Mathematics has been viewed as complex and difficult, which has led to negative attitude among students towards the subject. For students to analyze a mathematical problem is not easy, hence the huge effort by teachers and educational institutions attempting to change this attitude towards this science subject. It is clear that there is a great problem in the learning of mathematics since each year a growing number of students’ failures (in mathematics) are reflected in any part of the world. Similarly, we notice that most of the upper level students lack basic numeracy skills, and observe that students, who graduate from public institutions and to a lesser extent private school, have insufficient knowledge in the field of mathematical reasoning.  If math is discussed, it seems strange; ordinary people are not able to understand it. It is as if a few human beings were endowed with a kind of chip in their brains, allowing them to process these expertise. Nevertheless, what about others, who think that that they will never use mathematical knowledge in their social environment. This problem gets worse when they have a negative attitude due to their poor academic performance in mathematics (Morales, 2009); revealing that majority of these students (who have negative attitude) do not see a utility of mathematics in their lives.

The Secretariat of Public Education of Mexico (SEP) and the Panama Ministry of Education (MEDUCA) face a great challenge specifically in relation to math. The situations are:

1. Improve learning processes to reduce the difficulties that students have in understanding concepts,

2. Problem solving,

3. Transfer the contents to everyday situations and, in general,

4. Improve processes and mathematical thinking strategies that allow them to continue learning this science so that it hits the culture and society.

Failure and dropout rates are alarming, among evolving students in their education. As it is advanced in educa-tional levels, from elementary level to high school, failure and dropout rates grow significantly, decreasing terminal efficiency significantly, as shown below, in the case of higher education. The reported data vary according to the institution and the entity, so there is not a consensus. Table 1 shows conservative data about the rate of desertion and failure, according to indicators of the SNIEE - SEP of Mexico, MEDUCA of Panama and the DIGEPLEU of University of Panama (UP).

All of the above leads to the point that we are trying to show the importance of the development of an individual in the society who is able to criticize  logical arguments mathematical misconceptions or poorly prepared processes. This allows the evolution of the knowledge of science. These mathematical logical arguments can only be acquired through the development of a well-structured mathematical thinking. International education policy (NTCM Standards) points to the need that an individual should be able to guess how to build examples where the goodness of an information is displayed, i.e., that he may judge or evaluate their limitations as strengths. Never-theless, this indicates the importance of building a mathematical thought, which can only be achieved if the subject in question imitates a mathematician.

A mathematical thought is a scientific and critical thinking that is constructed of processes such as mathematical concepts in a useful manner for an individual within a society (García and Morales, 2012). This thinking is not easy to build in a school environment, if we do not use didactic activities; that allow interacting mathematical information necessary for the construction of the mathematical knowledge in the students. In that sense, it is noteworthy to observe the low performance obtained by Panama and Mexico in the PISA tests (program that measures the skills necessary of students 15 years old, in the school system of more than 20 countries at an international level math and reasoning). It will be that the Panamanian and Mexican school system made little effort; it is necessary that educational policies change with a primary goal: develop comprehensive individuals able to make suitable trials to build a society that solve their own problems. Complementing the above we can point the following: are there thoughts ingrained in students that do not let them travel from a naive thinking towards a mathematical thought? Sometimes these naive thoughts represent a concern in the educa-tional environment and the teacher often characterizes it as a negative aspect in the learning process, as in his stance, a mistake of the students in his mathematical work is a failure. Some authors have called it obstacle (Brousseau, 2006) in the sense that prevents other expertise new ideas to emerge.

A part of the problem of education lies not only in the ability or inability of students to understand certain topics, but in their attitude toward the school,  teacher and the subject. Authors propose that the success of a student in math class is related to the positive attitude towards the activity to carry out this matter and that includes personality traits that involve the intellectual and emotional spheres.  This  leads  to  the  observation  that attitudes in basic education depend on beliefs that are received from childhood being asserted by the verbal impact and the behavior of the family, in school and community life. Various studies (Guerrero and Blanco, 2002; Akey, 2006) reported that attitudes show a significant positive correlation with  motivation, discipline, learning and behavior in general. It is therefore of utmost importance to delve into their training. Among people we found different perceptions or ideas about mathematics leading to show certain attitudes towards it; and "various investigations have since revealed that the success and failure in mathematics depends on more than just knowledge of certain mathematical content requirements. Properly knowing facts, algorithms and procedures is not enough to ensure success"(Gómez-Chacón, 2009).

 “Is there a relationship between the affective and cognitive?” To find an answer to the question is the main motive that has led us to the present investigation. The authors of this paper believe that insofar as they investigate aspects of psychological nature in the education process, in this case the attitude, you will get information, which will make proposals to improve the teaching-learning process. Thus, the objective of the study is analyeze and compare the relationship between attitudes towards mathematics and school performance in college students of Panama and Mexico.

Due to the characteristics of the sample and of the research problem, it is a descriptive study - in which attitudes  and correlation - used to measure the degree of relationship that exists among the variables of the study. (Hernández et al., 2010). Its temporal scope corresponds to a cross-sectional study, as it is observed in a single point in time. Its scope, according to Bravo (2008), is micro sociological, since the phenomenon was investigated in small groups, without claim to generalize the results.

The study was conducted in two phases for the survey: in the first, we designed an instrument of scale of attitudes and applied it to the students of the Autonomous University of the State of Hidalgo (UAEH) and of the University of Panama (UP).  From the review of literature sources related to the object of study and analysis of items of other questionnaires (Auzmendi, 1992, Gómez-Chacón, 2000), were selected verbatim some of them, while other items were created, and modified for the construction of a scale to measure attitudes toward mathematics by these students. Then we proceeded to the organization and structure of the component items looking at their correspondence with the three components of attitudes: cognitive, affective and behavioral.

The type and amount of questions is then determined. Closed questions given the ease to interpret and evaluate the answers you need are considered. The scale was developed in a Likert-type format (Hernandez et al., 1991) with five response options (strongly agree (TA)-according (DA) - Undecided (I) - Disagree (ED) - totally disagree (TD)), depending on the degree of compliance with each of the aspects mentioned in the items. That is, a 5-point scale.

We proceeded to administer the questionnaire to a small sample of students in order to validate and evaluate its reliability (n = 247 students from Panama and Mexico). It was found that five indicators were not measured properly. The indicators were mathematical competence, assessment of school mathematics, trust, belief and motivation. Therefore, it was necessary  to  restructure  some  ítems (statements). For this research, a reliability index of 0.928 instru-ment used was obtained, and so the survey is valid and reliable.

Later, the questionnaire was given to judges who were active math teachers, to validate the content of the instrument. Based on feedback from the judges some adjustments were made to the scale.

This cohort was a total of 247 students for validation, 120 are from the Faculty of Exact Natural Sciences and Technology (UP) and 127 of the Institute of Basic Sciences and Engineering (UAEH). In the second phase, the same instrument for the correlational study of variables was applied to first year students of the same universities in 2012. The total sample was 1076 students, 530 from Panama and 546 from Mexico.

Figure 1 shows the whole structure linked to the concept of attitude that is related to their cognitive, affective and behavioral components discussed in this research.

The first phase of the study has an exploratory character, since it tried to get closer to the attitudes of the surveyed students (Bachelor and Engineering - scientific areas) for validation of the instrument, without taking into account the semester they were in. Meanwhile, the second phase groups were the total number of freshmen from which the population of students who had previously failed on the evaluated subject (mathematics) were removed; since these groups may represent a bias in information, affecting the variables studied.

The selection of the second phase was determined by a stratified sampling, which is used when the population is divided naturally into groups containing the variability of the population. The strata represented by the participating universities are set out in Tables 2 and 3. In these, the universities present the number of students tht enrolled in 2012, as well as population size and sample size estimated by career. For the determination of the sample size was established a confidence level of 95% and an estimated error of 5%. The population is composed of university freshmen of both sexes, from Mexico for the school year 2011-2012 of the ICBI of the University, and from Panama of the UP in the following faculties: Faculty of Exact Natural Sciences and Technology; Faculty of Architecture; Faculty of Electronics and Telecommunications.

In the research line called affective domain are located studies related to attitudes towards mathematics. This arises from the need to build theoretical framework derived from considering the teaching and learning of mathematical aspects such as: the conceptions, beliefs, motivations, powers, ideas, visions, beliefs, opinions, feelings, emotions and attitudes that have students and teachers toward mathematics, teaching, learning or assessment obtained from mathematical learning.

Pérez-Tyteca et al. (2011) conceptualized that students learn predisposition to respond positively or negatively to Mathematics, which determines their intention and influences their behavior in the field. Thus, in their study, aimed at students who had just entered the university, concluded that there are significant differences between the areas of knowledge of Technical Education, Health Sciences and Social Sciences. They also determined significant differences, statistically, between men and women in their anxiety about mathematics, where the former are those who have less anxiety.

Academic performance and their indicators

In this work, academic performance is defined operationally with the average of the qualifications obtained in the subject at the end of the course: January-July 2012 in Mexico, and March-July 2012 in Panama.

For practical purposes according to the hypothesis, we have defined four different categories for this variable, but the main one for this study is the outstanding academic performance. The student is considered as high merit individual; there is a high congruence between what is taught and what he proves to have at the end of the educational process and the condition of school success and failure focused on the student grades.

1. Insufficient performance: corresponds to a score of 0 for the student of UAEH and 0-60 for the student of the UP.

2. Poorly performance: this group consists of students with a score between 1-5 in UAEH and 61-70 for the student of the UP.

3. Average performance: this group consists of students with a score of 6-7 in UAEH and 71 to 80 students at the UP.

4. Outstanding performance: here are students who have a score in the qualification route of 8-10 in UAEH and 81 to 100 in the UP.

In the system of evaluation of school learning that governs the Autonomous University of the State of Hidalgo (UAEH), most of the ratings are based on the decimal system, from 0 to 10. At the University of Panama (UP), rating is assigned on a scale from 0 to 100, based on letters. These two systems in which the retrieved score translates in the categorization of the achievement of learning may vary from well done to poor learning. In this study, the criteria used in evaluation of both educational systems were adopted to conceptualize academic performance in mathematics (Table 4). In Mexico and Panama, academic performance is the process achieved by students on the basis of the programmed objectives.

Attitude and their indicators

Attitude is treated as a quantitative variable that is related to its components, cognitive, affective and behavioral. The attitude towards mathematics is defined, according to Petriz et al. (2010), as a series of provisions that make the individual to familiarize or not with certain mathematical contents.

This variable is treated as categorical; it is a scale graded in a positive and negative level, in terms of components, cognitive, affective and behavioral, using the scale developed by Morales (2009), adapted to the two countries. Each component possesses indicators, which are the scores obtained by sample on the scale of attitudes. Then, the measurement of this variable was carried out considering several categories for each of the components of attitude among a sample of students during the semester from January to July 2012. The categories that make up each of the components in the scale of attitude toward mathematics created for this study are presented in Table 5.

First comes  a  descriptive  analysis  to  characterize  the simple according to different variables included in the study. Measures of central tendency and dispersion were calculated. The results are presented in tables and figures.

Analysis of the academic achievement of students participating in mathematics

Figure 2 presents the level of academic performance achieved by the students of the sample of both countries. As noted above, took into account the conceptualization of performance proposed by Lent et al, (1994). So studies focused on the problems existing in the process of teaching and learning of mathematics have incor-porated affective and socio-cultural type variables, which have concluded that the cognitive factor is not the only participant in the learning, since it is a process shared between love and the context of the subject learning (Planchart et al., 2005).

Description of the attitudes in the total simple

The data collected with the attitude toward mathematics scale were analyzed initially using a frequency distribu-tion analysis organized in two ways: with the total sample and segregated by country. We found that students show a concentration in points 3 and 4 of the scale, which means that they have an attitude of indecision to partially positive. In addition, there is a low frequency in points 2 (negative attitude) and 5 (positive attitude) of the scale. If it well tends to be favorable in the beginning, the negative evolution that occurs over time and the persistence of this unfavorable nuance are very specific features that you should present to understand future reactions of the student and intervene appropriately in them (Auzmendi, 1992)  (Figure 3). 

This study took into account the following ethical guidelines: participants were informed of the study objec-tives, admission was voluntary and do not cause harm or discomfort in the session in which the Attitude  scale  was applied to mathematics. Anonymity and confidentiality of the data were respected. This implies that in all cases where the results can be presented in this study show global data and under no circumstances personal results.

Correlation between academic performance and attitude

Another type of analysis data on attitudes towards the mathematics consisted of assessing the relationship between them and academic performance in mathe-matics. The Spearman Correlation Coefficient was used for this. Correlated scores on the scale of attitude had scores of students in the school term from January to July 2012 (Table 6).

The results of the analysis suggest that academic achievement correlates positively with attitude. The value of the correlation coefficient ranged between 0.725 (ρ ≤ 0.01), students from Mexico and 0.829 (ρ < 0.01), students of Panama. That is, the positive attitude towards mathematics is related to increased academic performance in the field.  In this way, the results indicate that attitudes toward mathematics in freshmen of both universities are associated with academic performance in mathematics; particularly, there is a propensity to higher performance in the field corresponding to a positive attitude toward Mathematics (Figure 4). The implication of this, in accordance with Auzmendi (1992), is that: "attitudes affect the learning process and, at the same time, education has a broad power over them. Thus, is intended to better that which agrees or is consistent with our own attitudes or which produces greater pleasure, and a proper education can improve them in students in a given area"(p. 18). 

Lim et al. (2009), who concluded that attitudes towards this discipline are a multidimensional phenomenon, also studied these aspects recently; they found that these components influence the learning of students in the sense to provide them with an overview of the math with real world connections. The findings of this study are similar to those found by Álvarez and Soler (2010) in regards to that students perceive mathematics as a useful discipline, not only in the academic field but also in the labor one. However, they express mistrust and anxiety in situations that involve the use of mathematical procedures.

The result suggests that the greater the attitude towards mathematics the greater is students’ academic achievement. In addition, we evaluated the correlation between academic performance and each of the components of the attitude: the cognitive, the emotional and the behavioral. With regard to the gender difference in attitudes was found that the average for females is 3.28 points (s = 0.80); for males was 3.21 points (s = 0.71). Furthermore, by analyzing the behavior of attitudes according to the age of the students we found the following: Students with less than or equal to 18 years of age had a mean attitude of 3.21 points (s = 0.80). In contrast, over 18 years had an average of 3.27 points (s = 0.68) (Table 7). This result is inconsistent with the approach of some authors aforementioned, since there a common decrease in positive attitudes towards some school subjects related to science.

Analysis performed to contrast the differences between the mean scores on the scale of attitudes among male and female students showed that the difference is not significant.

There is a significant positive correlation between academic achievement and cognitive dimension in Panama (r =.637, ρ = 0) and Mexico (r =. 466, ρ = 0).  This indicates that there is a high probability that the cognitive development of the student directly affects academic performance in a positive way, implying that greater understanding of mathematical knowledge lrads to better academic performance. It is shown that the value obtained gives as a result a strong correlation between attitude and academic performance in Panama and Mexico, being the estimation of this value directly linked to the objective in this research. Apparently, the result corresponds to the expectation of the study: increased attitude towards  mathematics by the student leads to higher academic performance.

On the other hand, the cognitive development of an individual is intimately linked with solving problems. However, the majority of respondents are aware that solving a problem involves a comprehensive analysis, the application of concepts and a well-marked strategy as Pólya (2001). You can see that half of the students consider that they have feelings of anxiety that affects the resolution of mathematical problems and this is manifested in their poor academic performance. With this found correlation, you can set an interdependence between the cognitive development of a subject and its attitude towards resolutions of problems specifically for mathematics.

Taking into account what we have exposed here it can be considered positive to incorporate psycocentric and empirocentric approaches in the curricular treatment of mathematics again. The first requires you to do a math more linked to experience and involves the application of the principles of reality, necessity and usefulness. The second is to respect the characteristics of the person who learns and leads to the realization of objectives and activities according to their possibilities. The positive state of mind causes people to think, feel and act in ways that promote both the construction of resources and the generation of links (Ramírez and sources, 2013).

Consideration of the aforementioned approaches, as well as the use of appropriate organizational structures avoid, huge gaps currently occurring between the didactic proposals and possibilities of learning of students. That is why viable psycocentric and empirocentric approaches are integrated at the level of the curriculum planning, which is a modification of the learning programs and a more coherent adaptation to the cognitive potential of our students (Gairín, 1987, p.138). This means, for example, and among other things, abandoning the idea that for every school year there must be an increase of mathematical knowledge. Farias and Pérez (2010) show that to get students to learn is not enough to explain the subject and urge them to learn. It is necessary to arouse their attention, creating in them a genuine interest in the study, stimulate their desire to achieve the intended results and cultivate the taste by the schoolwork.

There have been elements that support the hypothesis initially formulated for this work, since there were significant correlations between the attitudes toward mathematics and academic performance by students, since students who have positive attitudes towards the mathematical learning have better grades and academic performance is outstanding. Within the aspects found, there are strong links between the developments of mathematical problems; (cognitive component) resolu-tions and the affective part of a subject are presented. It is recommended, that when a student registers at the university he/she must make a series of adjustments to adapt to the demands of this level of education. In this way, he/she will not be moving to another career because he/she is sure about what he/she wants to study. Frequently, these students come from an upper level where they have developed poor or inadequate study habits and may even have some deficiency in skills.

Studies on this subject, due to the shortcomings of a large number of students about basic math skills for performance in different areas of life are relevant to both education systems.

From this work, it is suggested to encourage the development of good attitudes toward math learning through educational and motivational activities by teachers, students and even throughout the educational system. That is, the teacher is one of the main actors of the educational phenomenon, since he/she not only transmits content, but also promotes values, beliefs, needs and, of course, attitudes. 

The authors have not declared any conflict of interests.

Research funded by the National Secretariat of Science and Technology (SENACYT) researcher’s new 2011 program and Institute of Studies  National  (IDEN) of the University of Panama and students of Psychology at the UDELAS.

Attitude: Having an attitude means being ready to respond in a given way to a social object. Attitude towards mathematics: number of provisions that expresses the individual to accept or not familiar with certain mathematical content.

Behavioral dimension: are verbal and nonverbal skills that show a behavioral adaptation to the situation and context that favors communicate effectively.

Dimension Attitude: Each of the magnitudes of a set used to define a phenomenon. The magnitudes vary attitudes are direction, intensity, prominence, degree of differen-tiation, action orientation, and content.

Educational Positioning: Fixed useful knowledge for people at a strategic time to give back to the society.

Construct: concepts that are directly manipulated by us, just as it is physical, but are inferable through conduct that is studying psychology.

Scale: perform a number of mathematical calculations of some nature in a tabular format to facilitate the task of performing these calculations to the public or a specific audience.