dkm2 task 4 (1)

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Western Governors University *

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GKM2

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Mathematics

Date

Apr 29, 2024

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pdf

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3

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John Brown DKM2 Task 4 4/23/24 A. Create an original, engaging, in-class activity that uses diverse historical contributions to a secondary geometry topic by doing the following: 1. Identify a content standard and an aligned secondary geometry topic that will be the basis of your in-class activity. The content standard is the Common Core State Standards for Mathematics (CCSSM) and the secondary geometry topic is the Properties of Quadrilaterals. Once such standard is: CCSS.MATH.CONTENT.5.G.B.3 The standard focuses on the relationships between different types of quadrilaterals and learning that certain properties are shared. For example, all rectangles have four right angles and squares are rectangles so all squares have four right angles. 2. Explain the diverse historical contributions that will be integrated into your in-class activity. One historical contribution that can be integrated into this activity is the development of geometry in ancient civilizations by focusing on the contributions of ancient Egyptians in understanding and using quadrilaterals. One way that the ancient Egyptians have demonstrated their knowledge of the properties of quadrilaterals was in the building of the pyramids. The sides of the pyramids are large quadrilateral faces made up of squares and rectangles. The measurements of precise angles and dimensions of each block were necessary to maintain the symmetry and stability that were required for the pyramids to last thousands of years. Lehner, M. (1997). The Complete Pyramids: Solving the Ancient Mysteries. Thames & Hudson. 3. Describe an original, engaging, in-class activity that aligns with the geometry topic and standard from part A1 and uses the diverse historical contributions from part A2. Note: Historical facts and video links alone are not sufficient. Examples of effective integration of history to engage students in learning mathematics include interesting stories about a mathematician involved in developing that mathematical topic, comparing historical and contemporary approaches to solving a problem, and discussing the historical impacts (cultural or technological) of applying the mathematics. I will call my in-class activity “Quadrilaterals through history”. During this activity students will explore the properties of quadrilaterals through a historical lens and try to understand how ancient Egypt civilizations contributed to our understanding of these shapes. The students will begin by discussing the importance of quadrilaterals in everyday life and
historical contexts. The teacher will show images of Egyptian pyramids and hieroglyphs and discuss how ancient Egyptians used quadrilaterals in their architecture and art. The students will create their own pyramids using quadrilaterals. The teacher will provide geometric tools for students to explore the properties of quadrilaterals. They can measure angles, sides, and diagonals to discover patterns and relationships. This will all lead to a discussion on how understanding the historical context enhances their understanding of quadrilaterals and geometry as a whole. a. Explain how students could engage with the historical component of the activity in part A3 to deepen their understanding of the geometry topic. Include specific examples of how the historical component from part A3 connects to student understanding of the geometry topic. Students engage with historical components by actively exploring how the ancient Egyptian civilization used quadrilaterals in their lives. For example, they connect the Egyptian use of quadrilaterals in pyramid construction to understand the relationship between base angles and side lengths. B. Explain how incorporating history into mathematical instruction improves student learning. Include evidence from one peer-reviewed research article as part of your explanation. Incorporating history into mathematical instruction enhances student learning by providing context, relevance, and a deeper understanding of mathematical concepts. Research by Rina Zazkis and Bharath Sriraman (2010) titled "History in Mathematics Education: The Historical Case of Negative Numbers" shows that historical narratives not only engage students but also help them grasp abstract concepts by connecting them to real-world contexts. By understanding the cultural and historical roots of mathematical concepts, students develop more appreciation for the subject and are more likely to retain knowledge and apply it effectively. C. Explore a significant event or discovery that was directly connected to the world’s understanding of probability and statistics as fields of mathematical study by doing the following: 1. Identify and briefly describe one of the following events or discoveries: • German tank problem • Trial of the Pyx • false positive paradox • Florence Nightingale and the Scutari barracks • Edmond Halley and annuities • Enigma machine • probability and statistics event or discovery of your choice Florence Nightingale and the Scutari Barracks:
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