# Correlation between intellectual capacity and ability of mathematical learning of grades 8 and 9 in junior schools in Ho Chi Minh city

The article presented the correlation between intellectual capacity and ability of mathematical learning of grades 8 and 9 in junior high schools in Ho Chi Minh City.

The Otis test was used to measure intellectual capacity giving the appropriate reliability index – grade 9 had an average score higher than that of grade 8.For the validity – the average scores of the 8 and 9 graders in junior high schools in Ho Chi Minh are significant different.

The general test set of ability and basic skills at level 21/22 in form A was used to measure mathematical learning ability. The results show that students sxored higher with theoretical questions than the practical ones.

The correlation between intellectual capacity and ability of mathematical learning of grades 8 and 9 is significant for general and particular aspects. Therefore, it is necessary to investigate students’ intellectual capacity before further decisions are made on mathematical learning contents for grades 8 and 9 in junior high schools.

**1. Introduction.**

Determining the task of educating and training the people of the country in the new stage, the 1992 Constitution of the Socialist Republic of Vietnam stated the macro objective of national education is to “enhance the intellectual level, train human resources, and foster talents”.

To make a specific step, the report of the Central Committee of the Communist Party of Vietnam at the 8th National Party Congress was more specific. That is “application of modern methods to foster students’ ability to solve problems, paying attention to fostering gifted students”.

At present, the school’s mission, as mentioned above, is to train “people of work, of autonomy, of dynamism and of creativity”, which requires the school to maximize its own student’s thinking abilities. In other words, the school must foster students’ thinking skills and learning methods.

Therefore, the study of “the concept of the capacity, the components that make up the capacity of Vietnamese students, its role in teaching, education from which to develop student’s ability and become one of the principles for developing general teaching content. The problem was to study the capacity and its components to make education and teaching more convenient in fostering capacity for students, especially self-study capacity”. (Nguyen, 1996, p.21).

Historically, mathematics in schools has been one of the subjects considered as the basis to best nurture students’ thinking ability. The purpose of teaching mathematics in high school is to develop students intellectually; especially, the operations such as analysis, synthesis, comparison, abstraction, generalization, and so on.

The ultimate purpose is to develop intellectual abilities so that students can solve problems independently and creatively. Therefore, it is necessary to consider the relationship between intellectual capacity and learning ability to have a better orientation to develop intelligence through students’ learning of mathematics.

**2. Methods.**

The research question is: Is there any correlation between students’ intellectual capacity and mathematical learning ability of Graders 8 and 9 in Vietnam?

**2.1. Terms.**

**2.1.1. Capacity.**

Capacity is specific psychological characteristics that create the conditions for speed, depth, and intensity of impact on the working objects. Thus, competency itself is an integral element of a particular activity, not just the correspondence or suitability of one side being the requirement of activity and the other being a combination of personal attributes (Tran, 1995, p.146).

Capacity is closely related to the trend. It could be said that human power is infinite. However, these abilities do notmanifest completely independently, but rather are related to other aspects such as affection as operating in a complete person.

**2.1.2. Intellectual ability.**

The intellectual capacity can manifest in the same cognitive aspect, knowing, quick understanding, quick remembering or thinking, finding out the rules quickly, manifested in imagination as rich imagination, immediate visualization, and exactly what others say, expressed in actions such as quickness, resourcefulness, flexibility, creativity; embodied in qualities such as curiosity, passion, interest in work, and perseverance… (Kharlamop, 1978, p.11).

**2.1.3. Purpose of teaching mathematics.**

Mathematics is not classified in natural sciences nor social sciences because its position and role in high school curriculumis:

– Essential tools to help students learn well in other subjects and help students work effectively in all fields.

– Help students develop intellectual capacities and qualities, such as training abstract thinking, rigorous logical reasoning, accurate thinking, logical thinking, scientific methods in thinking, in thinking essay, in learning, and in problem-solving such as observing, experimenting, groping, predicting, using thinking skills such as inductive, similar, proving, etc. thereby, fostering creative intelligence for students.

– Help students build the basis of the scientific worldview, educate patriotism in socialism, and train many valuable virtues such as disciplined, persistent, self-reliant labor, and love exactness and truth. In addition, mathematics could contribute to the student’s ability to perceive the beauty of creative laborand the beauty of the rich applications of mathematics.

In the other words, it could be said that mathematics help develop general learning skills and helps children orient and build models of intellectual and practical activities. Mathematics, in particular, helps develop the thinking at a high level that the purpose of cognitive education is aimed at.

It is also important to emphasize that a high level of thinking power is creativity in life. According to this view, once the capacity for thinking is developed, learners could apply creatively the principles and rules learned in practice to solve specific tasks.

In short, the purpose of teaching mathematics in secondary schools is to develop intellectual competencies to an optimal level. It could be also seen that the mind has many elements such as language, abstract thinking, spatial imagination, observing, memory, methods of thinking, intellectual qualities, etc.

Psychologically, intellectual qualities could include flexibility, independence, and creativity:

– The flexibility of the mind is manifested in the following main areas: The ability to change the direction of problem solving in accordance with the change of conditions, know how to find new methods to research and solve problems, easily switch from this type of intellectual activity to another one, overcome stereotypes attitude, machinery, and thinking along the trail. The ability to establish the dependence between knowledge in the opposite order known way (the reversibility of the thinking process). The ability to see a problem, a phenomenon under many different perspectives.

– The independence of the intelligence manifests itself in the ability to detect problems by itself and to find answers to them by themselves, not based on available solutions, not on the ideas and arguments of others. The flexibility and independence of thinking are the basis for creating critical thinking skills and creative thinking skills. Through the characteristics mentioned above, it could be concluded that the characteristics of “not stereotyping” and “not relying” on are the manifestations of creative thinking skills and the evaluation of other people’s thoughts and assessing ideas.

– Purpose of teaching mathematics in secondary schools. The teaching of mathematics must be done step by step for students: Understand the essence of a concept (distinguish between intrinsic and non-essential signs of the concept). Apply the concepts into specific problems, solving problems into practice (Hoang Chung, 1995, p.116).

The above work is very important in teaching mathematics because the formation of concepts is the basis of all students’ mathematical knowledge, which is the foundation of the ability to effectively use the knowledge and contributes to the development of intellectual capacity and materialistic worldview for learners (Leif, et al, 1970, p.180).

**2.2. Research methods.**

**2.2.1. Methods.**

The methods used in this study are literature review, testing, and statistical methods.

**2.2.2. Sampling.**

– 1,074 students in grades 8 and 9 at junior high schools in Ho Chi Minh City for the Otis test to investigate students’ intellectual capacity.

– 480 students in grade 8 at junior high schools in Ho Chi Minh City for the general test set of ability and basic skills at level 21/22 in form A to investigate students’ mathematical learning ability.

– 480 students in grade 8 at junior high schools in Ho Chi Minh City to investigate the correlation between students’ intellectual capacity and mathematical learning ability.

**2.2.3. Tools.**

– Otis quick-scoring ability test for the Beta was designed for grades 4 through 9. This test consists of 80 items to measure intellectual capacity (Otis, 1954). The use of the Otis scale in Ho Chi Minh City was carried out according to the following stages: Revision and standardization of the Otis scale in the 1995-1996 school year. The Otis scale was put into practice in the 1998-1999 school year. Otis testincludes the following factors:

+ Find antonyms (items 1, 10, 35, 38, 60);

+ Order the words in the alphabet A B C (items 2, 11, 20, 58);

+ Make the sentences according to the given words (items 28, 41, 43, 65, 80);

+ Find similarities by category (items 3, 17, 23, 29, 36, 72);

+ Find similarities in meaning (items 4, 6, 7, 9, 12, 14,15, 18, 22, 24,2 6, 42,47, 49, 57, 67, 79);

+ Arrange objects in a category (items 32, 33, 46, 51, 58, 68);

+ Find similarities in the picture (items 8, 16, 30, 50, 63);

+ Definition of words (items 13, 19, 27, 31, 39, 44,45, 53, 55, 59, 70);

+ Use words (items 21, 64, 66, 69, 74);

+ Calculating ability (items 25, 37, 50, 61, 75, 76);

+ Find the rules of a sequence of numbers (items 34, 52, 54, 56, 73, 77);

+ Understand the meaning of sentences (items 48, 62, 71, 78);

– The system of items to measure the ability to learn mathematics includes 80 items compiled from the general test set of ability and basic skills at level 21/22 in form A (Comprehensive Tests of Basic skills, 1989, pp.33-43). This exercise system was developed based on the theories of learning mathematics. Test of mathematical learning ability consisting of 80 multiple choice questions includes the following factors:

+ Ability to understand mathematical concepts (items 1-35).

+ Abstraction ability (items 36-45).

+ The ability to calculate arithmetic (items 46-80).

When collecting data, each student was asked to perform the two above tests in parallel. The correlation between the intellectual capacity and mathematical learning ability was measured.

To find the correlation between intellectual capacity and the ability to learn math, the study conducted simultaneous data collection for two tests. That means a student took 2 tests: the intellectual ability test and the general test set of ability and basic skills at level 21/22 in form A.

The scoring method for the multiple-choice tests and the above system of exercises was one (1) point for the correct answer and zero (0) points for the incorrect answer.

**3. Research findings and discussion.**

There are four parts in this section.

**3.1. The status of the intellectual capacity and ability to learn the mathematics of graders 8 and 9.**

Table 1. Results of the variances of the Otis test, and the general test set of ability and basic skills at level 21/22 in form A:

Scale: Otis test

N: 1074

M: 44.1099

SD: 10.25759

Reliability: .864

Scale: General test set of ability and basic skills at level 21/22 in form A.

N: 480

M: 45.98

SD: 10.483

Reliability:.872

Table 1 shows that the average score of Otis test is suitable with the intellectual capacity level of students in grades 8 and 9 in Ho Chi Minh City and is equivalent to one of the US students [with Otis test score of 45, IQ = 99 is equivalent to a student nearly 14 years old]. The average score of the General test set of ability and basic skills at level 21/22 in form A is suitable with the ability to learn the mathematics for graders 8 in Ho Chi Minh City.

**3.2. The status of the intellectual capacity of graders 8 and 9 with the Otis test.**

The following are the results evaluated through the Otis test.

The students achieved high level with the items: Find antonyms (1); Find similarities in the meaning (2); Find similarities by category (3); Making sentences according to the given words (4); and Definition of a word (5). However, the students achieved lower level with the items that require a higher level of thinking, which is more difficult for students: Use a word (6); Find similarities in the figure (7); Find the rule of a sequence of numbers (8); Sort objects by a category (9); Ability to calculate (10); Understand the meaning of sentences (11); and Arrange words according to the letters A B C (12).

Through the analysis above, it was found that students’ thinking development was related to the language development shown through some factors of the Otis test. In other words, the level of language development and thinking of graders 8 and 9 in Ho Chi Minh City was commensurate with age and grade.

Table 2 shows that there are statistical differences in grade 9 and grade 8 with 10 factors: Find antonyms; Arrange words according to the letters A B C; Making sentences according to the given words; Find similarities in the meaning; Find similarities in the figure; Definition of a word; Use a word; Ability to calculate; Find the rule of a sequence of numbers; and Understand the meaning of sentences. Grade 9 has higher average scores than grade 8.

There are not statistical differences in grade 9 and grade 8 with two factors: Find similarities by category, and Find similarities in the figure. In the other words, the intellectual development of grade 9 was almost higher than the that of grade 8. The validity of the Otis test is good.

Therefore, it could be said that learning activities contribute to students’ intellectual development. If the students wanted their intellectual capacity to be developed, they must participate in related cognitive development activities.

Table 4 shows that there are statistical differences regarding gender with six factors: Find antonyms; Arrange words according to the letters A B C; Find similarities in the meaning; Making sentences according to the given words; Definition of a word; and Understand the meaning of sentences. The female students had higher average scores than the male students.

Gender does not affect six factors: Find similarities by category; Sort objects by a category; Find similarities in the figure; Use a word; Ability to calculate; and Find the rule of a sequence of numbers.

**3.3. Grades 8 students’ ability to learn mathematics.**

The following are the results of 8th graders’ ability to learn mathematics.

Table 5 shows that the students achieve scores according to ranking with the items as following: Ability to understand mathematical concepts (1); Abstraction ability (2); [higher than average]; and the ability to calculate arithmetic (3) [lower than average].

The students had Ability to understand mathematical concepts and Abstraction ability better than Ability to calculate arithmetic. In the other words, they needed to improve their practice ability.

Table 6 shows that there are no statistical differences in average scores between male and female students in Ability to understand mathematical concepts; Abstraction ability; and Ability to calculate arithmetic. It could be said that male and female students had the equivalent ability to learn mathematics.

**3.4. Correlation between the intellectual capacity and the mathematics ability learning.**

For calculating a correlation between the intellectual capacity and the mathematics ability learning, the research sampling had to be equal in size. The investigation of the ability to learn mathematics was conducted on 480 8th graders. The author had to choose the same student number from the Otis test on the intellectual capacity.

The following are the results of the correlation between the intellectual capacity and the ability to learn mathematics in grades 8.

Table 6 shows that there is a statistical difference in correlation between intellectual capacity and the ability to learn mathematics. It could be said intellectual capacity contributes to the ability to learn mathematics.

Table 8 shows that there is a statistical difference in correlation between intellectual capacity and abstraction ability (one factor in ability to learn mathematics). It could be said the ability to learn mathematics requires more abstraction.

Table 9 shows there are statistical differences in correlation between the ability to learn mathematics and each factor in intellectual capacity. It can be said all the factors of intellectual capacity contribute to the ability to learn mathematics.

**4. Conclusion.**

Using the intellectual tests revised and standardized in the educational institutions to discover students with many levels of mental development; so that educators could “enhance the intellectual level, train human resources, and foster talents”.

Based on the psychological research findings, the educational institutions develop students’ intellectual qualities including flexibility, independence, and creativity in subject matters taught in junior high schools:

The flexibility of the mind was manifested in the following main areas:

– The ability to change the direction of problem solving in accordance with the change of conditions, know how to find new methods to research and solve problems, easily switch from this type of intellectual activity to another one, overcome stereotypes attitude, machinery, and thinking along the trail.

– The ability to establish the dependence between knowledge in the opposite order known way (the reversibility of the thinking process).

– The ability to see a problem, a phenomenon under many different perspectives.

The independence of the intelligence manifested itself in the ability to detect problems by itself and to find answers to them by themselves, not based on available solutions, not on the ideas and arguments of others. The flexibility and independence of thinking are the basis for creating critical thinking skills and creative thinking skills.

Through the characteristics mentioned above, it could be seen that the characteristics of “not stereotyping” and “not relying” on are the manifestations of creative thinking skills, and the evaluation of other people’s thoughts, and assessing ideas.

In short, we can develop the higher-order thinking skills for students – the current tendencies in education around the world. The Otis test is used to measure intellectual capacity giving the appropriate reliability index – grade 9 has an average score higher than that of grade 8.

The General test set of ability and basic skills at level 21/22 in form A is used to measure mathematical learning ability that shows the students have theoretical ability scores higher than the practical ones. The correlation between intellectual capacity and ability of mathematical learning of grade 8 is significant in general and for certain factors.

**References**

[1] Clinchy, B., Lief, J., & Young, P. (1977). Epistemological and moral development in girls from a traditional and a progressive high school. Journal of Educational Psychology, 69(4), 337-343.

[2] Educational Testing Service (1989). Comprehensive Tests of Basic skills (Form A levels 21/22. Fourth Edition). California: McGraw-Hill, Inc.

[3] Hoang, C. (1995). Phuong phap giang day Toan o truong trung hoc co so [Methods of Teaching Mathematics in Junior High Schools]. Hanoi: Education Publishing House.

[4] Kharlamop, I. F. (1978). Phat huy tinh tich cuc hoc tap cua hoc sinh nhu the nao? [How to develop students’ active learning?]. (Do Thi Trang and Nguyen Ngoc Quang, translation from Russia). Education Publishing House.

[5] Nguyen, M. P. (1996). Ve viec xac dinh noi dung mon hoc doi voi dinh huong cua hoc sinh cua phat trien nang luc [On the Identification of Subject Matter toward Students’ Orientation of the Capacity Development]. Journal of Education Research, (56), p.21.

[6] Otis, A. S. (1992). Manual of Directions for Beta Test (Form CM & DM and New Edition: Forms EM and FM). New York: Harcourt, Brace world, 1939-1954.

[7] Tran, B. H. (1995). Danh gia trong giao duc [Evaluation in Education]. Hanoi Publisher.

* **Conflict of Interest**: Author have no conflict of interest to declare.

* **Cite this article as**: Doan Van Dieu (2021). Correlation between intellectual capacity and ability of Mathematical learning of grades 8 and 9 in junior schools in Ho Chi Minh City. Ho Chi Minh City University of Education Journal of Science, 18(11), 1974-1986.

**Doan Van Dieu**

Ho Chi Minh City University of Education, Vietnam

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