Chapter 4 Math Test 2. txt
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Chapter 4 Math Test 2. txt
Math Test Two Chapter Four Notes
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. 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
: associate a number with a family of sets (number / cardinality)
: 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.