Logarithms through their history in mathematics education

2020 ◽  
pp. 29-41
Author(s):  
Sam Riley
Keyword(s):  
Mathematics Education ◽  
Textbook Analysis ◽  
First Century ◽  
Geometric Progression ◽  
Mathematical Beliefs ◽  
Exponential Equation ◽  
Mechanical Object

Over the first century and a half of their discovery, logarithms were seen and understood in a variety of ways. Depending on the mathematical beliefs of an author, they could choose to introduce logarithms as a geometric-mechanical object, or as an index of a geometric progression, or through an exponential equation. The choice of introduction then influenced how their reader viewed and used logarithms, and has implications for teachers today as they attempt to explain this topic. In looking over the works of three authors, Colin MacLaurin, William Frend, and George Peacock, we can see logarithms displayed in three different ways. In combining these presentations with our modern understanding of logarithms as a number, an operation, and a function, we can choose parts of the text that could help current students make sense of a difficult concept. Keywords: history, mathematicians, Cambridge, logarithms, textbook analysis

One Point of View: Passports to Opportunity

1986 ◽  
Vol 33 (9) ◽  
pp. 1
Author(s):  
B. Ross Taylor
Keyword(s):  
Elementary School ◽  
Mathematics Education ◽  
Elementary School Students ◽  
Information Society ◽  
Point Of View ◽  
First Century ◽  
School Students ◽  
Education Today ◽  
Twenty First Century

We are preparing today's elementary school students to live in the information society of the twenty-first century. In that society, whether one is a “have” or a “have not” will be determined largely by one' s education; the ability to do mathematics and solve problems will be essential. Today we have dramatic racial inequities in employment and income. We also have great disparities by race in students' achievement and participation in mathematics. To reduce the inequities in society tomorrow, we must address the disparitie in mathematics today. In my opinion, this challenge is the major issue in mathematics education today.

Problem Solving and Mathematical Beliefs

1988 ◽  
Vol 35 (5) ◽  
pp. 32-34 ◽  
Author(s):  
Martha L. Frank
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Programming Languages ◽  
Computer Programming ◽  
Mathematical Beliefs ◽  
Step Method ◽  
Problem Solvers

A frequently asked question in the decade since problem solving has become a popular topic in mathematics education is “How can we get students to become better problem solvers?” Answers to this question have focused on such in structional techniques as the introduction of problem-problemsolving strategies (“heuristics”), Polya's four-step method, or even the teaching of computer programming languages such as Logo or BASIC.

scholarly journals Mathematics education in the spotlight: Its purpose and some implications

2018 ◽  
Author(s):  
Jennie Golding
Keyword(s):  
Mathematics Education ◽  
Young People ◽  
Teacher Expertise ◽  
First Century ◽  
High Quality ◽  
Policy Context ◽  
Subject Specific ◽  
Twenty First Century ◽  
Specific Expertise

This article proposes a reframing of the purposes of mathematics education for the twenty-first century that combines apparently divergent philosophical approaches, arguing that the consequent empowerment should as a matter of individual equity be available to all young people (as well as of benefit to wider society). It suggests that the global mathematics attainment 'spotlight', and the English policy context in particular, offer both opportunities and constraints for the development of such a high-quality mathematics education. The article also discusses the challenging implications for the curriculum, and for the nature of teacher expertise, particularly subject-specific expertise, that is needed.

scholarly journals Complex Tasks: Potentials and Pitfalls

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1780
Author(s):  
Nina Bohlmann ◽  
Ralf Benölken
Keyword(s):  
Mathematics Education ◽  
Rapid Change ◽  
Analytical Investigation ◽  
Teaching Experiment ◽  
First Century ◽  
Mathematical Tasks ◽  
Complex Tasks ◽  
School Teaching ◽  
Twenty First Century ◽  
Twenty First Century Skills

Life in today’s world is characterized by complexity and rapid change. Twenty-first century skills and especially mathematical understanding are supposed to crucially contribute to meeting the demands of our world since mathematics offers strategies to structure or simplify complex problems. An open question is which teaching practices are appropriate to provide all students with such skills and to broaden the participation of underprivileged students. The present article explores these aspects by focusing on complex tasks, a practice that can be considered highly accepted in the context of mathematics education all over the world. We will concentrate on the perspective of the German mathematics education community as the foundation of our considerations. Based on an analytical investigation of mathematical literacy and twenty-first century skills (such as creativity, critical thinking, or problem-solving), we will address central ideas and characteristics of complex mathematical tasks. To complement the analytical approach, we will illustrate their characteristics as well as possible intersections with twenty-first century skills by presenting an elementary school teaching experiment. Finally, we will critically discuss the potentials and pitfalls of complex mathematical tasks from an abstract perspective and conclude by debating practical consequences for organizing mathematical learning-teaching-processes.

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