Cometancy 26 Learning Math Skills

Front 1

GREAT WORDS

Back 1

ASSOCIAATION
CONCEPT
PRINCIPLE
PROBLEM SOLVING

Front 2

DESC

Back 2

THE COMPETENS IS ABOUT DESINGING INSTRUCTION TO MEET THE STUDENTS WHERE THEY ARE AND TO HELP TEH AQUIRE INCREASING COMPLEX KNOW AND SKILLS

Front 3

Planning insstruction: Ausabel

Back 3

Concept maps were developed in the course of our research program where we sought to follow and understand changes in childrenÕs know ledge of science. This program was based on the learning psychology of David Ausubel (1963, 1968, 1978). The fundamental idea in Ausubel's cognitive psychology is that learning takes place by the assimilation of new concepts and propositions into existing concept propositional frameworks held by the learner.

Front 4

Planning Insturction Bloom

Back 4

another flashcard set

Front 5

Planning insturction Brownnell

Back 5

Focusing instruction on the meaningful development of important mathematical ideas increases the level of student learning.

There is a long history of research, going back to the work of Brownell (1945,1947), on the effects of teaching for meaning and understanding. Investigations have consistently shown that an emphasis on teaching for meaning has positive effects on student learning, including better initial learning, greater retention and an increased likelihood that the ideas will be used in new situations.

3. Students can learn both concepts and skills by solving problems.

Research suggests that students who develop conceptual understanding early perform best on procedural knowledge later. Students with good conceptual understanding are able to perform successfully on near-transfer tasks and to develop procedures and skills they have not been taught. Students with low levels of conceptual understanding need more practice in order to acquire procedural knowledge.

Front 6

Planning instruction of Gagne

Back 6

The purpose of this paper is to report how Gagne's model in "The Conditions of Learning" was adapted in order to develop activities, preobjectives, and test items for social studies concept instruction. One of the major problems in the field of social studies education is the looseness or nonspecificity of many of the definitions and terms which play such an important role in the planning, organization, and assessment of instruction. This looseness of definitions may contribute to a discrepancy between what teachers would like to teach and what they, in fact, teach. One way to improve instruction and increase student learning in the social studies is to develop precise definitions for the concepts used while simultaneously assisting teachers in the use of logical modes of instructional behavior

Front 7

Piaget

Back 7

four levels of development corresponding roughly to (1) infancy, (2) pre-school, (3) childhood, and (4) adolescence. Each stage is characterized by a general cognitive structure that affects all of the child's thinking Each stage represents the child's understanding of reality during that period, and each but the last is an inadequate approximation of reality. Development from one stage to the next is thus caused by the accumulation of errors in the child's understanding of the environment; this accumulation eventually causes such a degree of cognitive disequilibrium that thought structures require reorganizing.

The four development stages are described in Piaget's theory as

Sensorimotor stage: from birth to age 2 years (children experience the world through movement and senses and learn object permanence)
Preoperational stage: from ages 2 to 7 (acquisition of motor skills)
Concrete operational stage: from ages 7 to 11 (children begin to think logically about concrete events)
Formal operational stage: after age 11 (development of abstract reasoning).

[edit] Piaget's view of the child's mind
Piaget viewed children as little philosophers, which he called tiny thought-sacks and scientists building their own individual theories of knowledge

Front 8

The three type of Modalities

Back 8

visual
auditory
kinesthetic

Front 9

Each stage represents the child's understanding of reality during that period, and each but the last is an inadequate approximation of reality. Development from one stage to the next is thus caused by the accumulation of errors in the child's understanding of the environment; this accumulation eventually causes such a degree of cognitive disequilibrium that thought structures require reorganizing.

The four development stages are described in Piaget's theory as

Sensorimotor stage: from birth to age 2 years (children experience the world through movement and senses and learn object permanence)
Preoperational stage: from ages 2 to 7 (acquisition of motor skills)
Concrete operational stage: from ages 7 to 11 (children begin to think logically about concrete events)
Formal operational stage: after age 11 (development of abstract reasoning).

[edit] Piaget's view of the child's mind
Piaget viewed children as little philosophers, which he called tiny thought-sacks and scientists building their own individual theories of knowledge
ASSOCIATON

Back 9

WORDS OR SYMBOLS
Evem very young children associte the work, "triangle" with the, withough knowing the attributes and properties of triangle

Front 10

B. Concept--relational or concrete attributes

Back 10

Similar figures have relational attributes. The corresponding angles are equal and the rations of corrosponding sides are equal

Front 11

Types of learning-Principle-genaralizations, devlped rules

Back 11

Example-The area of a trapezoid is developed form the conceept of a trpaezoid and the are of (triangles, rectanghles, and or Parallelograms

Front 12

Tyes of learning-Problem solving

Back 12

Putting togther concepts and principles to solve a problem new to the learner. Example Given a compostie figure the student determines the area using the areas of triangles and rectangles

Front 13

DEVELOPENTAL LEARNING

Back 13

Instructional moves: Linkind betwen and among the following using modeloing, describing and recording by both teacher and studen. Concrete-manipulatives, models, hands on pictorial-pictures, diagrams, graphs, technology, abstract-symbols, words.

Front 14

Example 1 the nex unit in a fourth grade class is on multiplication. According to Piaget's theory of conceptual development, which one of the following activites is most apppropriate for the devlopment of multi-digit multiplicaion

Back 14

solutiopn: To be develoopmentally appropriate according to Piaget, the students at this developmenta stage-4th grade the students should begin new concepts with concrete modols

Front 15

example 2) Which of the following activities would best help develop the concepts of acute, obtruse, and right angles/

Back 15

The student investigates teh angle masures of a set of angles identifie as righ and conjecturs( math statement that appears to be true) simialar investigations are made for acute and obturse angles

Front 16

GREAT WORDS

Back 16

ASSOCIAATION
CONCEPT
PRINCIPLE
PROBLEM SOLVING

Front 17

DESC

Back 17

THE COMPETENS IS ABOUT DESINGING INSTRUCTION TO MEET THE STUDENTS WHERE THEY ARE AND TO HELP TEH AQUIRE INCREASING COMPLEX KNOW AND SKILLS

Front 18

Planning insstruction: Ausabel

Back 18

Concept maps were developed in the course of our research program where we sought to follow and understand changes in childrenÕs know ledge of science. This program was based on the learning psychology of David Ausubel (1963, 1968, 1978). The fundamental idea in Ausubel's cognitive psychology is that learning takes place by the assimilation of new concepts and propositions into existing concept propositional frameworks held by the learner.

Front 19

Planning Insturction Bloom

Back 19

another flashcard set

Front 20

Planning insturction Brownnell

Back 20

Focusing instruction on the meaningful development of important mathematical ideas increases the level of student learning.

There is a long history of research, going back to the work of Brownell (1945,1947), on the effects of teaching for meaning and understanding. Investigations have consistently shown that an emphasis on teaching for meaning has positive effects on student learning, including better initial learning, greater retention and an increased likelihood that the ideas will be used in new situations.

3. Students can learn both concepts and skills by solving problems.

Research suggests that students who develop conceptual understanding early perform best on procedural knowledge later. Students with good conceptual understanding are able to perform successfully on near-transfer tasks and to develop procedures and skills they have not been taught. Students with low levels of conceptual understanding need more practice in order to acquire procedural knowledge.

Front 21

Planning instruction of Gagne

Back 21

The purpose of this paper is to report how Gagne's model in "The Conditions of Learning" was adapted in order to develop activities, preobjectives, and test items for social studies concept instruction. One of the major problems in the field of social studies education is the looseness or nonspecificity of many of the definitions and terms which play such an important role in the planning, organization, and assessment of instruction. This looseness of definitions may contribute to a discrepancy between what teachers would like to teach and what they, in fact, teach. One way to improve instruction and increase student learning in the social studies is to develop precise definitions for the concepts used while simultaneously assisting teachers in the use of logical modes of instructional behavior

Front 22

Piaget

Back 22

four levels of development corresponding roughly to (1) infancy, (2) pre-school, (3) childhood, and (4) adolescence. Each stage is characterized by a general cognitive structure that affects all of the child's thinking Each stage represents the child's understanding of reality during that period, and each but the last is an inadequate approximation of reality. Development from one stage to the next is thus caused by the accumulation of errors in the child's understanding of the environment; this accumulation eventually causes such a degree of cognitive disequilibrium that thought structures require reorganizing.

The four development stages are described in Piaget's theory as

Sensorimotor stage: from birth to age 2 years (children experience the world through movement and senses and learn object permanence)
Preoperational stage: from ages 2 to 7 (acquisition of motor skills)
Concrete operational stage: from ages 7 to 11 (children begin to think logically about concrete events)
Formal operational stage: after age 11 (development of abstract reasoning).

[edit] Piaget's view of the child's mind
Piaget viewed children as little philosophers, which he called tiny thought-sacks and scientists building their own individual theories of knowledge

Front 23

The three type of Modalities

Back 23

visual
auditory
kinesthetic

Front 24

Each stage represents the child's understanding of reality during that period, and each but the last is an inadequate approximation of reality. Development from one stage to the next is thus caused by the accumulation of errors in the child's understanding of the environment; this accumulation eventually causes such a degree of cognitive disequilibrium that thought structures require reorganizing.

The four development stages are described in Piaget's theory as

Sensorimotor stage: from birth to age 2 years (children experience the world through movement and senses and learn object permanence)
Preoperational stage: from ages 2 to 7 (acquisition of motor skills)
Concrete operational stage: from ages 7 to 11 (children begin to think logically about concrete events)
Formal operational stage: after age 11 (development of abstract reasoning).

[edit] Piaget's view of the child's mind
Piaget viewed children as little philosophers, which he called tiny thought-sacks and scientists building their own individual theories of knowledge
ASSOCIATON

Back 24

WORDS OR SYMBOLS
Evem very young children associte the work, "triangle" with the, withough knowing the attributes and properties of triangle

Front 25

B. Concept--relational or concrete attributes

Back 25

Similar figures have relational attributes. The corresponding angles are equal and the rations of corrosponding sides are equal

Front 26

Types of learning-Principle-genaralizations, devlped rules

Back 26

Example-The area of a trapezoid is developed form the conceept of a trpaezoid and the are of (triangles, rectanghles, and or Parallelograms

Front 27

Tyes of learning-Problem solving

Back 27

Putting togther concepts and principles to solve a problem new to the learner. Example Given a compostie figure the student determines the area using the areas of triangles and rectangles

Front 28

DEVELOPENTAL LEARNING

Back 28

Instructional moves: Linkind betwen and among the following using modeloing, describing and recording by both teacher and studen. Concrete-manipulatives, models, hands on pictorial-pictures, diagrams, graphs, technology, abstract-symbols, words.

Front 29

Example 1 the nex unit in a fourth grade class is on multiplication. According to Piaget's theory of conceptual development, which one of the following activites is most apppropriate for the devlopment of multi-digit multiplicaion

Back 29

solutiopn: To be develoopmentally appropriate according to Piaget, the students at this developmenta stage-4th grade the students should begin new concepts with concrete modols

Front 30

example 2) Which of the following activities would best help develop the concepts of acute, obtruse, and right angles/

Back 30

The student investigates teh angle masures of a set of angles identifie as righ and conjecturs( math statement that appears to be true) simialar investigations are made for acute and obturse angles

Front 31

GREAT WORDS

Back 31

ASSOCIAATION
CONCEPT
PRINCIPLE
PROBLEM SOLVING

Front 32

DESC

Back 32

THE COMPETENS IS ABOUT DESINGING INSTRUCTION TO MEET THE STUDENTS WHERE THEY ARE AND TO HELP TEH AQUIRE INCREASING COMPLEX KNOW AND SKILLS

Front 33

Planning insstruction: Ausabel

Back 33

Concept maps were developed in the course of our research program where we sought to follow and understand changes in childrenÕs know ledge of science. This program was based on the learning psychology of David Ausubel (1963, 1968, 1978). The fundamental idea in Ausubel's cognitive psychology is that learning takes place by the assimilation of new concepts and propositions into existing concept propositional frameworks held by the learner.

Front 34

Planning Insturction Bloom

Back 34

another flashcard set

Front 35

Planning insturction Brownnell

Back 35

Focusing instruction on the meaningful development of important mathematical ideas increases the level of student learning.

There is a long history of research, going back to the work of Brownell (1945,1947), on the effects of teaching for meaning and understanding. Investigations have consistently shown that an emphasis on teaching for meaning has positive effects on student learning, including better initial learning, greater retention and an increased likelihood that the ideas will be used in new situations.

3. Students can learn both concepts and skills by solving problems.

Research suggests that students who develop conceptual understanding early perform best on procedural knowledge later. Students with good conceptual understanding are able to perform successfully on near-transfer tasks and to develop procedures and skills they have not been taught. Students with low levels of conceptual understanding need more practice in order to acquire procedural knowledge.

Front 36

Planning instruction of Gagne

Back 36

The purpose of this paper is to report how Gagne's model in "The Conditions of Learning" was adapted in order to develop activities, preobjectives, and test items for social studies concept instruction. One of the major problems in the field of social studies education is the looseness or nonspecificity of many of the definitions and terms which play such an important role in the planning, organization, and assessment of instruction. This looseness of definitions may contribute to a discrepancy between what teachers would like to teach and what they, in fact, teach. One way to improve instruction and increase student learning in the social studies is to develop precise definitions for the concepts used while simultaneously assisting teachers in the use of logical modes of instructional behavior

Front 37

Piaget

Back 37

four levels of development corresponding roughly to (1) infancy, (2) pre-school, (3) childhood, and (4) adolescence. Each stage is characterized by a general cognitive structure that affects all of the child's thinking Each stage represents the child's understanding of reality during that period, and each but the last is an inadequate approximation of reality. Development from one stage to the next is thus caused by the accumulation of errors in the child's understanding of the environment; this accumulation eventually causes such a degree of cognitive disequilibrium that thought structures require reorganizing.

The four development stages are described in Piaget's theory as

Sensorimotor stage: from birth to age 2 years (children experience the world through movement and senses and learn object permanence)
Preoperational stage: from ages 2 to 7 (acquisition of motor skills)
Concrete operational stage: from ages 7 to 11 (children begin to think logically about concrete events)
Formal operational stage: after age 11 (development of abstract reasoning).

[edit] Piaget's view of the child's mind
Piaget viewed children as little philosophers, which he called tiny thought-sacks and scientists building their own individual theories of knowledge

Front 38

The three type of Modalities

Back 38

visual
auditory
kinesthetic

Front 39

Each stage represents the child's understanding of reality during that period, and each but the last is an inadequate approximation of reality. Development from one stage to the next is thus caused by the accumulation of errors in the child's understanding of the environment; this accumulation eventually causes such a degree of cognitive disequilibrium that thought structures require reorganizing.

The four development stages are described in Piaget's theory as

Sensorimotor stage: from birth to age 2 years (children experience the world through movement and senses and learn object permanence)
Preoperational stage: from ages 2 to 7 (acquisition of motor skills)
Concrete operational stage: from ages 7 to 11 (children begin to think logically about concrete events)
Formal operational stage: after age 11 (development of abstract reasoning).

[edit] Piaget's view of the child's mind
Piaget viewed children as little philosophers, which he called tiny thought-sacks and scientists building their own individual theories of knowledge
ASSOCIATON

Back 39

WORDS OR SYMBOLS
Evem very young children associte the work, "triangle" with the, withough knowing the attributes and properties of triangle

Front 40

B. Concept--relational or concrete attributes

Back 40

Similar figures have relational attributes. The corresponding angles are equal and the rations of corrosponding sides are equal

Front 41

Types of learning-Principle-genaralizations, devlped rules

Back 41

Example-The area of a trapezoid is developed form the conceept of a trpaezoid and the are of (triangles, rectanghles, and or Parallelograms

Front 42

Tyes of learning-Problem solving

Back 42

Putting togther concepts and principles to solve a problem new to the learner. Example Given a compostie figure the student determines the area using the areas of triangles and rectangles

Front 43

DEVELOPENTAL LEARNING

Back 43

Instructional moves: Linkind betwen and among the following using modeloing, describing and recording by both teacher and studen. Concrete-manipulatives, models, hands on pictorial-pictures, diagrams, graphs, technology, abstract-symbols, words.

Front 44

Example 1 the nex unit in a fourth grade class is on multiplication. According to Piaget's theory of conceptual development, which one of the following activites is most apppropriate for the devlopment of multi-digit multiplicaion

Back 44

solutiopn: To be develoopmentally appropriate according to Piaget, the students at this developmenta stage-4th grade the students should begin new concepts with concrete modols

Front 45

example 2) Which of the following activities would best help develop the concepts of acute, obtruse, and right angles/

Back 45

The student investigates teh angle masures of a set of angles identifie as righ and conjecturs( math statement that appears to be true) simialar investigations are made for acute and obturse angles

Front 46

Grade 4 learning math skills

Back 46

4.14) Underlying processes and mathematical tools. The student applies Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

The student is expected to:

(A) identify the mathematics in everyday situations;

(B) solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;

(C) select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and

(D) use tools such as real objects, manipulatives, and technology to solve problems.

(4.15) Underlying processes and mathematical tools. The student communicates about Grade 4 mathematics using informal language.

The student is expected to:

(A) explain and record observations using objects, words, pictures, numbers, and technology; and

(B) relate informal language to mathematical language and symbols.

(4.16) Underlying processes and mathematical tools. The student uses logical reasoning.

The student is expected to:

(A) make generalizations from patterns or sets of examples and nonexamples; and

(B) justify why an answer is reasonable and explain the solution process.

Front 47

grade 5 math communication skills

Back 47

The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

The student is expected to:

(A) identify the mathematics in everyday situations;

(B) solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;

(C) select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and

(D) use tools such as real objects, manipulatives, and technology to solve problems.

(5.15) Underlying processes and mathematical tools. The student communicates about Grade 5 mathematics using informal language.

The student is expected to:

(A) explain and record observations using objects, words, pictures, numbers, and technology; and

(B) relate informal language to mathematical language and symbols.

(5.16) Underlying processes and mathematical tools. The student uses logical reasoning.

The student is expected to:

(A) make generalizations from patterns or sets of examples and nonexamples; and

(B) justify why an answer is reasonable and explain the solution process.

Front 48

grade 6 math communication skills

Back 48

(6.11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

The student is expected to:

(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;

(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and

(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.

(6.12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models.

The student is expected to:

(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and

(B) evaluate the effectiveness of different representations to communicate ideas.

(6.13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions.

The student is expected to:

(A) make conjectures from patterns or sets of examples and nonexamples; and

(B) validate his/her conclusions using mathematical properties and relationships.

Front 49

grade 7 math communication

Back 49

8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

The student is expected to:

(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;

(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and

(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.

(8.15) Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models.

The student is expected to:

(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and

(B) evaluate the effectiveness of different representations to communicate ideas.

(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions.

The student is expected to:

(A) make conjectures from patterns or sets of examples and nonexamples; and

(B) validate his/her conclusions using mathematical properties and relationships.

Front 50

grade 8th math communicatin

Back 50

.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

The student is expected to:

(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;

(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and

(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.

(8.15) Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models.

The student is expected to:

(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and

(B) evaluate the effectiveness of different representations to communicate ideas.

(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions.

The student is expected to:

(A) make conjectures from patterns or sets of examples and nonexamples; and

(B) validate his/her conclusions using mathematical properties and relationships.