A Comparison of U.S. and Chinese Geometry Standards through the Lens of van Hiele Levels

Zhou, Lili; Liu, Jinqing; Lo, Jane-Jane

doi:10.46328/ijemst.1848

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…Yet, CCSSM elementary standards begin with visual-level reasoning (K.G.A.1-3), which is theoretically outdated and unnecessarily delays development of elementary students' geometric reasoning. Moreover, there is an insufficient quantity and progression of descriptive level (i.e., property focused) standards to foster efficient growth to the informal deduction level (Zhou et al, 2022).…”

Section: Misapplication Of Van Hiele Theory In Ccssmmentioning

confidence: 99%

“…As Zhou, Liu, and Lo's (2022) analysis of the CCSSM geometry standards revealed, CCSSM provides insufficient experiences about properties to help children develop more advanced geometric reasoning required in secondary school and beyond. Despite properties being necessary to define every shape, the CCSSM does not provide a logical progression of properties.…”

Section: Current Shape Sequence In the Common Core State Standards Fo...mentioning

confidence: 99%

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Simplest Shapes First! But Let's Use Cognitive Science to Reconceive and Specify What “Simple” Means

Nurnberger‐Haag

Thompson²

2022

Mind Brain and Education

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Children's informal and formal learning experiences with geometric shapes currently result in misconceptions that persist into adulthood. Here, we combine research from mathematics education as well as cognitive science pertaining to concepts, categories, and learning strategies to propose a more optimal progression that is better specified and justified than the current standards. To do so, we reframed what constitutes a “simple” shape from perceptual simplicity to simplicity of properties. Our Property‐Based Shape Sequence uses property‐based criteria of what makes shapes “simple” and progresses in a way that affords opportunities for learners to develop hierarchical conceptions of two‐dimensional and three‐dimensional shapes. Our goals are threefold: (1) recommend an optimal, mathematically‐correct shape learning sequence, (2) correct misconceptions that adults and children harbor about shapes, and (3) encourage cross‐disciplinary collaborations between mathematics education and psychology researchers to validate the proposed learning sequence.

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Section: Misapplication Of Van Hiele Theory In Ccssmmentioning

confidence: 99%

Section: Current Shape Sequence In the Common Core State Standards Fo...mentioning

confidence: 99%

Simplest Shapes First! But Let's Use Cognitive Science to Reconceive and Specify What “Simple” Means

Nurnberger‐Haag

Thompson²

2022

Mind Brain and Education

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A comparative analysis of congruent triangle units in textbooks from China and the United States

Lo,

Zhou,

Liu

2024

Asian Journal for Mathematics Education

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In this article, we report findings from a comparative study of the introduction and development of triangle congruence in two textbooks: a high school geometry textbook from the United States and an eighth-grade mathematics textbook from China. Using the mathematics curriculum as a story (MCS) framework developed by Dietiker and additional coding schemes, we illustrate how each textbook designs its congruent triangle lessons with the goal to provide students a fertile ground for the development of geometry reasoning and proof. Through the analysis of the characters, actions, settings, and plots of each story, we identify both similarities and differences. Both textbooks introduced the same sets of side–angle criteria that proved the existence of the unique triangle as well as that did not support a unique triangle. Yet, the U.S. textbooks introduced side–angle–side first while the Chinese textbooks started with side–side–side. In addition, the findings demonstrate the illuminating power of the MCS framework to fill the gap of current textbook analysis research.

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The contribution of working memory and spatial perception to the ability to solve geometric problems

Galitskaya,

Drigas,

Antoniou

2024

Sci. Electronic Arch

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Geometry is a branch of mathematics that deals with the properties of space, including distance, shape, size, and the relative position of figures. It is one of the oldest branches of mathematics and has applications in various fields such as science, art, architecture, and even in areas seemingly unrelated to mathematics. Studies show that working memory and spatial perception contribute to students' geometry performance. This paper presents multiple studies demonstrating the brain regions activated when solving geometric problems. Interestingly, the brain areas activated when solving algebraic problems are different from those activated when solving geometric problems. Finally, multiple studies are presented that indicate students with learning difficulties lag in geometry, as solving geometric problems requires good reading and arithmetic skills.

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A Comparison of U.S. and Chinese Geometry Standards through the Lens of van Hiele Levels

Cited by 3 publications

References 13 publications

Simplest Shapes First! But Let's Use Cognitive Science to Reconceive and Specify What “Simple” Means

Simplest Shapes First! But Let's Use Cognitive Science to Reconceive and Specify What “Simple” Means

A comparative analysis of congruent triangle units in textbooks from China and the United States

The contribution of working memory and spatial perception to the ability to solve geometric problems

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