Math - Core Subjects EC-6 (291) UPDATED
ACTUAL Exam Questions and CORRECT
Answers
NCTM - CORRECT ANSWER -National Council of Teachers of Mathematics
Principles and Standards for School Mathematics (2000) - CORRECT ANSWER -6
principles:
1. Equity - high expectations and strong support for ALL students.
2. Curriculum - coherent, focused, well-articulated math concepts across all grades.
3. Teaching - understanding what is known and what is needed to learn while challenging
students to learn it well.
4. Learning - learn with understanding.
5. Assessment - support the learning and furnish useful info to teachers and students.
6. Technology - essential; its enhances and facilitates learning.
Divisor - CORRECT ANSWER -The number by which a dividend is divided.
Dividend - CORRECT ANSWER -A number that is divided by another number.
Quotient - CORRECT ANSWER -The answer to a division problem.
Inductive teaching - CORRECT ANSWER -Learning through examples.
Deductive teaching - CORRECT ANSWER -Learning step by step.
Nomenclature - CORRECT ANSWER -The act or process or an instance of naming
,nomenclature. A system or set of terms or symbols especially in a particular discipline (like
math).
Challenges faced in math by ELLs - CORRECT ANSWER -1. Math classroom tends to
assume students have prior knowledge of specialized terms.
2. The terms can have multiple meanings depending on the subject.
3. The vocabulary encompasses a variety of homophones (pronounced same, different meaning).
Denominator - CORRECT ANSWER -The quantity below the line in a fraction. It tells
how many equal parts are in the whole.
Numerator - CORRECT ANSWER -The top number of a fraction that tells how many
parts of a whole are being considered.
Minuend - CORRECT ANSWER -The number that is to be subtracted from.
Subtrahend - CORRECT ANSWER -The number that is to be subtracted.
Rational number - CORRECT ANSWER -Any number that can be expressed as a ratio or
quotient of two non-zero integers. Can be expressed as fractions or decimals.
Rote counting - CORRECT ANSWER -Verbal repetition of numbers.
Begins around 2-3 yo.
Autonomy - CORRECT ANSWER -Self-government, freedom, independence.
Discrete models - CORRECT ANSWER -Math based on distinct values; finite
possibilities. Ex. The use of counters.
,Continuous models - CORRECT ANSWER -Math based on the continuous number line;
real numbers; infinite possibilities.
Algorithm - CORRECT ANSWER -A step-by-step procedure for solving a problem.
Jean Piaget - CORRECT ANSWER -Developmental biologist.
Observed and recorded the intellectual abilities of infants, children, and adolescents.
4 stages of intellectual development.
Theory concerned with the growth of intelligence, the emergence and acquisition of schemata, or
schemes of a child using "developmental stages", to explain how children acquire new
information.
Preoperational thought - CORRECT ANSWER -A pattern of thinking that is egocentric,
centered, irreversible, and nontransformational.
Piaget's 4 stages of intellectual development - CORRECT ANSWER -1. Sensorimotor
Stage (birth-2 years)
2. Preoperational Stage (years 2-7)
3. Concrete Operational Stage (years 7-11)
4 Formal Operational Stage (years 11-adult)
Preoperational Stage - CORRECT ANSWER -Processes of symbolic functioning,
centration, intuitive thought, egocentrism, and inability to conserve.
, Concrete Operational Stage - CORRECT ANSWER -Exhibit developmental processes of
decentering, reversibility, conservation, serialization, classification, and elimitation of
egocentrism.
Formal Operation Stage - CORRECT ANSWER -Focus on the ability to use symbols and
think abstractly.
Problems in Preoperational Stage - CORRECT ANSWER -Sperry Smith
1. Centration - focusing on only one aspect of a situation or problem.
Ex. Differently shaped containers holding the same volume is not understandable yet.
2. Conservation - understanding that quantity, length, or number of items is unrelated to the
arrangement or appearance of the object or items.
Ex. Believing a nickel is with more than a dime because it's bigger.
Decentering - CORRECT ANSWER -Can take into account multiple aspects of a problem;
can form a conclusion based on reason rather than perception.
Reversibility - CORRECT ANSWER -Understands objects can be changed and returned to
original state; 4+4=8 and 8-4=4.
Conservation - CORRECT ANSWER -Understand quantity, length, or number of items is
unrelated to arrangement or appearance of the object.
Serialization - CORRECT ANSWER -Ability to arrange objects in an order according to
size, shape, or any other attribute.
ACTUAL Exam Questions and CORRECT
Answers
NCTM - CORRECT ANSWER -National Council of Teachers of Mathematics
Principles and Standards for School Mathematics (2000) - CORRECT ANSWER -6
principles:
1. Equity - high expectations and strong support for ALL students.
2. Curriculum - coherent, focused, well-articulated math concepts across all grades.
3. Teaching - understanding what is known and what is needed to learn while challenging
students to learn it well.
4. Learning - learn with understanding.
5. Assessment - support the learning and furnish useful info to teachers and students.
6. Technology - essential; its enhances and facilitates learning.
Divisor - CORRECT ANSWER -The number by which a dividend is divided.
Dividend - CORRECT ANSWER -A number that is divided by another number.
Quotient - CORRECT ANSWER -The answer to a division problem.
Inductive teaching - CORRECT ANSWER -Learning through examples.
Deductive teaching - CORRECT ANSWER -Learning step by step.
Nomenclature - CORRECT ANSWER -The act or process or an instance of naming
,nomenclature. A system or set of terms or symbols especially in a particular discipline (like
math).
Challenges faced in math by ELLs - CORRECT ANSWER -1. Math classroom tends to
assume students have prior knowledge of specialized terms.
2. The terms can have multiple meanings depending on the subject.
3. The vocabulary encompasses a variety of homophones (pronounced same, different meaning).
Denominator - CORRECT ANSWER -The quantity below the line in a fraction. It tells
how many equal parts are in the whole.
Numerator - CORRECT ANSWER -The top number of a fraction that tells how many
parts of a whole are being considered.
Minuend - CORRECT ANSWER -The number that is to be subtracted from.
Subtrahend - CORRECT ANSWER -The number that is to be subtracted.
Rational number - CORRECT ANSWER -Any number that can be expressed as a ratio or
quotient of two non-zero integers. Can be expressed as fractions or decimals.
Rote counting - CORRECT ANSWER -Verbal repetition of numbers.
Begins around 2-3 yo.
Autonomy - CORRECT ANSWER -Self-government, freedom, independence.
Discrete models - CORRECT ANSWER -Math based on distinct values; finite
possibilities. Ex. The use of counters.
,Continuous models - CORRECT ANSWER -Math based on the continuous number line;
real numbers; infinite possibilities.
Algorithm - CORRECT ANSWER -A step-by-step procedure for solving a problem.
Jean Piaget - CORRECT ANSWER -Developmental biologist.
Observed and recorded the intellectual abilities of infants, children, and adolescents.
4 stages of intellectual development.
Theory concerned with the growth of intelligence, the emergence and acquisition of schemata, or
schemes of a child using "developmental stages", to explain how children acquire new
information.
Preoperational thought - CORRECT ANSWER -A pattern of thinking that is egocentric,
centered, irreversible, and nontransformational.
Piaget's 4 stages of intellectual development - CORRECT ANSWER -1. Sensorimotor
Stage (birth-2 years)
2. Preoperational Stage (years 2-7)
3. Concrete Operational Stage (years 7-11)
4 Formal Operational Stage (years 11-adult)
Preoperational Stage - CORRECT ANSWER -Processes of symbolic functioning,
centration, intuitive thought, egocentrism, and inability to conserve.
, Concrete Operational Stage - CORRECT ANSWER -Exhibit developmental processes of
decentering, reversibility, conservation, serialization, classification, and elimitation of
egocentrism.
Formal Operation Stage - CORRECT ANSWER -Focus on the ability to use symbols and
think abstractly.
Problems in Preoperational Stage - CORRECT ANSWER -Sperry Smith
1. Centration - focusing on only one aspect of a situation or problem.
Ex. Differently shaped containers holding the same volume is not understandable yet.
2. Conservation - understanding that quantity, length, or number of items is unrelated to the
arrangement or appearance of the object or items.
Ex. Believing a nickel is with more than a dime because it's bigger.
Decentering - CORRECT ANSWER -Can take into account multiple aspects of a problem;
can form a conclusion based on reason rather than perception.
Reversibility - CORRECT ANSWER -Understands objects can be changed and returned to
original state; 4+4=8 and 8-4=4.
Conservation - CORRECT ANSWER -Understand quantity, length, or number of items is
unrelated to arrangement or appearance of the object.
Serialization - CORRECT ANSWER -Ability to arrange objects in an order according to
size, shape, or any other attribute.
