The DOI matches its Crossref record; 20 of the 20 references it cites were found in a registry or an index.
The development of proportional reasoning and the ratio concept Part I ? Differentiation of stages
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
- STATISTICAL PACKAGE FOR SOCIAL SCIENCES
(2014) · Statistical Methods in Psychiatry Research and SPSS · doi:10.1201/b17560-26 · Cited by 12,056
Statistical Package for the Social Sciences
Greatorex, M. (2015) · Wiley Encyclopedia of Management · doi:10.1002/9781118785317.weom090665 · Cited by 4,389
Non-Parametric Statistics for the Behavioral Sciences.
Stuart, A., & Siegel, S. (1957) · Economica · doi:10.2307/2551606 · Cited by 3,383
Torgerson, W. S. (1958) · Medical Entomology and Zoology · Cited by 2,920
BMD : biomedical computer programs
Dixon, W. J. (1965) · University of California Press eBooks · Cited by 2,673
The psychology of meaningful verbal learning.
Ausubel, D. P. (1963) · Cited by 2,568
Nonparametric Statistics for the Behavioral Sciences.
David, F. N., & Siegel, S. (1957) · Biometrika · doi:10.2307/2332896 · Cited by 1,362
Mathematics as an Educational Task
Freudenthal, H. (1972) · doi:10.1007/978-94-010-2903-2 · Cited by 1,336
A Basis for Scaling Qualitative Data
Guttman, L. (1944) · American Sociological Review · doi:10.2307/2086306 · Cited by 1,317
Stouffer, S. A. (1950) · Princeton University Press eBooks · Cited by 1,244
Cited by
Bilingualism: consequences for mind and brain
Bialystok, E., Craik, F. I. M., & Luk, G. (2012) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2012.03.001 · Cited by 1,386
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008) · Mathematical Thinking and Learning · doi:10.1080/10986060802229675 · Cited by 1,222
Functions, Graphs, and Graphing: Tasks, Learning, and Teaching
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990) · Review of Educational Research · doi:10.3102/00346543060001001 · Cited by 1,103
Rational Number, Ratio, and Proportion
Behr, M. J., Harel, G., Post, T., & Lesh, R. (2006) · Handbook of Research on Mathematics Teaching and Learning · doi:10.1108/978-1-60752-874-620251018 · Cited by 403
The relationship between bilingualism and the development of cognitive processes in problem-solving
Bialystok, E., & Majumder, S. (1998) · Applied Psycholinguistics · doi:10.1017/s0142716400010584 · Cited by 292
Metadata
- Authors
- Noelting, G.
- Venue
- Educational Studies in Mathematics
- Published
- 1980-05
- Volume
- 11
- Issue
- 2
- Pages
- 217-253
- ISSN
- 0013-1954 (ISSN-L)
- 1573-0816
- OpenAlex
- W2041436215
- Cited by
- 278
- References
- 20
- FWCI
- 4.78
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The development of proportional reasoning and the ratio concept Part I ? Differentiation of stages. https://app.cochat.ai/papers/10.1007/bf00304357
- The paper
- Noelting, G. (1980). The development of proportional reasoning and the ratio concept Part I ? Differentiation of stages. Educational Studies in Mathematics. https://doi.org/10.1007/bf00304357
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.
