A diagnostic assessment to middle school students’ proportional reasoning

Abstract

This study investigated Turkish middle school students' proportional reasoning and provided a diagnostic assessment of their strengths and weaknesses on the ratio and proportion concepts. A proportional reasoning test with 22 multiple-choice items was developed from the context of the loglinear cognitive diagnosis model. The test was developed around four core cognitive skills (attributes) that required in solving middle school ratio and proportion problems. These skills included understanding ratios, directly, inversely, and nonproportional relationships. The test was applied to 282 seventh grade students, and the collected data were analyzed using the Mplus software. The analysis showed that approximately 62% of the students were able to recognize directly proportional relationships. Whereas, roughly 48% of them were able to recognize inversely proportional relationships. Moreover, while 25% of the students did not master any of the four cognitive skills, 39.1% mastered all four of these skills. In addition, many students had difficulty distinguishing proportional relationships from nonproportional relationships. Diagnostic feedbacks on the students' strengths and weaknesses were provided based on the findings.

The Effect of Error Analysis-Based Learning on Proportional Reasoning Ability of Seventh-Grade Students

“…Reys et al (2009) regarded proportional reasoning as understanding proportional relationships and working with these relationships. Arican (2019b) and Lundberg (2022) considered the development of proportional reasoning as one of the most challenging aspects facing the individual in the ability on mathematical reasoning, as it requires the learner to be able to deal with multiple concepts and skills related to rational numbers, comparison, simplification, and operations on them, especially multiplication and division. These concepts and skills are learned over a long period by placing the learner in various life situations that he models, to be used in proportional reasoning.…”

A diagnostic comparison of Spanish and Turkish middle school students’ proportional reasoning

“…The test was specifically designed in order to measure middle school students’ mastery of the following four attributes: A1: Understanding the concept of a ratio and determining the value of a quantity in a given ratio. A2: Understanding directly proportional relationships and solving problems involving this type of relationships. A3: Understanding inversely proportional relationships and solving problems involving this type of relationships. A4: Understanding nonproportional relationships and solving problems involving this type of relationships. The four attributes were determined by examining relevant research, Turkish curriculum, and international standards (Arıcan, 2019). These attributes reflect competence in proportional reasoning, and their development follows concepts central to proportional reasoning (see Section 2.1).…”

“…The proportional reasoning research conducted in Spain and Turkey (e.g., Arıcan, 2018; Arıcan, 2019; Atabaş & Öner, 2016; Valverde Soto & Castro Martínez, 2009) shows that both Turkish and Spanish middle school students have similar difficulties understanding ratio, proportion, and proportional relationship concepts. In fact, as we will later show, the treatment of ratio and proportion topics in middle school curricula is very much similar in both countries.…”

Development of a Learning Trajectory for Early Proportional Reasoning: A Design Research

“…Diğer bir yandan, çalışmanın bu anlamdaki bulgularının sonucu olarak yedinci sınıf öğrencilerinin içler dışlar çarpımı gibi ezbere dayalı algoritmalara ihtiyaç duymadan gerçekçi durumlara dayanan çeşitli orantısal akıl yürütme etkinlikleri ile ilgili akıl yürütebilecekleri öne sürülebilir. Bu bulgu, özellikle ulusal alanda yapılan birçok çalışmada elde edilen öğrencilerin stratejilerinin çoğunlukla içler dışlar çarpımı gibi işleme dayalı algoritmalara dayandığını belirten çalışmaların (Arıcan, 2019;Atabaş ve Öner, 2017;Duatepe vd., 2005;Kahraman, Kul ve İskenderoğlu, 2019;Kaplan, İşleyen ve Öztürk, 2011;Özgün-Koca ve Altay, 2009) sonuçları ile birlikte düşünülebilir.…”