Teaching Mathematics to Non-Mathematics Majors through Problem Solving and New Technologies

The role of mathematics in several scientific disciplines is undisputed; work and everyday life take great advantage of its application. Nevertheless, students often tend to not particularly like it and to consider it of little interest. It is also believed that only people with a certain attitude are capable of mastering the subject. In consideration of this, we aimed to help science students develop mathematical competences by designing a course specifically oriented to applications and problem solving. We administered our course to students attending the first year of a program in biotechnology, asking them to work with technologies instilling curiosity and interest, thus achieving a better proficiency as a consequence. Two questionnaires, along with access and proficiency data, allowed us to collect information about students’ attitudes, beliefs, and activity, which we analyzed by means of descriptive statistics. The promotion of the interaction among learners made them active users of the contents, thus allowing for the adaptation of their learning paths according to their personal necessities, as well as the development of teamwork skills and flexibility. Finally, students recognized the usefulness of the problem-solving approach and the role played by software.

Cultural Challenge: Teaching Mathematics to Non-mathematicians

A “mathematics for non-mathematicians” course, commonly known as a “service” course is an undergraduate mathematics course developed for students who are not (going to become) mathematics majors. Besides calculus, such courses may include linear algebra, mathematical reasoning, differential equations, mathematical programming and modeling, discrete mathematics, mathematics for teachers, and so on. In this article we argue that a good, productive curricular design and teaching of service courses happen through a meaningful collaboration between a mathematics instructor and the department whose students are taking the course. This collaboration ensures that “non-mathematicians” see the relevance of learning mathematics for their discipline (say, by discussing authentic problems and examples), but also appreciate the relevance and benefits which mathematics brings to their overall education and skills set.

The role of expertise in the aesthetic evaluation of mathematical equations

There is a notion that mathematical equations can be considered aesthetic objects. However, whereas some aesthetic experiences are triggered primarily by the sensory properties of objects, for mathematical equations aesthetic judgments extend beyond their sensory qualities and are also informed by semantics and knowledge. Therefore, to the extent that expertise in mathematics represents the accumulation of domain knowledge, it should influence aesthetic judgments of equations. In a between-groups study design involving university students who majored in mathematics (i.e., experts) or not (i.e., laypeople), we found support for the hypothesis that mathematics majors exhibit more agreement in their aesthetic judgments of equations—reflecting a greater degree of shared variance driven by formal training in the domain. Furthermore, their judgments were driven more strongly by familiarity and meaning than was the case for laypeople. These results suggest that expertise via advanced training in mathematics alters (and sharpens) aesthetic judgments of mathematical equations.

Student Outcomes From a Large-Enrollment Introductory Course-Based Undergraduate Research Experience on Soil Microbiomes

In recent years, national reports have called for undergraduate laboratory education that engages students in authentic research experiences. As a result, a number of course-based undergraduate research experiences (CUREs) have been developed in biological sciences and some specifically in microbiology. Students benefit from CUREs much like in traditional mentored research experiences, where students carry out independent projects in faculty laboratories. These benefits include increased self-efficacy in research skills, enhanced identification as scientists, and higher graduation rates in science, technology, engineering, and mathematics majors. Because mentored research experiences are not readily available to every student, CUREs represent a potential mechanism to democratize the research experience by providing such opportunities to all students. However, many of existing CUREs described in the literature are designed for advanced undergraduates or are limited to a small number of students. Here, we report student outcomes from a large-enrollment introductory CURE on soil microbiomes that engages students in a real-world context with microbiology. In pre- and post-course surveys, students reported significant gains in self-efficacy on a number of research skills. These results are triangulated with post-course survey data on project ownership, sense of community, and CURE design elements such as collaboration, iteration, discovery, and relevance.

Creativity as a function of problem-solving expertise: posing new problems through investigations

This study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in problem-posing-through-investigations (PPI) in a dynamic geometry environment (DGE). The first type of expertise—MO—involved being a candidate or a member of the Israeli International Mathematical Olympiad team. The second type—MM—was comprised of mathematics majors who excelled in university mathematics. We conducted individual interviews with eight MO participants who were asked to perform PPI in geometry, without previous experience in performing a task of this kind. Eleven MMs tackled the same PPI task during a mathematics test at the end of a 52-h course that integrated PPI. To characterize connections between creativity and expertise, we analyzed participants’ performance on the PPI tasks according to proof skills (i.e., auxiliary constructions, the complexity of posed tasks, and correctness of their proofs) and creativity components (i.e., fluency, flexibility and originality of the discovered properties). Our findings demonstrate significant differences between PPI by MO participants and by MM participants as reflected in the more creative performance and more successful proving processes demonstrated by MO participants. We argue that problem posing and problem solving are inseparable when MO experts are engaged in PPI.

A Unique and Scalable Model for Increasing Research Engagement, STEM Persistence, and Entry into Doctoral Programs

Participation in the University of California, Los Angeles Program for Excellence in Education and Research in the Sciences (PEERS) program has a positive effect on closing gaps in research participation, graduation in science, technology, engineering, and mathematics majors, and enrollment into graduate and professional doctoral degree programs for underrepresented minority (URM) students. Hence, PEERS could serve as a model for other institutions looking for cost-effective ways to promote URM student success.

Mujeres en STEM, un reto educativo

Science, technology and innovation are elements to respond to the challenges that must be faced, such as, among others, climate change, renewable energies, the nutrition of humanity, health and the administration of resources. Currently, women have a low percentage of representation in science, technology, engineering and mathematics majors, STEM, for its acronym in English; the gender gap persists in the labor issue, where companies are required to allow women to enter leadership positions. The ONU, to respond to this evident disparity, in 2015 establishes an international day to recognize the important role it has in science and technology, which is proclaimed on February 11 as International Day of Women and Girls in the Science. This research analyzes the perception of women who were trained in STEM careers, with the purpose of knowing their perception in six aspects, namely; Perception of their academic training, ability to learn and solve problems in STEM areas, social, educational or family support, academic training, satisfaction in their work and the work environment, gender stereotypes and the analysis of the skills or competencies required.