Transdisciplinary Teaching Framework Aims to Improve Math Problem Solving in Colombian Primary School

Mathematics teaching in many primary classrooms remains cut off from the disciplines around it and from the cultural and social realities of the students it serves. A new qualitative action research study, published in Frontiers in Education, set out to characterize the factors that favor and disfavor problem solving in one Colombian primary school and to propose concrete indicators of what the authors call didactic suitability, a construct from the Onto-Semiotic Approach to mathematics education that evaluates the quality of teaching processes.

The research took place in a public primary school in southwestern Barranquilla, Colombia, an area characterized by socio-economic levels 1 and 2. Twelve primary education teachers from grades one through five, fifty-two third-grade students aged between eight and eleven, and the school management team participated. The school was selected intentionally because of the accessibility of its staff and management’s willingness to take part. The study was approved by the Ethics Committee of Universidad Simón Bolívar, with informed consent obtained from management, teachers, and the parents of participating students.

Methodologically, the researchers organized the work into three phases of a self-co-eco-formation cycle: auto-formation, in which the team became aware of the school’s reality; socio-formation, a period of reflective dialogue with teachers; and eco-formation, in which instruments were designed and applied to transform practice. Data collection combined a theoretical-methodological literature review, analysis of results from the Evaluar para Avanzar external test administered by Colombia’s Ministry of National Education and the Colombian Institute for the Evaluation of Education, structured interviews with teachers and students, questionnaire-workshops, and classroom observations.

The external test analysis produced some of the study’s most concrete technical findings. The EPA 2023-1 test consisted of twenty multiple-choice questions covering numerical-variational, spatial-metric, and random components, and it assessed communication, modeling and representation; reasoning and argumentation; and problem posing and solving. Across all fifty-two students, the three components showed remarkably similar average performances: 44.95 percent for numerical-variational, 44.87 percent for spatial-metric, and 44.23 percent for random items. The authors note that because the difference between components is less than one percentage point, no single component can be considered significantly weaker than the others.

The meaningful difficulties emerged at the item level rather than the component level. Within the spatial-metric set, specific questions showed marked struggles. Determining the final position of an element after three or more translations was answered correctly by only 25.00 percent of students. Finding the perimeter of a trapezoid from the length of its sides reached 36.54 percent correct, and finding the perimeter of a composite two-dimensional figure reached 38.46 percent. Recognizing the coverage of a shape with a non-standardized pattern scored 44.23 percent. By contrast, performing coverings with regular and irregular figures was answered correctly by 73.08 percent of students, showing that the difficulty was specific rather than uniform.

These item-level results, together with teacher interviews and classroom observations, led the research team to focus the study on measurement and metric thinking. In the reflective dialogue phase, teachers organized into teams by grade level and identified a cluster of problems: emotional difficulties among students, low results in the geometric-metric component and problem-solving competence, a lack of strategies for teaching problem solving, few interdisciplinary projects, little concrete material endowment, insufficient planning and reflection time for teacher teams, and in some cases incorrect interpretation of the mathematics curriculum referents.

The third phase probed measurement teaching directly. A questionnaire-workshop applied to teachers revealed notable weaknesses in their personal meanings around measurement: several limited the meaning of measuring to length alone, forgetting time, mass, area, and capacity; some omitted instruments such as clocks, stopwatches, calendars, and balances; and some mistakenly used the meter rather than the square meter as a unit of area. Strengths were also documented, including viewing patterns as standardized measures agreed upon by a community and recognizing strings, wool, clips, pencils, and body parts as non-conventional measurement patterns. A workshop-type class with third graders showed that all students could directly compare lengths between two objects of the same type, most struggled with indirect comparison using a third object, and few could iterate a pattern to indicate the measure of another object, although most could measure with a ruler once feedback was given on its initial placement.

Structured interviews with twenty-nine third-grade students mapped the sociocultural context that the researchers wanted to bring into the classroom. Students reported favorite toys including dolls, video games, bicycles, balls, and toy cars; favorite activities ranging from soccer and skating to board games and drawing; and parents or guardians working mostly in commerce, moto-taxis, clinics, or recycling. Family activities included watching movies, visiting parks and shopping centers, and playing board games. The researchers argue that these elements of the students’ lifeworld should function not merely as background context but as constitutive ingredients of mathematical activity.

From the convergence of all three phases, the team proposed nine indicators of didactic suitability organized into three integrated criteria. The epistemic-ecological indicators call on teachers to overcome their measurement knowledge gaps, treat patterns and units flexibly, and embed problem situations tied to nearby occupations such as dressmaking, carpentry, construction, and medicine. The cognitive-affective indicators direct teachers to build on favorable prior knowledge, such as direct length comparison and ruler use, while developing improvement plans for weaker areas like indirect comparison and pattern iteration, and to incorporate students’ family activities and interests. The mediational-interactional indicators recommend designing lessons around students’ favorite toys, software, soccer, and commerce-related environments, and structuring team work with defined roles and group sizes that allow the teacher to check and give feedback on every response.

The authors are careful to situate their contribution honestly. The study was conducted in a single school in a specific region of Colombia, the qualitative design and small sample limit statistical generalizability, and the analysis centered on measurement, one topic within the mathematics curriculum. They also explain what the transdisciplinary perspective added beyond the Onto-Semiotic Approach itself: recognition of the learner’s world, a dialogue of knowledge that integrates non-academic family practices into the curriculum, and a holistic grouping of the six classical facets of didactic suitability into three integrated criteria. The indicators, they emphasize, are not static checklists but a dynamic operational framework for assessing overall didactic suitability, and future work should implement and evaluate them in diverse educational settings, with the authors suggesting the approach could be calibrated to other mathematical domains and to vulnerable primary education contexts across Latin America.

Subject of Research: A qualitative action research study proposing indicators of didactic suitability for teaching mathematical problem solving and measurement in a Colombian primary school.

Article Title: Transdisciplinary perspective on problem solving: from didactic suitability in a primary school

Article References: Gómez Muñoz, M., & Pimienta Acosta, A. (2026). Transdisciplinary perspective on problem solving: from didactic suitability in a primary school. Frontiers in Education, 11, Article 1966258. https://doi.org/10.3389/feduc.2026.1966258

Image Credits: AI Generated

DOI: 10.3389/feduc.2026.1966258

Keywords: problem solving, didactic suitability, onto-semiotic approach, transdisciplinarity, primary education, mathematics teaching, measurement, teacher education, action research, Colombia, metric thinking, qualitative research