Algebraization Levels in the Study of Probability

Burgos, María; Batanero, Carmen; Godino, Juan D.

doi:10.3390/math10010091

Cited by 4 publications

(4 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although there are no articles that directly analyze the classification of parameters in probability problems, there are classifications that can be related to it. Probability problems have been studied by authors (Burgos et al, 2022) to classify tasks according to algebraic levels of reasoning -from proto-algebraic levels of mathematical activity to higher levels of algebraization and formalization. A description of these levels according to (Burgos et al, 2022) is as follows.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Probability problems have been studied by authors (Burgos et al, 2022) to classify tasks according to algebraic levels of reasoning -from proto-algebraic levels of mathematical activity to higher levels of algebraization and formalization. A description of these levels according to (Burgos et al, 2022) is as follows. Proto-algebraic level 1 is characterized by the introduction of some simple algebraic objects or processes.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The correspondence of these examples to other published classifications is determined. First, PPP's are compared with a classification of probability problems according to the six levels of algebraic reasoning given in (Burgos, Batanero, & Godino, 2022). Second, it is determined how the four levels of understanding and interpretation of the concept of parameters in algebra (Drijvers, 2003) correspond to parameters by authors' classification.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parameters in Formulations and Solutions of Introductory Probability Problems

Sondore

Daugulis

2022

SIE

View full text Add to dashboard Cite

Mathematical problems with parameters offer a higher semiotic complexity level of mathematical activities. The topicality of the research is determined by the fact that there are no studies on types of parameters in formulations and solutions of probability problems. The study aims are to analyse the current literature and propose an approach to classify parameters depending on their nature. Methodology - qualitative content analysis of probability problems from published textbooks and research papers. The main result - a parameter classification and interpretation scheme for introductory probability problems. The proposed parameter classification can help differentiate and individualise the study of probability theory and statistics.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parameters in Formulations and Solutions of Introductory Probability Problems

Sondore

Daugulis

2022

SIE

View full text Add to dashboard Cite

show abstract

“…Although the initial intention of the EAR levels model proposed in [37] is the description of the type of algebraic reasoning used in solving specific mathematical tasks from an epistemic viewpoint, it is possible to apply this model to analyze the nature of the mathematical activity expected or achieved by students when solving mathematical problems in different contexts. In Burgos and Godino [39] and Burgos et al [40], the EAR model is applied to identify the types of objects and processes put into play in solutions of a selection of problems involving proportional and probabilistic reasoning, respectively, showing the progression of mathematical activity from arithmetic and proto-algebraic levels to higher levels of formalization.…”

mentioning

confidence: 99%

Creation of Problems by Prospective Teachers to Develop Proportional and Algebraic Reasonings in a Probabilistic Context

Tizón-Escamilla,

Burgos

2023

Education Sciences

Self Cite

View full text Add to dashboard Cite

To promote optimal learning in their students, mathematics teachers must be proficient in problem posing, making this skill a cornerstone in teacher training programs. This study presents a formative action in which pre-service teachers are required to create and analyze a problem involving proportional reasoning within a probabilistic context. For this problem, they must identify the objects and processes involved in its resolution, recognize the degree of algebraic reasoning implied and identify potential difficulties for students. Subsequently, they need to formulate and analyze a new problem with variation, which mobilizes higher-level algebraic activity. Results indicate that prospective teachers struggle to pose problems that engage proportional reasoning, as well as to identify in their analysis which elements of proportional and algebraic reasoning are present in their solutions. Despite this fact, a significant percentage of participants adequately modify the original problem to address higher levels of algebraic reasoning, identifying in these cases the new algebraic objects and potential difficulties that might arise as the degree of generalization required in the solution increases. The study concludes by underscoring the importance of training in problem posing to enhance the knowledge and competences of prospective teachers concerning proportional and algebraic reasoning.

show abstract