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Didactics of mathematics for primary education - Iliana Dumitrescu
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ISBN: 978-606-28-1404-5
DOI: https://doi.org/10.5682/9786062814045
Publisher year: 2022
Edition: I
Pages:
Publisher: Editura Universitara
Author: Iliana Dumitrescu
Product Code:
9786062814045
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We learn every day, since we are born.
From the first day of life we begin to discover the world and learn how to adapt to the new.
We learn continuously, because we want to grow and live beautifully.
We learn to be better, better with us, better than us - those of yesterday, better with others, next to us...
From the first day of life we begin to discover the world and learn how to adapt to the new.
We learn continuously, because we want to grow and live beautifully.
We learn to be better, better with us, better than us - those of yesterday, better with others, next to us...
-
Didactics of mathematics for primary education
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ILIANA DUMITRESCU
Education
Doctor in Educational Sciences - Faculty of Psychology and Educational Sciences, University of Bucharest
Specializations: Pedagogy of primary and preschool education: Mathematics, Legal and Administrative Sciences
Methodist teacher, Trainer of trainers, Trainer, Evaluator of professional skills, Mentor, Educational management expert
Professional experience
Bachelor's/Master's program teacher, Faculty of Psychology and Educational Sciences, DPIPP, University of Bucharest, (Mathematics, Didactics of mathematics for primary and preschool education, Digital technologies in 21st century education)
Bachelor program teacher, Faculty of Education Sciences, Christian University "Dimitrie Cantemir" from Bucharest (Mathematics-primary and preschool education, Didactics of mathematics-primary and preschool education, Pedagogical practice-preschool education I, Pedagogical practice-primary education I)
Methodist teacher, House of the Didactic Body of the Municipality of Bucharest
Coordinator/trainer of accredited courses/Ministry of Education: Online class and home school, Digitization in the evaluation of students' skills, School inclusion management, Inclusive school, school for all, Evaluator of professional skills for pre-university teachers, CRED-Curriculum relevant, education open to all. Level II training-secondary education
Approved course coordinator/trainer/Ministry of Education: Competence assessment of primary and secondary school students, Development of didactic competences for assessment of learning through national exams, Competency assessor for certification and tenure, The role of the evaluator in inspections for tenure and certification in education, Definitely, Civic Courage, Online class and home school
Author/co-author of manuals and school aids
Scientific researcher III, deputy director, Institute of Education Sciences
Coordinator and author of curriculum for primary education (framework plan for primary education and school programs for the preparatory class, I, II), school programs for optional subjects
Coordinator and co-author of the impact study Implementation of the preparatory class in the Romanian educational system, 2013, Institute of Education Sciences
School program project evaluator
List of figures / 7
Applications / 11
I. MATHEMATICS IN THE NATIONAL CURRICULUM / 13
1.1. The purposes of primary education / 14
1.2. The National Curriculum. Key concepts / 19
1.3. Mathematics curriculum for primary education / 23
1.3.1. Program structure / 23
1.3.2. General competences and specific competences / 25
1.3.3. Learning contents / 30
1.3.4. Reflection of learning contents in the school textbook / 43
Bibliography / 48
II. METHODOLOGICAL REFERENCES REGARDING THE TEACHING OF MATHEMATICS IN PRIMARY EDUCATION / 49
2.1. Natural numbers / 50
2.1.1. The specificity of the preparatory class / 51
2.1.2. Natural numbers from 0 to 31. Preparatory class / 54
2.1.2.1. Entering natural numbers from 0 to 10 / 54
2.1.2.2. Entering natural numbers from 11 to 20 / 59
2.1.2.3. Entering natural numbers from 21 to 31 / 61
2.1.3. Natural numbers from 0 to 100. Class I / 61
2.1.4. Natural numbers smaller than 1,000,000. Classes II – IV / 63
2.1.5. Comparison, ordering and rounding of natural numbers / 67
2.1.5.1. Comparison and ordering of natural numbers / 67
2.1.5.2. Rounding of natural numbers / 68
2.2. Operations with natural numbers / 73
2.2.1. Addition and subtraction / 74
2.2.1.1. Addition and subtraction up to 10 / 75
a) Adding the numbers up to 10 / 75
b) Decreasing the numbers until 10 / 77
c) The connection between addition and subtraction / 79
2.2.1.2. Addition and subtraction in the center 0 → 20 / 81
a) Addition and subtraction in the center 0 → 20, without passing over order / 81
b) Addition and subtraction in the center 0 → 20, with passing over order / 83
2.2.1.3. Addition and subtraction in the center 0 → 100 / 88
2.2.1.4. Number 100 / 90
2.2.1.5. Addition and subtraction of natural numbers greater than 100 / 92
2.2.1.6. Finding an unknown number / 93
a) The reverse walking method / 93
b) Balance method / 97
2.2.2. Multiplication and division / 106
2.2.2.1. Teaching multiplication / 107
a) Multiplying a number by 10, 100, 1 000 / 109
b) Multiplying two numbers, one of which is written with a digit and the result does not exceed 10,000 / 110
c) Multiplying numbers when the factors have at most three digits / 112
2.2.2.2. Teaching division / 113
2.2.3. The order of operations / 125
2.3. Problem solving / 129
2.3.1. Problems that can be solved by a single operation / 131
2.3.2. Problems that are solved by two or more operations / 137
2.4. Fractions / 141
2.4.1. Representation, writing and reading of fractions / 142
2.4.2. Comparison of fractions / 145
2.4.2.1. Equal fractions / 145
2.4.2.2. Comparing a fraction with the whole / 146
2.4.2.3. Comparison of two fractions / 147
2.4.3. Adding and subtracting fractions with the same denominator / 148
2.5. Elements of geometry / 153
2.5.1. Elements of geometry in school programs for grades P-IV / 154
2.5.2. The specifics of teaching geometry elements / 155
2.5.3. Personalized reading of school programs / 158
2.6. Units of measure / 167
2.6.1. Units of measure in school programs for grades P-IV / 168
2.6.2. Conceptual clarifications / 169
2.6.3. Length measurement / 170
2.6.4. Measuring the capacity of vessels / 177
2.6.5. Measuring the mass of bodies / 177
2.6.6. Time measurement / 183
2.6.7. Measuring value. Money / 184
Bibliography / 188
Applications / 11
I. MATHEMATICS IN THE NATIONAL CURRICULUM / 13
1.1. The purposes of primary education / 14
1.2. The National Curriculum. Key concepts / 19
1.3. Mathematics curriculum for primary education / 23
1.3.1. Program structure / 23
1.3.2. General competences and specific competences / 25
1.3.3. Learning contents / 30
1.3.4. Reflection of learning contents in the school textbook / 43
Bibliography / 48
II. METHODOLOGICAL REFERENCES REGARDING THE TEACHING OF MATHEMATICS IN PRIMARY EDUCATION / 49
2.1. Natural numbers / 50
2.1.1. The specificity of the preparatory class / 51
2.1.2. Natural numbers from 0 to 31. Preparatory class / 54
2.1.2.1. Entering natural numbers from 0 to 10 / 54
2.1.2.2. Entering natural numbers from 11 to 20 / 59
2.1.2.3. Entering natural numbers from 21 to 31 / 61
2.1.3. Natural numbers from 0 to 100. Class I / 61
2.1.4. Natural numbers smaller than 1,000,000. Classes II – IV / 63
2.1.5. Comparison, ordering and rounding of natural numbers / 67
2.1.5.1. Comparison and ordering of natural numbers / 67
2.1.5.2. Rounding of natural numbers / 68
2.2. Operations with natural numbers / 73
2.2.1. Addition and subtraction / 74
2.2.1.1. Addition and subtraction up to 10 / 75
a) Adding the numbers up to 10 / 75
b) Decreasing the numbers until 10 / 77
c) The connection between addition and subtraction / 79
2.2.1.2. Addition and subtraction in the center 0 → 20 / 81
a) Addition and subtraction in the center 0 → 20, without passing over order / 81
b) Addition and subtraction in the center 0 → 20, with passing over order / 83
2.2.1.3. Addition and subtraction in the center 0 → 100 / 88
2.2.1.4. Number 100 / 90
2.2.1.5. Addition and subtraction of natural numbers greater than 100 / 92
2.2.1.6. Finding an unknown number / 93
a) The reverse walking method / 93
b) Balance method / 97
2.2.2. Multiplication and division / 106
2.2.2.1. Teaching multiplication / 107
a) Multiplying a number by 10, 100, 1 000 / 109
b) Multiplying two numbers, one of which is written with a digit and the result does not exceed 10,000 / 110
c) Multiplying numbers when the factors have at most three digits / 112
2.2.2.2. Teaching division / 113
2.2.3. The order of operations / 125
2.3. Problem solving / 129
2.3.1. Problems that can be solved by a single operation / 131
2.3.2. Problems that are solved by two or more operations / 137
2.4. Fractions / 141
2.4.1. Representation, writing and reading of fractions / 142
2.4.2. Comparison of fractions / 145
2.4.2.1. Equal fractions / 145
2.4.2.2. Comparing a fraction with the whole / 146
2.4.2.3. Comparison of two fractions / 147
2.4.3. Adding and subtracting fractions with the same denominator / 148
2.5. Elements of geometry / 153
2.5.1. Elements of geometry in school programs for grades P-IV / 154
2.5.2. The specifics of teaching geometry elements / 155
2.5.3. Personalized reading of school programs / 158
2.6. Units of measure / 167
2.6.1. Units of measure in school programs for grades P-IV / 168
2.6.2. Conceptual clarifications / 169
2.6.3. Length measurement / 170
2.6.4. Measuring the capacity of vessels / 177
2.6.5. Measuring the mass of bodies / 177
2.6.6. Time measurement / 183
2.6.7. Measuring value. Money / 184
Bibliography / 188
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