers, caregivers, and children with high-quality resources to support early mathematics learning in the context of meaningful, motivating, challenging, and achievable experiences.
... To understand which instruction may be important for developing early mathematical skills, we need to understand how mathematical skills develop in children. Learning Trajectories suggests that sequence matters in early mathematical development ( (Sarama and Clements, 2004); Clements & Sarama, 2007). Similar to children's other developmental milestones like early movement (stand, walk, skip), this theory suggests that there is a progression in mathematics learning such that certain foundational skills must be mastered before progressing to more complex ones. ...
Nine techniques for imaginative visualization exercises are included in this study. Running learning exercises where students complete tasks that directly support one or more of the concepts the teacher wants to cover in the lesson is a common way to teach visualization. We evaluate our own learning experiences as a team of educators and visualization researchers. Our experiences and actions include breaking the assignments up into smaller components, taking into account various educational resources, and promoting discussion. It is our aim that this document will inspire, motivate, and help other instructors with visualization exercises. Our observations offer a foundation for creating best practices in visualization education as well as a first starting point for techniques and strategies to create imaginative visualisation learning experiences.
Denne artikkelen har som mål å studere hvordan barnehagebarn gjør seg matematiske erfaringer gjennom å bruke digitale verktøy. Ved å ta et sosiokulturelt perspektiv på læring og utvikling studeres den sosiale interaksjonen mellom barn og voksne når disse diskuterer og samhandler med ulike digitale verktøy. Analysene av transkriberte dialoger i to grupper, hver bestående av en voksen og to barn, gir innblikk i det matematiske læringspotensialet som oppstår når barna interagerer med de digitale verktøyene. Dette læringspotensialet knytter seg til de matematiske begrepene telling og tallsymbol, deriblant matematiskteoretiske komponenter som sortering, subitizing, parkobling og kardinalprinsipp. Samtidig viser analysen at interaksjonen med de digitale verktøyene har potensiale til å gi ytterligere næring til approprieringsprosessen av de implisitte matematiske begrepene som finnes i applikasjonene.
In this qualitative case study, we investigated the role of an advanced math curriculum with language scaffolding on the development of geometric and visual-spatial reasoning skills in young mathematically promising English learners (MPELs). Specifically, we examined the effects of providing MPELs with challenging and supportive math curriculum to facilitate the development of mathematical potential through a geometry unit. Twenty-one MPELs were randomly assigned to either an intervention or a comparison class. The data sources included audio recordings of class sessions, documents of math tasks, field notes, and test scores. Findings revealed that in the intervention class, tasks required more cognitive demands, and students were encouraged to contribute to classroom discourse more than in the comparison class. MPELs in the intervention class demonstrated greater gains in geometric reasoning compared to their peers in the comparison class. These findings underscore the point that challenging and supportive curricula can effectively nurture the mathematical potential of underrepresented gifted students.
TR Bu araştırma, okul öncesi öğretmenlerinin eğitsel amaçlarla kullandığı dijital teknoloji (DT) ve uygulamaların, dokümantasyon, değerlendirme, veli iletişimi ve katılımı boyutlarında incelenmesini amaçlamaktadır. Nitel bir çalışma tasarlanarak İstanbul'da görev yapan 11 okul öncesi öğretmeni ile yarı yapılandırılmış görüşmeler gerçekleştirilmiştir. Veriler, içerik analizi tekniği ile analiz edilmiş ve bunun sonucunda dört ana tema ortaya çıkmıştır: eğitsel amaçlarla genel olarak teknoloji kullanımı, saklama ve paylaşma, değerlendirme, veli katılımı ve iletişimi. Bulgular, DT’lerin eğitimsel içerik, çocukların aktif katılımı, izleme ve inceleme imkânı, belgeleri paylaşma ve uzun süre saklama, çocukların öğrenmelerini görünür kılma, akran öğrenmesi, oyunlaştırma, içerik çeşitliliği, katılımın artması, anında ve kolay iletişim gibi faydalar sunduğunu göstermiştir. Öte yandan, malzeme ve donanım eksikliği, kötüye kullanım, pedagojik zorluklar, velilerin zorlayıcı tutum ve talepleri gibi çekinceler de ifade edilmiştir. Elde edilen bulgular, alan yazındaki ilgili araştırma ve uygulamalar ışığında tartışılmıştır. Özellikle, erken çocukluk eğitiminde eğitsel amaçlarla DT kullanımının dokümantasyon, değerlendirme ve veli katılımı ve iletişimi boyutlarındaki entegrasyonu ve bu boyutların kendi arasındaki bütünsellik gereğine dikkat çekilmiştir. ENG This study examines preschool teachers’ digital technologies (DT) use for educational purposes, focusing on documentation, assessment, parent communication, and participation. A qualitative design was employed, involving semi-structured interviews with 11 preschool teachers in Istanbul. Content analysis revealed four key themes: general use of technology for education, storage and sharing, assessment, and parent involvement. Findings indicate that DT provides benefits such as enhanced educational content, children’s active participation, monitoring and reviewing opportunities, long-term document storage, visibility of learning, peer learning, gamification, diverse content, increased participation, and instant communication. However, concerns such as insufficient materials, misuse, pedagogical challenges, and demanding parent attitudes were also identified. The discussion highlights the need to integrate DT in early childhood education, particularly in documentation, assessment, and parent involvement, emphasizing the importance of coherence across these areas.
This all takes some explanation. Building Blocks, the short name for our project, is producing several products. The first we produced, called "DLM Math," is available now; I'll discuss that below. The Building Blocks software stand alone product, for PreK to grade 2, is building on that base and will be field tested starting this summer and throughout the following year.
DLM Math, which is available now, is for preschool, although the software is also suitable for kindergarten.
For those who mostly want the software (which at this time is packaged with the "Math Guide" and some manipulatives), order the DLM Express Math Resource Package, ISBN 007-572-4543, which sells for 1,500, or the national version (English and Spanish), 007-572-6254 which sells for $2446.
To order, call SRA/McGraw-Hill at 888-772-4543 or see www.sra4kids.com.
Used to be #1505; erased accidentally
See Curriculum Research paper
See my book
Students using Everyday Mathematics (EM), developed to incorporate ideas from the NCTM Standards, were at normative U.S. levels on multidigit addition and subtraction symbolic computation on traditional, reform-based, and EM-specific test items. Heterogeneous EM 2nd graders scored higher than middle- to upper-middle-class U.S. traditional students on 2 number sense items, matched them on others, and were equivalent to a middle-class Japanese group. On a computation test, the EM 2nd graders outperformed the U.S. traditional students on 3 items involving 3-digit numbers and were outperformed on the 6 most difficult test items by the Japanese children. EM 3rd graders outscored traditional U.S. students on place value and numeration, reasoning, geometry, data, and number-story items.