This document provides an introduction to Euclid's geometry. It defines key terms like point, line, and plane used in Euclid's work. It explains that Euclid was the first to take a systematic deductive approach to geometry, establishing definitions, axioms, and proving theorems. It lists some of Euclid's definitions, five axioms, and provides an example of a proof from his work in "The Elements" establishing that two distinct lines cannot share more than one point.
Makalah belajar dan_pembelajaran_-pendidikan_matematika_2014linda_rosalina
Didalam Makalah ini terdapat materi-materi mengenai mata kulia belajar dan pembelajaran matematika.
adapun pokok bahasan yang dibahas dalam makalah ini, antara lain:
DAFTAR ISI
Halaman
DAFTAR ISI ii
BAB 1 HAKIKAT BELAJAR, MENGAJAR DAN PEMBELAJARAN 1
1.1 Pengertian belajar, mengajar, dan pembelajaran 1
1.2 Tujuan belajar dan pembelajaran 3
1.3 Faktor – faktor yang mempengaruhi belajar dan pembelajaran 4
1.4 Hubungan antara belajar dan pembelajaran 10
1.5 Rekayasa pembelajaran guru dan tindak belajar siswa 18
BAB 2 JENIS-JENIS DAN PRINSIP BELAJAR 20
2.1 Jenis Belajar Menurut Robert M.Gagne 20
2.2 Jenis Belajar Menurut Benyamin S.Bloom 22
2.3 Jenis Belajar Menurut UNESCO 24
2.4 Prinsip-prinsip Belajar 25
BAB 3 TEORI BELAJAR BEHAVIORISTK 29
3.1 Pengertian Teori Belajar Behavioristik 29
3.2 Ciri-ciri Teori Belajar Behavioristik 30
3.3 Tokoh-tokoh Aliran Behavioristik 30
3.4 Aplikasi Teori Belajar Behavioristik dalam Pembelajaran 57
3.5 Peran Guru dalam Teori Belajar Behavioristik 57
3.6 Peran Siswa dalam Teori Belajar Behavioristik 58
BAB 4 TEORI BELAJAR KOGNITIF 59
4.1 Teori Belajar Piaget 59
4.2 Teori Belajar Vygotsky 64
4.3 Teori Belajar Bruner 68
4.4 Teori Belajar Ausebel 69
BAB 5 TEORI BELAJAR HUMANISTIK 70
5.1 Pengertian Teori Belajar Humanistik 70
5.2 Tokoh dalam Teori Belajar Humanistik 70
BAB 6 TEORI BELAJAR SOSIAL 79
6.1 Pengertian Teori Belajar Sosial 79
6.2 Teori Belajar Sosial (Albert Bandura) 79
BAB 7 MOTIVASI BELAJAR 84
7.1 Pengertian Motivasi 84
7.2 Pentingnya Motivasi dalam Belajar 84
7.3 Jenis Motivasi 86
7.4 Sifat Motivasi 86
7.5 Motivasi dalam Belajar 87
7.6 Unsur-Unsur yang Mempengaruhi Motivasi Belajar 89
7.7 Upaya Meningkatkan Motivasi Belajar 91
BAB 8 KESULITAN BELAJAR 93
8.1 Pengertian Kesulitan Belajar 93
8.2 Faktor-Faktor Kesulitan Belajar 94
8.3 Jenis Kesulitan Belajar 98
8.4 Karakteristik Kesulitan Belajar 106
8.5 Cara Mengatasi Kesulitan Belajar 109
BAB 9 PENGERTIAN DAN JENIS-JENIS SUMBER BELAJAR 111
9.1 Pengertian Sumber Belajar 111
9.2 Fungsi Sumber Belajar 112
9.3 Jenis-Jenis Sumber Belajar 114
9.4 Kriteria Pemilihan Sumber Belajar 116
BAB 10 STRATEGI, PENDEKATAN, MODEL DAN METODE PEMBELAJARAN 117
10.1 Model Pembelajaran 117
10.2 Pendekatan Pembelajaran 129
10.3 Metode Pembelajaran 133
10.4 Strategi Pembelajaran 149
BAB 11 ANALISIS KASUS-KASUS PEMBELAJARAN MATEMATIKA 152
11.1 Pengertian Analisis Kasus Pembelajaran Matematika 152
11.2 Kasus Pembelajaran Matematika 152
11.3 Faktor Munculnya Kasus Pembelajaran Matematika 154
11.4 Pemecahan Kasus Pembelajaran Matematika 158
DAFTAR PUSTAKA 160
LAMPIRAN 163
Протокол №15/15ПС публичных слушаний по проекту межевания территории квартала, ограниченного Аэродромной улицей, улицей Фабрициуса, Туристской улицей, бульваром Яна Райниса (район Южное Тушино)
10 Steps for Transformation Education in India by Dr.Mahboob ali Khan Phd Healthcare consultant
Most of the steps needed to transform the quality of education in India do not require policy change or a new educational policy. Yet, these steps are not getting taken because there is no visible crisis pushing us to act. Only a few points in my list below – like the creation of a cadre of Indian education civil services, replacing the policy of schools within a kilometre of every habitation with a free transport to the nearest school policy – are policy-level issues.
Makalah belajar dan_pembelajaran_-pendidikan_matematika_2014linda_rosalina
Didalam Makalah ini terdapat materi-materi mengenai mata kulia belajar dan pembelajaran matematika.
adapun pokok bahasan yang dibahas dalam makalah ini, antara lain:
DAFTAR ISI
Halaman
DAFTAR ISI ii
BAB 1 HAKIKAT BELAJAR, MENGAJAR DAN PEMBELAJARAN 1
1.1 Pengertian belajar, mengajar, dan pembelajaran 1
1.2 Tujuan belajar dan pembelajaran 3
1.3 Faktor – faktor yang mempengaruhi belajar dan pembelajaran 4
1.4 Hubungan antara belajar dan pembelajaran 10
1.5 Rekayasa pembelajaran guru dan tindak belajar siswa 18
BAB 2 JENIS-JENIS DAN PRINSIP BELAJAR 20
2.1 Jenis Belajar Menurut Robert M.Gagne 20
2.2 Jenis Belajar Menurut Benyamin S.Bloom 22
2.3 Jenis Belajar Menurut UNESCO 24
2.4 Prinsip-prinsip Belajar 25
BAB 3 TEORI BELAJAR BEHAVIORISTK 29
3.1 Pengertian Teori Belajar Behavioristik 29
3.2 Ciri-ciri Teori Belajar Behavioristik 30
3.3 Tokoh-tokoh Aliran Behavioristik 30
3.4 Aplikasi Teori Belajar Behavioristik dalam Pembelajaran 57
3.5 Peran Guru dalam Teori Belajar Behavioristik 57
3.6 Peran Siswa dalam Teori Belajar Behavioristik 58
BAB 4 TEORI BELAJAR KOGNITIF 59
4.1 Teori Belajar Piaget 59
4.2 Teori Belajar Vygotsky 64
4.3 Teori Belajar Bruner 68
4.4 Teori Belajar Ausebel 69
BAB 5 TEORI BELAJAR HUMANISTIK 70
5.1 Pengertian Teori Belajar Humanistik 70
5.2 Tokoh dalam Teori Belajar Humanistik 70
BAB 6 TEORI BELAJAR SOSIAL 79
6.1 Pengertian Teori Belajar Sosial 79
6.2 Teori Belajar Sosial (Albert Bandura) 79
BAB 7 MOTIVASI BELAJAR 84
7.1 Pengertian Motivasi 84
7.2 Pentingnya Motivasi dalam Belajar 84
7.3 Jenis Motivasi 86
7.4 Sifat Motivasi 86
7.5 Motivasi dalam Belajar 87
7.6 Unsur-Unsur yang Mempengaruhi Motivasi Belajar 89
7.7 Upaya Meningkatkan Motivasi Belajar 91
BAB 8 KESULITAN BELAJAR 93
8.1 Pengertian Kesulitan Belajar 93
8.2 Faktor-Faktor Kesulitan Belajar 94
8.3 Jenis Kesulitan Belajar 98
8.4 Karakteristik Kesulitan Belajar 106
8.5 Cara Mengatasi Kesulitan Belajar 109
BAB 9 PENGERTIAN DAN JENIS-JENIS SUMBER BELAJAR 111
9.1 Pengertian Sumber Belajar 111
9.2 Fungsi Sumber Belajar 112
9.3 Jenis-Jenis Sumber Belajar 114
9.4 Kriteria Pemilihan Sumber Belajar 116
BAB 10 STRATEGI, PENDEKATAN, MODEL DAN METODE PEMBELAJARAN 117
10.1 Model Pembelajaran 117
10.2 Pendekatan Pembelajaran 129
10.3 Metode Pembelajaran 133
10.4 Strategi Pembelajaran 149
BAB 11 ANALISIS KASUS-KASUS PEMBELAJARAN MATEMATIKA 152
11.1 Pengertian Analisis Kasus Pembelajaran Matematika 152
11.2 Kasus Pembelajaran Matematika 152
11.3 Faktor Munculnya Kasus Pembelajaran Matematika 154
11.4 Pemecahan Kasus Pembelajaran Matematika 158
DAFTAR PUSTAKA 160
LAMPIRAN 163
Протокол №15/15ПС публичных слушаний по проекту межевания территории квартала, ограниченного Аэродромной улицей, улицей Фабрициуса, Туристской улицей, бульваром Яна Райниса (район Южное Тушино)
10 Steps for Transformation Education in India by Dr.Mahboob ali Khan Phd Healthcare consultant
Most of the steps needed to transform the quality of education in India do not require policy change or a new educational policy. Yet, these steps are not getting taken because there is no visible crisis pushing us to act. Only a few points in my list below – like the creation of a cadre of Indian education civil services, replacing the policy of schools within a kilometre of every habitation with a free transport to the nearest school policy – are policy-level issues.
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The word ‘Geometry’ comes from Greek words ‘geo’ meaning the ‘earth’ and ‘metrein’ meaning to ‘measure’. Geometry appears to have originated from the need for measuring land.
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The knowledge of geometry passed from Egyptians to the Greeks and many Greek mathematicians worked on geometry. The Greeks developed geometry in a systematic manner..
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4. INTRODUCTION
The word ‘Geometry’ comes from Greek words ‘geo’
meaning the ‘earth’ and ‘metrein’ meaning to ‘measure’.
Geometry appears to have originated from the need for
measuring land.
Nearly 5000 years ago geometry originated in Egypt as
an art of earth measurement. Egyptian geometry was the
statements of results.
The knowledge of geometry passed from Egyptians to
the Greeks and many Greek mathematicians worked on
geometry. The Greeks developed geometry in a systematic
manner..
5. Euclid was the first Greek Mathematician who initiated a new way of
thinking the study of geometry
He introduced the method of proving a geometrical result by deductive
reasoning based upon previously proved result and some self evident
specific assumptions called AXIOMS
The geometry of plane figure is known as ‘Euclidean Geometry’. Euclid
is known as the father of geometry.
His work is found in Thirteen books called ‘The Elements’.
6. EUCLID’S DEFINITONS
Some of the definitions made by Euclid involume I of
‘The Elements’ that we take for granted today are as follows :-
A point is that which has no part
A line is breadthless length
The ends of a line are points
A straight line is that whichhas lengthonly
7. Continued…..
The edges of a surface are lines
A plane surface is a surface which lies evenly with the straight
lines on itself
Axioms or postulates are the assumptions which are obvious
universal truths. They are not proved.
Theorems are statements which are proved, using definitions,
axioms, previously proved statements and deductive
reasoning.
8. EUCLID’S AXIOMs
SOME OF EUCLID’S AXIOMS WERE :-
Things which are equal to the same thing are equal to one
another.
i.e. if a=c and b=c then a=b.
Here a,b, and c are same kind of things.
If equals are added to equals, the wholes are equal.
9. Continued…..
i.e. if a=b and c=d, then a+c = b+d
Also a=b then this implies that a+c=b+c.
If equals are subtracted, the remainders are equal.
Things which coincide with one another are equal to one
another.
10. Continued…..
The whole is greater than the part.
That is if a > b then there exists c such that a =b + c. Here, b is
a part of a and therefore, a is greater than b.
Things which are double of the same things are equal to one
another.
Things which are halves of the same things are equal to one
another.
11. EUCLID’S FIVE POSTULATES
EUCLID’S POSTULATES WERE :-
POSTULATE 1:-
A straight line may be drawn from any one point to any other
point
Axiom :-
Given two distinct points, there is a unique line that passes
through them
12. Continued…..
POSTULATE 2 :-
A terminated line can be produced infinitely
POSTULATE 3 :-
A circle can be drawn with any centre and any radius
POSTULATE 4 :-
All right angles are equal to one another
13. Continued…..
POSTULATE 5 :-
If a straight line falling on two straight lines makes the
interior angles on the same side of it taken together less than
two right angles, then the two straight lines, if produced
indefinitely, meet on that side on which the sum of angles is
less than two right angles.
14. Example :-
In fig :- 01 the line EF falls on two lines AB and CD such that
the angle m + angle n < 180° on the right side of EF, then the
line eventually intersect on the right side of EF
fig :- o1
15. CONTINUED…..
THEOREM
Two distinct lines cannot have more than one point in
common
PROOF
Two lines ‘l’ and ‘m’ are given. We need to prove that they have
only one point in common
Let us suppose that the two lines intersects in two distinct
points, say P and Q
16. That is two line passes through two distinct points P and Q
But this assumptions clashes with the axiom that only one line can
pass through two distinct points
Therefore the assumption that two lines intersect in two distinct
points is wrong
Therefore we conclude that two distinct lines cannot have more than
one point in common