Recommendations for a “Target Understanding” of the Derivative Concept for First-Semester Calculus Teaching and Learning

Recommendations for a “Target Understanding” of the Derivative Concept for First-Semester... The derivative framework described by Zandieh (2000) has been an important tool in calculus education research, and many researchers have revisited the framework to elaborate on it, extend it, or refine certain aspects of it. We continue this process by using the framework to put forward a suggestion on what might constitute a “target understanding” of the derivative concept for first-semester calculus teaching and learning. We draw on empirical results from psychological research into analogical reasoning in order to create a guideline for such a “target understanding,” which includes a process-object comprehension of the ratio-limit-function layers in three distinct graphical-symbolic-verbal/rate-physical contexts. Our recommended target understanding creates a testable hypothesis, in that obtaining this target may allow students to apply their derivative understanding to additional contexts, as needed. We provide the results of an empirical study regarding this hypothesis and show that they support our recommendation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Research in Undergraduate Mathematics Education Springer Journals

Recommendations for a “Target Understanding” of the Derivative Concept for First-Semester Calculus Teaching and Learning

Loading next page...
 
/lp/springer_journal/recommendations-for-a-target-understanding-of-the-derivative-concept-Y5VwqsUDsv
Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG Switzerland
Subject
Education; Mathematics Education; Learning and Instruction
ISSN
2198-9745
eISSN
2198-9753
D.O.I.
10.1007/s40753-017-0057-2
Publisher site
See Article on Publisher Site

Abstract

The derivative framework described by Zandieh (2000) has been an important tool in calculus education research, and many researchers have revisited the framework to elaborate on it, extend it, or refine certain aspects of it. We continue this process by using the framework to put forward a suggestion on what might constitute a “target understanding” of the derivative concept for first-semester calculus teaching and learning. We draw on empirical results from psychological research into analogical reasoning in order to create a guideline for such a “target understanding,” which includes a process-object comprehension of the ratio-limit-function layers in three distinct graphical-symbolic-verbal/rate-physical contexts. Our recommended target understanding creates a testable hypothesis, in that obtaining this target may allow students to apply their derivative understanding to additional contexts, as needed. We provide the results of an empirical study regarding this hypothesis and show that they support our recommendation.

Journal

International Journal of Research in Undergraduate Mathematics EducationSpringer Journals

Published: Jun 29, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off