# Studying Without Math?

### What Mathematical Learning Requirements are expected for Studies outside STEM?

*Irene Neumann, Dunja Rohenroth & Aiso Heinze*

Many students leave school assuming they will never need mathematics again. However, the majority of them are confronted with mathematics in college - even if they have not chosen any of the so-called STEM courses of study (Science, Technology, Engineering, Mathematics). An IPN study shows that teachers at universities also expect mathematical knowledge and skills from first-year students outside STEM. In some cases, these learning requirements go well beyond basic knowledge and skills.

"Hello everyone," writes the prospective student with the username *klotzvormkopf* in the *Studis Online* forum, "are there any degree programs at all that have little to no math included and still offer relatively good career prospects (...)?" (Translation by the authors). Respondents are divided on this. Many are of the opinion that, for example, law and German studies are free of mathematics. Politics, education, psychology or business studies are also suggested, although user *Renate* advises against business studies: "(...) for someone who is an absolute math failure, it would be hell." (Translation by the authors). The Internet provides a large number of such websites offering advice on how to study without or with only a small mathematics component. STEM subjects are always excluded, but how valid is the advice for subjects outside STEM? What specific mathematical learning requirements are actually expected in these subjects?

The German national mathematics education standards define the mathematical competencies that students should have acquired before beginning their studies. This normative definition of what mathematical knowledge and skills are required to be able to study from the school's point of view stands in contrast to a rather unclear picture of expectations from the universities' point of view. The 2017 IPN Delphi study MaLeMINT (Mathematical Prerequisites for university STEM programs) yielded an empirically based catalog of mathematical learning requirements that comprehensively describes the expectations of university teachers in STEM study programs. Such a systematic description is still missing for subjects outside STEM. Commonly, mathematics is perceived to be hardly, or even not at all, necessary for these subjects. However, there are subjects outside STEM in which mathematics is relevant (such as psychology, medicine, economics, but also architecture, nutrition science, or communication science). It can be assumed that mathematical learning requirements are expected of more than 80% of all university students. The MaLeMINT-E project therefore aimed to extend the findings for STEM subjects to subjects outside STEM. Accordingly, the goal of the MaLeMINT-E project was to empirically describe the mathematical learning prerequisites necessary for non-STEM studies across disciplines and types of higher education institutions from the perspective of university teachers. In particular, MaLeMINT-E aimed to investigate, whether there is a consensus among university teachers in Germany for subjects outside STEM as well. To this end, a Delphi study was conducted building on the previous MaLeMINT study.

To identify expert participants, we first researched publicly available module handbooks and study information to find out which degree programs and courses include mathematical content beyond basic mathematical knowledge and skills. Then, we selected university lecturers who taught courses with mathematical content in these study programs from 2015 to 2019. Thus, a total of 1953 university teachers from 164 German universities were identified as experts for the Delphi study. From this total sample, 19 selected university teachers participated in the exploratory first Delphi round. The whole sample was contacted for rounds 2 and 3, and 547, respectively 337 participated.

The survey was based on the MaLeMINT catalog, which differentiates learning requirements for STEM studies regarding: (1) Mathematical Content, (2) Mathematical Processes, (3) Views about the Nature of Mathematics, and (4) Personal Characteristics. In the first, exploratory Delphi round, the learning prerequisites were presented to a smaller, criterion-referenced sample to investigate the extent to which this catalog can be applied to non-STEM fields of study. Results indicated, on the one hand, that the catalog can certainly serve as a basis for surveying university teachers outside STEM. On the other hand, this Delphi round already revealed that it might be useful to group subjects expecting similar mathematical learning requirements from first-year students. In subsequent rounds 2 and 3, the university teachers were therefore grouped according to the subjects they teach and asked to assess the given mathematical learning requirements. They each had the opportunity to evaluate, specify, or add to the aspects mentioned. Throughout the three rounds, we identified five subject groups in which similar mathematical learning requirements were expected and consensus among university instructors emerged (based on conservative consensus criteria).

After the third Delphi round a quite satisfactory, and in some cases even far-reaching, consensus was evident in all five study subject groups. Across all subject groups we found consensus on 48 of 188 learning requirements (26%). Of these, 41 learning requirements were judged necessary for all subject groups and 7 were judged not necessary. It is interesting to note that university instructors outside STEM regarded learning requirements as necessary in three of the four categories identified in the MaLeMINT study for the STEM subjects. Aspects on the nature of mathematics were the only ones deemed not necessary or did not result in consensus by university instructors in Subject Group 5, while university instructors in subject groups 1-4 also deemed learning requirements from this category necessary. With respect to the expected mathematical content, we found major differences between the five subject groups. Aspects of elementary geometry, for example, are specific to Subject Group 1, while aspects of calculus are expected primarily by university teachers for Subject Group 2 and 3. Content from analytic geometry and linear algebra is expected primarily in Subject Group 2. Stochastic aspects are expected much more broadly, except in Subject Group 1, where they hardly play a role, although the opinion in this group is not unanimous.

Regarding expected mathematical processes, there appears a greater degree of agreement across the subject groups. The most learning requirements are expected in Subject Group 2 and the fewest in Subject Group 5 - and here especially the basic processes such as the proficient handling of mathematical representations or standard mathematical notations. However, aspects of mathematical reasoning and proof, communicating, defining, problem solving, modeling, and researching - i.e., processes beyond basic "calculating" - are also expected by university instructors outside STEM, although not as comprehensively as by university instructors in STEM programs.

Views about the nature of mathematics are expected primarily in Subject Group 1 and 2. In Subject Group 3 and 4, the university teachers noted particular expectations regarding a conception of mathematics as learning to think precisely and abstractly and as a method for modeling phenomena and problems in other disciplines. All in all, understanding mathematics as a scientific discipline is thus also relevant for first-year students outside STEM.

Finally, we found a rather broad consensus with regard to expected personal characteristics. For example, across all subject groups, openness to mathematics, organizational and time management skills, the ability to work in a team, perseverance, the ability to concentrate or creativity were named as necessary learning requirements for first-year students by their participating university instructors.

#### Conclusion

The developed catalog shows that mathematics is important not only in STEM courses, but also in a large number of other subjects outside STEM. In some cases, expectations vary greatly between the fields of study. However, a relatively broad consensus can be found within individual subject groups. The catalog can thus serve as a source of information for teachers at schools, university instructors, and student advisors at universities, as well as for those involved in education policy and education administration. It can be used as a basis for providing prospective students with well-founded information about the mathematical competencies expected of university teachers in subjects outside STEM, thus complementing the diverse, sometimes speculative information in internet forums.

#### Delphi studies

Delphi studies are surveys of expert groups involving several rounds of questioning. In each round, the experts’ opinions are assessed, structured and then fed back to the expert group. The individual statements made by each person are not disclosed. This anonymous, multi-stage procedure enables successive consensus to be reached without being influenced by social or group dynamic effects, as can occur in group discussions, for example.

*Criteria for Consensus*

A mathematical learning prerequisite was assumed necessary if more than 2/3 of all participants in a subject or a subject group respectively deemed the prerequisite necessary.

A mathematical learning prerequisite was assumed not necessary if more than 3/4 of all participants in a subject or a subject group respectively deemed the prerequisite not necessary.

Subject Group | Subject Area |

1 | Architecture; Land Management, Landscape Design; Spatial Planning; Industrial Engineering with Focus on Economy |

2 | Psychology; Economics |

3 | Home Economics and Nutritional Science; Human Medicine; Pharmacy; Restorative Science; Veterinary Medicine; Dentistry |

4 | Library Science, Documentation; Education; Health Sciences (general); Media Studies; Political Science; Social Sciences; Sport, Sports Science |

5 | Communication Science/Journalism; Social Work; Administrative Sciences |

**Dr. Irene Neumann**

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**Dunja Rohenroth**

is a research scientist in the Department of Mathematics Education at the IPN and conducted the MaLeMINT-E study as part of her doctoral project.

**Prof. Dr. Aiso Heinze**

is director of the Department of Mathematics Education at the IPN.