The Influence of Numerical Ability and Abstract Thinking on Mathematical Problem Solving Pengaruh dan Berpikir

This research is ex post facto that aims to examine the influence of numerical ability and abstract thinking on mathematical problem-solving skills of eighth-grade students of SMP in Palopo. The population of this research is the student's class VIII students in Palopo, totalling 212 students, but the sample is 70 students have amounted to 10 students from each class. The selection of the samples used was a proportional random sampling technique. The research instrument used is the numerical ability test, abstract thinking test, and mathematics problem-solving test. The data was obtained by statistical analysis of descriptive and inferential statistics. The result of this research is an influence of numerical ability and abstract thinking on the mathematics problem-solving ability of eighth-grade students of SMP in Palopo. Numerical knowledge and abstract thinking have a contribution effect of 44.1% on students' mathematics problem-solving abilities. on eighth-grade students' junior high school in Palopo influences mathematical problem-solving ability with a contribution of 44%, and 3) Numerical ability and abstract thinking influence the mathematical problem-solving ability of eighth-grade students in a private junior high school in Palopo with an influence contribution of 43.4%.


Introduction
Problem-solving ability is one of the objectives of learning mathematics. Students learn mathematics to have good problem-solving skills to solve problems experienced in everyday life. Problem-solving ability in mathematics is the ability of students to solve mathematical problems by focusing on finding answers based on problem-solving steps. Mathematical problem-solving ability is the process of finding a solution to a given mathematical problem by involving previously learned knowledge. 1 The ability to solve problems varies from one student to another 2 . Several factors influence this difference. One of the factors that influence mathematical problem solving is numerical ability. Numerical ability has an essential role in students' learning and mathematical knowledge 3 , Developing numeric skills will help students to solve problems adequately 4 .
Numerical ability is defined as performing arithmetic operations quickly and precisely 5 . Completing calculation problems will be easier when students have good numerical skills. This ability helps students analyse mathematical problems logically and consistently and supports solving the problems given. The results of the research by Gunur, Makur, and Ramda. Furthermore, a large study concluded that there was a significant effect of numerical ability on students' problem-solving abilities 6 .
In addition to numerical ability, one factor affecting students' mathematical problem-solving skills is the ability to think abstractly. Mathematics is a science with an abstract object of study, so solving mathematical problems requires conceptual thinking skills 7 . Abstract thinking ability can be interpreted as a person's ability to think logically 8 by using symbols 9 . Students who have good abstract thinking skills will find it easier to describe mathematical situations/problems to be solved. It because the ability to think abstractly will require students to visualize, imagine, or represent a given problem 10 .
The results of Hasibuan, Mukhtar, and K's research concluded that students who have high abstract thinking skills have higher mathematics learning outcomes than students who have low conceptual thinking abilities 11 . Furthermore, Lyana, Sridana, and Kurniati concluded that there is a positive relationship between abstract thinking ability and students' mathematics learning achievement, so that if abstract thinking ability increases, learning achievement will also increase. 12 The results of an interview with the mathematics teachers showed; (1) Students who have good arithmetic operations skills tend to have good mathematical numerical abilities so that they are more able to solve the problems given, (2) Students with good abstraction skills tend to be easy to understand the mathematical material given so that they have good math skills.
Based on the description, this research examines the effect of numerical ability and abstract thinking on mathematics problem-solving for class VIII students in a private junior high school in Palopo. The difference between this research and previous research is that this study examines the numerical ability and problem-solving ability, abstract thinking and problem-solving skills, and numerical and abstract thinking skills of students together on students' problem-solving skills. Therefore, the results of this study are expected to be a reference for teachers in knowing students' mathematical problem-solving abilities through their numerical skills and abstract thinking.

Method
This research is ex-post facto research that aims to see the effect of numerical ability and abstract thinking on eighth-grade students' mathematical problem-solving in a private junior high school in Palopo. The population in the study was all students of class VIII Junior High School for the academic year 2020/2021, totaling 212 students divided into seven classes. The sample in this study amounted to 70 students. The selected sample consists of 10 students who represent each class. The sample selection technique used is the proportional random sampling technique. Data collection techniques using test techniques. The numerical ability test aims to measure students' numerical ability. The form of the numerical ability test used in this study is multiple choice. This test indicator (1) performs mathematical calculations, (2) thinks logically, (3) solves a problem, (4) recognizes patterns and relationships between numbers. Abstract thinking ability test aims to measure students' conceptual thinking ability. The form of abstract thinking test used in this research is an essay. The indicators of this test are (1) introduction, (2) Representation, (3) Structural Abstraction, (4) structural awareness. The mathematical problem-solving ability test aims to measure students' mathematical problem-solving abilities. The form of the mathematical problem-solving ability test used in this study is an essay. The test indicators (1) understand the problem, (2) draw up a settlement plan, (3) carry out the settlement plan, (4) check the results. The data collected will be analyzed using descriptive statistical analysis and inferential statistical analysis with the help of the IBM SPSS Statistics 20 application program. Inferential statistics used are simple linear regression to test the hypothesis. The first hypothesis is that numerical thinking ability influences math problem solving for class VIII students in a private junior high school in Palopo, and it was analyzed using a simple linear regression test. The second hypothesis is that abstract thinking ability affects mathematics problem solving for class VIII students in a private junior high school in Palopo, which is analyzed using simple linear regression and multiple linear regression. There are three research hypotheses, namely: a. Hypothesis 1; the effect of numerical thinking ability on mathematics problem solving for class VIII students in a private junior high school in Palopo, analyzed using a simple linear regression test. b. Hypothesis 2; the effect of abstract thinking ability on mathematics problem solving for class VIII students in a private junior high school in Palopo, analyzed using a simple linear regression test. c. Hypothesis 3; there is an effect of numerical ability and abstract thinking on math problem solving for class VIII students in a private junior high school in Palopo. It was analyzed using the multiple linear regression test Palopo and the multiple linear regression test with prerequisite tests, namely normality and linearity tests.

Students' Numerical Ability
An overview of the numerical abilities of grade VIII students in a private junior high school in Palopo can be seen in the following table. Source: Primary data analysis results (2021) The students' numerical ability data were further categorized into five groups. Based on this categorization, the distributive frequency and percentage of the numerical ability of class VIII students in a private junior high school in Palopo are obtained as follows. Based on Tables 1 and 2, it can be seen that the numerical ability of Class VIII students of SMP in Palopo is still relatively low. Students who have low skills are 37 students. The low numerical ability of students is due to the difficulty in solving questions related to logical thinking, solving problems and questions regarding pattern relationships between numbers due to the lack of students practicing answering questions. Learning is not optimal, which results in a lack of students understanding the material provided, which results in students' abstract abilities being low. Utami and Cahyono suggest that in the online learning process, students are not accustomed to carrying out online learning needs at home; students learn math material according to what they want. given by the teacher, not what they need, the goals or targets of students' online learning for mathematics lessons are still limited to obtaining satisfactory grades, not the abilities they should improve 12 .

Students' Abstract Thinking Ability
The description of the abstract thinking ability of class VIII students in a private junior high school in Palopo shows in the following table. Data on students' abstract thinking abilities were further categorized into five groups. Based on this categorization, the distributive frequency of abstract thinking of class VIII students in a private junior high school in Palopo is obtained as follows. Based on Tables 3 and 4, it can be seen that the students' abstract thinking ability is low. The low capacity of students' abstract thinking, because most students have difficulty in doing Representations, some have problems in doing Structural Abstraction and structural awareness. The COVID-19 pandemic has made learning mathematics done online and not optimally, resulting in students' abstract abilities being low. According to Dasa and Hudaidah, the lack of online mathematics learning during the pandemic is that students find it difficult to understand abstract mathematical material and require direct visualization. 13

Students' Mathematical Problem-Solving Ability
An overview of the mathematical problem solving abilities of class VIII students in a private junior high school in Palopo shows in the following table. Data on students' mathematical problem-solving abilities were further categorized into five groups. Based on this categorization, the distributive frequency of solving math problems for class VIII students in a private junior high school in Palopo is obtained below.  Tables 5 and 6, students' problem-solving abilities are classified as moderate, and this is because most students have difficulty in compiling a given problem-solving plan. This is in line with Buschman's opinion that the challenges experienced by students are because the strategies used are unusual and inefficient. 14

Results of Inferential Statistical Analysis
The purpose of inferential statistical analysis is to test the research hypotheses that have been formulated. Before testing the hypothesis, the prerequisite tests are carried out, namely the normality and linearity tests. The following are the results of the normality test of research data. Based on the results of the normality test with Kolmogorov-Smirnov the probability value for numerical ability data (X1) is 0.055 > 0.05, for abstract thinking ability data (X2) is 0.200 > 0.05, and for mathematical problemsolving data (Y) is 0.192 > 0.05 which means that numerical ability data, abstract thinking ability data and mathematical problem-solving data usually distributed.
The linearity test of the students' numerical and mathematical problemsolving abilities obtained a sig value. Deviation from linearity is 0.228 > 0.05, which means that it has a significant linear relationship between students' numerical ability (X1) and mathematical problem solving (Y). linearity test of abstract thinking and mathematical problem-solving ability of students obtained sig. Deviation from linearity is 0.062 > 0.05, which means that it has a significant linear relationship between abstract thinking (X2) and students' mathematical problem solving (Y).
Hypothesis 1 test was conducted to see the relationship between numerical ability and students' mathematical problem-solving ability. The statistical hypotheses are: H0: There is no effect of numerical ability on the mathematical problemsolving ability of class VIII students in a private junior high school in Palopo. H1: There is an effect of numerical ability on the mathematical problemsolving ability of eighth-grade students in a private junior high school in Palopo.
Based on the results of hypothesis 1 testing, a probability value of 0.001 <0.05, which means H0 rejected, and H1 is accepted, so it can be concluded that there is an influence of numerical ability on the mathematical problemsolving ability of eighth-grade students in a private junior high school in Palopo. The R square value of 0.136 was obtained, so it was interpreted that numerical ability had a 13.6% contribution effect on the mathematical problem-solving ability of class VIII students in a private junior high school in Palopo and 86.4% was influenced by other factors outside of numerical ability. Numerical skills are the basic skills that students need to solve problems in mathematics. The results of research by Gunur, Makur, and Ramda concluded that the better a person's numerical skills, the better his problem-solving ability. Furthermore, the research results of Ramadhan, Suaedi & Ilyas found that students who have high numerical skills tend to have high mathematical problem-solving abilities as well.
Hypothesis 2 test was conducted to see the relationship between abstract thinking and students' mathematical problem-solving abilities. H0: There is no effect of abstract thinking on the mathematical problemsolving ability of class VIII students in a private junior high school in Palopo. H1: There is an effect of abstract thinking on the mathematical problemsolving ability of class VIII students in a private junior high school in Palopo.
Based on the results of hypothesis 2 testing, a probability value of 0.000 <0.05 means that H0 is rejected and H1 is accepted so that it can be concluded that there is an effect of abstract thinking on the mathematical problemsolving ability of VIII students in a private junior high school in Palopo. It also obtained an R square value of 0.440 so that it interpreted that abstract thinking had a 44% contribution effect on the mathematical problem-solving ability of class VIII students in a private junior high school in Palopo, and 56% was influenced by other factors outside of abstract thinking. Wijayanti expressed similar results, abstract thinking is one of the competencies required for