1. What are the three shifts in mathematics standards?

The three shifts in mathematics standards include: focus, coherence, and rigor. With Focus, there is a stronger focus where standards focus, and allows teachers to teach fewer things, which allows more time for teachers to teach these vital standards, and for children to learn and internalize these important ideas. Coherence refers to the ability to make connections between ideas within and across grades to link those important topics and concepts. With rigor, the focus is on pursuing conceptual understanding, procedural skills and fluency, and application in relation to these major topics.

2. Briefly explain how does the shift from teaching many topics to focusing

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Not only do they recognize the number, they understand what that number is and how it is in relation with other numbers. They are recognizing what it means to be a numbers and are understanding that there are many different sets included in that one number. The example in the video used the number 7 to demonstrate cardinality. It discussed that cardinality is knowing that 7 is also 5 and 2, and that 5 and 2 equal 7. The first video mentioned students building conceptual understanding through awareness of cardinality in the first and second grade, but the second video mentioned the importance of importance of building the awareness of cardinality in kindergarten and building on this concept throughout the next early grades that students

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It is referencing how in the beginning grades students are learning all these ways and strategies to add and subtract in first and second grade and developing a more in-depth understanding of these concepts, and then moving the third and fourth grade to perform using the standard algorithm. It talks about the beauty of beginning by discovering and building fluency with these mathematical concepts in the early years in order to fluently transition into using the standard algorithm.

6. How can we help 1st and 2nd grade students understand number and operations?

We need to assist these students in understanding number and operations by helping them understand cardinality, equality, and decomposition. These are vital underpinnings for students to be able to perform and understand the operations they will be working with in their future grade levels. The way that students are understanding and developing strategies now when doing operations, will help them with the standard algorithm. We need to assist them in building fluency through conceptual