Reflection Day 21 (Math Methods Day 3)
Reflection on book (Early Childhood Mathematics)
--- Early Algebra (Pattern and Function) ---
Patterns are important in life
“The arrangement of sunflower seeds in the cone of the flower… Adults use patterns such as odd-even to locate a home by noting which street addresses are found on one side of the street” (p. 143).
“Children explore pattern on four levels: 1) recognize a pattern, 2) describe a pattern, 3) extend a pattern, and 4) create their own patterns” (p. 145).
Pattern Activities
- Real objects
- Pattern cards
- Extending a pattern
Pattern in music and art
- Repetitive phrases or rhythms in songs
- Paper weaving
--- Problem Solving (Addition and Subtraction) ---
“The teacher reads aloud the problem as many times as needed” (p. 161).
*Repeating the problem over helps the child understand. Repeating also goes along with Montessori philosophy.
“The children solve the problem, using whatever way they wish, and discuss their thinking” (p. 161).
*manipulatives, cubes, whatever needed should be available for child to use.
Polya’s four-step method: (the most common strategy for problem solving)
1. Understand the problem.
2. Devise a plan.
3. Carry out the plan.
4. Look back.
Cognitive background information for teachers: classes of problems
“The use of the 11 problem types also encourages children to learn the standard number sentences that mathematicians might use” – join, separate, part-part-whole, compare (p. 167).
Rules of operation
“These rules of operation govern what is mathematically possible using the addition and subtraction symbols” – the identity element, the commutative property, the associative property, transitivity of equality (p. 169-170).
Helping children write their own problems
“Children enjoy writing their own stories. Generally, they write problems they can solve” (p. 170).
Using what children know to learn the facts
“Teachers must keep individual records of the actual progress through the generally recognized sequence of learning” (p. 171).
--- Problem Solving (Multiplication and Divistion) ---
“Preschool children have the ability to understand the concept of equal shares, or dividing a collection into equal amounts” (p. 179).
“Multiplication is the operation used to fine a product when two factors are known” (p. 180).
Can do this with small children through: 1) classifying objects, and 2) skip counting
Problem solving strategies: 1) direct model, 2) counting strategies, 3) derived facts, and 4) standard math facts.
Classes of problems (p.182)
- Asymmetrical; numbers are not interchangeable.
- Symmetrical; numbers are interchangeable.
Rules of operation (p.188)
1) The identity element, 2) the commutative property, 3) the associative property, and 4) distributive property
Helping children write their own problems (p.189)
- Grouping situations
- Grid situations
- Selection situations
--- Reflection on class ---
Color is very important for number. It is easy to memorize and find patterns.
- Units: green
- Tens: blue
- Hundreds: red
- Thousands: green
Reflection on book (Early Childhood Mathematics)
--- Early Algebra (Pattern and Function) ---
Patterns are important in life
“The arrangement of sunflower seeds in the cone of the flower… Adults use patterns such as odd-even to locate a home by noting which street addresses are found on one side of the street” (p. 143).
“Children explore pattern on four levels: 1) recognize a pattern, 2) describe a pattern, 3) extend a pattern, and 4) create their own patterns” (p. 145).
Pattern Activities
- Real objects
- Pattern cards
- Extending a pattern
Pattern in music and art
- Repetitive phrases or rhythms in songs
- Paper weaving
--- Problem Solving (Addition and Subtraction) ---
“The teacher reads aloud the problem as many times as needed” (p. 161).
*Repeating the problem over helps the child understand. Repeating also goes along with Montessori philosophy.
“The children solve the problem, using whatever way they wish, and discuss their thinking” (p. 161).
*manipulatives, cubes, whatever needed should be available for child to use.
Polya’s four-step method: (the most common strategy for problem solving)
1. Understand the problem.
2. Devise a plan.
3. Carry out the plan.
4. Look back.
Cognitive background information for teachers: classes of problems
“The use of the 11 problem types also encourages children to learn the standard number sentences that mathematicians might use” – join, separate, part-part-whole, compare (p. 167).
Rules of operation
“These rules of operation govern what is mathematically possible using the addition and subtraction symbols” – the identity element, the commutative property, the associative property, transitivity of equality (p. 169-170).
Helping children write their own problems
“Children enjoy writing their own stories. Generally, they write problems they can solve” (p. 170).
Using what children know to learn the facts
“Teachers must keep individual records of the actual progress through the generally recognized sequence of learning” (p. 171).
--- Problem Solving (Multiplication and Divistion) ---
“Preschool children have the ability to understand the concept of equal shares, or dividing a collection into equal amounts” (p. 179).
“Multiplication is the operation used to fine a product when two factors are known” (p. 180).
Can do this with small children through: 1) classifying objects, and 2) skip counting
Problem solving strategies: 1) direct model, 2) counting strategies, 3) derived facts, and 4) standard math facts.
Classes of problems (p.182)
- Asymmetrical; numbers are not interchangeable.
- Symmetrical; numbers are interchangeable.
Rules of operation (p.188)
1) The identity element, 2) the commutative property, 3) the associative property, and 4) distributive property
Helping children write their own problems (p.189)
- Grouping situations
- Grid situations
- Selection situations
--- Reflection on class ---
Color is very important for number. It is easy to memorize and find patterns.
- Units: green
- Tens: blue
- Hundreds: red
- Thousands: green