How and what to teach on an elementary number theory course.

In summary, in the late 80’s and early 90’s, there was a focus on "calculus reform" and changes in the syllabus and emphasis, as well as changes in the order of doing things in calculus, thanks to technology. Similarly, in linear algebra, a curriculum study group produced effective teaching methods and highlighted curriculum changes. This work was published in the January 1993 issue of College Mathematics Journal. As for number theory, there has been similar work in researching and teaching the subject, such as the book "Learning and Teaching Number Theory: Research in Cognition and Instruction." Interested individuals can also refer to the resource "Math Teachers’ Circle: Learning and Teaching Number Theory" for more information."
  • #1
matqkks
285
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In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things also changed in calculus with the advantage of technology.
Similarly in linear algebra there was a linear algebra curriculum study group which produced some really good ways of teaching linear algebra and also highlighted curriculum changes. This was produced in the January 1993 College Mathematics Journal.
Has any similar work been covered in number theory. I am looking for what are the important topics to cover and any work or research on the teaching of number theory.
 
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  • #2
matqkks said:
In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things also changed in calculus with the advantage of technology.
Similarly in linear algebra there was a linear algebra curriculum study group which produced some really good ways of teaching linear algebra and also highlighted curriculum changes. This was produced in the January 1993 College Mathematics Journal.
Has any similar work been covered in number theory. I am looking for what are the important topics to cover and any work or research on the teaching of number theory.

Hi matqkks, :)

You might be interested in the following.

1) Learning and Teaching Number Theory: Research in Cognition and Instruction (Mathematics, Learning, and Cognition): Stephen R. Campbell, Rina Zazkis: 9781567506532: Amazon.com: Books

2) http://www.mathteacherscircle.org/resources/materials/numbertheory.pdf
 

What is the purpose of teaching elementary number theory?

The purpose of teaching elementary number theory is to introduce students to the fundamental concepts and principles of number theory, which is the branch of mathematics that deals with properties of numbers and their relationships. This course helps students develop critical thinking skills and problem-solving abilities, and lays the foundation for more advanced mathematical concepts.

What topics should be covered in an elementary number theory course?

The topics covered in an elementary number theory course typically include prime numbers, divisibility, factors and multiples, prime factorization, greatest common divisor and least common multiple, modular arithmetic, and basic properties of integers. Other topics may include divisibility rules, Euclid's algorithm, and theorems related to prime numbers.

How should I approach teaching elementary number theory?

When teaching elementary number theory, it is important to start with concrete examples and real-world applications to make the concepts more relatable to students. Use interactive activities and visual aids to engage students and encourage them to think critically. It is also important to provide practice problems and encourage students to work through them on their own to reinforce their understanding.

What are some common misconceptions about number theory?

One common misconception about number theory is that it is only useful for theoretical mathematics and has no practical applications. However, number theory has many real-world applications in fields such as cryptography, computer science, and physics. Another misconception is that all prime numbers are odd, when in fact 2 is the only even prime number.

How can I make the material more interesting for students?

To make the material more interesting for students, you can incorporate fun and engaging activities, such as games, puzzles, and real-life examples. You can also use technology, such as interactive apps or online simulations, to make the material more interactive. Additionally, you can encourage students to explore and discover connections between number theory and other areas of mathematics, making the material more relevant and interesting.

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