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Cardinality is understanding how many items are in a set. To do this, a student must first understand that each number in a count sequence represents a cumulative quantity, then the student learns that the last number represents the quantity of the set (e.g., counting to 10 means there are 10 items in the set).
Children advance through developmental stages of number concept. First is Pre-Numeral-Knowers when they have no understanding of Cardinality. Next is Subset-Knowers with two categories:
After they have achieved Three-Knower status, students acquire knowledge of all the numbers they can count relatively quickly in comparison. At this point, children have advanced from Subset-Knowers to Cardinal-Principle-Knowers.
CRA is a sequential instructional approach during which students move from working with concrete materials to creating representational drawings to using abstract symbols.
Students activate more cognitive processes by exploring and representing their understandings in visual form.
Continual use of foundational skills with different problems reinforces a conceptual understanding of math skills.
Daily review strengthens previous learning and can lead to fluent recall.
Thinking of and about patterns encourages learners to look for and understand the rules and relationships that are critical components of mathematical reasoning.
Free choice supports learner interests and promotes the development of more complex social interactions.
In guided inquiry, teachers help students use their own language for constructing knowledge by active listening and questioning.
Teaching students through guided play encourages them to take an active role in their learning and supports the development of a broad array of cognitive skills.
Spending time with new content helps move concepts and ideas into Long-term Memory.
Practicing until achieving several error-free attempts is critical for retention.
Math centers with math games, manipulatives, and activities support learner interests and promote the development of more complex math skills and social interactions.
Math games use numbers and Spatial Skills, allowing students to practice many math skills in a fun, applied context.
By talking through their thinking at each step of a process, teachers can model what learning looks like.
Providing physical representations of numbers and math concepts helps activate mental processes.
Easy access to seeing the relationships between numbers promotes number sense as students see these connections repeatedly.
Visual representations help students understand what a number represents as well as recognize relationships between numbers.
When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.
Math games and manipulatives for vision differences support math development for learners with visual needs.
Children's literature can be a welcoming way to help students learn math vocabulary and concepts.
Providing visuals to introduce, support, or review instruction activates more cognitive processes to support learning.
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