Roles and characteristics of problem solving in the mathematics curriculum: a review

Olivares, Daniela; Lupiáñez, José Luis; Alex, Isidoro Segovia

doi:10.1080/0020739x.2020.1738579

Cited by 25 publications

(22 citation statements)

References 55 publications

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“…In [31], Pólya lists four principles that should be followed when solving a mathematical problem: Understanding a problem, devising a plan, carrying out the plan and looking back on the work done. These four phases are still shared by most researchers as fundamental during the problem-solving process [11,33,[37][38][39][40]. They entail the ability of interpreting mathematically a real-word situation, choosing a solving strategy, developing the solving process, even changing strategy if needed, and reflecting on one's work and results [33].…”

Section: Doing and Assessing Problem Solving With Technologiesmentioning

confidence: 99%

Self-Assessment in the Development of Mathematical Problem-Solving Skills

2022

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Self-assessment, in the education framework, is a methodology that motivates students to play an active role in reviewing their performance. It is defined as “the evaluation or judgment of ‘the worth’ of one’s performance and the identification of one’s strengths and weaknesses with a view to improving one’s learning outcomes”. The goal of this research is to study the relationship between self-assessment and the development and improvement of problem-solving skills in Mathematics. In particular, the investigation focuses on how accurate the students’ self-evaluations are when compared to external ones, and if (and how) the accuracy in self-assessment changed among the various processes involved in the problem-solving activity. Participants are grade 11 students (in all 182 participants) in school year 2020/2021 who were asked to solve 8 real-world mathematical problems using an Advanced Computing Environment (ACE). Each problem was assessed by a tutor and self-assessed by students themselves, according to a shared rubric with five indicators: Comprehension of the problematic situation, identification of the solving strategy, development of the solving process, argumentation of the chosen strategy, and appropriate and effective use of the ACE. Through a quantitative analysis, students’ self-assessment and tutors’ assessment were compared; data were cross-checked with students’ answers to a questionnaire. The results show a general correlation between tutor assessment and self-assessment, with a tendency of students to underestimate their performance. Moreover, students were more precise in self-assessing in the indicators: Development of the solving process and use of the ACE, while they had major difficulties in self-assessment for the indicators: Comprehension of the problematic situation and argumentation.

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Section: Doing and Assessing Problem Solving With Technologiesmentioning

confidence: 99%

Self-Assessment in the Development of Mathematical Problem-Solving Skills

2022

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“…Esta necesidad latente se ha expresado en muchos países del mundo, quienes buscan tener estudiantes cada vez más competentes para enfrentarse a diversas situaciones propias de su entorno donde no solo sean capaces de aplicar los conocimientos aprendidos, sino que también sepan elegir una o más estrategias que le lleven a la solución del problema que enfrentan (Jäder, et al, 2019;Olivares et al, 2020).…”

Section: Introductionunclassified

“…En cuanto al área de matemática, hace algunos años atrás, los estudiantes que egresaban tenían serias deficiencias en cuanto a la resolución de problemas, esto se debía a que los docentes se habían dedicado a trabajar la parte operativa, los algoritmos y propiedades, dejando de lado la resolución de situaciones problemáticas contextualizadas y el manejo de estrategias heurísticas (Jäder, et al, 2019;Olivares et al, 2020).…”

Section: Introductionunclassified

“…El Minedu ha venido enfatizando la importancia de trabajar la matemática desde un punto no solo procedimental sino a nivel de competencias y desempeños diversificados en situaciones problemáticas contextualizadas (Guven, et al, 2016). Exige que los estudiantes aprendan a interactuar de manera creativa, autónoma, autorregulada y responsable con la gran cantidad de conocimientos que aprenden diariamente, demandando a la escuela y mucho más a los docentes, la enseñanza de estrategias diversas que los ayuden a resolver problemas en diversos contextos a partir de procesos conscientes y regulados, es decir, a partir de la reflexión de sus propios procesos cognitivos (Metacognición) (Olivares et al, 2020;Monarrez & Tchoshanov 2020).…”

Section: Introductionunclassified

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Estrategias resolutivas de Allan Schoenfeld y la solución de problemas matemáticos de alta demanda cognitiva en estudiantes de cuarto año de secundaria de un colegio ubicado en el distrito de Magdalena del Mar de Lima Metropolitana

Carhuatanta¹

2022

IJNE

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El presente estudio está enmarcado en el empleo de Estrategias Resolutivas de Allan Schoenfeld para la solución de problemas matemáticos de alta demanda cognitiva. El tipo de investigación fue descriptiva correlacional con un diseño pre – experimental longitudinal. La población estuvo conformada por 70 estudiantes entre dos secciones de cuarto año de secundaria de un colegio ubicado en Lima Metropolitana la cual fue tomada en su totalidad. En lo que respecta a las técnicas se utilizó la encuesta y como instrumentos se utilizaron una para recolectar los datos sociodemográficos tales como la situación personal, familiar, socioeconómica y de desempeño académico de cada uno de los estudiantes que conforman la población de estudio. Una Prueba de Conocimientos Previos en conceptos matemáticos, la Prueba de Problemas de Contexto elaborada con base a la prueba Pisa aplicadas años atrás que busca medir las estrategias resolutivas empleadas en la solución de dichos problemas y un instrumento para recoger la valoración de los estudiantes sobre las estrategias heurísticas. Los instrumentos fueron validados a través del juicio de expertos y se obtuvo un índice de Osterlind de 0.75. En cuanto a la confiablidad, tuvieron un alfa de Cronbach por encima del 0.80 para cada uno. Los resultados mostraron que luego de la intervención pedagógica, los estudiantes mejoraron su desempeño en cuanto a su capacidad para resolver problemas matemáticos y probando la hipótesis que existe relación entre las estrategias resolutivas según la propuesta de Allan Schoenfeld y la solución de problemas matemáticos de alta demanda cognitiva.

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“…Teachers' efforts are concentrated on the guidance of the learning process [12,13]. Synthesis of information, redesign of materials and resources, and curriculum alignment [14] are examples of demanding tasks expected from teachers, which have to lead students to direct their own learning [15,16] and self-understanding of concepts involved in a subject. In this sense, planning teaching activities that add real value to the master class is crucial.…”

Section: Introductionmentioning

confidence: 99%

Assessing the Impact of Attendance Modality on the Learning Performance of a Course on Machines and Mechanisms Theory

et al. 2021

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University education approaches related to the field of science, technology, engineering and mathematics (STEM), have generally particularized on teaching activity and learning programs which are commonly understood as reoriented lessons that fuse theoretic concepts interweaved with practical activities. In this context, team work has been widely acknowledged as a means to conduct practical and hands-on lessons, and has been revealed to be successful in the achievement of exercise resolution and design tasks. Besides this, methodologies sustained by ICT resources such as online or blended approaches, have also reported numerous benefits for students’ active learning. However, such benefits have to be fully validated within the particular teaching context, which may facilitate student achievement to a greater or lesser extent. In this work, we analyze the impact of attendance modalities on the learning performance of a STEM-related course on “Machines and Mechanisms Theory”, in which practical lessons are tackled through a team work approach. The validity of the results is reinforced by group testing and statistical tests with a sample of 128 participants. Students were arranged in a test group (online attendance) and in a control group (face-to-face attendance) to proceed with team work during the practical lessons. Thus, the efficacy of distance and in situ methodologies is compared. Moreover, additional variables have also been compared according to the historical record of the course, in regards to previous academic years. Finally, students’ insights about the collaborative side of this program, self-knowledge and satisfaction with the proposal have also been reported by a custom questionnaire. The results demonstrate greater performance and satisfaction amongst participants in the face-to-face modality. Such a modality is prooven to be statistically significant for the final achievement of students in detriment to online attendance.

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Roles and characteristics of problem solving in the mathematics curriculum: a review

Cited by 25 publications

References 55 publications

Self-Assessment in the Development of Mathematical Problem-Solving Skills

Self-Assessment in the Development of Mathematical Problem-Solving Skills

Estrategias resolutivas de Allan Schoenfeld y la solución de problemas matemáticos de alta demanda cognitiva en estudiantes de cuarto año de secundaria de un colegio ubicado en el distrito de Magdalena del Mar de Lima Metropolitana

Assessing the Impact of Attendance Modality on the Learning Performance of a Course on Machines and Mechanisms Theory

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