# Analysis of University STEM Students’ Mathematical, Linguistic, Rhetorical–Organizational Assignment Errors

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Error Analysis: Theoretical Background

#### 1.2. Our Study

## 2. Experimental Details

#### 2.1. Participants

#### 2.2. Data Collection

- Everything must be expressed in written form in a way that should be legible and understandable by a STEM student (in the first years).
- The bibliography must include all the sources used.
- The information to include is as follows:
- -
- Title of the essay and name of the students in the group;
- -
- Table of contents;
- -
- Introduction;
- -
- Description of the element, operation, classification, applications. If possible, videos of the item working can be attached;
- -
- Calculations: Propose 2 or 3 solved and explained examples of calculation and design so that they are understandable for self-study. In the case of the simplest elements (such as bearings, screws, belts, and springs), a greater number of exercises should be presented;
- -
- Conclusions;
- -
- Bibliography.

#### 2.3. Categorization of Errors

#### 2.3.1. Mathematical Errors

- Mathematical coherence in the management of formulas and units (from MAT-1 to MAT-9). They include errors in the system of units and their conversion, numerical calculations, errors in mathematical notation. As can be seen, this category is the one containing the highest number of errors, up to 9. After a first evaluation of the corpus, it was already observed that there were a large number of errors related to mathematical coherence. Given their number and variety, nine subcategories of these errors were proposed.
- Technical description of operation and applications (from MAT-10 to MAT-12): These are errors in the interpretation of data and their incorporation in the formulas used, omissions in definitions of the parameters used in the design, use of tables, or experimental graphs, or design standards.
- Decision-making (from MAT-13 to MAT-15): These errors are related to omissions in the explanation of the calculation method used, as well as omissions or mistakes in admissible convergence criteria in iterative mathematical processes.

#### 2.3.2. Linguistic Errors

- The first one includes errors concerning the syntax of the sentence. Questions such as the complexity of the sentences, the use of connectors, and the coherence in the use of verb tenses are considered here (from LING-1 to LING-5).
- The second group delves into the richness in the use of vocabulary (from LING-6 to LING-8).
- In the third group, the grammatical and ortho-typographical errors are considered (from LING-9 to LING-15).

#### 2.3.3. Rhetorical–Organizational Errors

- A visual one, which refers to the clarity of reading and the organization of all graphic material in relation to the layout of the page, graphs, paragraphs, and graphic representation (from ORG-1 to ORG-8).
- A second one, closely related to the rhetorical organization of the text, the coherence of the discourse and the interpretation of results, and its adaptation to the academic context (from ORG-9 to ORG-15).

## 3. Results and Discussion

#### 3.1. Mathematical Errors

#### 3.2. Linguistic Errors

#### 3.3. Rhetorical–Organizational Errors

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- James, C. Errors in Language L earning and Use; Routledge: London, UK, 1998; p. 320. [Google Scholar]
- Corder, S.P. Introducing Applied Linguistics; Penguin Books: Harmondsworth, UK, 1975. [Google Scholar]
- Cook, V. Linguistics and Second Language Acquisition; Modern Linguistics Series; Macmillan Education: London, UK, 1993; p. 333. [Google Scholar]
- Crystal, D. A Dictionary of Linguistics and Phonetics; The Language Library; Wiley: Hoboken, NJ, USA, 2009; p. 529. [Google Scholar]
- Corder, S.P. The significance of learners’ errors. Int. Rev. Appl. Linguist. Lang. Teach.
**1967**, 5, 161. [Google Scholar] [CrossRef] - Corder, S.P. Error analysis, interlanguage and second language acquisition. Lang. Teach. Linguist. Abstr.
**1975**, 8, 201–218. [Google Scholar] [CrossRef] - Corder, S.P. Error analysis and interlanguage. Can. Mod. Lang. Rev.
**1981**, 40, 649–650. [Google Scholar] - Selinker, L. Interlanguage. Int. Rev. Appl. Linguist. Lang. Teach.
**1972**, 10, 209–232. [Google Scholar] [CrossRef] - Ellis, R. Second Language Acquisition; Oxford Introduction to Language Study Series; Oxford University Press: Oxford, UK, 1997; p. 147. [Google Scholar]
- Fernández-López, S. Errores e interlengua en el aprendizaje del español como lengua extranjera. Didáctica Leng. Lit.
**1995**, 7, 203–216. [Google Scholar] - Zhan, H. Frequent errors in Chinese EFL learners’ topic-based writings. Engl. Lang. Teach.
**2015**, 8, 72. [Google Scholar] [CrossRef] [Green Version] - Leonardo, C.L. Las preposiciones en el habla no nativa de nivel intermedio: Análisis de la interlengua basado en corpus. RNLAEL
**2014**, 8, 5–27. [Google Scholar] [CrossRef] - Schachter, J. An error in error analysis. Lang. Learn.
**1974**, 24, 205–214. [Google Scholar] [CrossRef] - Larsen-Freeman, D.; Long, M.H.; Molina-Martos, I. Introducción al Estudio de la Adquisición de Segundas Lenguas; Gredos: Madrid, Spain, 1994. [Google Scholar]
- Radatz, H. Error analysis in mathematics education. J. Res. Math. Educ.
**1979**, 10, 163–172. [Google Scholar] [CrossRef] - Movshovitz-Hadar, N.; Zaslavsky, O.; Inbar, S. An empirical classification model for errors in high school mathematics. J. Res. Math. Educ.
**1987**, 18, 3–14. [Google Scholar] [CrossRef] - Socas, M. Dificultades, Obstáculos y Errores en el Aprendizaje de las Matemáticas en la Educación Secundaria; La Educación Matemática en la Enseñanza Secundaria; Rico, L., Ed.; Horsori: Barcelona, Spain, 1997; pp. 125–154. [Google Scholar]
- Astolfi, J.P. El “error”, un medio para enseñar. In Colección: Investigación y Enseñanza; Diada Editora: Sevilla, Spain, 2003. [Google Scholar]
- Araya, G.R.; Sánchez, C.M.; Mora, H.R. Errores matemáticos de estudiantes que ingresan a la universidad. Actual. Investig. Educ.
**2019**, 19, 104–136. [Google Scholar] [CrossRef] - Abrate, R.; Pochulu, M.; Vargas, J. Errores y Dificultades en Matemática: Análisis de Causas y Sugerencias de Trabajo; Universidad Nacional de Villa María: Buenos Aires, Argentina, 2006; p. 198. [Google Scholar]
- Borasi, R.; Siegel, M. Reading to learn mathematics: New connections, new questions, new challenges. Learn. Math.
**1990**, 10, 9–16. [Google Scholar] - Ashlock, R.B. Error Patterns in Computation; Using Error Patterns to Improve Instruction; Pearson: Columbus, NJ, USA, 2006; p. 98. [Google Scholar]
- Legutko, M. An analysis of students’ mathematical errors in the teaching-research process. In Handbook for Mathematics Teaching: Teacher Experiment. A Tool for Research; Czarnocha, B., Ed.; University of Rzeszόw: Rzeszόw, Poland, 2008; pp. 141–152. [Google Scholar]
- Daroczy, G.; Wolska, M.; Meurers, W.D.; Nuerk, H. Word problems: A review of linguistic and numerical factors contributing to their difficulty. Front. Psychol.
**2015**, 6, 348. [Google Scholar] [CrossRef] [PubMed] - Sanz, M.T.; López-Iñesta, E.; Garcia-Costa, D.; Grimaldo, F. Measuring arithmetic word problem complexity through reading comprehension and learning analytics. Mathematics
**2020**, 8, 1556. [Google Scholar] [CrossRef] - Martín, R.A.M.; Níkleva, D. Análisis de la competencia lingüístico-discursiva escrita de los alumnos de nuevo ingreso del Grado de Maestro en Educación Primaria. Rev. Signos
**2016**, 49, 48–70. [Google Scholar] [CrossRef] [Green Version] - I Feixas, M.J.; Vinyoles, A.A.; Bargalló, J.I. El uso de evidencias en la escritura cientinfica en los estudiantes de magisterio. Textos Didáctica Leng. Lit.
**2013**, 64, 40–46. [Google Scholar] - Rodríguez-Gómez, D.; Valldeoriola Roquet, J. Metodología de la Investigación; Universitat Oberta de Catalunya: Barcelona, Spain, 2009; p. 20. [Google Scholar]
- Dolz, J.; Gagnon, R.; Mosquera, S.; Sánchez-Abdchi, V. Producción Escrita y Dificultades de Aprendizaje; Graó: Barcelona, Spain, 2013; p. 91. [Google Scholar]
- Morales, A.O.; Espinoza, N. El desarrollo de la escritura de estudiantes universitarios. Lect. Vida
**2005**, 26, 26–37. [Google Scholar] - Berdanier, C.G.P.; Whitehair, C.; Kirn, A.; Satterfield, D. Analysis of social media forums to elicit narratives of graduate engineering student attrition. J. Eng. Educ.
**2020**, 109, 125–147. [Google Scholar] [CrossRef] - Leydens, J.A. Novice and insider perspectives on academic and workplace writing: Toward a continuum of rhetorical awareness. IEEE Trans. Prof. Commun.
**2008**, 51, 242–263. [Google Scholar] [CrossRef] - Carter, M.; Ferzli, M.; Wiebe, E.N. Writing to learn by learning to write in the disciplines. J. Bus. Tech. Commun.
**2007**, 21, 278–302. [Google Scholar] [CrossRef] - Ramírez-Echeverry, J.J.; Dussán, O.F.A.; García-Carrillo, A. Effects of an educational intervention on the technical writing competence of engineering students. Ing. Investig.
**2016**, 36, 39–49. [Google Scholar] [CrossRef] [Green Version] - Fox, J.; Artemeva, N. From diagnosis toward academic support: Developing a disciplinary, ESP-based writing task and rubric to identify the needs of entering undergraduate engineering students. Esp Today
**2017**, 5, 148–171. [Google Scholar] [CrossRef] [Green Version] - Bastola, N.M.; Hu, G. Supervisory feedback across disciplines: Does it meet students’ expectations? Assess. Eval. High. Educ.
**2020**. [Google Scholar] [CrossRef] - Daly, S.R.; Adams, R.S.; Bodner, G.M. What does it mean to design? A qualitative investigation of design professionals’ experiences. J. Eng. Educ.
**2012**, 101, 187–219. [Google Scholar] [CrossRef] [Green Version] - Mazzurco, A.; Crossin, E.; Chandrasekaran, S.; Daniel, S.; Sadewo, G.R.P. Empirical research studies of practicing engineers: A mapping review of journal articles 2000–2018. Eur. J. Eng. Educ.
**2020**, 1–24. [Google Scholar] [CrossRef] - Cantera, M.A.; Arevalo, M.; García-Marina, V.; Alves-Castro, M. A rubric to assess and improve technical writing in undergraduate engineering courses. Educ. Sci.
**2021**, 11, 146. [Google Scholar] [CrossRef] - Conrad, S. A comparison of practitioner and student writing in civil engineering. J. Eng. Educ.
**2017**, 106, 191–217. [Google Scholar] [CrossRef] - Schmitt, N.; Hemchua, S. An analysis of lexical errors in the English compositions of Thai learners. Prospect
**2006**, 21, 3–25. [Google Scholar]

**Figure 1.**Accumulated mathematical errors corresponding to the exercises (

**a**) by categories and (

**b**) by groups.

**Figure 2.**Accumulated mathematical errors corresponding to the essays (

**a**) by categories and (

**b**) by groups.

**Figure 3.**Accumulated linguistic errors corresponding to the exercises (

**a**) by categories and (

**b**) by groups.

**Figure 4.**Accumulated linguistic errors corresponding to the essays (

**a**) by categories and (

**b**) by groups.

**Figure 5.**Accumulated rhetorical–organizational errors corresponding to the exercises (

**a**) by categories and (

**b**) by groups.

**Figure 6.**Accumulated rhetorical–organizational errors corresponding to the essays (

**a**) by categories and (

**b**) by groups.

Mathematical Coherence: Managing Formulas and Units | Technical Description of Operation and Applications | Decision-Making |
---|---|---|

MAT-1 No International System of units | MAT-10 Does not define uses, applications, restrictions | MAT-13 Type of design under static or dynamic loads |

MAT-2 No English System of units | MAT-14 Justification of the applied design method (Goodman, Soderberg) | |

MAT-3 No engineering notation | MAT-11 Does not define basic design criteria. Does not identify simplifying hypotheses | |

MAT-4 Decimals: non-significant digits | MAT-15 Does not define convergence criteria in iteration problems | |

MAT-5 Numerical calculation error | MAT-12 Does not explain the coefficients of graphs or tables | |

MAT-6 Unit conversion error | ||

MAT-7 Does not enter / describe formula | ||

MAT-8 Dimensional analysis of wrong formulas | ||

MAT-9 Angle error (radians, degrees) |

Syntax | Lexicon | Grammar, Spelling, and Punctuation |
---|---|---|

LING-1 No connectors | LING-6 Poor lexicon, repetitions | LING-9 Spelling mistakes |

LING-2 Person changes, incoherence (me/us) | LING-10 Accent errors | |

LING-7 Colloquial and/or oral terms | LING-11 Punctuation errors | |

LING-3 Little variety of connectors | LING-12 Uppercase errors | |

LING-4 Verb tenses not coherent | LING-8 Words empty of content | LING-13 Subject-predicate concordance errors (anacolutha) |

LING-5 Syntactic errors that make understanding difficult | LING-14 Phrases without conjugated verb | |

LING-15 Lack of determiners, prepositions and/or conjunctions |

Clarity of Reading-Layout of the Page | Rhetorical Organization of the Text (Logical Organization of Discourse). Interpretation of Results |
---|---|

ORG-1 In disorder | ORG-9 Does not answer the question |

ORG-2 No paragraphs | ORG-10 Does not identify the type of analysis |

ORG-3 No page numbers, no references to tables/figures | ORG-11 Does not identify simplifying hypotheses |

ORG-4 Schema error | ORG-12 Does not interpret the results |

ORG-5 Table error | ORG-13 Negative results without explaining incompatibilities |

ORG-6 Aesthetic errors | ORG-14 Irrelevant conclusions |

ORG-7 Visual errors and poor supporting material | ORG-15 Bibliography errors |

ORG-8 No reference system, no references, no schemas, and no graphs |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Arévalo, M.-J.; Cantera, M.A.; García-Marina, V.; Alves-Castro, M.
Analysis of University STEM Students’ Mathematical, Linguistic, Rhetorical–Organizational Assignment Errors. *Educ. Sci.* **2021**, *11*, 173.
https://doi.org/10.3390/educsci11040173

**AMA Style**

Arévalo M-J, Cantera MA, García-Marina V, Alves-Castro M.
Analysis of University STEM Students’ Mathematical, Linguistic, Rhetorical–Organizational Assignment Errors. *Education Sciences*. 2021; 11(4):173.
https://doi.org/10.3390/educsci11040173

**Chicago/Turabian Style**

Arévalo, María-José, María Asun Cantera, Vanessa García-Marina, and Marian Alves-Castro.
2021. "Analysis of University STEM Students’ Mathematical, Linguistic, Rhetorical–Organizational Assignment Errors" *Education Sciences* 11, no. 4: 173.
https://doi.org/10.3390/educsci11040173