Categories to Assess the Understanding of University Students about a Mathematical Concept

Rodríguez-Vásquez, Flor Monserrat; Arenas-Peñaloza, Jhonatan

doi:10.17648/acta.scientiae.5892

Cited by 4 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This situation has triggered multiple investigations in mathematics education, from the historical, cognitive, and didactic parts. For example, from the cognitive side, a topic that has become relevant is the study or assessment of the understanding of a mathematical concept, where several models or theories that point to obtaining specific categories of understanding have been generated, aiming to strengthen the teaching or learning of mathematical concepts (Çalişici, 2018;Rodríguez-Vásquez & Arenas-Peñaloza, 2021).…”

Section: Introductionmentioning

confidence: 99%

Compresión del concepto razón a través del modelo de Pirie y Kieren

Arenas-Peñaloza

Rodríguez-Vásquez

2022

Acta Sci.

Self Cite

View full text Add to dashboard Cite

Background: Research in educational mathematics has shown that elementary school students poorly understand the concept of ratio due to the difficulties that emerge from its interpretation as a fraction. Objective: Therefore, based on the Pirie-Kieren theoretical model, we intend to analyse the comprehension process that appears when students solve tasks on ratio. Design: The approach is qualitative, and the research design was a case study. We used the field observation technique. Context and participants: The study was done in a primary school in the state of Guerrero, Mexico. The cases involved four students (11-12 years old) enrolled in the 6th grade. Data collection and analysis: The data was collected through a questionnaire (task) and an interview. For data analysis, the eight levels of understanding of the theoretical model were used. Results: The results indicate that the students do not manage to formalise their comprehension of the concept of ratio because of difficulties in applying mathematical strategies correctly when solving the proposed tasks. Conclusion: The results indicate that for students to reach higher levels of comprehension, it is necessary to carry out the dynamic process of repeating between levels as it makes one reflect on what is required to advance comprehension.

show abstract

Section: Introductionmentioning

confidence: 99%

Compresión del concepto razón a través del modelo de Pirie y Kieren

Arenas-Peñaloza

Rodríguez-Vásquez

2022

Acta Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

Onto-semiotic analysis of Colombian engineering students’ mathematical connections to problems-solving on vectors: A contribution to the natural and exact sciences

Rodríguez-Nieto,

Cabrales González,

Arenas-Peñaloza

et al. 2024

EURASIA J Math Sci Tech Ed

Self Cite

View full text Add to dashboard Cite

The mathematical connections Colombian engineering students activated when they solved vector problems were explored. The study was based on the extended theory of connections and the onto-semiotic approach. We followed a qualitative methodology that consisted of three stages: (1) selection of engineering students as participants; (2) application of a questionnaire with 15 tasks on vectors to the participating students; and (3) analysis of these data based on the theoretical articulation. The results show that students perform arithmetic operations with vectors, find the scalar and vector product, the norm of a vector, the angle between vectors, and unit vector based on mathematical connections (procedural, meaning, different representations, and implication), detail from an onto-semiotic point of view. However, some students have difficulty finding the angle between vectors because they misuse the norm. Furthermore, the new metaphorical connection based on mnemonics activated by the “law of the ear” is reported. The connections activated by engineering students to solve problems about vectors may have been influenced by the explanations provided by their calculus teacher, who promotes connections for the teaching and learning mathematical concepts.

show abstract

Analysis of primary school students’ process of understanding about the concept of ratio: A view from the Pirie-Kieren theory

Arenas-Peñaloza,

Silvera-Sarmiento,

Rodríguez-Nieto

et al. 2024

EURASIA J Math Sci Tech Ed

View full text Add to dashboard Cite

The understanding process of primary education students was analyzed when they solve tasks related to the concept of ratio. The study was based on the theoretical framework of Pirie and Kieren (1994). The methodology was qualitative with the case study method. The study was carried out in three stages: planning, development and analysis, using the field observation technique. Data collection was carried out through a task and an interview. The data were analyzed based on theoretical articulation. The results revealed that students lack the prior knowledge necessary to understand the concept of ratio. In conclusion, it can be noted that students do not present logical arguments to formalize the concept, and their understanding process is reduced to memorization or the use of mathematical strategies without understanding the relationship between the task and the mathematical concept.

show abstract

Categories to Assess the Understanding of University Students about a Mathematical Concept

Cited by 4 publications

References 0 publications

Compresión del concepto razón a través del modelo de Pirie y Kieren

Compresión del concepto razón a través del modelo de Pirie y Kieren

Onto-semiotic analysis of Colombian engineering students’ mathematical connections to problems-solving on vectors: A contribution to the natural and exact sciences

Analysis of primary school students’ process of understanding about the concept of ratio: A view from the Pirie-Kieren theory

Contact Info

Product

Resources

About