Foundational ways of thinking for understanding the idea of logarithm

Emily Kuper, Marilyn Carlson

Research output: Contribution to journalArticle

Abstract

This study explored two undergraduate precalculus students’ understandings of the idea of logarithm as they completed conceptually oriented exploratory lessons on exponential and logarithmic functions. The students participated in consecutive, individual teaching experiments that focused on Sparky – an animated mystical saguaro that doubled in height every week. The exponential lesson focused on developing students’ conceptions of growth factors and tupling (e.g., doubling) periods as a foundational understanding for conceptualizing logarithms and logarithmic properties meaningfully. This paper characterizes conceptions that are productive for students to acquire in introductory lessons on exponential and logarithmic growth, and discusses two understandings that were revealed to be foundational for students’ development of productive meanings for exponents, logarithms and logarithmic properties.

Original languageEnglish (US)
Article number100740
JournalJournal of Mathematical Behavior
Volume57
DOIs
StatePublished - Mar 2020

Fingerprint

Logarithm
Logarithmic
Students
student
Period Doubling
Growth Factors
Consecutive
Exponent
Intercellular Signaling Peptides and Proteins
Teaching
experiment
Experiment
Growth
Experiments

Keywords

  • Exponent
  • Exponential
  • Growth factor
  • Logarithm
  • Logarithmic
  • Tupling-period

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics

Cite this

Foundational ways of thinking for understanding the idea of logarithm. / Kuper, Emily; Carlson, Marilyn.

In: Journal of Mathematical Behavior, Vol. 57, 100740, 03.2020.

Research output: Contribution to journalArticle

@article{97a90ea0c80b4dbd888664b85dd86b39,
title = "Foundational ways of thinking for understanding the idea of logarithm",
abstract = "This study explored two undergraduate precalculus students’ understandings of the idea of logarithm as they completed conceptually oriented exploratory lessons on exponential and logarithmic functions. The students participated in consecutive, individual teaching experiments that focused on Sparky – an animated mystical saguaro that doubled in height every week. The exponential lesson focused on developing students’ conceptions of growth factors and tupling (e.g., doubling) periods as a foundational understanding for conceptualizing logarithms and logarithmic properties meaningfully. This paper characterizes conceptions that are productive for students to acquire in introductory lessons on exponential and logarithmic growth, and discusses two understandings that were revealed to be foundational for students’ development of productive meanings for exponents, logarithms and logarithmic properties.",
keywords = "Exponent, Exponential, Growth factor, Logarithm, Logarithmic, Tupling-period",
author = "Emily Kuper and Marilyn Carlson",
year = "2020",
month = "3",
doi = "10.1016/j.jmathb.2019.100740",
language = "English (US)",
volume = "57",
journal = "Journal of Mathematical Behavior",
issn = "0732-3123",
publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Foundational ways of thinking for understanding the idea of logarithm

AU - Kuper, Emily

AU - Carlson, Marilyn

PY - 2020/3

Y1 - 2020/3

N2 - This study explored two undergraduate precalculus students’ understandings of the idea of logarithm as they completed conceptually oriented exploratory lessons on exponential and logarithmic functions. The students participated in consecutive, individual teaching experiments that focused on Sparky – an animated mystical saguaro that doubled in height every week. The exponential lesson focused on developing students’ conceptions of growth factors and tupling (e.g., doubling) periods as a foundational understanding for conceptualizing logarithms and logarithmic properties meaningfully. This paper characterizes conceptions that are productive for students to acquire in introductory lessons on exponential and logarithmic growth, and discusses two understandings that were revealed to be foundational for students’ development of productive meanings for exponents, logarithms and logarithmic properties.

AB - This study explored two undergraduate precalculus students’ understandings of the idea of logarithm as they completed conceptually oriented exploratory lessons on exponential and logarithmic functions. The students participated in consecutive, individual teaching experiments that focused on Sparky – an animated mystical saguaro that doubled in height every week. The exponential lesson focused on developing students’ conceptions of growth factors and tupling (e.g., doubling) periods as a foundational understanding for conceptualizing logarithms and logarithmic properties meaningfully. This paper characterizes conceptions that are productive for students to acquire in introductory lessons on exponential and logarithmic growth, and discusses two understandings that were revealed to be foundational for students’ development of productive meanings for exponents, logarithms and logarithmic properties.

KW - Exponent

KW - Exponential

KW - Growth factor

KW - Logarithm

KW - Logarithmic

KW - Tupling-period

UR - http://www.scopus.com/inward/record.url?scp=85075196260&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075196260&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2019.100740

DO - 10.1016/j.jmathb.2019.100740

M3 - Article

AN - SCOPUS:85075196260

VL - 57

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

M1 - 100740

ER -