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Abstract

For early childhood, the domain of geometry and spatial reasoning is an important area of mathematics learning. Unfortunately, geometry and spatial thinking are often ignored or minimized in early education. We build a case for the importance of geometry and spatial thinking, review research on professional development for these teachers, and describe a series of research and development projects based on this body of knowledge. We conclude that research-based models hold the potential to make a significant difference in the learning of young children by catalyzing substantive change in the knowledge and beliefs of their teachers. KeywordsScaling up professional development–Geometry–Spatial reasoning–Learning trajectories–Early childhood
... Spatial thinking is associated with various disciplines and is correlated with achievements in both mathematics (e.g., Clements & Sarama, 2009;Mix, 2019;Mulligan et al., 2018), and other STEM disciplines (e.g., Newcombe, 2010Newcombe, , 2013Newcombe & Shipley, 2015;Pruden et al., 2011). However, there are few opportunities for students to engage in spatial thinking in school (Clements & Sarama, 2011;Sinclair & Bruce, 2015;Whiteley et al., 2015). Because spatial thinking is associated with achievements in mathematics in addition to achievements in other disciplines (Bruce et al., 2017), it is appropriate to investigate the ways of thinking involved in an iSTEM curricular approach with attention to spatial ways of thinking. ...
... To date, there are few iSTEM curriculum materials that emphasize mathematical concepts as the anchor discipline (English, 2016;Fitzallen, 2015), despite evidence of the benefits of iSTEM curricular approaches on mathematical achievement and development of mathematical understanding (Stohlmann, 2018). Additionally, there are few opportunities to engage in spatial thinking in schools (Clements & Sarama, 2011;Sinclair & Bruce, 2015;Whiteley et al., 2015), despite the role of spatial thinking in understanding both mathematics (e.g., Mix, 2019) and other disciplines (e.g., Newcombe & Shipley, 2015;Pruden et al., 2011). Our report illustrates a purposeful integration approach with a focus on mathematics in the context of science within an iSTEM unit. ...
Conference Paper
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Integrated science, technology, engineering, and mathematics (iSTEM) education allow learners to utilize multiple disciplinary perspectives. However, the discipline of mathematics remains underrepresented in iSTEM curriculum. To explore the nature of mathematical thinking with an iSTEM curricular approach that emphasizes mathematics, we investigated the thinking of a preservice mathematics teacher, Alex (pseudonym), who engaged in a task-based digital activity involving radian angle measure in the context of light reflection. Findings suggest that Alex's ways of thinking comprise mathematical terminology, concepts, and processes, including mathematical ways of thinking about light reflection. The findings in this report suggest that emphasizing mathematics in this iSTEM context provided an opportunity for new ways of thinking about radian angle measure, and about how angle measure relates to light reflection.
... These problems were also documented in US pre-school and primary school teachers, not just teacher candidates (Sarama & Clements, 2009). This was also seen to negatively affect the geometry content and techniques that American teachers taught to their students (Clements & Sarama, 2011). According to the results of the studies held in the UK, Scotland, Israel, Zimbabwe, and Malaysia, teachers also had various problems in terms of geometry skills (see Fujita & Jones, 2006a, 2006bMarkowitz & Patkin, 2020;Sunzuma & Maharaj, 2019). ...
... Other researchers documented deficiencies invisualizing and solving the geometric figures stemming from a lack classroom practice, lack of appropriate teaching methods and materials, lack of prior knowledge about basic geometric concepts, insufficient teacher-student interaction, lack of motivation in the classroom, and unsuitable learning environment (Chaudhary, 2019). Researchers have also documented problems with early geometry teaching, including a lack of problem-solving (Sulistiowati et al., 2019), a lack of collaborative learning (Chianson et al., 2010), insufficient technology support (Clements & Sarama, 2011;Rohendi et al., 2018) and not allocating time for geometry as much as the other topics in mathematics (such as counting) (Moss et al., 2015;Sarama, 2002). Even parents neglect geometry in favor of numeracy and counting (Zippert & Rittle-Johnson, 2020). ...
Article
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Mind mapping refers to the use of a specific graphic organizer to support learning. This paper describes the effect of mind mapping on pre-schoolers' geometric learning. Using a pre-and post-test control group quasi-experimental model, researchers found that the use of mind maps resulted in a statistically significant difference in geometry learning for pre-schoolers (mean age = 65.0 months). These results are discussed in terms of their ramifications for preschool geometry education, as well as for the use of mind maps with preschool children.
... Geometri dimensi tiga merupakan bagian dari geometri yang membahas bangun ruang atau bangun dimensi tiga dengan objek-objek yang bersifat abstrak (Negoro & Harahap, 2014). Objekobjek dimensi tiga seperti titik, garis, bidang, balok, kubus, bola, dan lain-lain, dimana semuanya adalah objek-objek yang diperoleh dari proses abtraksi berdasarkan benda-benda konkret yang ditemukan dalam keseharian (Clements & Sarama, 2011;Couto & Vale, 2014). Sehingga, sangat diharapkan upaya dari pendidik untuk mengembangkan pemahaman peserta didik pada konsep geometri sebaiknya dilakukan dengan aktivitas memanipulasi berbagai objek spasial atau bendabenda nyata (pengalaman kongkrit), brainstroming (konsep perumpamaan). ...
... Sehingga, sangat diharapkan upaya dari pendidik untuk mengembangkan pemahaman peserta didik pada konsep geometri sebaiknya dilakukan dengan aktivitas memanipulasi berbagai objek spasial atau bendabenda nyata (pengalaman kongkrit), brainstroming (konsep perumpamaan). Hal ini bertujuan agar peserta didik dapat memiliki pengetahuan yang sifatnya abstrak (abstract representation) tentang geometri dimensi tiga (Clements & Sarama, 2011;Browning et al., 2014;Panaoura, 2014). ...
Article
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Geogebra adalah software untuk mempelajari geometri dimensi tiga. Pengembangan buku digital berupa GeoGebra Book pada materi dimensi tiga diharapkan menjadi sumber belajar dan memfasilitasi peserta didik untuk belajar mandiri. Tujuan penelitian ini untuk mengetahui prosedur pengembangan dan kualitas GeoGebra Book pada materi dimensi tiga. Penelitian ini merupakan penelitian pengembangan menggunakan model ADDIE. Subjek penelitian terdiri dari ahli media, ahli materi, guru matematika, dan peserta didik kelas XI. Instrumen penelitian berupa lembar validasi untuk ahli materi dan ahli media, dan angket respon peserta didik. Data kualitatif yang dianalisis adalah data hasil studi literatur. Sedangkan data kuantitatif yang dianalisis adalah data hasil validasi dan respon peserta didik. Berdasarkan hasil penelitian disimpulkan bahwa (1) Geogebra Book materi dimensi tiga dikembangkan dengan menggunakan model ADDIE yang meliputi 5 tahapan yaitu: (a) tahap analyze, yaitu menganalisis kebutuhan media pembelajaran, materi pembelajaran, dan karakteristik peserta didik; (b) tahap design, yaitu mendesain media pembelajaran dan instrumen penelitian; (c) tahap development, yaitu membuat produk dan validasi ahli; (d) tahap implementation, setelah GeoGebra Book materi dimensi tiga dinyatakan valid, selanjutnya diimplementasikan terhadap guru dan peserta didik; dan (e) tahap evaluation, yaitu menganalisis hasil respon peserta didik. (2) Kualitas media GeoGebra Book pada materi dimensi tiga termasuk kategori sangat baik.
... Belajar matematika di kelas satu dan dua sekolah dasar di tahuntahun awal, sangat bergantung pada peran guru, karena merekalah yang pada akhirnya menentukan apa yang diterapkan di kelas mereka. Selain itu, Clements & Sarama (2011) berpendapat bahwa kepentingan yang lebih besar harus diberikan untuk pengembangan profesional guru untuk tujuan terlibat dalam geometri dengan anak-anak. Mereka juga menekankan bahwa pengetahuan dan keyakinan guru sekolah dasar tentang geometri harus ditingkatkan. ...
... Kurikulum menentukan bentuk lingkaran, segitiga, persegi, persegi panjang, elips, segiempat, segi lima dan segi enam. Sedangkan untuk bangun ruang (tiga dimensi), anak diharapkan dapat memberi nama bangun ruang dan mengenali bentuknya (Clements & Sarama, 2011). Kurikulum matematika sekolah dasar menunjukkan kubus, silinder, bola, kubus, prisma, kerucut dan limas. ...
Article
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Penelitian ini bertujuan untuk (1) menyelidiki pengetahuan guru sekolah dasar tentang bentuk-bentuk bangun datar dan bangun ruang, dan (2).mengeksplorasi sikap dan keyakinan guru sekolah dasar tentang geometri dan pengajarannya. Penelitian ini menggunakan pendekatan deskriptif dengan metode campuran penelitian kuantitatif dan kualitatif. Tiga puluh guru sekolah dasar di wilayah kecamatan Semarang Selatan sebagai partisipasi dalam penelitian ini dan menanggapi kuesioner yang terdiri dari item tertutup dan terbuka. Hasil temuan penelitian ini mendeskripsikan bahwa masih banyak guru sekolah dasar yang kurang memiliki pengetahuan tentang bentuk bangun datar dan bangun ruang. Temuan penelitian ini diperkuat dengan data yang menunjukkan bahwa mayoritas guru sekolah dasar tidak mendasarkan penjelasan mereka tentang bentuk geometri pada properti mereka, tetapi terutama hanya pada penampilan visual (gambar) geometris saja. Artinya dalam hal penegtahuan geometri, guru sekolah dasar kurang menguasai definisi dan sifat-sifat tentang bentuk bagun datar. Guru sekolah dasar memegang teguh pentingnya sikap dan keyakinan yang memotivasi untuk melibatkan anak-anak dalam kegiatan yang berhubungan dengan pembelajaran geometri. Para guru sekolah dasar ingin belajar geometri dengan cara yang eksperiensial dan menyenangkan. Mereka ingin mengubah pengalaman ini untuk anak-anak dan menyampaikannya kepada anak-anak sehingga mereka merasa bahwa belajar itu menyenangkan.
... Rittle-Johnson et al. (2019) found evidence that spatial reasoning in the early years is a strong predictor of future mathematics achievement. However, it has been noted that despite the clear importance of geometry and spatial reasoning for future mathematical progress, these areas are seldom explored in early years settings or related research (Clements & Sarama, 2011;National Council of Teachers of Mathematics, 2006), or in the education of early years teachers (Dindyal, 2015;Ginsburg et al., 2006;Moss et al., 2015). ...
... Stephen Hawking said "Equations are just the boring part of mathematics. I attempt to see things in terms of geometry" (Larsen, 2005, p. 43), yet geometry was the least popular area of mathematics among teachers surveyed by Clements and Sarama (2011). The van Hieles argued that geometric thinking could be accelerated by good teaching (Mason, 1998), making this a pressing issue. ...
Article
Mathematics in early years settings is often restricted to learning to count and identifying simple shapes. This is partly due to the narrow scope of many early years curricula and insufficient teacher training for exploring deeper mathematical concepts. We note that geometry is an area particularly neglected. In an innovative year-long project, a group of university-based mathematicians and early years teachers collaborated on a child-led exploration of ‘patterns in nature.’ The early years teachers ran the project within the setting, meeting regularly with the mathematicians to discuss potential areas of interest, and to highlight the children’s mathematical thinking. We found that, with the appropriate environment and guidance, the children naturally displayed deep levels of geometrical thinking and found enjoyment and satisfaction in the exploration of mathematical ideas. We define what we mean by the term ‘deep geometrical thinking’ and demonstrate this by looking at three excerpts through the lens of the van Hiele levels of geometric thought, finding that the children are capable of exhibiting thought at level 3 (abstraction), more advanced than previously thought of children of this age. Using a second taxonomy we also assess the range of skills across which they are demonstrating such geometric thought.
... The findings indicate that students do not possess sufficient knowledge of a concept's definition, implying a restricted concept image. It makes it harder for students to grasp and apply the concept definition (Clements & Sarama, 2011). Thus, teachers must create a learning situation that enables students to construct knowledge and maximize their potential. ...
Article
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The concept image comprises all the cognitive structures in an individual's mind connected with a specific notion. However, if the learning situation is not relevant to help students construct knowledge and provide meaningful experiences, it will affect their concept image. This study aims to examine the concept of the image of the Pythagorean theorem during online-based learning. The research is a qualitative approach, and the method is phenomenological to understand the meaning for the participants of their concept image. Initially, this study enrolled 66 students. Two students were selected as research subjects and acted as resource persons to provide adequate contextualization based on students who answered right and wrong. Data collection combines data from the outcomes of testing the Pythagorean theorem test, interviews, and literature studies. The data analysis technique employed is Interpretative Phenomenological Analysis (IPA). There are six categories of student concept image. Based on in-depth interviews with two students who answered correctly and incorrectly, students were given inconsistent meanings of the Pythagorean theorem due to the learning situation to improve students' understanding of the subject.
... Mathematical modelling with GeoGebra 3D Graphing Calculator or Autodesk ® Tinkercad ® could support students during the remote teaching and increase the learning outcome in modelling geometric shapes. Thus, the important spatial reasoning in geometry (Sinclair & Bruce, 2015) could be widely supported by these technologies (Clements & Sarama, 2011;Liu et al., 2019). The identification of the needed scaffolding, on how to use the augmented information (Bacca Acosta et al., 2019) plays an important role. ...
Article
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In reaction to the COVID-19 pandemic, the government of Luxembourg suspended in-school teaching and learning towards remote teaching. A survey conducted by the Ministry of Education after three weeks of confinement, showed that more than half of the parents faced difficulties when using remote teaching with their students. To tackle this new challenge, we adapted our research to the use of augmented reality, digital and physical mathematical modelling in remote mathematics education for elementary schools. The elementary school students (aged 5 to 12) created cultural artifacts (i.e., Easter egg cups) during the confinement. In this paper, we will describe mathematical modelling in remote teaching and further concentrate on parents' perspectives, who played an essential role in assisting their children. Moreover, we will discuss different didactical principles that emerged from the task design during the study through parents' eyes. Thus, understanding parents' perspectives became highly important in enabling us to improve task designs and related pedagogical approaches in remote teaching. The data collected in this study included semi-structured interviews with students, parents, and teachers as well as questionnaires and field notes. We followed an exploratory stance with our data analyses, primarily utilizing grounded theory (Corbin & Strauss, 1990, 2014) approaches. Through the insights we gained from our findings, we aim to explain how the parents perceived teaching and learning mathematical modelling in our experiments, how they scaffolded the given tasks, and what support they required and would need in future remote teaching.
... Knowledge about geometric shapes is considered a key element of young children's spatial thinking (Clements & Sarama, 2011) and includes both identifying shapes by name and understanding the defining features of shapes (National Research Council, 2009;van Hiele, 1999). One way to promote learning about geometric shapes is to include multiple exemplars that draw attention to, and allow for elaboration of, the defining features of shapes (e.g., rectangles with different dimensions or typical and atypical triangles; Clements, 2003;Fisher et al., 2013). ...
Article
Shape puzzles offer opportunities for families to talk about geometric concepts, which supports early spatial reasoning. However, puzzle features (i.e., similarity of shapes) may influence the nature of parent-child talk about shapes (e.g., labeling shapes vs. elaborating on shape properties). In this study, 128 dyads of parents and children (ages 30–47 months) completed both Typical and Highly Alignable (HA) shape puzzles. Compared to the HA puzzle, there was more shape labeling during the Typical puzzle; the HA puzzle elicited more elaborative shape talk (particularly comparing and contrasting shapes). Further, the HA puzzle elicited more elaborative shape talk when similar shapes were distributed on different rows rather than arranged side-by-side. Follow-up analyses found the HA puzzles were more difficult for children to complete. Findings suggest that including similar shapes and manipulating the arrangement of shapes may increase the difficulty of puzzles and elicit increased parent support and enhanced parent-child spatial language during puzzle play.
... A lack of effective teacher training for early math education has been regarded as one of the major barriers to support children's math learning in early childhood level (Ginsburg, Lee, & Boyd, 2008;Clements & Sarama, 2011). The recent research documents that well-designed intensive teachers training courses and on-site coaching have significantly improved teachers' CROSS-CULTURAL COMPARISONS 28 mathematics-related beliefs and knowledge, as well as children's mathematical skills (Hojnoski, Polignano, & Columba, 2016;Piasta, Logan, Pelatti, Capps, & Petrill, 2015). ...
Chapter
Thus far, we have focussed on the macro issues of the social, pedagogical, and economic perspectives of STEM discussed in Chap. 2; the impact of digital technologies on children’s learning in Chap. 3; and the role of play and play-based learning in Chap. 4. In this chapter, we turn our attention towards early childhood educators who are largely responsible for ensuring a positive experience of STEM for young children.
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We investigated criteria preschool children use to distinguish members of a class of shapes from other figures. We conducted individual clinical interviews of 97 children ages 3 to 6, emphasizing identification and descriptions of shapes and reasons for these identifications. We found that young children initially form schemas on the basis of feature analysis of visual forms. While these schemas are developing, children continue to rely primarily on visual matching to distinguish shapes. They are, however, also capable of recognizing components and simple properties of familiar shapes. Thus, evidence supports previous claims (Clements & Battista, 1992b) that a prerecognitive level exists before van Hiele Level 1 ("visual level") and that Level 1 should be reconceptualized as syncretic (i.e., a synthesis of verbal declarative and imagistic knowledge, each interacting with the other) instead of visual (Clements, 1992).
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“Teachers are the key to academic achievement for students.” This statement is widely accepted, but professional development in early childhood mathematics education faces a number of barriers. What are those barriers? What do teachers have to say about developing their own knowledge of the teaching and learning of mathematics? What should be done to address these problems? Answering these questions was the goal of a recent project funded by the National Science Foundation called “Planning for Professional Development in Pre-School Mathematics: Meeting the Challenge of Standards 2000.” This article shares some of the answers I found in the course of that project.
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The purpose of this research was to "scale up" the implementation of four research-based practices in inclusive classrooms. Twenty-nine teachers from six elementary schools participated in a 2-week professional development program and received extensive follow-up support from researchers throughout the school year. Our objective was to better understand the barriers and facilitators experienced by teachers determined to be high implementers (9), moderate implementers (9), and low implementers (11). Data sources included interviews, teacher logs, and classroom observations. Teachers across implementation levels lamented a lack of instructional time. Yet how teachers dealt with barriers differed. High-implementing (HI) teachers reported administrative support as their top facilitator, while five moderate-implementing (MI) teachers described a lack of administrative support. School effects were noted.