ummarize the below passage by including the setting or environment, content or subject, lesson or activity, and the organization of students or groups.  Entitled "Stock Up," this math class focuses on fraction and decimal concepts through a stock market simulation. The class features 19 gifted 6th graders from 8 schools, nine 11-year-olds, and ten 12-year-olds. All are native English speakers of high to low middle-class status and are state-identified as academically gifted. With no designated curriculum, I create and acquire my units and resources using gifted standards. I use "systems" and "relationships" concepts to teach accelerated math standards. I accommodate my students' exceptionalities through adequate challenges and higher-level thinkin

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Summarize the below passage by including the setting or environment, content or subject, lesson or activity, and the organization of students or groups. 

Entitled "Stock Up," this math class focuses on fraction and decimal concepts through a stock market simulation. The class features 19 gifted 6th graders from 8 schools, nine 11-year-olds, and ten 12-year-olds. All are native English speakers of high to low middle-class status and are state-identified as academically gifted. With no designated curriculum, I create and acquire my units and resources using gifted standards. I use "systems" and "relationships" concepts to teach accelerated math standards. I accommodate my students' exceptionalities through adequate challenges and higher-level thinking. Inquiry and social learning contexts are used to foster problem-solving skills, higher-order thinking, and student responsibility. Timid learners are often inhibited by low esteem and anxiety, engaged through individual work and small group collaboration. I assigned students' seats, dispersing confident communicators to ensure that the discussion spanned the room and allowing reluctant students to be heard. Students will make connections and represent mathematics in multiple ways. Applying knowledge of the connections through logical reasoning to formulate and evaluate conjectures requires higher-order thinking and a complex understanding of concepts. Engaging students in rich discourse fosters growth as they process, adapt, and personalize mathematics through the thoughts of others to reach and communicate understanding. The goals enable students to make connections between rational concepts and see how subgroups of a number system build on one another. This facilitation guides students to form conjectures individually, collaboratively (small groups), and collectively (whole class) to predict a fraction's decimal form. Intradisciplinary connections are made to divisibility rules, rational number forms, and the real number system. I introduced broker fees and had students express gains and losses as fractional investments change to necessitate rational numbers. My students noted 2000 that the New York Stock Exchange (NYSE) changed price reporting from fractions to decimals. "Stock Up" promotes analysis and problem-solving in an authentic context for understanding the properties of the real number system. Mastery of unit goals ensures numeric fluency, including the understanding and ability to problem-solve using various numeric representations. The whole-class discussion format supports the goals as it transforms our environment into a mathematical community. The whole-group discussion format is most useful in facilitating and assessing understanding because no student is more advantaged than the other in prerequisite knowledge. I created motivation by informing my students of their role as NYSE executives who must decide on the form of stock prices. We completed a "Need to Know Board," recording what we knew, needed to know, and how we could find our answer. They begin their plan by analyzing fractions and their decimal forms. They make conjectures to identify the decimal form of a fraction based on analysis of selected fractions and their decimal forms. We discuss and evaluate the conjectures through discussion, allowing my students to modify their thinking and repeat the process. Students complete and analyze the prime factorization of selected fractions' denominators based on my facilitation of discussion. Then, they correctly form conjectures to identify a fraction's decimal form without computation. Open-ended questions are used to elicit justification of reasoning considering their discoveries. The student's reasoning, varying views, and confidence in math reveal their understanding of the need to thoroughly test mathematical arguments for proof. I used calculators to sustain our focus on the relationship between fractions and decimals rather than the computation process. The excitement is apparent as students eagerly share about "disproving the theory." It enabled them to make connections, solve problems with conjectures, and communicate mathematically. Fairness, equity, and access to learning are evident in my understanding of students' individual and collective needs. I provided the relevance for success by using their natural curiosity to create stimulating, purposeful learning experiences. I made timid and intrapersonal learners comfortable participants in our whole-class discussion by providing the learners with opportunities to reason independently and in small groups. I generated discussion from 2 groups on the opposite side of the room to ensure fairness as I informally assessed understanding. Our whole-class discussion enabled mastery of learning goals as my students benefit from hearing the mathematical thoughts, reasoning, and evaluations of others. 

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