Designing Teaching: The Pythagorean Theorem

Wittmann, Erich Ch.

doi:10.1007/978-3-030-61570-3_7

Cited by 6 publications

(7 citation statements)

References 12 publications

(3 reference statements)

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“…The Pythagorean Theorem has been included in K-12 mathematics curriculum around the world because of its richness in mathematics reasoning, diverse historical and cultural origins, and accessibility to different levels of students (e.g. Wittmann, 2021). In many countries the theorem is given procedurally without justifications (e.g.…”

Section: Methodsmentioning

confidence: 99%

Teacher educator learning to implement equitable mathematics teaching using technology through lesson study

Huang,

Bonnesen,

Heath

et al. 2023

IJLLS

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PurposeThis paper examines how mathematics teacher educators (MTEs) learn to enact equitable mathematics instruction using technology through lesson study (LS).Design/methodology/approachA LS team with three MTEs conducted three iterations of LS on teaching the Pythagorean Theorem in an in-person, technology-mediated environment. Many forms of data were collected: Desmos activities, videos of research lessons (RLs), videos of MTE RL debriefings, artifacts of student learning in the Desmos Dashboard, and MTEs' written self-reflection. The authors investigate the teacher educators' learning through LS by analyzing the MTE debriefings of the RLs using Bannister’s (2015) framework for teacher learning in communities of practice.FindingsThe MTEs learned to enact equitable mathematics instruction using technology through addressing emerging issues related to intellectual authority and use of student thinking. Throughout the LS, the MTEs sought ways of promoting students' mathematical authority and using student thinking through features of the Desmos platform.Research limitations/implicationsThis study focuses on MTEs' learning without examining participating preservice teachers' learning. It demonstrates the benefits of LS for MTEs' professional learning.Practical implicationsThis study showcases how a research-based Desmos activity is used and refined to promote MTE learning how to implement equitable mathematics instruction.Originality/valueThe study contributes to better understanding of how LS could be used to develop MTEs' professional learning. Moreover, the dual process of participation and reification was concretized through diagnostic and prognostic frames in the LS context, which enriches the concept of community of practice.

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Section: Methodsmentioning

confidence: 99%

Teacher educator learning to implement equitable mathematics teaching using technology through lesson study

Huang,

Bonnesen,

Heath

et al. 2023

IJLLS

View full text Add to dashboard Cite

show abstract

“…The colorimetric equation in this study applies the CIE L*a*b* color system [ 16 ] together with the Pythagorean theorem [ 24 ]. Specifically, the Pythagorean theorem is applied to navigate the relationship between the −a* and +b* axes in CIE L*a*b*.…”

Section: Methodsmentioning

confidence: 99%

“…Expressing and handling the hue as θ facilitates processing of collected data allows for creation of the eventual phone application. The colorimetric equation in this study applies the CIE L*a*b* color system [16] together with the Pythagorean theorem [24]. Specifically, the Pythagorean theorem is applied to navigate the relationship between the −a* and +b* axes in CIE L*a*b*.…”

Section: Creating a Colorimetric Equation To Transform The Spectromet...mentioning

confidence: 99%

Developing a Colorimetric Equation and a Colorimetric Model to Create a Smartphone Application That Identifies the Ripening Stage of Lady Finger Bananas in Thailand

Tanut,

Tatomwong,

Buachard

2023

Sensors

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This article develops a colorimetric equation and a colorimetric model to create a smartphone application that identifies the ripening stage of the lady finger banana (LFB) (Musa AA group ‘Kluai Khai’, กล้วยไข่ “gluay kai” in Thai). The mobile application photographs an LFB, automatically analyzes the color of the banana, and tells the user the number of days until the banana ripens and the number of days the banana will remain edible. The application is called the Automatic Banana Ripeness Indicator (ABRI, pronounced like “Aubrey”), and the rapid analysis that it provides is useful to anyone involved in the storage and distribution of bananas. The colorimetric equation interprets the skin color with the CIE L*a*b* color model in conjunction with the Pythagorean theorem. The colorimetric model has three parts. First, COCO-SSD object detection locates and identifies the banana in the image. Second, the Automatic Power-Law Transformation, developed here, adjusts the illumination to a standard derived from the average of a set of laboratory images. After removing the image background and converting the image to L*a*b*, the data are sent to the colorimetric equation to calculate the ripening stage. Results show that ABRI correctly detects a banana with 91.45% accuracy and the Automatic Power-Law Transformation correctly adjusts the image illumination with 95.72% accuracy. The colorimetric equation correctly identifies the ripening stage of all incoming images. ABRI is thus an accurate and robust tool that quickly, conveniently, and reliably provides the user with any LFB’s ripening stage and the remaining days for consumption.

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“…The earlier research (Lo, Zhou, & Liu, 1968) separated proofs into four sections, including algebraic, geometric, quaternionic, and dynamic. However, it is insufficient for teachers to solely focus on proving theories (Wittmann, 2020), which emphasizes the need for real-life applications (Baki et al, 2009).…”

Section: Teaching and Learning The Pythagorean Theoremmentioning

confidence: 99%

Comparative Analysis of Contents on the Pythagorean Theorem in Mathematics Textbooks from America and China

Chen

2024

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Recent studies have demonstrated that textbook analysis is an essential method of review in mathematics education. This study conducted a comparative analysis of textbooks from America and China to evaluate how students are expected to learn information pertaining to the Pythagorean theorem. This was accomplished using the 5D model approach, specifically focusing on contents, mathematical activities, complexity levels, answering forms, and contextual features. The results showed that Chinese textbooks were slightly more complex, focused on proving the Pythagorean theorem, and presented students with real-life problems. In contrast, American textbooks were mainly concentrated on basic mathematics concepts. These findings suggest that American students should solve more items that require deep thinking, while Chinese students should improve their communication skills by practicing open-ended questions. Future studies can add to the literature by investigating other mathematics materials across a greater number of countries, thus contributing to a more globalized conversation on relevant education methods.

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Designing Teaching: The Pythagorean Theorem

Cited by 6 publications

References 12 publications

Teacher educator learning to implement equitable mathematics teaching using technology through lesson study

Teacher educator learning to implement equitable mathematics teaching using technology through lesson study

Developing a Colorimetric Equation and a Colorimetric Model to Create a Smartphone Application That Identifies the Ripening Stage of Lady Finger Bananas in Thailand

Comparative Analysis of Contents on the Pythagorean Theorem in Mathematics Textbooks from America and China

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