Analysis of Students Mathematical Reasoning Abilities on Number Topics

Mathematical reasoning skills are critical for students to solve math problems. The research objective was to determine the reasoning ability of junior high school students in solving number problems. This research is a qualitative descriptive study with case studies. The research subjects were 27 students consisting of 14 female students and 13 male students. A total of 10 questions were tested containing five multiple-choice questions, and five description questions. From the results of data analysis, 3% of students had high reasoning abilities, 43% of students had moderate reasoning abilities, 30% of students had low reasoning abilities, 13% of students had meagre reasoning abilities.


PENDAHULUAN
The field of mathematics is often used as material for competency testing to continue education at a certain level. Mathematics is also used as a benchmark for selecting employees in a company (Krzemien et al., 2017). In education, mathematics has been included in the curriculum at all levels of education from kindergarten to college (Stout, 2019). In addition, the intensity of the lesson hours for mathematics is also more than for other subjects. This means that mathematics is essential for the life of all ages.
The existence of mathematics is caused by the human mind related to ideas or reason which is divided into four fields, namely algebra, arithmetic, analysis and geometry. (Ayan & Isiksal-Bostan, 2019). Thus, actually from an early age, someone has been trained to reason by studying mathematics. The main characteristic of mathematics is the method of reasoning (Jonsson et al., 2016). This peculiarity is what makes reasoning an inseparable part of mathematics.
However, the students' ability in reasoning type questions is still very minimal. The achievement of students in Indonesia in the 2011 TIMSS (Trends in International Mathematics and Science Study) at the junior high school level in the cognitive dimension, namely knowing (knowledge) is 37%, applying is 23% and reasoning is 17% (Saal et al., 2019). The three cognitive dimensions can be seen that reasoning is the lowest. The reasoning is a logical thinking process in concluding the form of knowledge. The result of this reasoning process will give us the knowledge to solve problems. The criteria for the truth of each individual are, of course, different, this is because accurate perceptions differ according to their knowledge. The data shows that students who think mathematically are reasonable (74%). Students in Indonesia tend to have good mathematical reasoning skills. Students with high mathematical abilities can estimate the problem-solving process and analyze mathematical situations appropriately, can formulate valid arguments, and be able to draw logical conclusions (Nurhayati, 2013). Meanwhile, students with mathematical abilities are estimating the completion process correctly but not in detail. Students with low math abilities are less able to analyze mathematical situations and compile valid arguments with less systematic settlement steps and are unable to draw logical conclusions.
This study used TIMSS model questions to measure students' mathematical reasoning abilities. The material to be discussed in this study numbers consisting of whole numbers and fractions. These questions have different dimensions of cognitive assessment, one of which is reasoning. In the cognitive domain of reasoning, multiple-choice questions and descriptions include the ability to analyze, generalize, integrate, justify, and solve non-routine problems. (Mullis et al., 2016). In addition, the TIMSS model questions not only use formulas but also require students to use their reasoning skills in the process of solving them.
The research objective was to determine the reasoning ability of junior high school students in solving number problems. The reasoning is one of the crucial aspects needed in mathematics, and the topic discussed was the numbers to be measured using questions from TIMSS.

Method
This research is a qualitative descriptive study with a case study which aims to describe students' mathematical reasoning abilities in solving number problems. A total of 27 students from junior high schools were involved to fill out the research instruments. The instrument used in the study was a test of reasoning and observation abilities. The results of the study were analyzed using indicators that were concluded from the TIMSS 2015 mathematics Framework, which is used to determine the reasoning ability of the subjects in table 3.

Finding and Discussion
Based on the results of observations of researchers when the instrument was tested, the class conditions were quite conducive. Some students seemed confused by the questions given, occasionally someone whispered to their friends to ask the meaning of the questions, or someone asked the answers. Students feel the problem is different from what was taught. In contrast, the results of the distribution of the reasoning ability to answer student questions in each indicator measured through the students' correct answers can be seen in table 5. Based on Table 5, most students can answer correctly on indicators to determine, describe or use relationships between numbers with a percentage of 89%. Meanwhile, students' reasoning abilities on indicators connecting various elements of knowledge, related to representation, and procedures for solving problems were still not good with a percentage of 30%. In addition, the achievement of students' mathematical reasoning abilities, according to the categories, is presented in Table  6. Based on these categories, most students have mathematical reasoning abilities in the moderate category, namely as much as 43%. The analysis of students' reasoning abilities in each category is with indicators of determining, describing or using relationships between numbers.

Answers to subjects with high reasoning abilities
Analysis of the subject's answer shows that the subject correctly determines, describes or uses the relationship between numbers. From the results of students' answers to item no. 4 high-ability students are seen to understand the pattern formed from each sequence of similarities with the subtraction operation for number 3.By looking at the first line, three minus 3, then in the second line, three minus 2, up to the fourth line, number 3 minus 0. This means that between the first line and the next line, the number that is subtracted from the number 3 is getting smaller by the difference of 1. Based on this understanding, the students succeeded in determining that in the fifth row, the number 3 was subtracted from the number (-1). Likewise, the result of the reduction is 4. From the results of students' answers to item no. 4, there was an error writing the sign. Students intending to write "5-1 = 4" in the answer. Students only managed to see the pattern that was on the right side of each similarity. The pattern of the right side forms a sequence of 0, 1, 2, 3 so that the student manages to determine that the next number is 4. However, the student fails to see the pattern that is on the left side of the similarity.

Answers to subjects with moderate reasoning abilities
Based on the answer on the right side, with his intuition, he wrote the subtraction for the left side which he thought was easy, namely "5-1".

Answers to subjects with low reasoning abilities
From the results of students' answers to item no. 4, students with low abilities appear to be able to see the pattern formed from the right side of each line of similarity but fail to see the pattern formed on the left side. Furthermore, it appears that students have not mastered the subtraction operation of integers. This is shown by writing 3-7 according to which the result is 4.

Figure 3. Answers to low proficiency subjects
Based on the test results, students' reasoning abilities are high, medium and low. Highly skilled students can analyze mathematical situations using patterns and relationships appropriately, and systematic work steps, can formulate valid arguments and be able to draw logical conclusions (Kan et al., 2019). Students with moderate abilities can analyze mathematical situations using patterns and relationships appropriately, and unsystematic steps, so they are less able to formulate valid arguments and are less able to draw logical conclusions (Alexander et al., 2016). Low-ability students can analyze mathematical situations using patterns and relationships appropriately, but the steps are less systematic, so they are less able to formulate valid arguments, and are less able to draw logical conclusions (Gürbüz & Erdem, 2016).
Herutomo (2014) states that errors are caused by students representing and interpreting the information presented in questions in the form of story questions. An error is caused by ignorance of the concept of the subject because to understand the meaning of the questions that have been presented, and the subject must master the material and know the concepts related to the problem (Fyfe & Brown, 2018). In addition, Savitri (2014), concluded that most students only understand the concept. So that when faced with a new problem, they experience the confusion that leads to mistakes. The causes of errors in students with the Field Dependence (FD) cognitive style group are more dominated by incomplete student reasoning and students' inadequate ability to understand and remember the material they have received (Krzemien et al., 2017).
The errors experienced by students in solving story problems in the aspect of understanding the problem are errors in interpreting language and mathematical models (Kan et al., 2019). The causes of errors in the aspect of understanding language are students' low mathematical abilities and incomplete/wrong student reasoning.

Conclusion
Students who are highly capable of reasoning can analyze mathematical situations using patterns and relationships appropriately, and systematic work steps, can formulate valid arguments and be able to draw logical conclusions. Low ability students are less able to formulate valid arguments and less able to draw logical conclusions. Students' reasoning abilities can be improved by changing learning methods, such as providing www.psychologyandeducation.net particular practice questions that require reasoning so that students are accustomed and able to reason well.