An analysis of proportional reasoning ability of junior high school students

Abstract

This study aims to describe proportional reasoning skills and students’ difficul­ties in solving proportional reasoning problems. The population of this research was 3480 seventh-grade students of state junior high schools in the Yogyakarta region. The samples were 158 students chosen using proportionate stratified random sampling that represent four categories of school (very high, high, me­dium, low) based on the average scores of the national examination in mathe­matics in 2016. Data were collected through essay tests and interviews. Data were analyzed quantitatively and qualitatively. The result showed that the stu­dents in very high and high category schools had moderate proportional rea­soning ability. Students in medium and low category schools had low propor­tional reasoning ability. Students’ difficulties in solving proportional reasoning problems vary based on the type of the problem, such as the difficulty in finding the multiplicative relationship contained in the problem, the difficulty in under­standing the value of inverse proportion, and the difficulty in explaining the obtained solution of the problems.

Junior High School Students' Proportional Reasoning Ability in the Domain Comparison: A Gap in Results Between Indicators

“…The two proportions stated in the two figures above are formed from direct proportion relationships, so they are not in accordance with the context of the problem given which should use indirect proportion relationships. The finding of research (Mardika & Mahmudi, 2021) also showed the same thing that students are more proficient in solving direct proportion problems than indirect proportion. The unique in this study is that there are no students who can state the indirect proportion relationship given in the problem.…”

“…In mathematics learning, students often have difficulties in solving proportional reasoning problems. The difficulties faced by students are in finding multiplicative relationships, understanding inverse value comparisons, and explaining the results obtained (Mardika & Mahmudi, 2021), distinguishing proportional from nonproportional situations (Tjoe & Torre, 2014). Frequent errors in solving proportional reasoning problems are caused by confusion in identifying unit values and algorithmbased errors in the computational process (Soyak & Isiksal, 2017).…”

“…Similar research conducted by Prayitno et al (2018) only used proportional reasoning questions of missing value problem type on direct proportion, the results showed that the proportional reasoning ability of VIII grade students has not reached the optimal stage. Further research conducted by Mardika & Mahmudi (2021) used three proportional reasoning problems, namely 1) missing value problem on direct proportion; 2) missing value problem on indirect proportion; and 3) comparison problem. In addition, Zulkarnaen (2017) also conducted a study aimed to analyze the proportional reasoning ability of grade X students using three problems, namely 1) missing value problem; 2) numerical comparison; and 3) qualitative prediction; by classifying students based on high, medium, and low school categories.…”

Student Proportional Reasoning on Missing Value Problems Based on Multiplicative Concepts

“…Students are able to connect problems with their own experience since the problem context is familiar to them. The problem solving strategies chosen by students are always based on the experiences and routine habits of students in solving simple problems rather than solving complex problems (Chai & Kong, 2017;Mardika & Mahmudi, 2021).…”

Penalaran Proporsional Siswa dalam Strategi Worked Example

“…Berapa harga 2 buku Ani?" [15]. Dalam menyelesaikan soal tersebut, siswa hanya menjumlahkan dan mengurangi angka, tanpa menggunakan proporsi.…”