Representations and Proportional Reasoning in a Problem Solving Context. (c2015)

2015 ◽  
Author(s):  
Rana Aboul Hosn
Keyword(s):  
Problem Solving ◽  
Proportional Reasoning

STUDENTS’ PROPORTIONAL REASONING IN MATHEMATICS THROUGH COVID-19 PANDEMIC CONTEXT

2021 ◽  
Vol 10 (3) ◽  
pp. 1670
Author(s):  
Rohati Rohati ◽  
Turmudi Turmudi ◽  
Kusnandi Kusnandi
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Junior High School ◽  
Real World ◽  
Proportional Reasoning ◽  
Learning Activities ◽  
School Students ◽  
Reasoning Skills ◽  
Almost All

Abstract The aim of this study was to ascertain high school students' proportional reasoning in the sense of the COVID-19 pandemic. How do students' thoughts flow when confronted with problems requiring proportional reasoning? This research is a mixed study by collecting data through problem-solving questions to 253 junior high school students in Muaro Jambi, Jambi Province, Indonesia. The problem-solving activities are based on real-world scenarios and require reasoning that is proportional and pertinent to the COVID-19 pandemic context. Due to the ongoing COVID-19 pandemic, the test is administered through the Whatsapp framework. Students' responses are examined in detail to ascertain their proportional reasoning skills. The results indicate that almost all students correctly answered the first question. However, only a small percentage of students were able to answer to and make the correct argument for the second question. The findings indicated that students demonstrated a reasonable level of proportional reasoning when confronted with the COVID-19 pandemic situation. According to the findings of this report, it is important for teachers of mathematics to establish learning activities and problem-solving tasks that help students improve their proportional reasoning skills. Keywords: COVID-19; Problem Solving; Proportional Reasoning; Real-World Situations AbstrakTujuan dari penelitian ini adalah untuk menggali penalaran proporsional siswa SMA  dengan konteks pandemi COVID-19. Bagaimana alur pemikiran siswa ketika dihadapkan pada masalah yang membutuhkan penalaran proporsional? Penelitian ini merupakan penelitian campuran dengan pengumpulan data melalui pertanyaan pemecahan masalah kepada 253 siswa SMP di Muaro Jambi, Provinsi Jambi, Indonesia. Kegiatan pemecahan masalah didasarkan pada skenario dunia nyata dan membutuhkan penalaran yang proporsional dan relevan dengan konteks pandemi COVID-19. Karena pandemi COVID-19 yang sedang berlangsung, tes dikirim melalui aplikasi Whatsapp. Tanggapan siswa diperiksa secara rinci untuk memastikan kemampuan penalaran proporsional mereka. Hasilnya menunjukkan bahwa hampir semua siswa menjawab pertanyaan pertama dengan benar. Namun, hanya sebagian kecil siswa yang mampu menjawab dan membuat argumen yang benar untuk pertanyaan kedua. Hasil penelitian menunjukkan bahwa siswa memiliki alur penalaran proporsional yang cukup baik dengan menggunakan konteks kondisi pandemi COVID-19. Menurut temuan  ini, penting bagi guru matematika untuk menetapkan kegiatan pembelajaran dan tugas pemecahan masalah yang membantu siswa meningkatkan keterampilan penalaran proporsional mereka. Kata kunci: COVID-19; Pemecahan Masalah; Penalaran Proporsional; Situasi Dunia

International Perspectives: The Triple Jump: A Potential Area for Problem Solving and Investigation

1998 ◽  
Vol 4 (2) ◽  
pp. 104-108
Author(s):  
Doug Clarke
Keyword(s):  
Problem Solving ◽  
Proportional Reasoning ◽  
International Perspectives ◽  
Key Concepts ◽  
Potential Area

Many teachers comment that interesting appucations of ratio are hard to find. Teachers also find that many students have difficulty with proportional reasoning in general, and ratio in particular. In this article, I talk through a process that led to the discovery of the role of ratios and percentages in discussions about triple jump performances, and to a range of tasks that provide important information about students' understanding of key concepts in mathematics.

A Comparison of the Proportional Reasoning Abilities of Learning Disabled and Non-Learning Disabled Children and Adolescents

1983 ◽  
Vol 6 (3) ◽  
pp. 313-320
Author(s):  
Rose Sinicrope ◽  
Lori Bell Mick
Keyword(s):  
Problem Solving ◽  
School District ◽  
Children And Adolescents ◽  
Proportional Reasoning ◽  
Learning Disabled ◽  
Disabled Children ◽  
Symbolic Form ◽  
Disabled Students ◽  
Reasoning Abilities

Noelting's (1980a, 1980b) three parallel instruments on proportional reasoning—two presenting problem-solving tasks in the ratio and division interpretations of fractions and one presenting the tasks in the purely symbolic form of numerical fractions—were administered to 6 female and 41 male learning disabled students, grades four through eight. Performances on the instruments were then compared to the performances of 120 non-learning disabled students in grades five through nine of the same school district. The purpose of the study was to determine whether learning disabled students differed in their development of proportional reasoning and whether their disability was in the use of symbols and language and not in their ability to solve proportional problems. Developmental scalograms, PPR>0.93, resulted in support of the hypothesis that the proportional reasoning abilities of the learning disabled student are developmental and thus not unlike those of the non-learning disabled student. A comparison of the three means for the two groups revealed a reversal in performance with the learning disabled students more successful at problem solving and the non-learning disabled students more successful at the purely symbolic form of numerical fractions. Unlike the non-learning disabled students, the learning disabled students' inability to express a strategy did not indicate an inability to solve the problem.

Ratio and Proportion: Connecting Content and Children's Thinking

1993 ◽  
Vol 24 (1) ◽  
pp. 41-61 ◽  
Author(s):  
Susan J. Lamon
Keyword(s):  
Problem Solving ◽  
Proportional Reasoning ◽  
Sixth Grade ◽  
Student Thinking ◽  
Semantic Type ◽  
Clinical Interviews ◽  
Ratio And Proportion ◽  
Problem Situations ◽  
Semantic Types ◽  
Children’S Thinking

Twenty-four sixth-grade children participated in clinical interviews on ratio and proportion before they had received any instruction in the domain. A framework involving problems of four semantic types was used to develop the interview questions, and student thinking was analyzed within the semantic types in terms of mathematical components critical to proportional reasoning. Two components, relative thinking and unitizing, were consistently related to higher levels of sophistication in a student's overall problem-solving ability within a semantic type. Part-part-whole problems failed to elicit any proportional reasoning because they could be solved using less sophisticated methods. Stretcher/shrinker problems were the most difficult because students failed to recognize the multiplicative nature of the problem situations. Student thinking was most sophisticated in the case of associated sets when problems were presented in a concrete pictorial mode.

Investigating a Tier 1 Intervention Focused on Proportional Reasoning: A Follow-Up Study

2017 ◽  
Vol 83 (4) ◽  
pp. 340-358 ◽  
Author(s):  
Asha K. Jitendra ◽  
Michael R. Harwell ◽  
Stacy R. Karl ◽  
Gregory R. Simonson ◽  
Susan C. Slater
Keyword(s):  
Problem Solving ◽  
Treatment Group ◽  
Mathematical Problem ◽  
Proportional Reasoning ◽  
Controlled Study ◽  
Tier 1 ◽  
Mathematics Difficulties ◽  
Based Instruction ◽  
Business As Usual

This randomized controlled study investigated the efficacy of a Tier 1 intervention—schema-based instruction—designed to help students with and without mathematics difficulties (MD) develop proportional reasoning. Twenty seventh-grade teachers/classrooms were randomly assigned to a treatment condition (schema-based instruction) or control condition (business as usual). Participants included 373 students, of whom 253 demonstrated MD. A measure of proportional problem solving (PPS) was administered at pre- and posttesting and at 11 weeks following treatment, along with a general mathematical problem-solving measure at pre- and posttesting. For the full sample, posttest differences favoring the treatment group were statistically significant for all measures. For students with MD, posttest differences favored the treatment group for the PPS posttest and PPS delayed posttest but not for general problem-solving posttest.

Proportional Reasoning: Lessons from Research in Data and Chance

2004 ◽  
Vol 10 (2) ◽  
pp. 104-109
Author(s):  
Jane Watson ◽  
J. Shaughnessy
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Mathematics Curriculum ◽  
Proportional Reasoning ◽  
School Mathematics ◽  
School Level ◽  
Principles And Standards ◽  
Middle School Level

PRINCIPLES AND STANDARDS FOR SCHOOL Mathematics (NCTM 2000) places proportionality among the major concepts connecting different topics in the mathematics curriculum at the middle school level (p. 217). What concerns us about many of the problems presented to students, however, is that they are often posed purely as a ratio or proportion from the start. Often the statement of a problem is a giveaway that a proportion is involved. For example, the question “If 15 students out of 20 get a problem correct, how many students in a class of 28 would we expect to get the problem correct?” does not tap the depth of proportional reasoning that is required for meaningful problem solving.

scholarly journals Investigation of Proportional Reasoning Problem Solving Processes of Seventh Grade Students: A Mixed Method Research

2021 ◽  
Vol 3 (1) ◽  
pp. 48-67
Author(s):  
Mesut Öztürk ◽  
Ümit Demir ◽  
Yaşar Akkan
Keyword(s):  
Problem Solving ◽  
Mixed Method ◽  
Quantitative Data ◽  
Qualitative Data ◽  
Proportional Reasoning ◽  
Mixed Method Research ◽  
Seventh Grade ◽  
Qualitative Comparison ◽  
Skill Test ◽  
Reasoning Problem

This study was carried out to examine proportional reasoning problem solving processes of seventh grade students. This study was conducted with the explanatory sequential mixed method design. In this respect, firstly, quantitative data from 56 students were collected and analyzed. Then, qualitative data of the study was collected from six students selected according to their success and analyzed. The quantitative data of the study was consisted of a proportional reasoning skill test and analyzed using predictive statistics. The qualitative data of the study were collected through activity cards and the think-aloud protocol, and content analysis was applied to the collected qualitative data. The findings of the study showed that students were most successful at qualitative comparison. On the other hand, the least success was observed for quantitative comparison, and female students were found to be more successful in proportional reasoning problems.

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