Using History to Teach Mathematics: The Case of Logarithms

Panagiotou, Evangelos N.

doi:10.1007/s11191-010-9276-5

Cited by 12 publications

(10 citation statements)

References 29 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It might be due to participants' inability to get the definition of logarithm and build connection to exponents. In this case, we made use of common conception that logarithm was the invers of raising to a power (exponents), thus we did not confirm the historical development of logarithm which emphasized the concept of geometric and arithmetic sequences (Fauvel, 1995;Katz, 1995;Panagiotou, 2011) as the basic theme when introducing logarithm. So, for instance, teachers should provide powerful explanation repetitively that c a b  can be expressed as log a b c  by using numerical example such as 3 2 2 8 log 8 3    .…”

Section: Graph Of Logarithm and Logarithmic Functionmentioning

confidence: 91%

How Do College Students Solve Logarithm Questions?

Aziz

Pramudiani

Purnomo

2017

Int. J. Emerg. Math. Educ.

View full text Add to dashboard Cite

AbstrakTujuan dari penelitian ini adalah untuk menyelidiki jawaban mahasiswa dalam menyelesaikan permasalahan logaritma. Penelitian ini menggunakan penelitian kualitiatif deskriptif. Partisipan penelitian ini adalah empat belas mahasiswa Indonesia yang terdaftar di berbagai perguruan tinggi di Ankara, Turki. Mereka menyelesaikan sepuluh pertanyaan logaritma yang diklasifikasikan menurut bagian-bagian dari topik logaritma. Setelah menganalisis jawaban tertulis mereka, wawancara dilakukan untuk mendapatkan penjelasan lebih lanjut tentang strategi mereka dan kesalahan yang umum dilakukannya. Penelitian ini menemukan bahwa berdasarkan pekerjaan masing-masing partisipan dalam menjawab pertanyaan logaritma, terdapat beberapa strategi yang dapat teridentifikasi, diantaranya (a) pengolahan basis, (b) terfokus pada aturan, (c) pemisahan, (d) loncatan berpikir, dan (e) penyesuaian. Bersamaan dengan itu, beberapa partisipan melakukan kesalahan karena memiliki miskonsepsi tentang logaritma, pemahaman aritmatika yang kurang kuat, dan penyalahgunaan konsep aljabar. Implikasi dari temuan ini difokuskan pada belajar dan mengajar logaritma yang disajikan lebih lanjut di dalam artikel.Kata Kunci: permasalahan logaritma, kesalahan umum mahasiswa, strategi mahasiswa, mahasiswa perguruan tinggi Abstract The purpose of the study was to investigate college students' work with logarithm questions. Qualitative descriptive research is chosen to reach the research goal. The participants of the study were fourteen Indonesian students who were enrolled at different universities in Ankara, Turkey. They worked to solve ten logarithm questions which were classified according to the contents. After analysing their written responses, interviews were conducted to obtain further explanation about their strategies and common mistakes. The study found that participants' works in dealing with logarithm questions comprised of (a) processing base, (b) holding the rule, (c) separating, (d) jumping, and (e) conditioning. Therewith, several participants made common mistake because of misconception about logarithm, arithmetical problems, and misuse of algebra concept. Implication of the finding of the study for teaching and learning logarithm were presented.

show abstract

Section: Graph Of Logarithm and Logarithmic Functionmentioning

confidence: 91%

How Do College Students Solve Logarithm Questions?

Aziz

Pramudiani

Purnomo

2017

Int. J. Emerg. Math. Educ.

View full text Add to dashboard Cite

show abstract

“…Early works of Archimedes and Euclid contributed to the development of the multiplicative world and arithmetic and geometric series. Chuquet argued that multiplication of two numbers might be simplified to the addition of their natural orders [3]. For instance, 2 • 4 = 8 corresponded to 1+2 = 3.…”

Section: Historical Overview Of Thementioning

confidence: 99%

Historical Overview of Logarithms and Implications for Teaching

2023

Proceeding Book of 3rd International Conference on Scientific and Academic Research ICSAR 2023

View full text Add to dashboard Cite

Historically, the invention and development of logarithms and logarithmic functions are so important that the power of modern calculations are rooted in these efforts. It is known that the development of logarithms was not quick and at least took half a century. The early attempts included a desire to advance multiplications and divisions with the help of tables that could be used once for all. This desire is no longer valid since computers and calculators can easily do very long and complex calculations. Thus, there needs to be a change in the objectives and the content of teaching logarithms so that the focus is on the conceptual part rather than the computational part. The benefits of using history in teaching mathematics have long been discussed. However, providing a clear road map for the use of available historical resources in teaching mathematics is rather rare. Investigating the historical development of mathematical concepts can provide many implications for teaching mathematics. Although this conceptual paper provides a very brief historical overview of the development of logarithms, an essential concept in advance mathematics, and a draft outline of a teaching sequence for teaching logarithms in high school classrooms it provides a clear introductory road map for teaching logarithms based on an history-integrated approach.

show abstract

“…This is the conceptualization of "logarithms" by Napier and Briggs in the early 17th century and the "logarithmic curves" of Newton, Huygens and Agnesi at the end of the same century. A historical review of the emergence of logarithms can be found in Panagiotou (2011) andFerrari (2008). We will refer to the common covariational reasoning of both functions as logarithmic-exponential covariational reasoning.…”

Section: Purpose Of Researchmentioning

confidence: 99%