C285 Task 4 Tyler P

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Western Governors University *

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C285

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Mathematics

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Apr 3, 2024

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Tyler Phanhthavilay December 9, 2023 C285 Task 4 A1. Content Standard: Common Core State Standards for Mathematics (CCSSM) – High School Geometry: CCSS.MATH.CONTENT.HSG.CO.A ( High School: Geometry | Common Core State Standards Initiative , n.d.). Aligned Secondary Geometry Topic : Congruence and Similarity A2. Historical Contribution: The teacher would integrate the historical contribution of ancient Greek mathematicians known as Euclid, and their work towards the concepts of geometry. More specifically, how Euclid’s “Elements” showed the foundations of congruence and similarity of shapes. Euclid showed the similarity of triangles and created proofs and theorems such as that the sum of all the angles within a triangle would equate to 180 degrees. Integrating the theorems that Euclid had created throughout history into an activity would engage the students and show how the concepts they were learning were something this mathematician created a long time ago. Euclid also used tools such as the ruler and compass to facilitate geometry concepts (Artmann, 2019). Another mathematician who made great impact on the foundation of geometry was Pythagoras who was a Greek philosopher around 500 BCE. He not only helped the foundation of geometry to form but he also advanced it. One example of this can be demonstrated by a theorem he named after himself called, “Pythagoras Theorem.” This theorem states that if given a right triangle, the hypotenuse can be computed by the squares on both legs. This is demonstrated with: Now this historic mathematician can be incorporated into the lesson as a very important theorem to know as it is taught in almost every math classroom. To set the importance, the teacher would read about his history as a mathematician, who he was influenced by and make sure to state his name a bunch. Then the students would match his name to this theorem after hearing it so many times which was reinforced by the teacher (Mark, 2019). A3. In-class Activity: Euclidean Explorations: Geometry’s Mysteries

Tyler Phanhthavilay December 9, 2023 C285 Task 4 Objectives: Students will explore congruence and similarity with geometry concepts through a historical perspective. They will understand the contribution of Euclid and the mathematical impacts that he provided to the works of geometry. Materials: 1. Copies of Euclid’s “Elements” with excerpts and summaries. 2. Rulers, Protractors, Compasses 3. Whiteboard 4. Markers 5. Notebook and Pencil Procedure: -Intro : I would read the excerpt of Euclid and explain the historical context of this Greek Mathematician. Explain the importance of Euclid’s “Elements” in geometric principals and the framework of geometry (Artmann, 2019). Discussion : Have the classroom answer a set of questions that tested their knowledge on Euclid’s “Elements” that showed their understanding of congruence and similarity. Walk around the classroom and answer questions and clear misconceptions. Hands-on Activity : Split the students into groups of 4-5 and give them a specific theorem from Euclid’s “Elements.” Have the students use the tools to try and replicate the theorems by making their own examples. Then have each group to demonstrate their theorem on the whiteboard while having the other students take notes on that theorem that related to Euclid. Then after, engage discussion with the class to talk about what they noticed, similarities between theorems and questions they may have. Application : Give the students real-world questions that they can solve with their theorems and knowledge about congruence and similarity. Have the students answer the questions and then discuss how Euclidean principals an impact and influence on modern questions have that we still answer today that relate to mathematics and architecture. A3a. The students could gain a deeper understanding of congruence and similarity through the history of Euclid because it gives them a higher level of engagement as it connects a person and their history to the math concepts they learn. The cultural impact of Euclid’s work gives ideas of how geometry is connected to society back then and then they can think and brainstorm about how it relates to modern day society. Then as they compare the old geometric methods and see how it developed into the modern ones that they will use for later lessons it allows them to see the development and the thought process of the geometrical concepts. This allows them to gain critical thinking skills when solving geometrical questions as they have a broader view to connect to geometry. Learning the most basic and raw explanations of math concepts will allow

Tyler Phanhthavilay December 9, 2023 C285 Task 4 the students to grasp the concepts easier and have a better understanding of the subject in general (Artmann, 2019). B. Incorporating History into Mathematical Instruction: By bringing in History into Mathematical instruction enhances student learning in a lot of ways such as, contextualization of the math concepts. In the article, it explains that there was a Math Reform movement in 1950-1970 where it talks about the failures in the fields of governance, ideology, economics, and sociology. By incorporating history of math to students, it enhances and deepens their learning by showing how math evolved over time and how it gave context for better strategies and approaches for other societies (Menghini, 2020). C1. German Tank Problem The German tank problem was a statistical issue that occurred during World War II. Allied forces wanted to figure out how many tanks were created by the Germans by looking at the serial numbers from the ones retrieved. Although, the Germans wanted to mislead the Allies by putting a random set of serial numbers on their Mark V Tanks. Yet, the Allied statisticians more specifically the British intelligence analyst Patrick D. Mainland created a method that estimated the total number of tanks. He used statistical inference from the serial numbers to figure it out (Stephanie, 2016). C2. Impact on Probability and Statistics The German tank problem made a lot of progression in the fields of statistics because it used a real-life application of statistical inference. This method allowed for the Allies to estimate the total number of tanks based on the serial numbers. It showed the concepts of probability sampling and estimation techniques. This brought a spotlight into statistical analysis through the military intelligence and made making informed decision and guessing reasonable through limited data by using statistics. Through it they estimated that there were 245 tanks produced per month which was 10 off the correct answer giving a very high validity to the field of statistics (learnwithalbert, 2016). C3. History in the Classroom One way I could introduce history and incorporate it within a lesson to engage the students is through simulation exercises. First the teacher would give background information on the German Tank Problem and then how the statisticians found a very accurate estimation on the production. After this, I would have the students go on their laptops to a simulation where they act as intelligence analysts by giving them tank serial numbers and using those with statistic models and formulas to estimate the total tanks produced per month. This would have the students engaged in the assignment while learning and practicing statistic problems. It would also have them more motivated as it shows real life application to the work they are learning.

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