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.

Expanding participation in problem solving in a diverse middle school mathematics classroom

2010 ◽  
Vol 22 (1) ◽  
pp. 91-118 ◽  
Author(s):  
Keith Weber ◽  
Iuliana Radu ◽  
Mary Mueller ◽  
Arthur Powell ◽  
Carolyn Maher
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Mathematics Classroom ◽  
Middle School Mathematics ◽  
School Mathematics

scholarly journals Examining Mathematical Problem-Solving Beliefs among Rwandan Secondary School Teachers

2021 ◽  
Vol 20 (7) ◽  
pp. 227-240
Author(s):  
Aline Dorimana ◽  
Alphonse Uworwabayeho ◽  
Gabriel Nizeyimana
Keyword(s):  
Problem Solving ◽  
Secondary School Teachers ◽  
Mathematics Classroom ◽  
Mathematical Problem ◽  
Real Life ◽  
Mathematical Problem Solving ◽  
Teachers Beliefs ◽  
Mathematical Problems ◽  
Teacher Professional

This study explored teachers' beliefs about mathematical problem-solving. It involved 36 identified teachers of Kayonza District in Rwanda via an explanatory mixed-method approach. The findings indicate that most teachers show a positive attitude towards advancing problem-solving in the mathematics classroom. However, they expose different views on its implementation. Role of problem-solving, Mathematical problems, and Problem-solving in Mathematics were identified as main themes. Problem-solving was highlighted as an approach that helps teachers use time adequately and helps students develop critical thinking and reasoning that enable them to face challenges in real life. The study recommends teacher professional development initiatives with their capacity to bring problem-solving to standard.

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.

Using Writing Strategies in Math to Increase Metacognitive Skills for the Gifted Learner

2017 ◽  
Vol 40 (1) ◽  
pp. 43-47 ◽  
Author(s):  
Heather Knox
Keyword(s):  
Academic Success ◽  
Problem Solving ◽  
Mathematics Classroom ◽  
Metacognitive Skills ◽  
Problem Solving Skills ◽  
Gifted Learners ◽  
Solution Strategies ◽  
Multiple Strategies ◽  
Problem Solving Process ◽  
Metacognitive Ability

Metacognition is vital for a student’s academic success. Gifted learners are no exception. By enhancing metacognition, gifted learners can identify multiple strategies to use in a situation, evaluate those strategies, and determine the most effective given the scenario. Increased metacognitive ability can prove useful for gifted learners in the mathematics classroom by improving their problem-solving skills and conceptual understanding of mathematical content. Implemented effectively, writing is one way to increase a student’s metacognitive ability. Journal writing in the mathematics classroom can help students by clarifying their thought process while further developing content knowledge. Implementing writing can lead to increased understanding of the problem, identification of additional strategies that can be used to solve the problem, and reflective thinking during the problem-solving process. Reflective writing in mathematics can help students evaluate solution strategies and identify strengths and areas of improvement in their mathematical understanding.

Connecting Research to Teaching: Affective Responses to Problem Solving

1993 ◽  
Vol 86 (9) ◽  
pp. 761-763 ◽  
Author(s):  
Douglas B. McLeod
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Affective Responses ◽  
School Mathematics ◽  
Affective Reactions ◽  
Reform Mathematics ◽  
Mathematical Ideas ◽  
Mathematics Classrooms ◽  
The Future ◽  
Nonroutine Problems

The vision of the mathematics classroom that IS presented 1n the Natwnal Council of Teachers of Mathematics's Curriculum and Eualuation Standards for School Mathematics (1989) has inspired many of us to want to change the way in which we teach. We want to pose challenging problems, to see our students work cooperatively, and to have productive discussions with students about significant mathematical ideas. But as Ball and Schroeder have pointed out, that vision is “much more difficult to realize than to endorse” (1992, 69). We will encounter many difficulties as we move toward that ideal classroom of the future; getting students to respond positively to nonroutine problems or other tasks that require higher-orderthinking skills is one difficulty that teachers often face. Research suggests that students' affective reactions to nonroutine problems can be a source of both difficulty and support as we work to reform mathematics classrooms.

scholarly journals Toward Developing a Real-World Computational Thinking Test Tool from Existing Models

2019 ◽  
Vol 8 (2S6) ◽  
pp. 389-393
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Liberal Arts ◽  
Real Life ◽  
Computational Thinking ◽  
Validity And Reliability ◽  
Test Tool ◽  
Verification Methods ◽  
Problem Solving Process ◽  
Thinking Tools

Various researches are always being carried out to measure the effectiveness of software education. We analyzed previously developed computational thinking tools and studied their practical application and verification methods. Using this information, we developed a 20-item questionnaire to categorize the tools by the abilities they measured: analysis, design, implementation, and reasoning. We surveyed college freshman and 204 students in computer programming subjects in liberal arts and then conducted an exploratory factor analysis to analyze the validity and reliability of our questionnaire test tool. Our test showed that previously used computational testing tools lacked the ability to measure problem-solving processes based on computational thinking. To solve this problem, we revised the questionnaire items to consider the problem-solving process based on computational thinking and proposed a tool that can check the computational thinking through the material of real life using the students’ empirical knowledge. The statistical analysis was as follows: analysis ability (reliability α = .895); design ability (reliability α = .727); implementation ability (reliability α = .745), and reasoning ability (reliability α = .833). To measure computing errors, you need a testing tool that can address real-world problems. We aimed to develop a research tool for measuring computational thinking based on the case of applying and revising existing test tools.

scholarly journals Kemampuan Komunikasi Matematis dalam Menyelesaikan Soal Transformasi Geometri Ditinjau dari Gender

2021 ◽  
Vol 5 (1) ◽  
pp. 26
Author(s):  
Rizky Dian Pertiwi ◽  
Tatag Yuli Eko Siswono
Keyword(s):  
Problem Solving ◽  
Communication Skills ◽  
Female Students ◽  
Male Students ◽  
Geometric Transformation ◽  
Mathematical Communication ◽  
Male And Female ◽  
Geometric Transformations ◽  
Transformation Problems ◽  
Problem Solving Process

Abstrak — Kemampuan komunikasi matematis adalah kecakapan seseorang dalam menggunakan istilah matematika untuk menyalurkan pemikirannya secara sistematis baik secara lisan maupun tulis. Kemampuan komunikasi matematis dapat diketahui dari kemampuan siswa dalam menyelesaikan soal matematika dan kemampuan dalam mengkomunikasikan hasilnya kepada orang lain. Pengetahuan mengenai transformasi geometri berperan penting dalam perkembangan matematika siswa di sekolah karena dapat membangun kemampuan spasial, kemampuan penalaran serta membantu siswa dalam menganalisis situasi matematis. Penelitian ini bertujuan untuk mendeskripsikan kemampuan komunikasi matematis dalam menyelesaikan soal transformasi geometri yang ditinjau dari gender. Jenis penelitian ini adalah penelitian kualitatif dengan pendekatan deskriptif. Subjek penelitian ini adalah dua orang siswa laki laki dan dua orang siswa perempuan di salah satu sekolah menengah Kota Mojokerto dikarenakan penelitian ini mendeskripsikan bagaimana kemampuan komunikasi matematis yang ditunjukkan oleh siswa laki-laki dan perempuan. Berdasarkan analisis data dalam penelitian dapat disimpulkan bahwa (1) Kemampuan komunikasi matematis siswa lakilaki lebih unggul dibandingkan siswa perempuan dalam kemampuan menyajikan informasi serta dalam kemampuan menggunakan bahasa matematika yang logis dan sistematis dalam proses penyelesaian soal. Sedangkan pada kemampuan menggunakan representasi matematis dalam menyatakan gagasan matematis untuk menyelesaikan soal transformasi geometri, siswa laki-laki dan perempuan memiliki kemampuan yang sama. (2) Siswa laki-laki lebih mampu menyelesaikan soal transformasi geometri dengan lebih tepat dibandingkan siswa perempuan. (3) Siswa laki-laki lebih unggul dalam menjawab soal secara tertulis, sedangkan siswa perempuan memiliki kemampuan yang baik dalam menyajikan jawaban secara lisan atauverbal.Kata kunci: kemampuan komunikasi matematis, transformasi geometri, gender.Abstract — Mathematical communication skills are a person's ability to use mathematical terms to express their thoughts systematically both spoken and written. Mathematical communication skills can be seen from the ability of students to solve mathematic problems and the ability to communicate the results to others. Knowledge of geometric transformations plays an important role in the development of student’s mathematics in school because it can build spatial abilities, reasoning abilities and help students analyze mathematical situations. This study aims to describe written mathematical communication skills in solvinggeometric transformation problems in terms of gender. This type of research is a qualitative research with a descriptive approach. The subjects of this study are two male students and two female students in one of senior high school in Mojokerto because this study describes how mathematical communication skills are showed by male and female students. The results showed that (1) Male students' mathematical communication skills are superior to female students in the ability to present information and in the ability to use logical and systematic mathematical language in the problem solving process. Meanwhile, the abilityto use mathematical representations in expressing mathematical ideas to solve geometric transformation problems, male and female students have the same abilities. (2) Male students are more able to solve geometric transformation problems more precisely than female students. (3) Male students are superior inanswering questions in writing, while female students have good abilities in present the answer orally or verbally.Keywords: mathematical communication skills, problem solving, gender.

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).

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