The DOI matches its Crossref record; 55 of the 55 references it cites were found in a registry or an index.
Together yet separate: Students’ associating amounts of change in quantities involved in rate of change
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“A student engaging in static shape thinking would interpret a graph as a being a manipulable shape (e.g., a graph of an absolute value function as being a BV^), but not necessarily iconically (e.g., a graph representing change in a liquid's volume and height in a filling bottle as being shaped like a bottle (see also Johnson, 2015b)).”
From A link between students’ discernment of variation in unidirectional change and their use of quantitative variational reasoning (2018) · cites this paper as Johnson, 2015b
Citations
Cites
Handbook of Qualitative Research
Crozier, G., Denzin, N., & Lincoln, Y. (1994) · British Journal of Educational Studies · doi:10.2307/3121684 · Cited by 26,666
Basics of Qualitative Research (3rd ed.): Techniques and Procedures for Developing Grounded Theory
Corbin, J., & Strauss, A. (2008) · SAGE · doi:10.4135/9781452230153 · Cited by 12,136
The SAGE handbook of qualitative research
(2005) · Choice Reviews Online · doi:10.5860/choice.43-1330 · Cited by 10,183
(2008) · Cited by 7,674
Handbook of research on mathematics teaching and learning
(1992) · Choice Reviews Online · doi:10.5860/choice.30-2122 · Cited by 6,121
The Sage Handbook of Qualitative Research[1]
(2006) · Qualitative Research in Organizations and Management An International Journal · doi:10.1108/17465640610666642 · Cited by 5,866
(2024) · Intersectional Advocacy · doi:10.1017/9781009433075.010 · Cited by 4,041
Second Handbook of Research on Mathematics Teaching and Learning.
Lester, F. (2007) · Cited by 3,090
Handbook of Complementary Methods in Education Research
(2012) · Routledge eBooks · doi:10.4324/9780203874769 · Cited by 2,029
Hamel, J., Dufour, S., & Fortin, D. (1993) · Medical Entomology and Zoology · Cited by 1,240
Research works printed but not linked: 6
- Cantoral, R., & Farfán, M. (1998). Pensamiento y lenguaje variacional en la introducción al análisis [Thought and variational language in the introduction to analysis]. Épsilon, 42(3), 353–369.
- Castillo-Garsow, C. (2010). Teaching the Verhulst model: A teaching experiment in covariational reasoning and exponential growth (Unpublished doctoral dissertation). Arizona State University, Phoenix, AZ.
- Clagett, M. (1968). Nicole Oresme and the medieval geometry of qualities and motions. Madison: University of Wisconsin Press.
- Heinz, K. (2000). Conceptions of ratio in a class of preservice and practicing teachers (Unpublished doctoral dissertation). The Pennsylvania State University, University Park, PA.
- Johnson, H. L. (2010). Making sense of rate of change: Secondary students' reasoning about changing quantities (Unpublished doctoral dissertation). The Pennsylvania State University, University Park, PA.
- Thompson, P. W. (2012). Invited commentary—Advances in research on quantitative reasoning. In R. Mayes & L. L. Hatfield (Eds.), Quantitative reasoning and mathematical modeling: A driver for STEM integrated education and teaching in context (Vol. 2, pp. 143–148). Laramie: University of Wyoming College of Education.
Cited by
Johnson, H. L., & McClintock, E. (2018) · Educational Studies in Mathematics · doi:10.1007/s10649-017-9799-7 · Cited by 23
“…would interpret a graph as a being a manipulable shape (e.g., a graph of an absolute value function as being a B V ^ ), but not necessarily iconically (e.g., a graph representing change in a liquid ’ s volume and height in a filling bottle as being shaped like a bottle (see also Johnson, 2015b)).”
BackgroundSelf-citation
Metadata
- Authors
- Johnson, H. L.
- Affiliations
- University of Colorado Denver (US)
- Corresponding author
- Johnson, Heather L.
- ORCID
- Johnson, Heather L.
- Venue
- Educational Studies in Mathematics
- Published
- 2015-01-27
- Volume
- 89
- Issue
- 1
- Pages
- 89-110
- ISSN
- 0013-1954 (ISSN-L)
- 1573-0816
- OpenAlex
- W2050921353
- Cited by
- 58
- References
- 55
- Citations by year
- 2026: 6 · 2025: 6 · 2024: 8 · 2023: 7 · 2022: 3 · 2021: 4 · 2020: 10 · 2019: 6 · 2018: 2 · 2017: 3 · 2016: 2 · 2015: 1
- FWCI
- 12.26
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Educational Studies in Mathematics (publishedVersion)
- Funders
- Pennsylvania State University
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Social Sciences › Education › Mathematics Education and Pedagogy
- Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
- Keywords
- rate of change, quantitative reasoning, multiple representations, Cartesian graphs, student reasoning, algebraic thinking
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Cite CoChat for the checks on this page, and the paper for its own findings.
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- CoChat. (2026). Citation check: Together yet separate: Students’ associating amounts of change in quantities involved in rate of change. https://app.cochat.ai/papers/10.1007/s10649-014-9590-y
- The paper
- Johnson, H. L. (2015). Together yet separate: Students’ associating amounts of change in quantities involved in rate of change. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-014-9590-y
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
