Strategies for Problem Solving, Critical Analysis, and Goal Setting

2021 ◽  
Vol 43 (1) ◽  
pp. 41-55
Author(s):  
Zoi A. Traga Philippakos ◽  
Hailey Mathison Wilson ◽  
Karen Picerno
Keyword(s):  
Problem Solving ◽  
Goal Setting ◽  
Oral Language ◽  
Critical Analysis ◽  
Thinking Skills ◽  
Transfer Of Knowledge ◽  
Knowledge And Skills ◽  
Challenging Tasks ◽  
And Mathematics ◽  
Support Students

Problem solving requires the application of critical reading and thinking skills and the use of relevant strategies to reach a solution. Independent learners are able to apply taught strategies across contexts and often complete challenging tasks unassisted. The purpose of this paper is to explain how a process of analysis of assignments and evaluation can be applied in reading, writing, and with modifications in mathematics. This work draws on genre-based strategies, on oral language and dialogic pedagogy, and demonstrates how they can be applied across the curriculum to support students’ transfer of knowledge and skills from writing instruction to responses to reading and mathematics aiding them in reflection and eventually independence. Further, the paper provides guidelines for teachers’ explanations to promote critical thinking, questioning, and goal setting.

Computational Thinking and Mathematics

2016 ◽  
pp. 853-865
Author(s):  
Thiago Schumacher Barcelos ◽  
Ismar Frango Silveira
Keyword(s):  
Problem Solving ◽  
Computer Science ◽  
Basic Education ◽  
National Curriculum ◽  
Computational Thinking ◽  
Thinking Skills ◽  
Educational Systems ◽  
Curriculum Guidelines ◽  
And Mathematics ◽  
The One

On the one hand, ensuring that students archive adequate levels of Mathematical knowledge by the time they finish basic education is a challenge for the educational systems in several countries. On the other hand, the pervasiveness of computer-based devices in everyday situations poses a fundamental question about Computer Science being part of those known as basic sciences. The development of Computer Science (CS) is historically related to Mathematics; however, CS is said to have singular reasoning mechanics for problem solving, whose applications go beyond the frontiers of Computing itself. These problem-solving skills have been defined as Computational Thinking skills. In this chapter, the possible relationships between Math and Computational Thinking skills are discussed in the perspective of national curriculum guidelines for Mathematics of Brazil, Chile, and United States. Three skills that can be jointly developed by both areas are identified in a literature review. Some challenges and implications for educational research and practice are also discussed.

Computational Thinking and Mathematics

2014 ◽  
pp. 922-934
Author(s):  
Thiago Schumacher Barcelos ◽  
Ismar Frango Silveira
Keyword(s):  
Problem Solving ◽  
Computer Science ◽  
Basic Education ◽  
National Curriculum ◽  
Computational Thinking ◽  
Thinking Skills ◽  
Educational Systems ◽  
Curriculum Guidelines ◽  
And Mathematics ◽  
The One

On the one hand, ensuring that students archive adequate levels of Mathematical knowledge by the time they finish basic education is a challenge for the educational systems in several countries. On the other hand, the pervasiveness of computer-based devices in everyday situations poses a fundamental question about Computer Science being part of those known as basic sciences. The development of Computer Science (CS) is historically related to Mathematics; however, CS is said to have singular reasoning mechanics for problem solving, whose applications go beyond the frontiers of Computing itself. These problem-solving skills have been defined as Computational Thinking skills. In this chapter, the possible relationships between Math and Computational Thinking skills are discussed in the perspective of national curriculum guidelines for Mathematics of Brazil, Chile, and United States. Three skills that can be jointly developed by both areas are identified in a literature review. Some challenges and implications for educational research and practice are also discussed.

scholarly journals Characteristics of HOTS Oriented Learning at the Elementary School Level

2020 ◽  
Vol 3 (4) ◽  
pp. 873
Author(s):  
Isti Aulia Maspupah
Keyword(s):  
Elementary School ◽  
Critical Thinking ◽  
Problem Solving ◽  
Creative Thinking ◽  
Higher Order Thinking ◽  
Thinking Skills ◽  
Higher Order ◽  
School Level ◽  
Transfer Of Knowledge ◽  
Higher Order Thinking Skills

<p><em>Teachers are always required to always update the changes that occur, so that learning is able to prepare students to face the changes that occur. One of the important things that can be done by teachers is to develop HOTS-oriented learning so that students become accustomed to critical thinking so that they are able to develop their creativity. The purpose of this study is to determine the concept of higher order thinking skills, aspects of higher order thinking skills, HOTS-oriented learning characteristics. The results of this study are: Higher order thinking skills are thinking skills that are not just remembering, restating, and also referring without processing, but thinking skills to examine information critically, creatively, and able to solve problems, Skill-oriented learning higher order thinking is learning that involves 3 (three) aspects of higher order thinking skills, namely: transfer of knowledge, critical and creative thinking, and problem solving. The characteristics of HOTS-oriented learning must make students active in thinking.</em></p>

Science Education and Our Future

1997 ◽  
Vol 3 (1) ◽  
pp. 240-252
Author(s):  
Yervant Terzian
Keyword(s):  
Science Education ◽  
Problem Solving ◽  
Communication Skills ◽  
Thinking Skills ◽  
Critical Thinking Skills ◽  
General Science ◽  
Problem Solving Skills ◽  
Basic Understanding ◽  
Understanding Of Science ◽  
And Mathematics

We need a workforce with basic understanding of science and mathematics; with problem-solving skills; with communication skills; with critical thinking skills; with skills to understand statistics and probabilities. In general, science education will improve when students realize that in order to get better jobs they need to understand science, mathematics, and technology. The following presents my ten pragmatic suggestions for the improvement of science education in general. 

scholarly journals Two finnish girls and mathematics: Similar achievement level, same core curriculum, different competences

2015 ◽  
Vol 3 (1) ◽  
pp. 137-150
Author(s):  
Hanna Viitala
Keyword(s):  
Problem Solving ◽  
Core Curriculum ◽  
Basic Education ◽  
Mathematical Thinking ◽  
Real Life ◽  
Thinking Skills ◽  
Achievement Level ◽  
Core Content ◽  
Learning Mathematics ◽  
And Mathematics

Mathematical thinking and problem solving are essential parts of learning mathematics described in the Finnish National Core Curriculum for Basic Education. Evaluations on both have been done at national and international level. However, in a request for deeper understanding of pupils’ mathematical thinking we need to move beyond paper tests. This paper is a first look into the mathematical thinking of two Finnish girls, Emma and Nora, in their final year of Finnish comprehensive school. After solving a real-life situated problem in a classroom, the girls talk about mathematics and problem solving in an interview. The focus of the analysis is on the learning objectives, core content and final-assessment criteria related to thinking skills and methods in the Finnish curriculum. Also some results on metacognition and affect will be reported. The results suggest that while both pupils have similar achievement level in mathematics, their competences are different: Emma is more competent in problem solving and Nora is more self-confident and self-guided in learning mathematics and can more easily recognize mathematics outside school.

Engaging Students through Technology

2004 ◽  
Vol 9 (6) ◽  
pp. 300-305
Author(s):  
A. Kursat Erbas ◽  
Sarah Ledford ◽  
Drew Polly ◽  
Chandra H. Orrill
Keyword(s):  
Problem Solving ◽  
Mathematics Teaching ◽  
Mathematical Knowledge ◽  
Multiple Representations ◽  
Time Constraints ◽  
Mathematical Concepts ◽  
Problem Situations ◽  
Use Of Technology ◽  
And Mathematics ◽  
Support Students

The use of technology provides an effective way for promoting multiple representations in problem solving and mathematics. Multiple representations allow students to experience different ways of thinking, develop better insights and understandings of problem situations, and increase comprehension about mathematical concepts. Even with all the benefits of multiple representations, however, teachers find it difficult to incorporate open-ended problem solving that capitalizes on these representations because of time constraints and limitations of traditional mathematics teaching. Technology can become a vital and exciting tool in allowing students to explore multiple representations and mathematical situations and relationships (NCTM 2000). Technology empowers students who may have limited mathematical knowledge and limited symbolic and numeric manipulation skills to investigate problem situations. Technology not only frees the students from tedious and repetitive computations but actually encourages the use of multiple representations. Students can easily move from a spreadsheet to a graph or geometry software in their quest for solutions to a given problem. When supported by the teacher, these tools of technology provide students with opportunities to investigate and manipulate mathematical situations to observe, experiment with, and make conjectures about patterns, relationships, tendencies, and generalizations. Teachers should emphasize and encourage the use of multiple representations to support students' thinking and understanding of concepts and problem-solving situations in all areas of mathematics.

scholarly journals Culture and mathematics learning: Identifying students’ mathematics connection

2019 ◽  
Vol 12 (1) ◽  
pp. 82-93
Author(s):  
Al Kusaeri ◽  
Habib Husnial Pardi ◽  
Abdul Quddus
Keyword(s):  
Data Analysis ◽  
Problem Solving ◽  
Mathematics Learning ◽  
Learning Culture ◽  
Cultural Products ◽  
Mathematical Objects ◽  
Formal Mathematics ◽  
Mathematical Problems ◽  
And Mathematics ◽  
Support Students

[English]: Mathematics connection support students finding various possible strategies in problem-solving. Cultural products can be used as mathematical objects in learning. This article, part of a study that designed culture-based learning, aims to identify students' mathematics connection. Data was collected through a test given to 341 students and unstructured interviews of nine students selected based on the completion of the test, which fulfills mathematization steps. Data analysis began by classifying students’ answers based on mathematization, identifying mathematics connection of students according to mathematization, analyzing students’ mathematics connection, and drawing conclusions about mathematics connection and the constraints found. The results showed that students' mathematics connections include three categories, namely understanding connection, representation connection, and justification connection. Students with justification connection solved mathematical problems according to mathematization steps, from the identification of mathematical objects to formal mathematics. Meanwhile, students with understanding and representation connection solved their respective mathematical problems up to the concrete and formal stages. The findings reveal that culture-based mathematics learning provides space to understand students' mathematics connection. Further research is required to prove that it can be used to develop students' mathematics connection. Keywords: Mathematics learning, Culture, Mathematics connection [Bahasa]: Koneksi matematika mendukung siswa menemukan berbagai kemungkinan strategi dalam penyelesaian masalah. Produk budaya memungkinkan dapat dijadikan objek matematika dalam pembelajaran. Artikel ini merupakan bagian dari penelitian yang merancang desain pembelajaran berbasis budaya lokal yang bertujuan mengidentifikasi kemampuan koneksi matematika siswa. Data dikumpulkan melalui tes yang diberikan kepada 341 siswa dan wawancara tidak terstruktur terhadap 9 siswa yang dipilih berdasarkan penyelesaian tes sesuai proses matematisasi. Analisis data diawali dengan klasifikasi jawaban siswa berdasarkan tahapan matematisasi, identifikasi kemampuan koneksi matematika sesuai tahapan matematisasi, analisis kemampuan koneksi matematis, dan penarikan simpulan terkait kemampuan koneksi matematika serta kendala yang ditemukan. Hasil penelitian menunjukkan bahwa kemampuan koneksi matematika siswa meliputi tiga kategori yaitu koneksi pemahaman, koneksi representasi, dan koneksi justifikasi. Siswa dengan kemampuan koneksi justifikasi bisa menyelesaikan masalah matematika sesuai tahapan matematisasi, dari identifikasi objek matematika sampai matematika formal. Sementara itu, siswa yang memiliki kemampuan koneksi pemahaman dan representasi menyelesaikan masalah matematika masing-masing sampai pada tahap model kongkret dan model formal. Hasil penelitian menunjukkan bahwa pembelajaran berbasis budaya memberikan ruang untuk memahami kemampuan koneksi matematika siswa. Penelitian lebih lanjut dibutuhkan untuk menunjukkan pembelajaran berbasis budaya bisa digunakan untuk mengembangkan kemampuan koneksi matematika siswa. Kata Kunci: Pembelajaran matematika, Budaya, Koneksi matematika

THE SOLUTION OF PROBLEMS ON THE COMPUTER: NUMBER, PLOT, SYMBOL

2019 ◽  
pp. 55-63
Author(s):  
V. F. Ochkov ◽  
Yu. V. Chudova ◽  
A. N. Dolgushev
Keyword(s):  
Problem Solving ◽  
Critical Analysis ◽  
Mathematical Constants

The article presents a critical analysis of the methods of analytical, numerical and graphical problem solving on a computer. Problems are solved on the optimal dimensions of hollow geometric bodies (tanks for storing liquids), on the animation of the hinge mechanism, and on the dimensions of the Nautilus submarine. А new set of mathematical constants (numbers and expressions in the radicals), based on the optimization of geometric bodies is presented.

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