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The first one is a test if a child has understood conservation of matter. It is an example of a conservation task. These belong to the tests used in the framework of Piaget to test what stage of development a child is in.
Here is a video demonstration of the cookie task. HereHere is another question on this site pertaining to a different conservation task.

The second one is an example of a false-belief task test for the Theory of Mind. See here for some criticism of the false-belief task, questioning if it truly tests what it aims to test.

I don't think it's appropriate to say either of these is used to test if children are "thinking on their own" for what it's worth. They're about developmental stages.

The first one is a test if a child has understood conservation of matter. It is an example of a conservation task. These belong to the tests used in the framework of Piaget to test what stage of development a child is in.
Here is a video demonstration of the cookie task. Here is another question on this site pertaining to a different conservation task.

The second one is an example of a false-belief task test for the Theory of Mind. See here for some criticism of the false-belief task, questioning if it truly tests what it aims to test.

I don't think it's appropriate to say either of these is used to test if children are "thinking on their own" for what it's worth. They're about developmental stages.

The first one is a test if a child has understood conservation of matter. It is an example of a conservation task. These belong to the tests used in the framework of Piaget to test what stage of development a child is in.
Here is a video demonstration of the cookie task. Here is another question on this site pertaining to a different conservation task.

The second one is an example of a false-belief task test for the Theory of Mind. See here for some criticism of the false-belief task, questioning if it truly tests what it aims to test.

I don't think it's appropriate to say either of these is used to test if children are "thinking on their own" for what it's worth. They're about developmental stages.

3 added 220 characters in body
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The first one is a test if a child has understood conservation of matter. It is an example of a conservation task. These belong to the tests used in the framework of Piaget to test what stage of development a child is in.   
Here is a video demonstration of the cookie task. Here is another question on this site pertaining to a different conservation task.

The second one is an example of a false-belief task test for the Theory of Mind. See here for some criticism of the false-belief task, questioning if it truly tests what it aims to test.

I don't think it's appropriate to say either of these is used to test if children are "thinking on their own" for what it's worth. They're about developmental stages.

The first one is a test if a child has understood conservation of matter. It is an example of a conservation task. These belong to the tests used in the framework of Piaget to test what stage of development a child is in.  Here is a video demonstration of the cookie task.

The second one is an example of a false-belief task test for the Theory of Mind. See here for some criticism of the false-belief task, questioning if it truly tests what it aims to test.

I don't think it's appropriate to say either of these is used to test if children are "thinking on their own" for what it's worth. They're about developmental stages.

The first one is a test if a child has understood conservation of matter. It is an example of a conservation task. These belong to the tests used in the framework of Piaget to test what stage of development a child is in. 
Here is a video demonstration of the cookie task. Here is another question on this site pertaining to a different conservation task.

The second one is an example of a false-belief task test for the Theory of Mind. See here for some criticism of the false-belief task, questioning if it truly tests what it aims to test.

I don't think it's appropriate to say either of these is used to test if children are "thinking on their own" for what it's worth. They're about developmental stages.

2 added 36 characters in body
source | link

The first one is a test if a child has understood conservation of matter. It is an example of a conservation task. These belong to the tests used in the framework of Piaget to test what stage of development a child is in. Here is a video demonstration of the cookie task.

The second one is an example of a false-belief task test for the Theory of Mind. See here for some criticism of the false-belief task, questioning if it truly tests what it aims to test.

I don't think it's appropriate to say either of these is used to test if children are "thinking on their own" for what it's worth. They're about developmental stages.

The first one is a test if a child has understood conservation of matter. It is an example of a conservation task. These belong to the tests used in the framework of Piaget to test what stage of development a child is in. Here is a video demonstration of the cookie task.

The second one is an example of a false-belief task test for the Theory of Mind. See here for some criticism of the false-belief task, questioning if it truly tests what it aims to test.

I don't think it's appropriate to say either of these is used to test if children are "thinking on their own" for what it's worth.

The first one is a test if a child has understood conservation of matter. It is an example of a conservation task. These belong to the tests used in the framework of Piaget to test what stage of development a child is in. Here is a video demonstration of the cookie task.

The second one is an example of a false-belief task test for the Theory of Mind. See here for some criticism of the false-belief task, questioning if it truly tests what it aims to test.

I don't think it's appropriate to say either of these is used to test if children are "thinking on their own" for what it's worth. They're about developmental stages.

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