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Reflections on academic achievement in mathematics in standardized assessments: the case of Mexican students.^[1]

Karla María Díaz- López^[2]

Center for Technical and Higher Education, CETYS University, Mexico

E-mail: karla.díaz@ cetys.edu.mx

Ana Gabriela Kong -Toledo^[3]

Center for Technical and Higher Education, CETYS University, Mexico

E-mail: ana.kong@cetys.edu.mx

Para citar este artículo /To reference this article /Para citar este artigo

Díaz-López, K. &. Kong-Toledo, A. (2020). Reflections on academic achievement in mathematics in standardized assessments: the case of Mexican students. Revista Electrónica en Educación y Pedagogía, 4(7), pp-pp.78-90 doi: http://dx.doi.org/10.15658/rev.electron.educ.pedagog20.11040707

Received: febrero, 14 de 2020 /Reviewed: marzo, 11 de 2020 / Accepted: abril, 02 de 2020

Abstract: At the international level, mathematics learning occupies an instrumental place in curriculums and programmes as its purpose compromises the development of reasoning skills and problem solving in everyday life. This article aimed to analyze the results of the academic achievement of Mexican students in this field, whereby a documentary review of the historical results obtained in two tests in which the subject is evaluated was carried out. The reflection done points to the need to focus on teaching-learning processes and, in particular, to rescue the role of teachers. Likewise, the relevance of observing on time and directly what happens in classrooms is assessed as a road or as an early response to influence improvement, thereby claiming the potential of the school field in academic achievement.

Keywords. Education, evaluation (Thesaurus); mathematical competence, factors associated with learning (authors' keywords).

Resumen: En el ámbito internacional el aprendizaje de las Matemáticas ocupa un lugar instrumental en los planes y programas de estudio, dado que su propósito compromete el desarrollo de habilidades de razonamiento y resolución de problemas de la vida cotidiana. En el presente artículo se planteó como objetivo analizar los resultados del logro académico de estudiantes mexicanos en dicha materia, para lo cual se realizó una revisión documental de los resultados históricos obtenidos en dos pruebas en las que se evalúa la asignatura. A manera de reflexión se apunta la necesidad de centrar la mirada en los procesos de enseñanza-aprendizaje y, en particular, rescatar el papel de los docentes. Asimismo, como una vía o respuesta anticipada para incidir en la mejora, se valora la pertinencia de observar puntualmente y de manera directa lo que ocurre en las aulas, y con ello reivindicar el potencial del ámbito escolar en el logro académico.

Palabras clave. Educación, evaluación (Tesauro); competencia matemática, factores asociados al aprendizaje (palabras clave de los autores).

Reflexões sobre o desempenho acadêmico em matemática em avaliações padronizadas: o caso de estudantes mexicanos

Resumo: A nível internacional, a aprendizagem da Matemática ocupa um lugar instrumental nos planos e programas de estudo, uma vez que o seu objetivo compromete o desenvolvimento de capacidades de raciocínio e resolução de problemas do quotidiano. O presente artigo teve como objetivo analisar os resultados do aproveitamento acadêmico de estudantes mexicanos nesta disciplina, para o qual foi realizada uma revisão documental dos resultados históricos obtidos em duas provas nas quais a disciplina é avaliada. Como reflexão, aponta-se a necessidade de enfocar os processos de ensino-aprendizagem e, em particular, resgatar o papel do professor. Assim mesmo como um caminho ou resposta antecipada para a melhoria, valoriza-se a pertinência de observar de forma pontual e direta o que acontece na sala de aula, reivindicando o potencial do ambiente escolar no desempenho escolar.

Palavras-chave. Educação, avaliação (Tesauros); competência matemática, fatores associados à aprendizagem (palavras-chave dos autores).

Introduction

In Mexico, as in other countries, the government is responsible for guaranteeing education, a right stipulated in Article 3 of the Political Constitution of the United Mexican States (Diario Oficial de la Federación (DOF), 2019). Thus, compulsory education goes from 3 to 17 years old. This education must be carried out without discrimination based on language, ethnic origin, social or any other condition. It should be noted that, in that country, one of the purposes of education is the achievement of meaningful learning. In the particular case of upper secondary education, a level that goes between 15 and 17 years, since 2008 important changes have been implemented due to the limited development of basic competencies that are essential to ensure their participation in the society of the 21st century. In particular, the subject of mathematics holds a central and instrumental place in the curricula, since its fundamental objective involves the development of reasoning skills, as well as creative problem solving (Secretaría de Educación Pública [SEP], 2018). It should be pointed out that one of the most relevant changes in the current Mexican educational model is that it emphasizes the need for teachers to use contextualized problems as part of their teaching practice, so that their students can identify the degree of applicability of the subject’s content, in their immediate environment and in everyday life.

In a remarkable way, in the last two decades the learning of Mathematics, given its instrumental character, has gained relevance both in the international and national level. As an example of this, there are the evaluations that measure academic achievement in this subject, given that the integration of students into working and social life requires making decisions and issuing judgments. Thus, learning Mathematics facilitates young people to put into practice skills that contribute to problem solving and the analysis of situations. According to the Organization for Economic Cooperation and Development (OECD), the mathematical competence is associated with the ability to analyze, reason, and communicate effectively and at the same time, to pose, solve, and understand mathematical problems in various situations (OECD, 2016b).

Reference Framework

The OECD implements the Program for International Student Assessment (PISA), which is applied every three years, where all its members participate. This evaluation is created with the purpose of allowing the participating countries to take the necessary measures to address areas of opportunity evidenced by the results. PISA evaluates the competences that students have at the end of their compulsory basic education stage, which, in turn, has allowed to discover the competences with which young people of 15 years will begin their higher education or enter their working lives. In this program three areas are evaluated: Reading, Science and Mathematics. Thus, the latter corresponds to the young person's ability to reason, analyze and communicate mathematical operations (OECD, 2019a).

With regard to national tests, since the last decade, evaluations have been implemented to measure the academic achievement of students at the compulsory education levels. Specifically, in 2006, the Test for National Evaluation of Academic Achievement in Schools (ENLACE^[4]) was created and applied for eight consecutive years. This test invariably evaluated students in the subjects of Language and Communication and Mathematics from the third to sixth grade of elementary school and the three grades of high school. In 2015, the Ministry of Public Education (SEP^[5]) and the National Institute for the Evaluation of Education (INEE^[6]) created (replacing ENLACE) the National Plan for the Evaluation of Learning (PLANEA^[7]), which is applied to students in the third grade of preschool, primary school, secondary school and the last grade of high school, based on a sample design. Through this evaluation, it is possible to identify the extent to which students achieve mastery of the set of instrumental learnings they have acquired at the end of the different obligatory educational levels. According to the INEE (2018a), the purposes of PLANEA are:

1. To know the extent to which students at different levels of compulsory education achieve a set of key learnings established in the curriculum.

2. To provide information to federal and local educational authorities and decentralized agencies on the achievement of key learning by students in compulsory education, as well as on the gaps that exist between different population groups; all of this with the aim of contributing to educational policy decisions.

3. To provide society in general with information about the state of compulsory education in terms of what students are learning, as well as the differences in learning among different groups of the school population.

4. To provide information and knowledge to the teaching and administrative teams of elementary and middle schools about what their students are expected to learn in the studied areas, the level of learning achievement they reach, and the size of the teaching and learning challenge they face (p. 10).

In upper secondary education, PLANEA is aligned with the Common Curricular Framework (CCB); which has 100 multiple-choice items, 50 for Language and Communication and another 50 for Mathematics. It is important to emphasize that the results should not affect the performance of schools or teachers; specifically, it provides relevant information to improve the quality of student learning (SEP, 2017). The structure of the test allows the measurement of the mastery of a certain number of key learnings in the subject of Mathematics, given that the students demonstrate how they can use and transform their knowledge into tools that allow them to provide solutions to problems related to their environment, through the analysis, interpretation and evaluation of situations.

On the other hand, it should be noted that both evaluations have made significant efforts to identify some contextual factors that account for variations in results (INEE, 2015; INEE, 2017a; INEE, 2017b; INEE, 2018b). Likewise, empirical studies have reported the influence of variables from the socio-familiar, personal and school environment on learning achievement (Becerra-González and Reidl-Martínez, 2015; Díaz and Caso, 2018; Flores, 2014; Gaxiola and Armenta, 2016). Regarding the school variables, the teaching methodology, the didactics employed by the teacher and the classroom context stand out (Godino, 2014; Jurado, 2016; Simón and Alonso-Tapia, 2016), these variables are often overlooked in the evaluations described. Additionally, in the last decade, research work has focused on the teaching-learning strategies used by teachers in the classroom, in identifying whether they are prepared to teach the subject in question, as well as the analysis of their professional training (Barallobres, 2016; Pochulu, Font y Rodríguez, 2016; Posada y Godino, 2017).

In the last two decades, periodic evaluations have been implemented to measure the learning acquired by students; Mexico has participated in PISA  since 2000, it also has the National Plan for the Evaluation of Learning (PLANEA), which replaced the National Evaluation of Academic Achievement in Schools (ENLACE) in 2015. The following sections describe and interpret the historical results of these two evaluations.

Taking into account the described context, the relevance of Mathematics learning is undeniable. For this reason, this article presents reflections based on the analysis of the results of the academic achievement obtained by Mexican students who are in compulsory education, hence, the most relevant evaluations, both international and national, are reviewed.

Methodology

In the investigative exercise, a qualitative methodology was used through the documentary review method according to Hernández, Fernández and Baptista (2014). These are studies where the studied variables are not manipulated, but rather phenomena are observed as they occur in their natural context, and then analyzed. It should be noted that the documentary review is the dynamic process that consists essentially of the collection, classification, recovery and distribution of information (Delgado-Amaya and Herreño-Vargas, 2018).

In line with what Garcia, Ruge and Quintero (2016) have said, the first step in the construction of the documentary review consisted in specifying organized and significant components, in this case the historical results in Mathematics of Mexican youth in the Program for International Student Assessment (PISA), which covers the period from 2003^[8] to the present year, and in the National Plan for the Evaluation of Learning (PLANEA), which covers the period from 2015 to date. Taking into account what Casallas, Rodríguez and Ladino (2017) have said, the categories established for PISA were: a) results from all evaluation periods; b) national average score; c) average score of OECD member countries; and d) average score of participating countries. With regard to PLANEA, the categories identified were: a) levels of achievement in mathematics; b) level of achievement by type of administrative control; and c) scores at each level for each evaluation period.

Results and discussion

PISA

Table 1 shows the results obtained by Mexican students in PISA, it also shows the comparison of the score with the average of the participating countries. An increase of 23 points was observed between the results of 2003 and 2015. However, in relation to the results of 2009, 2012 and 2015 there was a decrease in the score with an average of five points between each evaluation. At the same time, there was an 80 point difference, compared to the OECD average score, in the 2018 application.

Table 1

Results of the mathematical competition of Mexican students in PISA

Mexico's average score	Application year	Mathematical competence	OECD average score	Application year	Mathematical competence
	2003	385		2003	500
	2006	406		2006	497
	2009	419		2009	499
	2012	413		2012	496
	2015	408		2015	490
	2018	409		2018	489

Note. Own elaboration. Sources: Diaz, M., Flores, G. y Martínez, F., 2007, p. 293; OECD, 2004, p. 92; OECD, 2011, pp. 61-62; OECD, 2014, p. 5; OECD, 2019b, p. 17; Schleicher, A., 2016, p. 5.

In order to interpret the results obtained by Mexican students, and later reflect on their implications, it is necessary to understand how and what this program evaluates. In principle, it is necessary to comment that six levels of mastery of the Mathematics competency are considered. Therefore, the description of each level is presented below (OECD, 2006, pp. 15-16):

Level 6 (more than 668 points). Students who reach this level are able to conceptualize, generalize, and use information based on their research and modeling to solve complex problems. They can relate different sources of information. They demonstrate advanced mathematical thinking and reasoning. They can apply their knowledge and skills in mathematics to face new situations. They can formulate and communicate their actions and thoughts accurately.

Level 5 (from 607 to 668 points) At this level, students can develop and work with models for complex situations. They can select, compare and evaluate appropriate strategies for solving complex problems related to these models. They can work strategically by making extensive use of well-developed reasoning skills, association representations, and symbolic and formal characterizations.

Level 4 (545 to 606 points). Students are able to work effectively with explicit models for specific complex situations. They can select and integrate different representations, including symbols, and associate them directly with real-world situations. They can use well-developed skills and reason flexibly with some understanding in these contexts. They can construct and communicate explanations and arguments.

Level 3 (483 to 544 points). Those at this level are able to execute clearly described procedures, including those that require sequential decisions. They can select and apply simple problem-solving strategies. They can interpret and use representations based on different sources of information, as well as reason directly from them. They can generate short communications to report their interpretations.

Level 2 (421 to 482 points). In the second level, students can interpret and recognize situations in contexts that require only direct inferences. They can extract relevant information from a single source and make use of a single type of representation. They can use basic algorithms, formulas, conventions or procedures. They are able to make literal interpretations of the results.

Level 1 (358 to 420 points). Students are able to answer questions involving familiar contexts where all relevant information is present and questions are clearly defined. They are able to identify information and develop routine procedures according to direct instructions in explicit situations. They can carry out actions that are obvious and follow them immediately from a stimulus.

Below level 1 (less than 358 points). These are students who are not capable of performing the most basic math tasks required by PISA.

Once the results have been described, it is convenient to present some of the general interpretations. Thus, the average scores obtained by the Mexican youth in the six applications place them at level 1, as well as below the average scores of the participating countries.

Mexican students have difficulties in mathematically representing everyday situations, for example, comparing the total distance between two alternative routes, or converting prices to a currency different from the one commonly used in their country (OECD, 2016a).

It should be pointed out that the levels of competence used in each evaluation to measure Mathematics have not changed; likewise, the variations in the scores of the six applications have not registered a statistically significant difference, that is, the young people who participated in 2003 and those who participated in 2018 have the same competence level, placing us in the last places of the ranking of the participating countries. It is also a concern that in the last application in 2018, only 44% of the students reached level 2 or higher (OECD, 2019c).

The OECD (2016b), concluded that academic achievement in this subject, includes a solid predictive factor about the decision to continue with an educational process at the upper middle level or higher, as well as with the subsequent economic income forecasts.

PLANEA

Table 2 shows the number of reagents used for each of the key learnings, highlighting those related to the numerical sense and algebraic thinking, as well as changes and relationships.

Table 2

Key lessons from the thematic axes in the PLANEA evaluation for Mathematics in higher education

Mathematics
Thematic axes	Number of  reagents
Number sense and algebraic thinking	18
Changes and relationships	17
Shape, space, and size	5
Information Management	10
Total reagents	50

Note: Own elaboration. Source: Secretariat of Public Education (SEP), (2017).

The results obtained through PLANEA are grouped into four levels of achievement, which translates into the key learning that the students had to acquire gradually during their academic trajectory in high school. For the evaluation of academic achievement in Mathematics, four levels of mastery are considered. Table 3 details the characteristics of each one, as well as the different fields that are evaluated.

Table 3

PLANEA achievement levels according to the field of assessment in Mathematics in higher education

Numerical sense and algebraic thinking
Level I		Students solve problems that involve basic operations with whole numbers or that result in a whole number. However, they have difficulty employing more elaborate arithmetic algorithms and significant difficulties in mastering algebra
Level II		They solve additive problems with common denominator fractions and involve the direct calculation of  ratios or percentages.
Level III		They perform operations involving integers and grouping signs. They perform polynomial multiplications. They solve additive problems of fractions and involve the approach of equations.
Level IV		They perform operations involving real numbers and grouping signs. They solve multiplicative problems of mixed fractions. They subtract polynomials and divide polynomials between monomials
Changes and relationships
Level I		Students solve missing value problems on direct proportionality tables. They identify the maximum value reached by a phenomenon from its graph. However, they have difficulty recognizing and establishing algebraically the relationship of dependence between two variables.
Level II		They solve missing value problems in inverse proportionality tables. They identify the linear function that models a phenomenon.
Level III		They determine whether data in a table have relationships of proportionality. They solve proportionality problems. They interpret the relationships and parameters of the linear function within a situation. They perform the sum of functions and evaluate positive numbers in them.
Level IV		Subtract functions and evaluate negative numbers in them. Determine the domain and range of a function as well as the value of the dependent and the equation of a line from its graph.
Shape, space, and size
Level I	Students have difficulty applying the properties of geometric shapes to solve problems.
Level II	They solve problems involving the calculation of angles at the intersection of lines by directly applying a single property.
Level III		They solve problems that involve calculating angles at the intersection of lines by applying more than one property. They determine why two triangles are similar.
Level IV		They solve problems applying the Pythagorean theorem to calculate legs to determine if a triangle is a rectangle.
Information Management
Level I		Students solve mode and arithmetic average problems for listed data. They interpret the possibility of occurrence of events in an experiment from a frequency graph. However, they have difficulty establishing measures of central tendency when data are not listed or calculating probabilities.
Level II		They solve mode problems when the data are organized in several tables. They determine the value of a missing data set to adjust its arithmetic mean to a pre-set value. They compare and interpret the probabilities associated with the events of a random experience
Level III		They calculate the probability of a simple event. They interpret and abstract information that is presented in graphs. They calculate the probability of compound events.
Level IV		They solve arithmetic mean problems when data is presented in histograms. They determine the median of a data set for an even number of data

Note: Own elaboration. Source: National Institute for the Evaluation of Education (INEE), 2017a, p. 38-40.

In terms of results, Table 4 presents a comparison between the level of achievement for each type of management control. It should be mentioned that level 4 is interpreted as the maximum mastery of mathematical knowledge, while level 1 is the lowest, and as such it gives evidence of the deficiencies in analyzing, interpreting, and performing operations. State campuses are noted for having a higher number of students in Tier I compared to the other types of administrative controls and a lower number in Tier IV. The 2017 national results show that only 2.5% of students are achieving at the Tier IV level, i.e., learning what is needed.

Table 4

Percentage of Students at Each Achievement Level and by Type of Administrative Control in the Mathematics Subject of the Last Application in High School

Type of administrative control	Percentages at each level
	Level I	Level II	Level III	Level IV
State	73.0%	20.6%	5.2%	1.1%
Federal	62.6%	26.1%	9.0%	2.3%
Private	61.0%	22.9%	11.0%	5.1%
Autonomous	52.0%	29.8%	13.4%	4.8%
National	66.2%	23.3%	8.0%	2.5%

Note: Own elaboration. Source: National Institute for the Evaluation of Education (INEE), 2017a, p. 9.

Table 5 shows the results of all PLANEA applications. It should be noted that the test was not applied in the years 2018, 2019 and 2020 in upper secondary education. Due to the fact that a rethinking was carried out by the INEE, it was established that the application would be every three years (INEE, 2018c). Therefore, the application that had been established for March 31 and April 1, 2020 was cancelled due to the health contingency caused by COVID 19, causing its application to be postponed until further notice (Diario Oficial de la Federación (DOF), 2020).

Table 5

Historical Results for PLANEA Mathematics Achievement Level in High School

Year	Percentages at each level
	Level I	Level II	Level III	Level IV
2015	51.3%	29.9%	12.4%	6.4%
2016	49.2%	30.0%	14.4%	6.3%
2017	66.2%	23.3%	8%	2.5%

Note: Own elaboration. Sources: (Secretariat of Public Education (SEP), 2016, p. 1; National Institute for the Evaluation of Education (INEE), 2017, p. 7)

In this way, it is interpreted that in both the 2015 and 2017 applications, more than half of the students have insufficient academic achievement in Mathematics, it is alarming that in 2017 only 2.5% of the students register an adequate level of achievement. Because the levels are related to key learning outcomes in the curriculum, most students would be expected to achieve results that would place them in the two highest levels. National educational failure in mathematics achievement is undeniable.

Conclusions

The poor results obtained by Mexican students, both in PISA and in PLANEA, show insufficient academic achievement in Mathematics. According to Osuna and Diaz (2019) it is a manifestation of the difficulties that students have in formulating, employing and interpreting Mathematics in a variety of contexts. In this regard, Marquez (2017) noted that PISA measures the skills that young people have acquired during their academic lives; therefore, its results are considered the intellectual capital that a country has, in this case, there is a concern about the deficit of intellectual capital shown in this subject.

In the search for an improvement in the results which show the achievement here, SEP has emphasized the prevailing need to increase the quality of teaching, so it has promoted changes aimed at highlighting the work of teachers, among which the following stand out: the incorporation of professionalization and training processes for teachers, together with the definition of the teachers' skills profile. Likewise, changes have been made in the curricula, among which the need for teachers to contextualize the contents dealt with in the classroom stands out. Thus, a reflection derived from this analysis of results, is the need to observe in a direct, detailed and deep way what happens in classrooms regarding the complex teaching - learning processes, as a way to influence the urgent improvement of the results in Mathematics that occupies and worries the Mexican educational system. It is undeniable that teachers have a significant influence on the achievement of students' learning, therefore, through the implementation of appropriate didactics in the classroom it is possible to promote a positive change.

The OECD (2016c) identifies that there are three major groups of teaching strategies used by teachers of Mathematics, Active Learning, Activation and direct instruction, where according to the TALIS-PISA study (Backhoff, Baroja, Guevara, Morán and Vázquez-Lira, 2017) Active Learning^[9] is the only one that positively impacts student learning.

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^[1] Article derived from the research project Characterization of the teaching of Mathematics in Baja California Technological Baccalaureates endorsed and funded by the Sectoral Research Fund for the Evaluation of Education / National Council of Science and Technology [CONACYT] Mexico.

^[2] PhD in Educational Sciences, Universidad Autónoma de Baja California. Teacher, Center for Technical and Higher Education, CETYS University. ORCID: https://orcid.org/0000-0002-0890-5328. E-mail: karla.díaz@cetys.edu.mx. Ensenada Baja California, Mexico.

^[3] Master in Education, Center for University Studies of Baja California. Researcher, CETYS University. ORCID: https://orcid.org/0000-0002-2360-0637. E-mail: ana.kong@cetys.edu.mx, Mexicali, Baja California, Mexico.

^[4] Spanish Acronym

^[5] Spanish Acronym

^[6] Spanish Acronym

^[7] Spanish Acronym

^[8] It should be noted that Mexico participated since the 2000 implementation although the student sample was not representative, unlike the 2003 application.

^[9] Understanding that Active Learning involves students in two ways: doing and thinking about the things they are doing. Therefore, the student does not just take notes and listen, but are an active part of their learning. It becomes a central part of the formative process and is responsible for it (Parra, Monobe and Barceló, 2018).