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HW3
Math Shifts
1. what is this shift, and why is this shift needed?
2. what opportunities does this shift present?
3. what challenges does this shift present?
focus strongly where standards focus
1. The shift is from racing to cover many topics in a mile-wide, inch-deep curriculum to spend more time focusing deeply on the major work of each grades. This shift is needed so that students can gain strong foundations.
2. This shift provide what area each grade needs to focus on. In Grades K-2: concepts, skills, and problem solving related to addition and subtraction. In grades 3-5: concepts, skills, and problem solving related to multiplication and division of whole numbers and fractions. In grade 6: Ratios and proportional relationships, and early algebraic expressions and equations. In grade 7: Ratios and proportional relationships, and arithmetic of rational numbers. In grade 8: Linear algebra and linear functions. This shift present an opportunity for student to gain strong foundations before moving on to next grade level, including a solid understanding of concepts, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the classroom.
3. One challenge might be there will be some gap between students’ math level within the same grade. There are variations in family structure. For example, some parent have more time to practice with their children, so those children might master the topic sooner than other children. If a student already mastered addition and subtraction in first grade, spending another year in addition and subtraction during second grade, parent might think this is a waste of time.
coherence: Think across grades and link to major topics within grades
1. This shift is changed from designing learning mathematics as disconnected topics to designing around coherent progressions from grade to grade. This shift is needed because learning is connected across grades, it’s a progression of learning, and it should never be disconnected.
2. This shift provides opportunity for students to extent their knowledge base on previous learning. For example, in first grade, students learn adding and subtracting within two digits, build up the foundation, then in second grade, students can move on learning adding and subtracting within triple numbers.
3. One of the challenges could be a student failed to master previous topic. For example, if a student failed to master multiplication and division in third grade, then in fourth grade, that student will have difficulty to learn multiplication and division with fractions. Teachers need to provide struggling students with extra support, back, and help them build up the previous knowledge first. Another example, some international students might have difficulty in the classroom, not because they are struggling with the subject, it’s because the main issue is they are struggling with English. Therefore, what they should do first, should be focus on improving their English first.
rigor in major topics
1. This shift is educators will need to pursue the three aspects of rigor: conceptual understanding, procedural skills and fluency, and application. This shift is needed because educators need to help students to have a deep, authentic command of mathematical concepts.
2. This shift provides opportunities for students to see math as more than a set of mnemonics or discrete procedures. Also provides opportunities for students to apply math in context with fast and accurate calculation.
3. Some students might require more practice than others in order to achieve fluency. The challenge might be how much homework practice should teachers be assigning for students. If teachers assign more practice homework for struggling students, those particular students might think is unfair, or even might hurt their self-esteem.
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