DIDACTIC ANALYSIS OF CURRICULAR MATERIALS BY FUTURE TEACHERS

Bethzabe Cotrado

Universidad Nacional del Altiplano (UNA), Puno, Peru; bcotrado@unap.edu.pe

María Burgos

Universidad de Granada (UGR), Granada, Spain; mariaburgos@ugr.es

Pablo Beltrán-Pellicer

Universidad de Zaragoza (Unizar), Zaragoza, Spain; pbeltran@unizar.es

Alfredo Castro

Universidad Nacional del Altiplano (UNA), Puno, Peru; acastroq@unap.edu.pe

Note on authorship

This article is part of the doctoral thesis Idoneidad didáctica de la probabilidad en documentos normativos y materiales curriculares de educación secundaria. Implicaciones para la formación de profesores developed by Bethzabe Cotrado, responsible for the collection of information, description, analysis, and writing of the article. María Burgos and Pablo Beltrán-Pellicer are the thesis directors, who have contributed to guiding the theoretical framework, analyzing and validating the data, as well as reviewing and writing the article. Alfredo Castro has participated in the collection of information and analysis of the obtained results.

Facets	Description	Frequencies
Epistemic	Meaningful, concrete tasks, brief definitions	4
Affective	Attractive, well-illustrated, catches the student’s attention, motivational	9
Interactional	Clear and precise, instructive	5
Interactional	Promotes interaction between teacher and student	1
Cognitive	Appropriate to the student’s age and interest, connects with the student’s real life	5
Mediational	Easy to use or handle	5
Ecologic	Aim or purpose well defined	3
Others	General, does not specify characteristics	4

Facets	Incipient features of indicators	Frequencies
Epistemic	Includes problems contextualized and from everyday life.	7
	Propose several exercises	2
	Makes use of graphical representations	7
	Presents some definitions of probability	3
	Explains the formulas and use Laplace’s rule	3
	The steps are very well explained	2
	Allows students to justify their answers	1
Affective	Contains attractive images and colours	12
	Motivates the student with simple exercises	7
	Encourages an active role of the student	2
Interactional	Shows open-ended questions, examples and solutions to guide subsequent problems	6
	Problems are clear and well-ordered	6
	Shows interaction between teacher and student	2
Cognitive	The statements are understandable and for different learning levels	4
	It includes and evaluation	2
	The problems contain questions that generate cognitive conflicts	1
	Use errors as a source of learning	1
Mediational	It includes spaces to solve the problems	6
Ecological	The material is in accordance with Minedu guidelines	2

Components	Evidence of use of indicators	Frequency
Problem-situation	Lack of problem situations relating different meanings of probability	4
	Absence of situations from a context familiar to the student	2
	Lack of situations where the student can generate, experiment, and simulate problems	9
Components	Evidence of use of indicators	Frequency
Languages	Uses different registers and representations	19
Languages	The linguistic registers are appropriate to the educational level to which they are addressed	19
Concepts	Concepts are relative to the educational level of the students, but are not clear	4
Concepts	Absence of situations where the student can generate or negotiate definitions	5
Procedures	Some steps are not explained or justified	2
Procedures	Lack of situations where the student can generate or negotiate procedures	1
Propositions	Laplace’s rule is used, the other properties are insufficient (they do not involve impossible and certain events)	2
Propositions	There are no situations in which the student generates propositions	4
Arguments	There are few arguments to justify propositions and procedures	1
Relations	The meanings of probability are not articulated	2
Relations	Mathematical objects are connected to each other	1
Epistemic conflicts	Some epistemic errors or conflicts are present	6
Epistemic conflicts	Absence of definitions (probable event, impossible event)	5

Components	Evidence of use of indicators	Frequency
Evaluation	UA3 presents evaluation situations with different levels of comprehension	16
Evaluation	Lack of self-assessment situations	3
Individual differences	The situations respond to different difficulty level	11
Previous knowledge	There is a shortage of introductory situations that lead to the differentiation between random and deterministic experiments	3
Cognitive conflicts	In AU2, error is used as a source of learning	2
Cognitive conflicts	Equiprobability biases are not anticipated	3

Dimension	Improvement proposal	Frequency
Epistemic	Include a complete theoretical explanation of the concepts Address the different meanings of probability Correct errors in the statements (titles in the graphics, eliminate confusing images) and take care in the use of symbols, tables, graphics Pose situations with multiple solutions	11
Interactional	Propose activities to work in groups, promoting dialogue and communication	5
Mediational	Include the use of physical or technological materials and resources	3
Affective	Emphasize the usefulness of the content Use situations closer to the student, motivating Foster emotional reflection of the student on mathematics	5
Cognitive	Consider previous knowledge required or give a warning about it Use various problem-solving methods Provide more examples with greater diversity and progressively increasing complexity Use incorrect solutions to emphasize errors as a learning source Use self-evaluation rubric	9

Brasil