Ph.D., in Education. Research Professor at the University of the Autonomous Regions of the Nicaraguan Caribbean Coast.

Esta investigación ha analizado las creencias sobre la resolución de problemas matemáticos. Se trata de una investigación cuantitativa basada en un diseño “Ex Post Facto” en el que se proporcionó una escala de dominio afectivo (creencias, actitudes y emociones) a 118 mujeres y hombres, profesores de primaria de la Costa Caribe nicaragüense. Los análisis sugieren que los docentes tienen creencias positivas que se manifiestan en factores como la confianza, la seguridad, la perseverancia, la satisfacción, la curiosidad, el gusto, la motivación y la utilidad para funcionar con éxito en la resolución de problemas matemáticos. Además, que las creencias sobre la resolución de problemas no difieren según la edad, el género, la etnia, los años de experiencia y el tipo de escuela (urbana y rural). Se concluye que es necesario seguir avanzando en los procesos de formación y capacitación de los docentes de educación primaria con un mayor énfasis en los procesos de resignificación de experiencias y prácticas matemáticas contextualizadas a las comunidades.

This research has analyzed beliefs about solving mathematical problems. This is quantitative research based on an “Ex Post Facto” design where a scale of affective domain (beliefs, attitudes, and emotions) was provided to 118 women and men, primary school teachers from the Nicaraguan Caribbean Coast. The analyses suggest that teachers have positive beliefs that are manifested in factors such as confidence, security, perseverance, satisfaction, curiosity, liking, motivation, and usefulness to function successfully in solving mathematical problems. In addition, that beliefs about problem-solving do not differ according to age, gender, ethnicity, years of experience, and type of school (urban and rural). It is concluded that it is necessary to continue advancing in the processes of education and training of primary education teachers with a greater emphasis on the processes of resignification of experiences and mathematical practices contextualized to the communities.

Before the COVID-19 pandemic, a learning crisis was reported in relation to mathematical competences, due to the fact that the learning outcomes were unsatisfactory due to low levels of understanding and high social inequalities (

The literature shows that the beliefs and attitudes towards mathematics of elementary school teachers can disrupt the learning of their future students. For example, in the study by

In this article, we analyze the beliefs of primary school teachers about problem-solving based on a study with Nicaraguan teachers, carried out in the context of the COVID-19 pandemic. The data that inform this article come from the online application of an affective domain questionnaire (

Beliefs are defined as a subjective and not always shared knowledge system that is modified as a consequence of the interactions of the environmen

Beliefs are considered to be “a judgment of truth or the falsity of a proposition to identify beliefs from the teachers’ narratives” (

In fact, if a teacher perceived himself as having little ability to teach mathematics (belief), he would develop a dislike for that area of knowledge (attitude), and would even feel anxious when he had to teach it (anxiety), consequently, as far as possible avoid teaching math (behavior) (

Research on teachers’ beliefs about mathematics are interesting due to their reflection, or possible influence on students (

In solving a mathematical problem, an affective situation is associated with the involved subject, who puts into play not only operative and discursive practices to answer the problem, but also mobilizes beliefs, attitudes, emotions, and values that condition, to a greater or lesser degree and in a different sense, the required cognitive response (

- Identify the beliefs of primary school teachers about solving mathematical problems.

- Explain the relationships between the beliefs of primary school teachers about problem-solving.

- Check if the beliefs of primary school teachers about the resolution differ with the variables gender, age and ethnicity.

- Study if the beliefs of primary school teachers about the resolution differ with the variables teaching experience and type of school.

It is a quantitative study that focuses on the treatment of data through the categorization and description of the properties, characteristics and profiles of the people, groups, communities, processes and objects that have been subjected to analysis (

We worked with a sample of 118 primary school teachers belonging to communities of the Autonomous Regions of the Caribbean Coast of Nicaragua. In this research, as we can see in Table

Table

Characteristic
Percentage
(%, n) or mean SD
Age in year (n=118)
< 20
25.40 (30)

Characteristic
Percentage
(%, n) or mean SD
20-29
50.00 (59)
30
24.60 (29)
Mean (SD)
24.81 (4.72)
Gender (n=118)
Male
48.30 (57)
Female
51.70 (61)
Ethnicity (n=118)
Mestizo
75.40 (89)
Afro descendant (Creole)
15.30 (18)
Miskito (Indigenous)
9.30 (11)
Teaching experience (years) (n=118)
< 5
40.70 (48)
5-9
48.30 (57)
10
11.00 (13)
Mean (SD)
7.20 (3.48)
School type (n=118)
Urban
44.10 (52)
Rural
55.90 (66)

The
affective domain instrument was used in solving mathematical problems
(

Beliefs about the nature of mathematical problems and their teaching and learning. It aims to analyze and seek a greater understanding of teachers’ role and value in problem-solving and their learning. Consisting of 5 items. The score for this category is obtained by adding items from 1 to

Beliefs about oneself as a mathematical problem solver. It is about exploring the self-image of the teacher in initial training with respect to his abilities and capacities as a solver of mathematical problems. Made up of 6 items. The score for this category is achieved by adding items from 6 to 11.

Attitudes and emotional reactions towards solving mathematical problems. It is about knowing and analyzing the attitudes and emotional reactions that teachers manifest in problem-solving. Made up of 8 items. The score for this category is achieved by adding items from 12 to 20

Assessment of the training received in teaching studies in relation to solving mathematical problems. It is about analyzing the teacher’s assessment of the changes that his/her training has produced in her coping with problem-solving. This category is configured with item 21

In all the items, the possible answers range from 1 to 4, Likert scale. These alternative answers are: 1 = Strongly disagree; 2 = Disagree; 3 = Agree; and 4 = Strongly agree. The instrument on affective dominance in solving mathematical problems allows obtaining, in addition to a global score on beliefs, four more scores referring to each of the categories that are evaluated

To guarantee the quality of the measurement, a psychometric study was applied to the instrument, to check its validity and reliability values. The internal consistency value of the instrument items was calculated, obtaining a Cronbach’s alpha value of 96% reliability. Regarding validity, a principal component analysis (PCA) was carried out, in this sense, the Kaiser-Meyer-Olkin measure of sampling adequacy shows a value of 0.777. On another hand, the Bartlett sphericity test offered results that indicated that the analysis is relevant (Chi-square = 774.585; gl = 210; sig. 0.000). In addition, the value of the determinant matrix was calculated, which is equivalent to 0.001, this value is different from 1. Ultimately, the principal components analysis shows an adequate model.

The administration of the instrument was carried out by the author during the 2021 academic year using Google Forms. Before the administration of the instrument, the objectives of the study were informed, emphasizing the right not to participate and the confidentiality of the process. Participants were asked not to reveal their identity to ensure that the completion of this instrument was for academic purposes only. Prior to data collection, the prior, free and informed consent of the primary education teachers was obtained, as well as the authorization of the educational institutions of the Caribbean Coast of Nicaragua.

Data were analyzed using the Statistical Package for Social Sciences (SPSS), version 25. Frequencies, percentages, means, and standard deviation were used to summarize the data. An internal consistency analysis of the instrument, a principal component analysis to determine the quality and validity of the measure and parametric tests were applied.

In Table

Table

Statement
Response %
Scores mean (SD)
Strongly disagree
In disagreement
Agree
Strongly agree
1. Most
math problems are usually solved in a few minutes, if you know the formula,
rule, or procedure that the teacher explained or that is in the textbook.
8.50
10.20
38.10
43.20
3.16 (0.94)
2. When
trying to solve a problem, the result is more important than the process
followed.
10.20
14.40
36.40
39.00
3.04 (0.97)
3.
Knowing how to solve the problems that the teacher proposes in class, it is
possible to solve others of the same type if only the data has changed.
9.30
14.40
33.10
43.20
3.10 (0.97)
4. The
skills or abilities used in math classes to solve problems have nothing to do
with those used to solve problems in everyday life.
6.80
6.80
23.70
62.70
3.42 (0.89)
5. Find
different ways and methods to solve problems.
5.10
16.90
33.90
44.10
3.17 (0.89)
Total scoreª
Median (range)
15 (5-20)

Median (SD)
15.89 (3.08)
Variance
9.54
Total score/full score %
79%

ªMaximum score = 20

In Table

Table 3: Beliefs about oneself as a mathematical problem solver

Statement
Response %
Scores mean (SD)
Strongly disagree
In disagreement
Agree
Strongly agree
6. When more study time is devoted to
mathematics, better results are obtained in solving problems.
9.30
20.30
34.70
35.60
2.97 (0.96)
7. When I solve a problem, I often
doubt whether the result is correct.
6.80
13.60
36.40
43.20
3.16 (0.90)
8. I am confident in myself when
faced with math problems.
5.90
6.80
28.00
59.30
3.41 (0.86)
9. I am calm and collected when
solving math problems.
5.90
5.90
34.70
53.40
3.36 (0.84)
10. When I try to solve a problem, I
usually find the correct result.
5.1
15.30
39.00
40.70
3.15 (0.86)
11. Luck influences the successful
solving of a math problem.
6.80
8.50
33.10
51.70
3.30 (0.89)
Total scoreª
Median (range)
16 (8-24)
Median (SD)
19.33 (3.33)
Variance
11.14
Total score/full score %
80%

ªMaximum score = 24

It can be seen in Table

Table 4: Attitudes and emotional reactions towards solving mathematical problems

Statement
Response %
Scores mean (SD)
Strongly disagree
In disagreement
Agree
Strongly agree
12. In the face of a complicated
problem, I often give up easily.
9.30
8.50
42.40
39.80
3.13 (0.92)
13. When faced with a problem, I am
very curious to know the solution.
7.60
16.10
29.70
46.60
3.15 (0.95)
14. I am distressed and afraid when
the teacher offers me “by surprise” to solve a problem.
34.70
41.50
10.20
13.60
1.96 (1.03)
15. When I solve problems in a group,
I have more confidence in myself.
10.20
10.20
30.50
49.20
3.19 (0.98)
16. When I get stuck or block in
solving a problem, I start to feel insecure, desperate, nervous.
39.80
42.40
9.30
8.50
1.84 (0.91)
17. If I can’t find the solution to a
problem, I have the feeling of having failed and wasting my time.
28.00
57.60
5.90
8.50
1.65 (0.92)
18. It gives me great satisfaction to
be able to solve a mathematical problem successfully.
6.80
8.50
38.10
46.60
3.25 (0.87)

Statement
Response %
Scores mean (SD)
Strongly disagree
In disagreement
Agree
Strongly agree
19. When I failed in my attempts to
solve a problem, he tried again.
12.70
14.40
40.7
32.20
2.92 (0.98)
20. Solving a problem requires
effort, perseverance, and patience.
5.10
4.20
36.40
54.20
3.40 (0.79)
Total scoreª
Median (range)
15 (15-30)
Median (SD)
24.48 (2.58)
Variance
6.66
Total score/full score %
68%

ªMaximum score = 36

The teachers state that they strongly agree / agree (82.20%; M = 3.13; SD = 0.92) that in the teaching profession they have discovered other ways of approaching mathematical problems, this can be seen in Table 5.

Table

Statement
Response %
Scores mean (SD)
Strongly disagree
In disagreement
Agree
Strongly agree
21. In teaching, I have
discovered other ways of approaching mathematical problems.
5.10
8.50
39.00
47.50
3.29 (0.82)
Total scoreª
Median (range)
3 (1-4)
Median (SD)
3.28 (0.82)
Variance
0.68
Total score/full score %
3 (1-4)

ªMaximum score = 4

Regarding the correlation of the different categories with each other, all the correlations were statistically significant at levels of 0.001, in Table 6, relevant associations are observed. The correlations between the various categories are statistically significant and of moderate or high intensity, so we believe that, although they constitute different aspects of beliefs, each of these aspects can influence the others. For example, beliefs about oneself as a mathematical problem solver are correlated with attitudes and emotional reactions towards solving mathematical problems (r = 0.617), that is, the levels of confidence and security in their abilities, capacities, and possibilities to succeed in solving a problem is due to the level of perseverance, satisfaction, curiosity, and security in problem-solving.

Table

Categories’
Categoric 1
Categoric 2
Categoric 3
Categoric 4
Categoric 1: Beliefs about the nature
of mathematical problems and their teaching and learning
1
Categoric 2: Beliefs about oneself as
a mathematical problem solver
0.471**
1
Categoric 3: Attitudes and emotional
reactions towards solving mathematical problems.
0.560**
0.617**
1
Categoric 4: Assessment of the
training received in teaching studies in relation to solving mathematical
problems
0.503**
0.354**
0.468**
1

* The correlation is significant with p 0001

** The correlation is significant with p <0.001

Similarly, beliefs about the nature of mathematical problems and their teaching and learning are related to attitudes and emotional reactions towards problem-solving (r = 0.560), this indicates that teachers who reported higher levels of utility, applicability, and importance to solve a mathematical problem had attitudes and emotional reactions of satisfaction, curiosity, and security towards problem-solving. On the other hand, beliefs about the nature of mathematical problems and their teaching and learning were positively correlated with the assessment of the training received in teacher studies in relation to the resolution of mathematical problems (r = 0.503), which implies that the teacher’s vision of how to learn to solve mathematical problems produces a change in the approach to solving due to teaching studies or training throughout their academic career. In addition, the training received in teacher education is correlated with attitudes and positive emotional reactions in problem-solving (r = 0.468), this indicates that attitudes such as liking, motivation, usefulness, and confidence towards problem-solving.

Another relevant aspect is that beliefs about the nature of mathematical problems and their teaching and learning correlate with beliefs about oneself as a mathematical problem solver (r = 0.471), this indicates that teachers try to analyze and understand mathematical problems with the help of your skills and abilities as a problem solver. And finally, it was found that the assessment of the training received in teaching studies is significantly related to beliefs about oneself as a solver of mathematical problems (r = 0.354), this indicates, in such a way that teachers receive a training increases their capacities and possibilities to function successfully in problem solving.

The Kruskal-Wallis test was applied to try to explain, verify, study, and know if the variables age, gender, ethnicity, teaching experience, and what type of school influence beliefs towards mathematics in problem-solving this is shown in Table 7.

Table 7: Analysis of non-parametric tests

Categories
Age
Gender
Ethnicity
Teaching Experience
School Type
x2
p
x2
p
x2
p
x2
p
x2
p
Categoric 1: Beliefs about the nature
of mathematical problems and their teaching and learning
2.33
0.313
0.005
0.939
5.07
0.079
6.68
0.035
0.150
0.698
Categoric 2: Beliefs about oneself as
a mathematical problem solver
3.10
0.212
4.69
0.983
11.24
0.004
1.85
0.396
0.490
0.484
Categoric 3: Attitudes and emotional
reactions towards solving mathematical problems.
3.72
0.156
0.477
0.490
4.03
0.134
2.26
0.323
0.020
0.885
Categoric 4: Assessment of the
training received in teaching studies in relation to solving mathematical
problems
5.33
0.070
0.064
0.800
1.65
0.439
0.99
0.608
0.003
0.953

It can be seen that the age variable does not influence beliefs towards mathematics in problem solving (Category 1: X2= 2.33; 0.313 <0.05; Category 2: X2= 3.10; 0.212 <0.05; Category 3: X2= 3.72; 0.156 <0.05; Category 4: X2= 5.33; 0.070 <0.05). Regarding gender, it was found that there are no statistically significant differences between women and men in relation to beliefs towards mathematics because the bilateral significance values are greater than 0.05 (Category 1: X2= 0.005; 0.939 <0.05; Category 2: X2= 4.69; 0.983 <0.05; Category 3: X2= 0.477; 0.490 <0.05; Category 4: X2= 0.064; 0.800 <0.05), this means that both women and men have similar belief systems. Also, it can be observed that being an urban or rural schoolteacher does not influence beliefs towards mathematics in problem-solving. (Category 1: X2 = 0.150; 0.698 <0.05; Category 2: X2= 0.49087; 0.484 <0.05; Category 3: X2= 0.020; 0.885 <0.05; Category 4: X2= 0.003; 0.953 <0.05).

On the other hand, when analyzing the ethnicity variable, it was found that there are no significant differences in some categories (Category 1: X2= 5.07; 0.079 <0.05; Category 3: X2= 4.03; 0.134 <0.05; Category 4: X2= 1.65; 0.439 <0.05). Although in category 2, regarding beliefs about oneself as a mathematical problem solver, differences are shown between teachers (Category 2: X2= 11.24; 0.004 <0.05) with a significant effect size (ε2 = 0.0961) in favor of the mestizo ethnic group, which can be corroborated with the results of the test of comparisons by pairs of Table 8. It was also found that the variable teaching experience does not influence some categories (Category 2: X2= 1.85; 0.396 < 0.05; Category 3: X2= 2.26; 0.323 <0.05; Category 4: X2= 0.99; 0.608 <0.05), but if the teaching experience influences beliefs about the nature of mathematical problems and their teaching and learning (ε2 = 0.0571).

Table 8: Dwass-Steel-Critchlow-Fligner Pairwise Comparisons

Ethnicity
Mean (SD)
Pairwise comparisons
W
p
Mestizo
19.88 (3.04)
Mestizo – Creole
-4.56
0.004
Creole
16.72 (4.04)
Mestizo – Miskitus
-1.62
0.488
Miskitus
19.18 (2.35)
Creole – Miskitus
2.43
0.199
Teaching Experience
Mean (SD)
Pairwise comparisons
W
p
< 5
15.39 (3.20)
0 < 5 9
2.97
0.08
5-9
16.59 (2.71)
0 < 5 10
-0.90
0.799
10
14.69 (3.68)
5 < 10 +
-2.92
0.097

Teachers who have between five and nine years of experience have a broader vision of how to learn and teach how to solve mathematical problems (See Table 8).

The objective of the study was to analyze the beliefs of primary school teachers about problem-solving in the context of COVID-19, and their relationship with demographic variables such as gender, ethnicity, age, teaching experience, and type of school. In this research, teachers’ beliefs could propagate the idea of better achievement and improve the teaching and learning of mathematics (Tarmizi and Tarmizi, 2010). Therefore, it was identified that the beliefs of primary education teachers about solving mathematical problems are generally high (M = 67.11; SD = 9.95), coinciding with the study by Yavuz and Erbay (2015) in which they say that primary school teachers have positive perceptions of problem-solving.

Referring to the significant correlations between the categories evaluated, it can be indicated that the teachers’ beliefs about solving mathematical problems become factors such as confidence, security, perseverance, satisfaction, curiosity, liking, motivation, and usefulness to function successfully in the resolution of mathematical problems, which implies the need to continue advancing in the training processes throughout their academic career, coinciding with what Flores-López and Auzmendi (2018) express that when solving mathematical problems beliefs are activated, emotions and attitudes in a positive way.

It was determined that teachers’ beliefs about solving mathematical problems do not differ according to age, this means that young and adult teachers tend to have the same type of beliefs about problem-solving both in their learning processes and in their teaching shared with their future students. Also, it was found that the beliefs of teachers about solving mathematical problems do not influence according to gender (women and men), coinciding with the research of Sağlam and Dost (2014) and Yavuz and Erbay (2015) that states that the beliefs of teachers on problem-solving do not differ according to gender, although Bekirogullari et al. (2011) reported that the gender variable has a positive influence in favor of women. However, Arli et al. (2011) affirm that, if the beliefs of women and men differed or not according to gender, it could change according to the context of the research participants.

The teachers surveyed in this study belong to different ethnic groups (mestizo, Afro-descendant and indigenous), however, ethnicity is not a determining factor in beliefs about solving mathematical problems. Therefore, these findings suggest a greater investigation be carried out on various socio-cultural factors of these ethnic populations since it was found that beliefs about oneself as a solver of mathematical problems manifest significant differences in ethnic groups in favor of the mestizo, therefore, in the studies by Flores-López and Auzmendi (2015) suggested the powerful influence of the multicultural context on the beliefs and attitudes towards problem-solving of future teachers.

It was found that teachers ‘beliefs about problem-solving do not differ according to their teaching experience, relating to the study by Yu (2009) that reported that the teaching experience does not influence the teachers’ beliefs, likewise, they are consistent with the beliefs reported by Lebrija et al. (2010) from the perspective that the years of experiences do not seem to make a difference between their beliefs, but rather that they share similar beliefs, although, in the section beliefs about the nature of mathematical problems and their teaching and learning, few differences appear with regarding your teaching experience. Also, it was discovered that teachers’ beliefs about solving mathematical problems do not differ according to their type of school (urban or rural). The reason for this situation may be the fact that the schools are in the same region, therefore, teachers develop a process of planning and evaluation of mathematical content in a collaborative and articulated way. Furthermore, the teachers’ environments do not differ in general terms.

In light of these findings, it is necessary to advance in the education and training processes of primary education teachers with a greater emphasis on pedagogical and technological knowledge of the content, in the community construction of knowledge, wisdom, and practices, in teaching problem solving and beliefs, attitudes and emotions in solving mathematical problems. Taking as a reference that beliefs about mathematics are formed throughout life, it is also recommended that teachers develop the beliefs related to the mathematics of students from elementary school.