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While similarities certainly exist between the Common Core and previous standards, there do exist some key differences. This week we will take a look at these three key shifts:
1. Greater focus on fewer topics
2. More coherence
The developers of the Common Core have aimed to create standards that focus on fewer topics while delving deeper into each topic so that students have a much more comprehensive grasp of the material. By avoiding a “mile wide, inch deep” approach, students will have time to better understand all aspects of a concept and its interconnectedness to other mathematical topics. To achieve this deeper focus, students will need to be given plenty of time to work with each given topic until they have truly acquired a deep, enduring understanding of it.
To that end, different grade bands focus on different mathematical strands. For example, students in Grades K-2 will spend the majority of their time focusing on addition and subtraction – along with the related concepts, skills, and problem solving. Meanwhile, 3rd through 5th graders will investigate multiplication and division concepts. Finally, middle school students will work with ratios, proportions, and algebra in 6th grade; ratios, proportions, and rational numbers in 7th; and linear functions and algebra in 8th grade.
This shift reflects the importance of understanding the interplay, connections, and relationships between various math concepts. By creating standards that “build new understanding onto foundations built in previous years”, students extend their previous learning from year to year. Here is one example of this progression:
“In 4th grade, students must “apply and extend previous understandings of multiplication to multiply a fraction by a whole number” (Standard 4.NF.4). This extends to 5th grade, when students are expected to build on that skill to “apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction” (Standard 5.NF.4).”
This shift encompasses conceptual understanding, procedural skills and fluency, and application. In other words, students need to understand mathematical concepts (like place value) deeply and fully. In addition, they need to develop automaticity with basic facts, along with developing “speed and accuracy in their calculation”. Lastly, they need to “correctly [apply]… mathematical knowledge [that applies]… their conceptual understanding and procedural fluency” (from www.corestandards.org/key-shifts-in-mathematics).
Because content at different grade levels has changed, it’s vital for the curriculum to reflect those changes; and it is just as important to ensure that teachers are aware of what has moved to a different grade level. Teachers can specifically help students by becoming aware of gaps that may have occurred between old curricula and new – and then filling in those gaps as much as possible to help students move forward with ease and confidence.
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