Row 1
Prenumber Development
Fostering foundational math concepts like classifying, comparing, seriation, and recognizing patterns
Classify objects...
By shapes, size, color, gender, and many others
Counting Principles
Rote vs. Rational Counting
Patterns are arrangemet...
Of numbers, shapes, or objects that follows a specific, repeating rule or sequence
Developmet research by Piaget and others
Early Number Development
Briefly describe one of the image example of Comparing and Ordering
Image 1: gingerbread man and hearts
Image 2: Bonnie and Sammy's leaves
Image 3: (a) cuisenaire rods and cards or (b) connecting blocks
Image 4: greater than, less than, or equal to numbers
Counting Strategies (2)
Counting on, Counting back, and Skip Counting
Briefly describe one of the image examples of Counting Principles
Image 1: correct counting (rational counting)
Image 2: correct counting but incorrect correspondence (counts too fast) (rote counting)
Image 3: correct counting but incorrect correspondence (points too fast) (rote counting)
One-to-one Correspondence is...
Comparing and Ordering
Number benchmarks --- perceptual anchors that become internalized from many concrete experinces is...
Developing Benchmarks
Classification (in math)
how objects are grouped based on their similar characteristics or different characteristics
Think back to the examples of Patterns, and describe one of the images
Image 1: green square, red circle, blue triangle, (repeat)
Image 2: blue square, green triangle, (repeat)
Image 3: apple, grapes, apple, grapes, apple, (repeat) or cherry, cherry, strawberry, strawberry, cherry, (repeat)
Image 4: large bowling ball, large bowling ball, small bowling ball, small bowling ball, (repeat)
Comparing and Ordering
Comparison of quantities is another important part of learning to count and is essential to developing number awareness
Early Development
Children can compare amounts and identify which is more or less even without counting, and these activities can also create opportunities to practice counting skills
Using visual comparisons supports the ability to recognize small quantities
Prenumber Development is two stages, what are the stages?
2. Patterns
Briefly describe Activity 1 from Day 1
Made as many groups of categories to classify different forks
Briefly describe Activity 2 from Day 1
Subitizing coloring sheet: students had to color the correct spaces to the correct number group from different examples to show counting
The phenomenon of _________ of number that a given number does not vary reflects how children think
Conservation
1-4 Important Counting Principles
Each object to be counted must be assigned one and only one number name
The number name list must be used in a fixed order every time a group of objects is counted
The order in which the objects are counted doesn't matter; order-irrelevance rule
The last number name used gives the number of objects; cardinality rule
Think back to the examples of Classification, and describe one of the images
Image 1: circle, square, triangle (shape, color, size)
Image 2: number of sizes a shape has (4 sides, 3 sides, 2 sides)
Image 3: Compare and Contrast of what shapes are blue or not blue, what shapes are pentagons or not pentagons, and what shapes are both blue and pentagons
Image 4: coins (how much each coin is worth, size of coin, color of coin)
Subitizing
The skill to "instantly see how many" in a group is called subitizing, from the Latin word meaning "suddenly"
Conservation (principle)
Quanity remains the same even when its appearannce or arrangement changes
Developing Benchmarks
Cultural Connection: Japan
5 and 10 are later used with the ten-frame and the Japanese soroban (similar to an abacus) to promote counting, quick recognition of counting, and mental computation
Classification
Fundamental to learning about the real worl, and it can be done with or without numbers
Counting Strategies
Once mastery of rational counting has been reached, more efficient and sophisticated counted strategies should be encouraged