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

2013 ◽  
Vol 9 (3) ◽  
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).

Assessing Mathematics Classroom Goal Structures in a Sample of Italian Students During Sixth Grade

2016 ◽  
Vol 36 (2) ◽  
pp. 182-187
Author(s):  
Donatella Poliandri ◽  
Stefania Sette ◽  
Emanuela Vinci ◽  
Sara Romiti
Keyword(s):  
Mathematics Achievement ◽  
Adaptive Learning ◽  
Mathematics Classroom ◽  
Sixth Grade ◽  
Confirmatory Factor Analyses ◽  
Goal Structures ◽  
Confirmatory Factor ◽  
And Performance ◽  
And Mathematics ◽  
Approach Goals

The present study analyzed the factor validity of the Patterns of Adaptive Learning Scale (PALS) to assess students’ perceptions of mathematics classroom goal structures. Participants were N = 7,773 Italian students aged from 11 to 15 years ( M = 11.97, SD = 0.50). The confirmatory factor analysis replicated a three-factor structure (i.e., mastery, performance-avoidance, and performance-approach goals) of the scale. Multigroup confirmatory factor analyses supported configural, metric, and scalar measurement invariance of the scale across gender. Moreover, the students’ mathematics achievement was positively related to mastery goals and negatively associated with performance-avoidance goals. The use of the scale may help teachers to understand the relations between classroom goal structures and mathematics achievement during middle school.

How Does Your Mathematical Garden Grow?

2007 ◽  
Vol 13 (2) ◽  
pp. 68-76
Author(s):  
Shari A. Beck ◽  
Vanessa E. Huse ◽  
Brenda R. Reed
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Real Life ◽  
Middle School Mathematics ◽  
Content Standards ◽  
Mathematical Communication ◽  
Mathematical Ideas ◽  
Application Problem ◽  
Multiple Process ◽  
Problem Solving Process

Imagine a middle school mathematics classroom where students are actively engaged in a real-life application problem incorporating multiple Process and Content Standards as outlined by NCTM (2000). Sounds of mathematical communication arise as students use multiple representations to help connect mathematical ideas throughout the problem-solving process. Students apply various types of reasoning and explore alternate methods of proof while working attentively on applications that incorporate Number and Operations, Algebra, Geometry, and Measurement.

scholarly journals Analisis Tingkat Kemampuan Metakognitif Mahasiswa Melalui Mai (Metacognitive Awareness Inventory) Pada Eksperimen Berbasis Problem Solving

Kodifikasia ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 35
Author(s):  
Faninda Novika Pertiwi ◽  
Ahmadi Ahmadi ◽  
Wirawan Fadly
Keyword(s):  
Problem Solving ◽  
Metacognitive Awareness ◽  
Metacognitive Awareness Inventory

Pembelajaran fisika harus bermakna, yaitu didalamnya menekankan pada fisika sebagai produk, sebagai proses, dan sebagai sikap. Dua hal dalam pembelajaran fisika yang tidak dapat dipisahkan yaitu pengamatan dalam eksperimen dan telaah teori. Eksperimen fisika hendaknya memungkinkan mahasiswa terlibat langsung dalam segala proses mulai dari tahap merumuskan tujuan eksperimen sampai mengambil kesimpulan dari eksperimen yang telah dilakukan. Salah satu metode yang dapat memfasilitasi keberhasilan tujuan eksperimen fisika adalah dengan metode problem solving. Tujuan dari penelitian ini adalah untuk menganalisis tingkat kemampuan metakognitif mahasiswa yang melaksanakan eksperimen fisika dasar berbasis problem solving di IAIN Ponorogo melalui MAI (Metacognitive Awareness Inventory) serta untuk menjelaskan keterkaitan antar indikator (perencanaan diri, pemonitoran diri, dan evaluasi diri) pada kemampuan metakognitif mahasiswa. Data yang dihasilkan penelitian ini adalah data kemampuan metakognitif mahasiswa yang telah diukur menggunakan lembar kuesioner MAI (Metacognitive Awareness Inventory). Analisis data yang digunakan yaitu analisis korelasi product moment. Hasil penelitian yang didapatkan yaitu bahwa eksperimen fisika dasar berbasis problem solving ini sangat baik untuk mengoptimalkan kemampuan metakognitif mahasiswa. Hal ini terbukti ketika eksperimen fisika dasar yang dilaksanakan berbasis problem solving ternyata tingkat kemampuan metakognitif mahasiswa mencapai 153,459 yang artinya tingkat kemampuan metakognitif mahasiswa pada kategori super (berkembang sangat baik). Hal ini menandakan bahwa mahasiswa menggunakan kesadaran metakognitif secara teratur untuk mengukur proses berpikir dan belajarnya secara mandiri. Selain tingkat kemampuan metakognitif, ternyata ada keterkaitan antar ketiga indikator kemampuan metakognitif. Keterkaitan indikator perencanaan diri dan pemonitoran diri adalah sebesar 0,901, keterkaitan indikator pemonitoran diri dan evaluasi diri adalah sebesar 0,891, dan keterkaitan indikator perencanaan diri dan evaluasi diri adalah sebesar 0,926. Ketiganya menunjukkan korelasi positif yang sangat kuat.

scholarly journals Experiences in Learning Problem-Solving through Computational Thinking

2018 ◽  
Vol 18 (02) ◽  
pp. e15 ◽  
Author(s):  
Jacqueline M. Fernández ◽  
Mariela E. Zúñiga ◽  
María V. Rosas ◽  
Roberto A. Guerrero
Keyword(s):  
Problem Solving ◽  
Computer Science ◽  
Computational Thinking ◽  
First Year ◽  
Learning Problem ◽  
Introductory Course ◽  
San Luis ◽  
National University ◽  
And Mathematics ◽  
Problem Solving Process

Computational Thinking (CT) represents a possible alternative for improving students’ academic performance in higher level degree related to Science, Technology, Engineering and Mathematics (STEM). This work describes two different experimental proposals with the aim of introducing computational thinking to the problem solving issue. The first one was an introductory course in the Faculty of Physical, Mathematical and Natural Sciences (FCFMyN) in 2017, for students enrolled in computer science related careers. The other experience was a first attempt to introduce CT to students and teachers belonging to not computer related faculties at the National University of San Luis (UNSL). Both initiatives use CT as a mean of improving the problem solving process based on the four following elementary concepts: Decomposition, Abstraction, Recognition of patterns and Algorithm. The results of the experiences indicate the relevance of including CT in the learning problem solving issue in different fields. The experiences also conclude that a mandatory CT related course is necessary for those careers having computational problems solving and/or programming related subjects during the first year of their curricula. Part of this work was presented at the XXIII Argentine Congress of Computer Science (CACIC).

scholarly journals Analysis of Teacher-Student Interaction in the Joint Solving of Non-Routine Problems in Primary Education Classrooms

2020 ◽  
Vol 12 (24) ◽  
pp. 10428
Author(s):  
Beatriz Sánchez-Barbero ◽  
José María Chamoso ◽  
Santiago Vicente ◽  
Javier Rosales
Keyword(s):  
Problem Solving ◽  
Primary Education ◽  
Mathematics Classroom ◽  
Student Interaction ◽  
Process Selection ◽  
Teacher Student ◽  
Cognitive Difficulty ◽  
Teacher Student Interaction ◽  
Teachers And Students ◽  
Problem Solving Process

The analysis of teacher–student interaction when jointly solving routine problems in the primary education mathematics classroom has revealed that there is scarce reasoning and little participation on students’ part. To analyze whether this fact is due to the routine nature of the problems, a sample of teachers who solved, together with their students, a routine problem involving three questions with different cognitive difficulty levels (task 1) was analyzed, describing on which part of the problem-solving process (selection of information or reasoning) they focused their interaction. Results showed that they barely focused the interaction on reasoning, and participation of students was scarce, regardless of the cognitive difficulty of the question to be answered. To check whether these results could be due to the routine nature of the problem, a nonroutine problem (task 2) was solved by the same sample of teachers and students. The results revealed an increase in both reasoning and participation of students in processes that required complex reasoning. This being so, the main conclusion of the present study is that including nonroutine problem solving in the primary education classroom as a challenging task is a reasonable way to increase students’ ability to use their own reasoning to solve problems, and to promote greater teacher–student collaboration. These two aspects are relevant for students to become creative, critical, and reflective citizens.

Cognitive Style, Operativity, and Mathematics Achievement

1983 ◽  
Vol 14 (5) ◽  
pp. 344-353
Author(s):  
James J. Roberge ◽  
Barbara K. Flexer
Keyword(s):  
Problem Solving ◽  
Mathematics Achievement ◽  
Propositional Logic ◽  
Eighth Graders ◽  
Field Independent ◽  
Field Dependent ◽  
Educational Implications ◽  
Concrete Operational ◽  
And Mathematics ◽  
Operational Development

Previous investigations of the effects of field dependence-independence or the level of operational development on the mathematics achievement of children in the lower elementary school grades have involved the administration of concrete operational tasks (e.g., classification, conservation, and seriation). The present study was designed to examine the influence of these factors on the mathematics achievement of sixth, seventh, and eighth graders by using formal operational tasks (i.e., combinations, propositional logic, and proportionality). Results were analyzed using total mathematics achievement test scores as well as scores on subtests of computation, concepts, and problem solving. Field-independent students scored significantly higher than field-dependent students on the total mathematics, concepts, and problem-solving tests. High-operational students scored significantly higher than their low-operational peers on all tests. Educational implications of the findings are discussed.

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