Acquiring the principles of mathematics and science (Summary)

[Sir real]

How can I write a summary of the following article?

Task: Write a summary (120 words) from the article below.

ACQUIRING THE PRINCIPLES OF MATHEMATICS AND SCIENCE

A. It has been pointed out that learning mathematics and science is not so much learning facts as learning ways of thinking. It has also been emphasised that in order to learn science, people often have to change the way they think in ordinary situations. For example, in order to understand even simple concepts such as heat and temperature, ways of thinking of temperature as a measure of heat must be abandoned and a distinction between 'temperature' and 'heat' must be learned. These changes in ways of thinking are often referred to as conceptual changes. But how do conceptual changes happen? How do young people change their ways of thinking as they develop and as they learn in school?

B. Traditional instruction based on telling students how modern scientists think does not seem to be very successful. Students may learn the definitions, the formulae, the terminology, and yet still maintain their previous conceptions. This difficulty has been illustrated many times, for example, when instructed students are interviewed about heat and temperature. It is often identified by teachers as a difficulty in applying the concepts learned in the classroom; students may be able to repeat a formula but fail to use the concept represented by the formula when they explain observed events.

C. The psychologist Piaget suggested an interesting hypothesis relating to the process of cognitive change in children. Cognitive change was expected to result from the pupils' own intellectual activity. When confronted with a result that challenges their thinking - that is, when faced with conflict - pupils realise that they need to think again about their own ways of solving problems, regardless of whether the problem is one in mathematics or in science. He hypothesised that conflict brings about disequilibrium, and then triggers equilibration processes that ultimately produce cognitive change. For this reason, according to Piaget and his colleagues, in order for pupils to progress in their thinking they need to be actively engaged in solving problems that will challenge their current mode of reasoning. However, Piaget also pointed out that young children do not always discard their ideas in the face of contradictory evidence. They may actually discard the evidence and keep their theory.

 

[emsr2d2]

When do you have to submit your summary to your teacher for marking or grading?

 

[Tarheel]

Have you ever written a summary before? What stands out?

 

[Sir real]

When do you have to submit your summary to your teacher for marking or grading

This is not an assignment. I just want to have a better grasp at the idea of this article, maybe other articles and reading passages too.

 

[Sir real]

Have you ever written a summary before? What stands out?

I haven't, this might be the first summary. I guess the conceptual changes and how students can progress their ways of thinking by solving problems rather than learning facts stands out the most.

 

[Tarheel]

I would say that learning mathematics and science is not about learning facts as much as it is about learning new ways of thinking.

 

[emsr2d2]

Instead of asking us "How can I write a summary of the following article?", try searching the internet for general instructions on how to write summaries, then try to write the summary yourself and post it here. You'll learn a lot more that way.

 

[probus]

Have you tried chatgpt? It's far from perfect but it can be a great help with such tasks.

 

[teechar]

How can I write a summary of the following article?
Task: Write a summary (120 words) from the article below.

Are you preparing for some test?

ACQUIRING THE PRINCIPLES OF MATHEMATICS AND SCIENCE

Please cite properly where you got the text you quoted (author, publisher, year of publication, and provide a link if there is one).

 

[Sir real]

I have completed the summary, can you tell me if I am wrong somewhere.

The summary:

In the article “Acquiring the principles of mathematics and science” the writer discussed that learning mathematics and science is rather learning how to think differently than memorizing subjects’ facts. Traditionally, students were taught on how a scientist thinks and learned about the subject’s theory, which appears to be unsuccessful as students can recite the theory but fail to apply it to explain when they see an experiment. The writer also said that to learn mathematics and science, people need to think outside the box. The example was given as temperature and heat are not one but must be distinguished from each other, which the different thoughts on the example is also referred to as conceptual or cognitive changes. Piaget - a psychologist - hypothesized that to improve the students' cognitive changes, they have to achieve the skill of problem solving intentionally to adjust their rational behaviour.

 

[Sir real]

Please cite properly where you got the text you quoted (author, publisher, year of publication, and provide a link if there is one).

Oh, these are the 3 paragraphs of a reading from the book IELTS practice tests plus 3, the authors are Vanessa Jakeman and Clare McDowell

 

[teechar]

In the article “Acquiring the principles of mathematics and science” the writer [ 1] discussed [ 2] that learning mathematics and science is rather learning how to think differently than memorizing subjects’ facts from those subjects.

1- Use the present (not past) simple for summarizing a report.
2- "discussed that" is wrong. Use another reporting verb (e.g. states/argues that).
3- Avoid repetition in close proximity. Here, I'm talking about "learning".

[ 4] Traditionally, students were taught on how a scientist thinks and learned about the subject’s theory, which appears to be unsuccessful as students can recite the theory but fail to apply it to explain when they see an experiment.

4- That is not what the article says! It just points out the shortcomings of some traditional methods of teaching. You need to reword that part.

The writer also said that [ 5] To learn mathematics and science, people need to think outside the box.

[ 5]: In a summary, it is assumed you are not adding any input. Therefore, there is no need to keep referring back to the author.

The example was given as temperature and heat are not one but must be distinguished from each other, which the different thoughts on the example is also referred to as conceptual or cognitive changes.

Generally, examples are not included in summaries.

Piaget - a psychologist - hypothesized that to improve the students' cognitive changes, they students have to ...

The part below is wrong, especially "... their rational behaviour".

achieve the skill of problem solving intentionally to adjust their rational behaviour.

You also omitted the last part in section C, which I think should be included in the summary.

 

[Sir real]

I have revised the summary and I do not know if the last sentence which is about the reluctance of children in changing their previous idea when they are confronted with contradictory facts is necessary to put in the summary?

The summary:

In the article “Acquiring the principles of mathematics and science” the writer states that learning mathematics and science is rather learning how to think differently than memorizing facts from those subjects. Traditional teaching methods which focus on explaining how scientists think and emphasizing the theories of maths and science appears to be unsuccessful as students still keep their prior misconceptions and they can recite the theory but fail to apply it to explain when they see an experiment. To learn mathematics and science, people need to think outside the box, which is also referred to as conceptual or cognitive changes. Piaget - a psychologist - hypothesized that when students encounter a dispute in the outcome, they would rethink on their own the ways to solve problems. This will result in imbalance and again create a process of balancing to produce cognitive changes. Piaget and his coworkers affirm that to improve cognitive changes, pupils have to achieve the skill of problem solving intentionally, challenging their means of rationalizing.

 

[emsr2d2]

Oh, these are the 3 paragraphs of a reading from the book "IELTS Practice Tests Plus 3". The authors are Vanessa Jakeman and Clare McDowell.

Note my corrections above. Remember to capitalise book titles correctly.

 

[teechar]

I have revised the summary, and I do not but I don't know if the last sentence, which is about the children's reluctance of children in changing to change their previous idea preconception when they are confronted with contradictory facts, is necessary to put in the summary. ?

The summary:

In the article “Acquiring the principles of mathematics and science” the writer states that learning mathematics and science is rather learning how to think differently rather than memorizing facts from those subjects. Traditional teaching methods which focus on explaining how scientists think and emphasizing the theories of maths and science appear s to be unsuccessful as students still keep their prior misconceptions; and they can recite recall the theory but fail to apply it in actual situations. to explain when they see an experiment. To learn mathematics and science, people need to think outside the box, which is also referred to as conceptual or cognitive changes. Piaget - a psychologist - hypothesized that when students encounter a dispute in the outcome, challenging situation, they would re likely think on their own the and try to devise ways to solve such problems. This will result in imbalance and again create a process of balancing to produce cognitive changes. Piaget and his coworkers affirm that to improve cognitive changes, pupils have to achieve the skill of problem solving intentionally, challenging their means of rationalizing.

It's up to you whether you want to include that last part. I have already outlined my view on that.

 

[Tarheel]

Can you explain what you mean by "think outside the box"?

 

[5jj]

It's a fairly common expression: https://en.wikipedia.org/wiki/Think...tside the box (also,or from a new perspective.

 

[Tarheel]

Yes. It didn't start off that way, but now it's so common it's become trite. Also, I suspect that some people use it without knowing what it means. (I'm not sure myself.)