Factors affecting the numeracy skills of students from mountainous ethnic minority regions in Vietnam: Learners’ perspectives

Abstract

This paper analyzes factors that affect the numeracy skills of secondary school students from mountainous and ethnic minority regions in Vietnam from the perspective of the students to create suitable strategies for teachers, parents, and the government to enhance their numeracy skills. Data from 755 students in 8 secondary schools in 8 provinces in the northern region of Vietnam were analyzed. The results showed eight factors that impact the numeracy levels of secondary students in mountainous regions. Student’s efforts and language skills were most influential, and teachers did not have a substantial effect. The paper offers suggestions to equip teachers in these regions with more knowledge and skills to support students in developing their numeracy skills.

Keywords:

• numeracy skill
• mountainous region
• Vietnam
• secondary students
• parents
• teachers

PUBLIC INTEREST STATEMENT

Although there have been many researches regarding factors that affect students’ numeracy skills, our research group believes that there is room for further analysis. Our study stands out because it was performed on 755 secondary students who are mature enough to assess the impact of various factors on their numeracy. These students currently live in some of the most economically deficient regions of Vietnam. Our results show that internal factors including language, passion, and effort have the most substantial impact on student’s numeracy.

1. Introduction

Since 2018, Vietnam has been in the course of renovating its secondary school curriculum in order to prepare the necessary human resources for the Fourth Industrial Revolution. The Vietnamese general education curriculum has prioritized the establishment of a new system of crucial skills for students, and considers numeracy a general skill for all. Brown et al. (1998) defined “numeracy” as the ability to process, interpret, and communicate numerical information in various contexts. Australian educational researchers believe that numeracy includes knowledge, skills, behaviors, and dispositions that students need to apply in various situations (Tout et al., 2020). This includes the acknowledgment of the role of mathematics in daily life and the tendency to use mathematical knowledge and skills in a meaningful way. Numeracy is a critical skill that builds bridges between mathematics and the real world (Steen, 2001; Tout et al., 2020). Sabidin et al. (2017) noted that numeracy requires students to use their knowledge and skills to solve numerical issues in real-life situations. While discussing the role of numeracy, Tariq and Durrani (2012) noted that researchers, tutors, and policymakers focus on the decline in undergraduates’ numeracy skills as it is necessary to maintain and advance in subjects, but also post-graduate employment. Adults with low levels of literacy and numeracy skills encounter limitations in their work, community, and home lives, including finding and keeping jobs and supporting their children’s learning (Grunau, 2020; Hong et al., 2020; Lopes et al., 2020; Tariq & Durrani, 2012).

Studies on the numeracy skills of students have sparked interest from many researchers. Melhuish et al. (2008) investigated the strong influence of social contexts on cognitive development and academic success, and the development of other aspects of children including literacy and numeracy skills, although the result may differ across cultures. Enu et al. (2015) pointed out a few primary factors that influence learners’ mathematics achievement like their behaviors and attitudes toward learning mathematics, their socioeconomic backgrounds including their parents’ academic and financial capabilities, and the type of schools and teachers. Missall et al. (2015, p356) emphasized that “children from lower socioeconomic and ethnic minority backgrounds tend to enter school with less developed mathematical skills.” Strickland et al. (2020)) found the participation of children in numeracy-activities at home and in the kindergarten-level offers a noticeable boost to their performance in higher levels. Aunio et al. (2019) examined 442 first grade students in South Africa and found that perceptive and language skills, as well as the opportunity to learn mathematics in pre-school are crucial factors that influence students’ numeracy skills in the first grade.

With 27 minority groups encompassing 7 distinctive language families, the Northern mountainous region of Vietnam is one of the most vital economic and social areas in the country. However, the undeveloped infrastructure owing to the remoteness of the terrains that house their residential areas has learning barriers (Nguyen et al., 2020). Moreover, the current mathematics education program for all 54 ethnic groups developed by the Vietnam Ministry of Education and Training has been facing many obstacles (Nguyen et al., 2020). The reason is that it tend to homogenize all 54 ethnic groups and does not offer room to account for the culture and socioeconomic backgrounds while the culture of each ethnic group and the students’ socioeconomic status play a decisive role in their educational outcomes (Melhuish et al., 2008; Missall et al., 2015; Nguyen et al., 2020).

The Vietnamese mathematics curriculum has focused on three learning areas: 1) Arithmetic, operations, and algebra; 2) Space, shapes, and measurement; and 3) Statistics (data handling) and probability (MoET, 2018). At every stage, teachers are expected to follow the curriculum chronologically, and to spend five hours a week on teaching mathematics. Teachers make use of mathematics textbooks supplied by the public education authorities to supplement their pedagogies. There have been numerous efforts to improve mathematics education in the Northern mountainous region of Vietnam; however, the results are not as expected (MoET, 2018).

Numeracy is not the same as mathematics, nor is it alternative to mathematics. Numeracy encompasses the knowledge, skills, behavior and dispositions that students need to use mathematics in a wide range of situations (Tout et al., 2020). So, research on factors affecting the numeracy skills of ethnic minority students is crucial for the staff and policymakers to narrow the gap in quality of mathematics education between the mountainous and developed regions and to create human resource strategies for minority regions in Vietnam. Therefore, this study was conducted to clarify i) the influence of internal factors including the acknowledgment of the usefulness of mathematics on students’ numeracy skills; ii) the influence of parents (including their beliefs with respect to the subject and in their children’s abilities, economics conditions, and provision of time for their children to study) on students’ numeracy skills; and iii) the influence of teachers (including beliefs in the subject and their teaching methods) on students’ numeracy skills. All three factors have a substantial impact on the numeracy skills of students in northern Vietnam’s ethnic minority areas.

2. Literature review

In order to understand the factors that influence on the students’ numeracy skills, we would clarify these factors below.

2.1. Language

Various studies have highlighted the impact of language (both of the students’ language skills and the language that is used as a medium of education) on the numeracy skills of children (Aunio et al., 2019; Rahman et al., 2010; Rosenthal et al., 1983; Zhang, 2016). Aunio et al. (2019) noted that although language does not affect every aspect of numeracy skills, children who lack language skills score lower, particularly in solving word problems in mathematics. They emphasized that second-language learners face greater difficulties in learning mathematics especially if their knowledge of the second language is weak (Aunio et al., 2019).

2.2. Effort

Effort refers to the amount of time and energy that students expend in meeting their formal academic requirements as established by their teachers and/or schools (Carbonaro, 2005). It has played a central role in shaping students’ attitudes toward and thoughts on learning and achievement. Students’ perceptions of effort may have a substantial impact on their achievement when they influence their self-regulated learning (Carbonaro, 2005; Dunlosky et al., 2020; Hopland & Nyhus, 2016).

2.3. Interest

According to Krapp et al. (1992), interest emerges from an individual’s interactions with their environment. Azmidar et al. (2017, p1) defined “interest known as a condition or situation was related to individual wishes or necessities. It’s can also define as the preference in someone’s soul together with happiness”. It is thus necessary to cultivate interest in studies among students. The higher the interest in learning, the more positive the students’ attitude toward the subject. Interest can be situational or personal. The former is produced by a number of conditions and/or concrete objects in the environment. Students with personal interest are characterized by their massive effort in looking for new information and a positive attitude toward learning (Azmidar et al., 2017; Krapp et al., 1992). The benefits of having a personal interest include greater focus on learning activities, the ability to learn and work on something in the long term, appropriate learning strategies, and satisfaction with what one does in order to achieve their goals. Azmidar et al. (2017) emphasized that the level of students’ interest has an immense influence on their learning, especially their attentive and objectives in learning.

2.4. Anxiety

Anxiety is a crucial factor that affects students while studying mathematics (Tariq & Durrani, 2012 Bed Acharya, 2017). It is a feeling of tension or fear that interferes with one’s ability to manipulate numbers and solve mathematical problems in everyday life and academic environments (Tariq & Durrani, 2012). Acharya (2017) indicated that anxiety refers to the stress, nervousness, lack of confidence, and sometimes fear. It has a negative effect on students’ learning processes in mathematics and other subjects. It is an emotional state that appears in normal life circumstances and is inseparable from human survival. It is rooted in the fear of facing the subject, which includes classes, homework, and tests (Velazco et al., 2021).

2.5. Time learning

Although the relationship between time spent on homework and subsequent student achievement is clearly inconsistent (Cattaneo et al., 2017; Gettinger, 1984; Godwin et al., 2021; Nasrullah_phd & Khan_phd, 2015). A few studies (Cattaneo et al., 2017; Godwin et al., 2021; Kidron & Lindsay, 2014; Nasrullah_phd & Khan_phd, 2015) have presented a positive relationship, where high-performing students spend more time doing homework, optimize their time, and do more teacher-assigned homework than do low-performing students. Kidron and Lindsay (2014) and Jez and Wassmer (2015) suggested that the time at school is not enough for many students to gain knowledge. They believe that increased learning time can lead to personal growth opportunities, including higher self-confidence, better interpersonal and study skills, and greater commitment to school and learning. Increased learning time is intended to benefit all students, especially those with limited learning opportunities. However, Kidron and Lindsay (2014), Jez and Wassmer (2015), Cattaneo et al. (2017) also noted that there is insufficient evidence to suggest that increased learning time is effective in promoting the academic outcomes for all students in all settings. Jez and Wassmer (2015) emphasized that: educators and policy makers should pause as they consider increasing instructional time by lengthening the school day or cutting recess in hopes of increasing students’ learning outcomes. If time alone is a poor predictor of learning, simply adding more instructional time is unlikely to achieve the desired results. Nevertheless, the belief that improving academic achievement is as simple as increasing instructional time is pervasive and evident in current trends in how schools are allocating instructional time (Jez & Wassmer, 2015, p.14).

2.6. Self-efficacy

Previous research has found consistent relations between students’ self-efficacy and achievement goals (Å. Diseth et al., 2012; Komarraju & Nadler, 2013; Liem et al., 2008). For example, Liem et al. (2008) explained that self-efficacy refers to the students’ beliefs and confidence in accomplishing an academic task. They found that students’ self-efficacy was a positive predictor of performance outcomes in various academic areas such as mathematics, science, and reading. Diseth et al. (2012) suggested that self-efficacy refers to people’s beliefs around their capabilities to produce designated levels of performance under the influence of problems in their lives. They emphasized that students’ competence predicts mastery in goal achievement, both directly and indirectly via self-efficacy. The association between high self-efficacy and academic achievement has also been demonstrated in various settings (Abuya et al., 2018; Komarraju & Nadler, 2013; Rahman et al., 2010), where self-efficacy has been defined as people’s assessment of their ability to take actions that can influence the outcomes of events or situations that affect their lives.

2.7. Parents

Considine and Zappalà (2002) claimed that those with good social and economic status tend to help their children achieve better intellectual outcomes. Melhuish et al. (2008) noted that parents’ education is the most substantial stimulus for students’ performance, where a mother’s education has the most significant impact on the first few years in a child’s life. They showed how mothers can create activities to provoke their children’s intelligence by supplying various instruments to help them develop their skills. In the process of raising a child, activities such as reading books, using diversified knowledge, building quick reflexes, and keeping communications cordial can have a direct effect on a child’s positive development. Parents who come from healthy economic and educational backgrounds are more capable of using complex activities to improve their children’s cognition.

Enu et al. (2015) also believed that the economic background is usually indicated by combining the parents’ academic level, employment status, and income. In most explorations of students’ academic performance, it is not surprising that a student’s socioeconomic status is a major factor in predicting their academic achievements, which means that successes in education depend heavily on parents’ conditions.

To further certify results from Melhuish et al. (2008) regarding the role of parents on their children’s numeracy skills, Missall et al. (2015) has executed his study using a larger sample with a sizeable number of Latino families and more economic diversity than in previous studies conducted in the United State. Missall et al. concluded that the children of those who believed in the significance of learning the subject tended to do well in it. This means that what parents believe about math is related to how they can use their mathematics knowledge and experience to support their children math learning (Missall et al., 2015).

Acharya (2017) believed that parents played a pivotal role in supporting their children’s studies, helped them achieve better results, and adjusted their behaviors. Encouragement from parents can help students at every stage of education. Those who succeed in helping their children tend to receive similar triumphs for themselves.

Abuya et al. (2018) stated that higher parental education influences positive family interaction patterns, which can lead to greater academic achievement and achievement-oriented attitudes over time of their children. The parental education and family interaction foster positive experiences in children, which can lead to the adoption of cognitive scripts, beliefs, and values in children who maintain their behavior over time- in this case academic and achievement-related behavior (Abuya et al., 2018; Missall et al., 2015). Moreover, Abuya et al. (2018) found “a positive association between mothers’ education and achievement, with the effects on achievement larger with increased levels of fathers’ education” (Abuya et al., 2018, p.7).

Bradley (2019) highlighted the relationship between a child’s promising academic results and their parents’ incentives to achieve skills like connecting letters with sounds. The most vital attribute is that parents can help their children improve their skills and motivation for studying.

2.8. Teachers

In studied done by Ernest (1989), he identified that “Official pressure for reforms in the teaching of mathematics overlook a key factor: the psychological foundations of the practice of teaching mathematics, including the teacher’s knowledge, beliefs and attitudes”. Thus, in this study he presented a model of knowledge, beliefs and attitudes of the mathematics teacher, and their relationship with practice. He also emphasized that a teacher’s view of the nature of mathematics provides a basis for their mental model for the teaching and learning of mathematics. Teachers’ beliefs have a powerful impact on teaching through processes such as the selection of content and emphasis, styles of teaching, and modes of learning (Ernest, 1989).

Raymond (1997) suggested a number of complex associations concerning perceptions of how beliefs are formed by teaching activities and why there are contradictions between teachers’ beliefs and how they are erected via practical endeavors. The author also supposed that teachers convey knowledge to students via daily classroom activities, which is imperative in increasing their confidence in the subject. Goos et al. (2020) asserted that the faith that teachers have in their students with respect to mathematics and numeracy abilities tends to affect their learning progress significantly because teachers have a major impact on their classrooms in terms of their comprehension of teaching, studying, and assessing.

Enu et al. (2015) affirmed that teachers have a major impact on constantly achieving higher standards, which are emphasized in schools and educational systems world over. He believed that the success of a subject depends on various factors, one of which is the teachers. Acharya (2017) argued that a child’s academic performance depends heavily on how their teachers work and host their educational activities. He emphasized that the positive attitude of a teacher can create a positive impact on their students.

3. Current studies

Studies have indicated a strong relationship among language (Aunio et al., 2019), cognitive (including short- and long-term memory) and spatial awareness (Aunio et al., 2019; Locuniak & Jordan, 2008), parents’ economic and academic statuses, and the opportunity for students to approach the kindergarten education (Aunio et al., 2019; LeFevre et al., 2010; Locuniak & Jordan, 2008; Melhuish et al., 2008) with their students’ numeracy skills. However, research has mostly focused on final-year kindergarten and primary school students. Very few studies have focused on secondary school students. Most studies on developmental dynamics in early numeracy have been conducted in rich educational contexts, namely in the US, Europe, Singapore, and Australia; studies outside these contexts are non-existent (Aunio et al., 2019). The current study can fill a major gap in research by focusing on secondary school students in Vietnam, a developing nation and investigating the influence of various factors including language, effort, interest, time, teachers, and families on students’ learning mathematics.

4. Methods

Numeracy encompasses the knowledge, skills, behaviors, and dispositions that students need in order to use mathematics in a wide range of situations (Victoria State Government, 2020). A person needs to be able to think and communicate quantitatively, make sense of the data, have spatial awareness, understand patterns and sequences, and recognize situations where mathematical reasoning can be applied to solve problems (The Department of Education and Skills, 2011). It is the ability to understand the usefulness of mathematics and apply it to solve word problems (E0). Eight factors are assumed to influence the numeracy among ethnic minority students in northern Vietnam: language skills (E1), effort (E2), math interest (E3) and anxiety (E4), time-consuming problem (E5), self-efficacy (E6), teacher (E7), and parental care (E8). The model is as follows (see Figure 1):

Figure 1. The model of factors that impact on students’ numeracy skills.

The following hypotheses were developed:

• Hypothesis 1 (H1): Language is correlated with numeracy.

• Hypothesis 2 (H2): Effort is positively correlated with numeracy.

• Hypothesis 3 (H3): Interest is positively correlated with numeracy.

• Hypothesis 4 (H4): Anxiety is negatively correlated with numeracy.

• Hypothesis 5 (H5): Time is positively correlated with numeracy.

• Hypothesis 6 (H6): Self-efficacy is positively correlated with numeracy.

• Hypothesis 7 (H7): Teacher is positively correlated with numeracy.

• Hypothesis 8 (H8): Family is positively correlated with numeracy.

4.1. Participants

The sample in this cross-sectional study comprised 755 middle school students (410 girls, 345 boys) from grades 6 to 8 in 8 provinces in northern Vietnam. In each province, one school was chosen using the convenience sampling method where 30 to 35 students were randomly selected for each grade.

The children’s ethnicities were as follows: Kinh (206), Tay (171), Dao (100), Nung (88), Giay (67), Muong (67), San Chi (20), Hmong (16), Cao Lan (6), Thai (5), Hoa-Chinese (3), San Chay (2), Lao (2), and San Diu (1).

4.2. Measures

We used a survey that comprised two sections. The first section collected personal and demographic data, including name, code, ethnicity/race, sex, date of birth, grade, school, and household income. All questions in this section were forced- answers, except for name. The second section comprised 58 questions that focused on mathematics-related beliefs where students assessed the impact of different factors on their numeracy skills and how they thought and felt about the subject. All items were rated on a 4-point Likert scale (1=strongly disagree, 2=disagree, 3=agree, and 4=strongly agree). The researchers designed and discussed the questionnaires several times to evaluate the quality of the questions. All of questionnaires were sent to 12 senior teachers in 6 secondary schools in Thai Nguyen and Lao Cai, and 4 experts working at the Vietnam Institute of Educational Sciences and Thai Nguyen University of Education. After receiving feedback from the teachers and experts, the questionnaires were adjusted to eliminate observational variables in order to avoid duplication. The questionnaire is presented in Table 1.

Table 1. The Questionnaire

Code	Question
E0	NUMERACY (USEFULNESS OF MATHEMATICS AND THE ABILITY TO USE IT TO SOLVE WORD PROBLEMS)
E01	Mathematics is only important for mathematicians, economists, and scientists; and not for everybody.
E02	You enjoy solving real-life issues more than textbook questions.
E03	Mathematics helps us better understand the world we live in.
E04	You can recognize the situation in daily life that can use your knowledge of mathematics to solve them.
E05	You can use mathematics in your daily activities.
E06	You can apply your mathematics knowledge in other subjects.
E07	The only reason you study mathematics is that it is compulsory.
E08	You believe you can use mathematics in your future job.
E09	You need to study mathematics for your future job.
E1	LANGUAGE SKILLS
E11	Your knowledge of Vietnamese helps you study mathematics better.
E12	You enjoy learning mathematics even though it is not written in your mother tongue.
E13	You feel confident using Vietnamese.
E14	You usually use Vietnamese outside school.
E15	Studying mathematics at school helps you develop the ability to use Vietnamese.
E16	You face difficulties communicating with teachers and other students during mathematics classes.
E2	EFFORT
E21	Through hard work, you have got better at mathematics.
E22	Hard work can help everyone improve their mathematics skills.
E23	Studying mathematics can help you become smarter.
E24	Hard work can help you improve your numeracy skills.
E3	MATHEMATICS INTEREST
E31	You love reading stories on mathematics.
E32	You are interested in what you have learned in mathematics.
E33	You enjoy learning mathematics.
E34	You are excited about mathematics classes.
E4	MATHEMATICS ANXIETY
E41	You usually struggle during mathematics classes.
E42	You are always worried about getting a low score in mathematics.
E43	You are always stressed while doing mathematics homework.
E44	You feel helpless while trying to solve a mathematics problem.
E45	You are afraid to give a wrong answer in mathematics class.
E46	You struggle to apply mathematics to other subjects.
E5	MATHEMATICS SELF-EFFICACY
E51	You feel confident about using mathematics in your daily life.
E52	You can complete your mathematics homework.
E53	You feel like you can study mathematics in the coming years.
E54	You are confident about acing your mathematics exams.
E55	You feel confident asking questions in mathematics classes.
E6	TEACHERS’ INTEREST IN THE STUDENTS’ LEARNING PROCESS
E61	Your teachers recognize when you try your best, even when your results are not good.
E62	Your teachers believe that errors are acceptable, as long as you are trying.
E63	Your teachers care about your feelings in mathematics classes.
E64	Your teachers want you to understand the lessons, not just remember them.
E65	Your teachers understand the issues you face.
E66	Your teachers give you time to discover new questions and solve them.
E67	Your teachers try to make mathematics lessons exciting.
E68	Your teachers want you to feel excited when you learn something new.
E69	Your teachers listen attentively when you ask or voice your opinions.
E610	Your teachers do not care about how you feel during class.
E7	TIME SPENT ON THE SUBJECT
E71	You can solve questions although they may take you a long time to do so.
E72	Time-consuming questions do not discourage you.
E73	You can solve hard questions if you truly focus.
E74	You are not good at solving questions that take a lot of time to analyze.
E75	You will not try to solve questions if you cannot quickly find the solution.
E8	FAMILY INTEREST
E81	Besides studying at school, your parents let you study mathematics at your teachers’ extra classes.
E82	Outside of school, you have to work to help your parents.
E83	Your parents believe studying is important.
E84	Your parents help you understand most mathematics lessons taught at school.
E85	Your parents understand your struggles in studying mathematics at school.
E86	You only study mathematics at home in the evenings.
E87	If you cannot solve a mathematics problem, your parents help you.
E88	Besides school, you have to do housework to help your parents.
E89	Your parents support you when you struggle to study mathematics at home.

4.3. Procedures

The Thai Nguyen University, a leading agency for research sent consent forms to the Departments of Education and Training across 8 provinces, namely Thai Nguyen, Bac Kan, Lang Son, Ha Giang, Son La, Lai Chau, Dien Bien, and Quang Ninh. The consent forms, were in Vietnamese. The Departments of Education and Training and secondary schools in the provinces under study selected the students; the research group did not participate in this process. Our only criteria were that the schools selected had to be situated in the poorer areas within the provinces, and had to have many ethnic minority students on their rolls. We received the signed consent forms from students who agreed to participate. The students then gathered to answer the questions within 60 minutes.

4.4. Missing data

There were some missing data. Of the 58 subscale items, 1 had 15 missing responses, 5 had 3 missing responses, 12 had 2 missing responses, and 15 had 1 missing response. As the total number of missing responses per item was small, they did not affect the results of the study. Therefore, the sample size was 755.

5. Data analysis and results

The exploratory factor analysis (EFA) method was used to evaluate the convergence validity and discriminant validity of the measurement scale. To analyze the trustworthiness of the scale, we evaluated the Cronbach’s Alpha>0.5 and Corrected Item-Total Correlation>0.3 (Nunnally, 1975) using SPSS 20. After the first round, factors E66, E67, E68, E83, E85, and E89 were eliminated as their Cronbach’s Alpha was<0.5 and Corrected Item-Total Correlation was<0.3. Other variables satisfied the requirements for Cronbach’s Alpha and Corrected Item-Total Correlation. The Cronbach’s Alpha for all factors ranged from 0.7 to 0.9 and the Corrected Item-Total Correlation for all factors was higher than 0.35. Therefore, they were all reliable. The exact levels are given in Table 2.

Table 2. Reliability of the factors

Factors	Observed variables	Cronbach’s Alpha	Minimum corrected item-total correlation
E0	E01, E02, E03, E04, E05, E06, E07, E08, E09	0.901	0.625
E1	E11, E12, E13, E14, E15, E16	0.781	0.447
E2	E21, E22, E23, E24	0.705	0.455
E3	E31, E32, E33, E34	0.716	0.382
E4	E41, E42, E43, E44, E45, E46	0.773	0.353
E5	E51, E52, E53, E54, E55	0.798	0.383
E6	E61, E62, E63, E64, E65, E69, E610	0.845	0.461
E7	E71, E72, E73, E74, E75	0.823	0.354
E8	E81, E82, E84, E86, E87, E88	0.761	0.384

Using factor analysis, we discovered the impact of independent variables (E1-E8) on the dependent variable (E0) in the theoretical model. We focused on some factors in the Kaiser-Meyer-Olkin (KMO) test and Bartlett’s test of sphericity, using Varimax rotation with a minimum factor loading of 0.500 and a quote factor of 8. Table 3 presents the results.

Table 3. KMO and Bartlett’s Test

KMO and Bartlett’s Test
Kaiser-Meyer-Olkin Measure of Sampling Adequacy		0.835
Bartlett’s Test of Sphericity	Approx. Chi-Square	11030.949
	df	0.903
	Sig.	0.000

The KMO result was 0.835. Thus, the factor analysis was suitable for the data gathered. As the sig of Bartlett’s test was 0.000 (less than 0.05), it is clear that there were connections among the variables observed. The rotation matrix divided the 43 observed variables into 8 factors, all of which had a factor loading of more than 0.5 (Hair et al., 2010). The smallest and biggest were E56 (0.501) and E74 (0.8), respectively. The observed variables have strong relationships with the factors. By conducting a Pearson correlation factor analysis, we examined the strong linear relationship between E0 (dependent variable) with independent variables and identified multicollinearity as many independent variables had strong relationships. The results show that E0 (usefulness of mathematics and the ability to use mathematics to solve word problems) had strong relationships with other variables thanks to sig values being less than 0.001. The Pearson r between E0 and other variables had a value that ranged between 0.212 and 0.419, showing a noticeable relationship these variables (see Table 4).

Table 4. The Pearson correlation among variables

		E0	E1	E2	E3	E4	E5	E6	E7	E8
E0	Pearson Correlation	1	0.402**	0.417**	0.419**	0.212**	0.413**	0.299**	0.409**	0.233**
	Sig. (2-tailed)		0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
E1	Pearson Correlation		1	0.060	0.167**	0.028	0.075*	−0.030	0.038	−0.041
	Sig. (2-tailed)			0.102	0.000	0.445	0.039	0.418	0.300	0.261
E2	Pearson Correlation			1	0.247**	0.027	0.249**	0.205**	0.260**	0.066
	Sig. (2-tailed)				0.000	0.457	0.000	0.000	0.000	0.072
E3	Pearson Correlation			.	1	0.018	0.267**	0.171**	0.246**	0.042
	Sig. (2-tailed)					0.621	0.000	0.000	0.000	0.245
E4	Pearson Correlation					1	−0.001	−0.054	−0.017	−0.005
	Sig. (2-tailed)						0.988	0.142	0.638	0.895
E5	Pearson Correlation						1	0.221**	0.246**	0.119**
	Sig. (2-tailed)							0.000	0.000	0.001
E6	Pearson Correlation							1	0.328**	0.293**
	Sig. (2-tailed)								0.000	0.000
E7	Pearson Correlation								1	0.166**
	Sig. (2-tailed)									0.000
E8	Pearson Correlation									1
	Sig. (2-tailed)

Note: **. Correlation is significant at the 0.01 level (2-tailed).

*Correlation is significant at the 0.05 level (2-tailed).

Multivariable regression analyses were conducted between independent variables E1 to E8 and the dependent variable E0 to indicate the regression correlation $Bi$ in the regression equation:

$E0=\beta 1E1+\beta 2E2+\beta 3E3+\beta 4E4+\beta 5E5+\beta 6E6+\beta 7E7+\beta 8E8+\epsilon$

The results are shown in Table 5.

Table 5. Results of multivariable regression and multicollinearity analysis

Variable	F-test sig	Adjusted R Square	Durbin-Watson	Standardized beta regression coefficient	Sig.	VIF
E1	0.000	0.565	1.901	0.340	0.000	1.037
E2				0.217	0.000	1.158
E3				0.182	0.000	1.179
E4				0.203	0.000	1.006
E5				0.199	0.000	1.170
E6				0.094	0.000	1.248
E7				0.194	0.000	1.229
E8				0.142	0.000	1.106

The F-test sig was 0.000 (less than 0.05). Therefore, the regression analysis was suitable. Table 5 presents the Durbin-Watson to assess the serial autocorrelation, which was 1.901 (between 1.5 and 2.5); therefore, there was no serial autocorrelation (Qiao, 1999). The adjusted R square of 0.565 means that independent variables explain 56.5% of the variations in the dependent variable, with the remaining 43.5% owing to external variables and random errors. All variables had at of less than 0.05. Thus, they were meaningful and affected E0. The VIF coefficient for all variables was less than 2. Thus, data did not violate the multicollinearity hypothesis. From the coefficients, we constructed two regression equations as follows (see Figure 2):

$\begin{array}{rl}& E0=0.340\times E1+0.217\times E2+0.182\times E3+0.203\times E4+0.199\times E5+0.094\times E6\\ & +0.194\times E7+0.142\times E8+\epsilon \end{array}$

Figure 2. The P-plot of the Regression Standardized Residual.

The regression standardized residual model shows that data points were close to the diagonal line. Therefore, residuals have an almost normal distribution, and the normal distribution assumption is not violated (see Figure 3).

Figure 3. The Scatterplot.

According to the scatterplot, data points surround the zero-ordinate line and tend to form a straight line. Therefore, the linearity hypothesis is not violated. The regression model is shown in Figure 4.

Figure 4. The regression model between E0 and independent variables.

6. Discussion

The regression model demonstrates alignment with previous studies (Aunio et al., 2019; Rahman et al., 2010; Rosenthal et al., 1983). The results show that language has a huge impact on students’ achievements, as Kim et al. (2012) declared that “language shapes mathematical learning.” Most students believed that speaking Vietnamese fluently could help them understand the subject and they were confident in using Vietnamese in their studies and external communications. Studies such Rosenthal et al. (1983), and Kim et al. (2012) demonstrated the difference in achievements between students who studied mathematics in their mother tongue and in a second language. Students considered effort one of the most crucial influences on their achievements as it directly caused changes in learning, which is consistent with Dunlosky et al. (2020), Carbonaro (2005), and Hopland and Nyhus (2016). Students had a more positive attitude toward learning mathematics as many items we set for this variable included “Hard work can help improve one’s mathematics skills, “Through hard work, you can learn mathematics better,” and “Hard work can help improve numeracy skills.” Students believe that effort can help them improve their results, and they experience this. Although Carbonaro (2005) believed that it is challenging to unify students’ efforts with the completion of homework, we believe that finishing homework is a signal of effort.

Interest in studying had a correlation with the numeracy skills of ethnic minority students. Azmidar et al. (2017) indicated that interest has a noticeably positive impact on students’ achievements. However, there are some contradictions as interest is an internal factor that influences learning and student learning outcomes, as it only demonstrates a small relationship (correlation = 0.18). This suggests a difference between the mentality of the Vietnamese northern ethnic minority students, who tend to study with a clear goal and are not influenced by interest.

The regression model indicates a positive correlation between anxiety and numeracy. This contradicts 2021), who described “mathematic anxiety includes tension and emotions that affect the ability to manipulate numbers and tackle issues associated with mathematics in day- to-day” (Luu-Thi et al., 2021, pp1–14). Or Lailiyah et al. (2021), who defined it as students experiencing apprehension, aversion, tension, worry, frustration, and fear while carrying out mathematical tasks; and noted that they cannot develop their full capacity as a result. Tariq and Durrani (2012) affirmed that correlations between students’ composite scores for numerical competence and “mathematics anxiety” scale and sub-scales were negative and statistically significant. 2021) highlighted a weak positive correlation between mathematics anxiety and average mathematics score (r = 0.064, p < 0.05). They discovered that the higher the mathematics anxiety level, the higher the average mathematics score. Thus, we can hypothesize that the impact of mathematics anxiety on numeracy skills depends on the cultural context. The higher the anxiety level for Vietnamese mountainous ethnic minority students, the more they try to ace the subject.

The Pearson correlation analysis results show the relationship between numeracy and self-efficacy (r = 0.199, p = 0.000). The correlation coefficient values show that there was a significant positive relationship. Self-efficacy had weak relationships with numeracy. These results align with previous studies, which have shown a positive correlation between self-efficacy and students’ academic achievement (Diseth et al., 2012; Komarraju & Nadler, 2013). Komarraju and Nadler (2013) noted that self-efficacy expectancies are important in predicting academic achievement. Students who are more confident and self-assured are more likely to report higher levels of academic performance. However, there are differences between our research outputs and those of Diseth et al. (2012) and Komarraju and Nadler (2013), who presented a substantial relationship (with correlation coefficients of r = 0.56 and β = 0.30 with p < 0.01) between self-efficacy and students’ academic achievement. Our correlation coefficient remains low at r = 0.199 at p < 0.00, because studies conducted by other authors have focused on older students who may have acknowledged the role of self-efficacy in their academic achievement.

Studies have reported a statistically positive relationship between studying time (which includes extra time at school and self-study) and academic achievement (Cattaneo et al., 2017; Jez & Wassmer, 2015; Kidron & Lindsay, 2014). According to Godwin et al., “A common belief in education is that better learning outcomes should result the more time students spend on a given task” (Godwin et al., 2021, p1). Owing to the students’ economic conditions, most secondary students who answered the questionnaire attended one session at school (usually from 7.30 AM − 11.30 AM) and spent the remaining time studying by themselves. Therefore, our surveys focused on the impact of self-study on numeracy skills. The results show a weak relationship between self-study time and numeracy skills (r = 0.194 with p = 0.000), which explains that students had not fully recognized the role of enhanced self-study on academic achievement, or that self-study without guidance from teachers was not enough to acknowledge improvements.

The results suggest that parents also have an impact on their children’s numeracy skills, which aligns with the findings of Melhuish et al. (2008), LeFevre et al. (2010), Missall et al. (2015), Abuya et al. (2018), and Liu et al. (2019). Studies have highlighted a substantial correlation among academic level, economic status, parental expectations, and the overall numeracy skills of students. The impact can be seen through orthodox activities such as encouraging or helping children read numbers, count the number of objects in a group, and add and subtract using objects, as well as unorthodox activities including e-games and real‐world tasks (LeFevre et al., 2010; Liu et al., 2019; Missall et al., 2015). However, the studies mentioned have focused only on kindergarten and/or pre-primary students. Our study focuses on secondary students. Thus, the report depends solely on the students’ responses. Therefore, although the results show a positive connection between the parents’ support and numeracy skills, this connection is relatively weak, and proves that parents living in remote and mountainous areas in Vietnam have paid attention to their children’s numeracy skills, but have not supported their children’s mathematics learning much.

7. Conclusion and implications

Numeracy can be understood as the ability to use mathematics to solve real-life problems, which plays a crucial role in our daily lives and each nation’s economic advancement. To develop students’ mathematical and numeracy competences, one of the most vital facets is to make experiences around the subject exciting in order to build trust and approach students easily. These experiences should insinuate persistence with mathematics for students. Many authors, such as Melhuish et al. (2008), Missall et al. (2015), Jez and Wassmer (2015), Dunlosky et al. (2020) have focused on researching factors that affect numeracy in order to propose solutions to improve it. These include early learning and home environment, mathematical activities in the home and parental beliefs about mathematics (Missall et al., 2015); early numeracy, parent involvement, and home experiences (LeFevre et al., 2010; mothers’ education, self-efficacy (Abuya et al., 2018); and students’ efforts, self-regulated learning (Dunlosky et al., 2020). We identified that multiethnicity and multilingualism in Vietnam create barriers for students from remote and mountainous areas while learning mathematics. This aligns with Simmons and Singleton (2008), who claimed that the limited ability of phonological awareness affected aspects of arithmetic that involve the manipulation of verbal codes such as counting speed and number recall. Our research also indicates the substantial impact of intrinsic factors like interest, effort, anxiety, and self-efficacy on students’ numeracy skills. This solidifies the trustworthiness of the findings in Sansone and Smith (2000), Dunlosky et al. (2020), Carbonaro (2005), and Hopland and Nyhus (2016).

Teachers and parents also have major impacts on students’ numeracy skills. This contradicts the findings in Melhuish et al. (2008), Missall et al. (2015), and Liu et al. (2019). This paradox exists as our research subjects were secondary students who were independent in handling their studies. The illiteracy rates are high in remote regions, and this causes parents to struggle to support their children when they learn mathematics. Melhuish et al. (2008, p109) claimed that “The influences upon parenting and how parenting may influence educational achievement are not simple matters. Poverty, parental education, culture, ethnicity, parental age, health, and other factors are all likely to be important”. We will continue to study the impact of teachers in order to present more detailed results on the impact on students’ numeracy skills and propose suggestions to enhance the effect.

The result of this study helps students indicate the impact of various factors on their numeracy skill so that they can adjust intrinsic elements to enhance their numeracy skill. The findings in this study also show that policies for disadvantaged parents living in mountainous areas that encourage active parenting can help promote children’s numeracy skills and facilitate academic achievement. However, the responsibility for students’ numeracy skills development should not be placed solely on parents. Moreover, the finding from this study help teachers realize that they need to change their teaching methods in order to has more positive effect on the development of students’ numeracy skills.

We believe teachers should engage constructivism in designing learning scenarios for students. They can also use more practical Mathematics issues so that students understand the importance of mastering the subject. The government can also adopt policies for teachers in remote schools to improve their knowledge and teaching skills. The provision of good quality teachers will have major benefits, particularly when the teachers work closely with students.

8. Limitations and future research

Our study has a few limitations. First, only students were surveyed, and teachers and parents were excluded. Future research can extract more meaningful results by surveying students, teachers, and parents. Second, the theoretical model is relatively simple as independent variables (E1–E8) converge to the dependent one (E0), which shows a relationship between these factors. However, our correlation coefficients were lower than those in the literature. Finally, the selection of the research sample was not completely random as it still depended on secondary schools. This means we may have left out students who were interested in the subject or cared about factors that affect their numeracy skills.

Author contributions

Ha Cao Thi contributed to conception, design of the study and wrote the first draft of the manuscript. Thao Phan Thi Phuong and Bich Tran Ngoc organized the database, and Tuan Anh Le performed the statistical analysis. All authors contributed to manuscript revision, read, and approved the submitted version.

Acknowledgments

We appreciate the cooperation and enthusiasm of the students and schools that participated in this study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study was funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 503.01-2020.300. We would like to thank the Thai Nguyen University of Education for their support and all schools, teachers, and students for participating in this study.

Notes on contributors

Ha Cao Thi

Assoc. Prof. Dr. Ha Cao Thi is a senior lecturer at the Vietnam National University, Hanoi. She completed her master’s degree in Hanoi National University of Education and she earned her PhD in The Vietnam National Institute of Educational Sciences. She started her career as a lecturer at the Thai Nguyen University, now she is a senior lecturer at the Vietnam National University, Hanoi. Research areas of interest include: Mathematics education for students, developing students’ thinking in teaching mathematics, curriculum and instruction.

Tuan Anh Le

Dr. Tuan Anh Le is a senior lecturer at the Hanoi National University of Education, Hanoi.

Bich Tran Ngoc

Dr. Bich Tran Ngoc is a lecturer at the Thai Nguyen University.

Thao Phan Thi Phuong

Dr. Thao Phan Thi Phuong is a lecturer at the Thai Nguyen University.