Analysis of the Relationships between Mathematics Achievement, Reflective Thinking of Problem Solving and Metacognitive Awareness

Tujuan kajian eksperimental kuasi ini ialah untuk menentukan kesan pembelajaran koperatif ke atas kemahiran menyelesaikan masalah, kesedaran metakognitif, pencapaian Matematik, sikap terhadap Matematik dan sikap terhadap penyelesaian masalah pelajar–pelajar matrikulasi. Kumpulan rawatan (n = 36) adalah kumpulan koperatif, manakala kumpulan kawalan (n = 34) menerima pengajaran secara tradisional. Bagi mengawal perbezaan pemboleh ubah–pemboleh ubah yang bergerak balas, ujian pra diberikan kepada kedua–dua kumpulan sebelum pengajaran. Selepas 17 minggu pengajaran, kedua–dua kumpulan diberikan ujian pos. Lima jenis alat kajian digunakan bagi mendapatkan data: Ujian penyelesaian masalah Matematik, ujian pencapaian Matematik, soal–selidik kesedaran metakognitif, soal–selidik sikap terhadap Matematik dan soal–selidik sikap terhadap penyelesaian masalah. Bagi menentukan perbezaan antara kumpulan rawatan dan kawalan, data ujian pra dan ujian pos dianalisis dengan menggunakan analisis varian multivariat (MANOVA), diikuti dengan analisis varian univariat (ANOVA). Dapatan kajian daripada MANOVA menunjukkan terdapat perbezaan secara keseluruhan yang signifikan memihak kepada kumpulan koperatif dalam kemahiran menyelesaikan masalah, pencapaian Matematik, kesedaran metakognitif, sikap terhadap Matematik dan sikap terhadap penyelesaian masalah. Bagaimanapun, analisis ANOVA mendapati hanya pencapaian Matematik dan kemahiran menyelesaikan masalah mempunyai perbezaan signifikan antara kumpulan koperatif dan tradisional. Hasil kajian menunjukkan pelajar dalam kelas pembelajaran koperatif mengatasi pelajar dalam kelas tradisional dalam ujian pos pencapaian dan kemahiran menyelesaikan masalah. Saiz kesan adalah sederhana dan dengan itu, kesan rawatan adalah bermakna secara praktisnya. Kata kunci: Pembelajaran koperatif, kemahiran menyelesaikan masalah, kesedaran metakognitif, pencapaian Matematik, sikap terhadap Matematik dan sikap terhadap penyelesaian masalah The purpose of this quasi–experimental study was to determine the effects of cooperative learning on matriculation college students’ Mathematics achievement, attitude towards Mathematics, attitude towards problem solving, metacognitive awareness and problem solving skills. The treatment group (n = 36) was given a cooperative learning environment while the control group (n = 34) received instruction in a traditional learning environment. In order to control the differences in the dependent variables, a pre–test was administered. After 17 weeks of instruction, both groups were given a post–test. Five types of instruments were employed to collect the data: the problem solving test, the Mathematics achievement test, the metacognitive awareness instrument, the attitude towards Mathematics instrument and the attitude towards problem solving instrument. The pre-test and post–test data were analyzed using Multivariate Analysis of Variance (MANOVA), followed by univariate Analysis of Variance (ANOVA). The MANOVA results revealed the overall significant differences favouring the cooperative learning group in the areas of problem solving skills, Mathematics achievement, metacognitive awareness, attitude towards Mathematics and attitude towards problem solving. However, the ANOVA showed only Mathematics achievement and problem solving skills were found to be statistically significant. The results indicated that students in the cooperative learning class outperformed students in the traditional class on post test achievement and problem solving skills scores. The effect size was moderate and therefore practically meaningful. Key words: Cooperative learning, Mathematics achievement, attitude towards Mathematics, attitude towards problem solving, metacognitive awareness and problem solving skills.

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Learner metacognition and mathematics achievement during problem-solving in a mathematics classroom

The Journal for Transdisciplinary Research in Southern Africa ◽

10.4102/td.v9i3.194 ◽

2013 ◽

Vol 9 (3) ◽

Cited By ~ 2

Author(s):

Stephan Du Toit ◽

Gawie Du Toit

Keyword(s):

Problem Solving ◽

Mathematics Achievement ◽

Mathematics Classroom ◽

Metacognitive Awareness ◽

Quantitative Methodology ◽

Two Phase ◽

Phase Approach ◽

And Mathematics ◽

Problem Solving Process ◽

Metacognitive Awareness Inventory

In this investigation the level of learner metacognition as well as the level of mathematics achievement during problem-solving in a mathematics classroom was investigated. Learner metacognition plays a pivotal role during the problem-solving process and when the problem-solving is successful it can be viewed as evidence of high achievement in mathematics. Data were collected from one intact Grade 11 class of 25 girls. A word problem was given to the learners to solve individually. The learners recorded their thoughts relating to the problem as well as the calculations that corresponded to their thoughts. The level of achievement of the learners were analysed by noting calculation and conceptual errors in the solving of the problem. The learners’ level of metacognition was determined by analysing the written account of their thoughts and comparing it to the items on an adapted Metacognitive Awareness Inventory (MAI). Strong evidence was obtained from the recorded thoughts of learners that their metacognitive behaviours corresponded to the first three phases of Polya’s problem-solving model, but there was no evidence of metacognitive behaviours that corresponded with Polya’s fourth phase (Looking back) of problem-solving. It was further determined that the learners’ metacognitive awareness during the problem-solving session did not relate to the subscale Evaluation of the MAI. It was thus evident that the learners were not reflecting on the validity and correctness of their own solution. In this study a qualitative one- phase approach was used to examine the process of intervention, as well as a two-phase approach on the qualitative data which was also embedded in the quantitative methodology prior to and after the intervention phase (two-phase approach).

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PROFIL BERPIKIR REFLEKTIF SISWA SD DALAM PEMECAHAN MASALAH PECAHAN BERDASARKAN KEMAMPUAN MATEMATIKA

EDUKASI ◽

10.33387/j.edu.v14i2.194 ◽

2016 ◽

Vol 14 (2) ◽

Author(s):

Hery Suharna ◽

Agung Lukito Nusantara ◽

I Ketut Budayasa

Keyword(s):

Elementary School ◽

Problem Solving ◽

Elementary School Students ◽

Reflective Thinking ◽

Research Subjects ◽

Math Skills ◽

School Students ◽

Calculation Skills ◽

High Ability Students ◽

Selection Of

The research reveals a profile of reflective thinking of elementary school students in problem solving fractions based on his mathematical abilities. The instruments used in data collection is Test Problem Solving (TPM), interview. Selection of research subjects in a way given test is based on the ability of mathematics, namely mathematical skills of high, medium and low and further categorized and taken at least 2 people to serve as subjects. The research objective is: describe the profile of reflective thinking that math skills of elementary school students High, medium, and low. Based on the results of the study found reflective thinking profile and high ability students were as follows: (a) the step to understand the problems students have information/knowledge or data that is used to respond, comes from inside (internal) and can explain what has been done; (B) the planned step problem solving students have information/knowledge or data that is used to respond, comes from inside (internal) and can explain what has been done; (C) on measures to implement the plan in terms of information/knowledge or data used by students to respond, comes from inside (internal), could explain what has been done, realized the error and fix it, and communicate ideas with a symbol or image, and (d) the checking step back, namely information/knowledge or data that is used by students to respond, comes from inside (internal) and can explain what has been done. Profile of reflective thinking ability students lowly mathematics, namely: (a) at the stage of understanding the problem, students can determine known and asked in the problem, but the students' difficulties to explain the identification of the facts that have been done, the students explained the understanding vocabulary, and feel of existing data the matter is enough; (B) at the stage of implementing the plan, the students explained, organize and represent data on the issue, describes how to select the operation in solving a problem though students are not sure, and students' difficulty in explaining what he had done; (C) at the stage of implementing the plan, the student has information on calculation skills although the answer is not correct. Students difficulty in explaining about the skills calculations have been done, trying to communicate their ideas in the form of symbols or images, even if students rather difficult to describe, and realized there was an error when using a calculation skills and improve it; (D) at the stage of check, students' difficulties in explaining whether obtained estimates it approached, it makes senseKeywords: reflective thinking, problem solving, fractions, and math skills.

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Nature education: Outdoor learning of map literacy skills and reflective thinking skill towards problem-solving

Thinking Skills and Creativity ◽

10.1016/j.tsc.2021.100815 ◽

2021 ◽

Vol 40 ◽

pp. 100815

Author(s):

Elif Aladağ ◽

Alaattin Arıkan ◽

Hatice Özenoğlu

Keyword(s):

Problem Solving ◽

Reflective Thinking ◽

Literacy Skills ◽

Outdoor Learning ◽

Thinking Skill ◽

Nature Education

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How Indonesian Students Use the Polya’s General Problem Solving Steps

Southeast Asian Mathematics Education Journal ◽

10.46517/seamej.v8i1.62 ◽

2018 ◽

Vol 8 (1) ◽

pp. 39-48

Author(s):

Hari Pratikno ◽

Endah Retnowati

Keyword(s):

Problem Solving ◽

Mathematics Achievement ◽

Secondary School ◽

General Problem ◽

High Ability ◽

School Students ◽

Junior Secondary School ◽

Junior Secondary ◽

Mathematical Problems ◽

Low Ability

General problem-solving steps consist of understanding the problem, developing a plan, implementing the plan and checking the result. The purpose of this study is to explore how well Indonesia junior secondary school students apply these four steps in solving mathematical problems, especially on plane geometry topics. Using a qualitative approach, with a sample of nine students, of which three students were from the low mathematics achievement category, three from the medium and three from the high category, were given a test and instructed to write the answers to each question step by step. The results were described and categorized into four groups. The first group consisted of students who used all of the four steps. The second and the third were for students who used the first three steps or the first two steps respectively. The fourth group was for those who could only show the first step. The study indicated that for this sample the level of mathematic ability corresponded to how the students applied their problem-solving steps. It was found that students with high ability were included in the first group, while those with moderate ability were in the second group. Low ability students were categorized into group four. Nevertheless, there was one student with high ability who did not to do the checking step and there was one student with low ability who was able to develop a plan.

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