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数学

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Andrius Kulikauskas

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Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

Book.MathActivity istorija

Paslėpti nežymius pakeitimus - Rodyti galutinio teksto pakeitimus

2019 kovo 03 d., 22:08 atliko AndriusKulikauskas -
Pakeistos 41-44 eilutės iš
* List unlike units.
į:
* List unlike units.
* Extend the domain.
* Every right triangle is half a rectangle.
* Every triangle is two right triangles
.
2019 kovo 03 d., 22:08 atliko AndriusKulikauskas -
Pakeista 40 eilutė iš:
* Add like units.
į:
* Combine like units.
2019 kovo 03 d., 22:08 atliko AndriusKulikauskas -
Pakeistos 39-41 eilutės iš
* Every answer is an amount and a unit. These are the grounds for recognizing differences (amounts) and similarities (units). "Comparing apples and oranges."
į:
* Every answer is an amount and a unit. These are the grounds for recognizing differences (amounts) and similarities (units). "Comparing apples and oranges."
* Add like units.
* List unlike units.
2019 kovo 03 d., 21:30 atliko AndriusKulikauskas -
Pakeistos 13-14 eilutės iš
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į:
>>bgcolor=#FFFFC0<<
Pakeista 17 eilutė iš:
į:
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2019 kovo 03 d., 21:29 atliko AndriusKulikauskas -
Pridėtos 25-30 eilutės:
A math result is an Alexandrian pattern which brings together:
* the forces in tension: the axioms or principles that it involves
* the instances, particular and general: the objects (of whatever degree of abstraction) that it holds for
* the logic that holds it together, the rule of thumb: an argumentation (a proof or demonstration)
* the way of figuring things out that brought it together
Ištrintos 34-39 eilutės:
Consider the relation between:
* an argumentation (a proof or demonstration)
* the axioms or principles that it involves
* the objects (of whatever degree of abstraction) that it holds for
* the way of figuring things out that brought it together
Pakeistos 37-40 eilutės iš
Math should derive from logic, from perfect duality, and variation from it. The relation between logic and metalogic is given by our interpretation of a variable with reference to one of four levels. This establishes an analogy between logic, set theory, category theory and...? See [[logic]].
į:
Math should derive from logic, from perfect duality, and variation from it. The relation between logic and metalogic is given by our interpretation of a variable with reference to one of four levels. This establishes an analogy between logic, set theory, category theory and...? See [[logic]].

List basic principles of math:
* Every answer is an amount and a unit. These are the grounds for recognizing differences (amounts) and similarities (units). "Comparing apples and oranges."
2019 kovo 03 d., 21:16 atliko AndriusKulikauskas -
Pakeista 20 eilutė iš:
Attach:mathactivity-investigate.png
į:
%center%Attach:mathactivity-investigate.png
Pakeista 22 eilutė iš:
Attach:mathactivity-distinguish.png
į:
%center%Attach:mathactivity-distinguish.png
2019 kovo 03 d., 17:58 atliko AndriusKulikauskas -
Pakeistos 22-37 eilutės iš

Mathematical activities
* Characterizing objects
** Counting
- characterizing a set
* Identifying objects
* Constructing objects
* Checking objects (if they satisfy conditions and which conditions they satisfy)
* Calculating
* Proving
* Understanding
* Learning
* Teaching
* Giving an answer
* Asking a question
* Figuring out the answer
į:
Attach:mathactivity-distinguish.png
---------------

Counting:
characterizing a set.
2019 kovo 03 d., 17:54 atliko AndriusKulikauskas -
Pridėtos 18-21 eilutės:

---------------
Attach:mathactivity-investigate.png
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2019 kovo 03 d., 14:18 atliko AndriusKulikauskas -
Pridėtos 10-11 eilutės:

Given a theory, as in geometry, collect and study the questions that arise.
2019 kovo 03 d., 14:17 atliko AndriusKulikauskas -
Pridėtos 8-9 eilutės:

Study the most basic math, what is taught in grade school. Study geometries as theories.
2019 kovo 03 d., 14:15 atliko AndriusKulikauskas -
Pridėtos 26-28 eilutės:
* Giving an answer
* Asking a question
* Figuring out the answer
2019 kovo 03 d., 14:14 atliko AndriusKulikauskas -
Pakeista 7 eilutė iš:
Consider math as the most general discipline for figuring things out, for relating questions and answers, in the spirit of games of understanding.
į:
Consider math as the most general discipline for figuring things out, for relating questions and answers, in the spirit of games of understanding. Look for the role of duality and deviation from it.
Pakeista 28 eilutė iš:
Note: the action becomes an object in its own right. For example, an object is characterized by whether it is an instance of itself or is not. The multiset of instances is then is characterized by distinguishing a set of distinct instances. A set is characterized by counting it. But the count is not a set but a list. In this way, algebra unfolds to yield counting.
į:
Note: the action becomes an object in its own right. For example, an object is characterized by whether it is an instance of itself or is not. The multiset of instances is then characterized by distinguishing a set of distinct instances. A set is characterized by counting it. But the count is not a set but a list. In this way, algebra unfolds to yield counting.
2019 kovo 03 d., 14:07 atliko AndriusKulikauskas -
Pakeista 7 eilutė iš:
Consider math as the most general discipline for figuring things out, for relating questions and answers, in the spirit of games.
į:
Consider math as the most general discipline for figuring things out, for relating questions and answers, in the spirit of games of understanding.
2019 kovo 03 d., 14:06 atliko AndriusKulikauskas -
Pridėtos 6-7 eilutės:

Consider math as the most general discipline for figuring things out, for relating questions and answers, in the spirit of games.
2019 vasario 03 d., 21:01 atliko AndriusKulikauskas -
Pakeista 36 eilutė iš:
Math should derive from logic, from perfect duality, and variation from it. The relation between logic and metalogic is given by our interpretation of a variable with reference to one of four levels. This establishes an analogy between logic, set theory, category theory and...?
į:
Math should derive from logic, from perfect duality, and variation from it. The relation between logic and metalogic is given by our interpretation of a variable with reference to one of four levels. This establishes an analogy between logic, set theory, category theory and...? See [[logic]].
2019 vasario 03 d., 21:00 atliko AndriusKulikauskas -
Pakeistos 34-36 eilutės iš
Study polymorphism of principles of basic math
į:
Study polymorphism of principles of basic math

Math should derive from logic, from perfect duality, and variation from it. The relation between logic and metalogic is given by our interpretation of a variable with reference to one of four levels. This establishes an analogy between logic, set theory, category theory and...?
2019 sausio 30 d., 10:09 atliko AndriusKulikauskas -
Pakeistos 32-34 eilutės iš
* the way of figuring things out that brought it together
į:
* the way of figuring things out that brought it together

Study polymorphism of principles of basic math
2019 sausio 29 d., 22:42 atliko AndriusKulikauskas -
Pridėtos 28-32 eilutės:
Consider the relation between:
* an argumentation (a proof or demonstration)
* the axioms or principles that it involves
* the objects (of whatever degree of abstraction) that it holds for
* the way of figuring things out that brought it together
2019 sausio 26 d., 23:43 atliko AndriusKulikauskas -
Pridėtos 10-11 eilutės:
* Consider how all aspects of math may be generated.
* Relate that to the ways of figuring things out, and in particular, the three-cycle.
2019 sausio 26 d., 23:42 atliko AndriusKulikauskas -
Pridėta 16 eilutė:
* Checking objects (if they satisfy conditions and which conditions they satisfy)
2019 sausio 26 d., 23:41 atliko AndriusKulikauskas -
Pakeista 23 eilutė iš:
Note: the action becomes an object in its own right. For example, a set is characterized by counting it. But the count is not a set but a list. In this way, algebra unfolds to yield counting.
į:
Note: the action becomes an object in its own right. For example, an object is characterized by whether it is an instance of itself or is not. The multiset of instances is then is characterized by distinguishing a set of distinct instances. A set is characterized by counting it. But the count is not a set but a list. In this way, algebra unfolds to yield counting.
2019 sausio 26 d., 23:38 atliko AndriusKulikauskas -
Pakeista 23 eilutė iš:
Note: the action becomes an object in its own right. For example, a set is characterized by counting it. But the count is not a set but a list.
į:
Note: the action becomes an object in its own right. For example, a set is characterized by counting it. But the count is not a set but a list. In this way, algebra unfolds to yield counting.
2019 sausio 26 d., 23:37 atliko AndriusKulikauskas -
Pridėtos 21-23 eilutės:


Note: the action becomes an object in its own right. For example, a set is characterized by counting it. But the count is not a set but a list.
2019 sausio 26 d., 23:34 atliko AndriusKulikauskas -
Pridėta 13 eilutė:
** Counting - characterizing a set
2019 sausio 26 d., 23:34 atliko AndriusKulikauskas -
Pridėtos 12-14 eilutės:
* Characterizing objects
* Identifying objects
* Constructing objects
2019 sausio 26 d., 23:33 atliko AndriusKulikauskas -
Pridėtos 10-16 eilutės:

Mathematical activities
* Calculating
* Proving
* Understanding
* Learning
* Teaching
2019 sausio 26 d., 23:33 atliko AndriusKulikauskas -
Pakeistos 7-10 eilutės iš
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į:
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What kinds of mathematical activity are there, how are they related and what do they involve?
2019 sausio 26 d., 23:32 atliko AndriusKulikauskas -
Pridėtos 1-7 eilutės:
>>bgcolor=#E9F5FC<<
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See: [[Math Big Picture]]

'''Understand mathematics by describing it as an activity.'''
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MathActivity


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Puslapis paskutinį kartą pakeistas 2019 kovo 03 d., 22:08
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