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What are the Pre-Number Skills?
- 1. Classifying (enactive)
- 2. Finding the Relation between two sets (enactive)
- 3. Conserving Relations (enactive to iconic)
- 4. Classifying on the basis of the As-Many Relation
- 5. Ordering on the basis of the More-Than and Less-Than Relations (iconic)
Why do we teach Pre-Number Skills?
- 1. birth to age 7
- 2. skills have to have in place before being introduced to idea of number
- 3. pre-operational (lack ability to conserve)
- 4. use measurement and quantity interchangeably when describing different sets
- 5. based on a heirarchy
Four Important Understandings for Developing Pre-Number Concepts
- 1. set of things has a number property, and the number property is stable. (CARDINALITY)
- 2. always make a set with one more or one fewer. (ORDINALITY)
- 3. whole numbers, we can determine how many objects are in a set, either by recognizing number patterns or by counting.
- 4. whole numbers, we compare two sets and find whether one set has as many as, more than, or less than the other set.
Classifying Pre-Number Skill
- 1. Selects objects having a SPECIFIC attitude
- 2. Sorting objects on the basis of GENERAL attitude
- 3. DUPLICATING a pattern
- 4. EXTENDING a pattern
Finding the relation between two sets Pre-Number Skill
- 1. As Many As Relation
- 2. More-Than and Less-Than Relation
Definition of Subitizing
- 1. being able to perceive in your brain how many in a set without having to count each individual piece
- 2. brain recognizes patterns in way elements are laid out
Classifying on the basis of As-Many Relation Pre-Number Skill
children are able to match pictures of various amounts of objects to the picture of the number symbol
Ordering on the basis of More-Than and Less-Than Relations Pre-Number Skill
children are able to put cards in order from least to greatest; children are able to put a card either before, middle, or end
Finding and Using the Properties of Relations
- 1. Reflexive Property
- 2. Symmetric
- 3. Transitive
- 1. A=A
- 2. mirror images
- 3. identical sets in every way
- 1. A=B, then B=A
- 2. does not matter way they are placed, as long as same information given
- 3. green orange = orange green
- 4. numbers can be symmetric without objects being identical
- 5. five dogs + three dogs = 2 trucks + 6 trucks
- 1. A=B, B=C, then A=C
- 2. require 3 sets of information
- 3. Sally has seven barbies. Her mom went to Wal-Mart and picked out the seven outfits with seven pairs of shoes inside. (7 barbies = 7 outfits, 7 outfits = 7 shoes, then 7 barbies = 7 shoes)
One To One Matching Test in Relation with One To One Correspondence
- 1. Children use the one to one matching test to determine the condition of one to one correspondence.
- 2. manipulatives match up
- 1. rote counting: memorize numbers without meaning
- 2. meaningful counting: concept to number word
Readiness Skills for Learning Numbers 1-10
- Step 1: associate a number with a family of sets (number / cardinality)
- Step 2: number / numeral association
- (abstract idea to written sign "4")
Counting Meaningful Skills
- 1. count each item once and only once
- 2. have a way of keeping track of what has been counted already
- 3. know the counting sequence
Definition of Counting
knowing that the last number said represents everything that has been counted so far
Kindergarten and First Grade Counting Experiences
- 1. count all of a set (every element of a set beginning with one)
- 2. count from a set (count on from a known number either forward or backward) = MATURATIONAL
Readiness Step for Addition and Subtration
children count from a set and must have access to model
Definition of Cardinal Numbers
- 1. idea of cardinality
- 2. numbers that tell how many
Definition of Ordinal Numbers
- 1. idea of ordinality
- 2. before, after, or next
- 3. numbers that tell position more closely related to before or after
What about 0?
- 1. hard to demonstrate
- 2. ask questions that correspond to cardinality of "0"
Greater than 10
- 1. establish ones place before explaining "0"
- 2. helps develop idea of place value
- 3. good questions are a must in this activity
- 4. develop numbers 11-19 first
How to assess student performance using PREVENTATIVE TEACHING?
- 1. must be able to look through the great array of learning goals and identify those that are key.
- 2. many tools can be used to assess learning, very few of them include pencil and paper testing.
- 3. learn to collect, maintain, and study examples of student work to demonstrate mastery.
- 4. understand how children master these concepts and what difficulties they encounter when learning them.