Investigations: Vehicles for Learning and Doing Mathematics

1996 ◽  
Vol 178 (2) ◽  
pp. 35-49 ◽  
Author(s):  
Carole Greenes
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Solution Method ◽  
Professional Organizations ◽  
Mathematical Concepts ◽  
Educational Benefits ◽  
Problem Situations ◽  
Mathematics Educators ◽  
Solution Methods ◽  
Problem Solving Strategies

Professional organizations of mathematics educators and mathematicians are calling for major reforms in the teaching and learning of mathematics. Among those reforms are a shift in emphasis in curriculum from mastery of lists of unrelated mathematical concepts and skills to exploration of rich mathematical topics and problem situations, and a shift in learning from memorizing and replicating algorithmic procedures to investigating and solving complex problems. To help students achieve proficiency in solving problems, the curriculum must focus on development of the major concepts of mathematics, the enhancement and enlargement of students' repertoires of problem-solving strategies and reasoning methods, and the refinement of communication and collaboration skills. Because they present intriguing problems whose solutions or solution methods are not immediately obvious, and require the application of concepts from different areas of mathematics, and, in some instances, knowledge from other content areas, investigations are powerful vehicles for helping students achieve expertise in solving problems. The nature of investigations and their educational benefits are described. Three types of investigations, whimsical, real, and mathematical, are defined and illustrated. For each investigation, the mathematical content and problem-solving strategies are identified, and a solution method is presented. The responsibilities of the teacher, before, during and after an investigation are described.

Teaching and Learning of Mathematics in Lower Primary in Schools in Ghana

2021 ◽  
pp. 136-154
Author(s):  
Frank Quansah
Keyword(s):  
Problem Solving ◽  
Human Activity ◽  
Teaching And Learning ◽  
Qualitative Approach ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Making Sense ◽  
The World ◽  
Problem Solving Strategies ◽  
Research Questions

Mathematics is a fundamental human activity – a way of making sense of the world. Children possess a natural curiosity and interest in mathematics and come to school with an understanding of mathematical concepts and problem-solving strategies that they have discovered through explorations of the world around them. The purpose of this study is to find out how mathematics is being taught and learnt among primary one pupils in basic schools in Ghana. A qualitative approach was employed to provide answers to the research questions raised. It was found that teachers employed variety of procedures for teaching mathematics. However, there were some problems encountered in the teaching and learning of mathematics.

Coordinate Geometry: A Powerful Tool for Solving Problems

1990 ◽  
Vol 83 (4) ◽  
pp. 264-268
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematics Standards ◽  
Problem Situations ◽  
Coordinate Geometry

In calling for reform in the teaching and learning of mathematics, the Curriculum and Evaluation Standards for School Mathematics (Standards) developed by NCTM (1989) envisions mathematics study in which students reason and communicate about mathematical ideas that emerge from problem situations. A fundamental premise of the Standards, in fact, is the belief that “mathematical problem solving … is nearly synonymous with doing mathematics” (p. 137). And the ability to solve problems, we are told, is facilitated when students have opportunities to explore “connections” among different branches of mathematics.

A Problem is Something You Don't Want to Have: Problem Solving by Kindergartners

2005 ◽  
Vol 12 (3) ◽  
pp. 146-154
Author(s):  
Lynne Outhred ◽  
Sarah Sardelich
Keyword(s):  
Problem Solving ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Social Process ◽  
Mathematical Concepts ◽  
Mathematics Teaching And Learning ◽  
Mental Actions

Although Adrian, when asked by his teacher what a problem is, was adamant that problems are to be avoided, educators believe problem solving is central to mathematics teaching and learning (NCTM 2000). Problem solving supports students as they apply their skills and their knowledge of mathematical concepts and processes to a range of different contexts and as they construct knowledge by reflecting on their own physical and mental actions. When children solve problems together, learning is a social process in which they learn not only from the teacher but also by discussing, arguing, and negotiating with their peers.

scholarly journals Componentes de conocimiento del profesor para la enseñanza de la resolución de problemas en educación primaria

2019 ◽  
Vol 13 (2) ◽  
pp. 104-129
Author(s):  
Juan Luis Piñeiro ◽  
Elena Castro-Rodríguez ◽  
Enrique Castro
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Pedagogical Knowledge ◽  
Primary Teacher ◽  
Problem Resolution ◽  
Resolution Process ◽  
Mathematics Educators ◽  
Teaching Problem ◽  
Educación Primaria

La importancia que presenta la resolución de problemas en la enseñanza y aprendizaje de la matemática es una premisa aceptada en la comunidad de educadores matemáticos. No obstante, los marcos que describen o caracterizan el conocimiento de los profesores sobre las matemáticas escolares han dado poca relevancia a este proceso. Partiendo de revisiones curriculares y teóricas, presentamos una organización del conocimiento del profesor de educación primaria sobre la resolución de problemas de matemáticas. En ella diferenciamos un conocimiento sobre la resolución de problemas del que emergen los componentes relativos al concepto de problema, proceso de resolución y disposición para afrontar un problema; y un conocimiento pedagógico sobre la resolución de problemas en el que distinguimos un componente referido al aprendizaje y otro a la enseñanza. Nuestra reflexión ratifica la idea que la naturaleza distinta de un proceso como la resolución de problemas provoca un conocimiento que los modelos han omitido.Teacher knowledge components for teaching problem solving in primary educationProblem solving is central in teaching and learning of mathematics, an accepted premise in the community of mathematics educators. However, the frameworks that describe or characterize teachers' knowledge have given little relevance to this process. Starting from curricular and theoretical revisions, we present a proposal of organization for the knowledge of primary teacher about problem solving. We differentiate a knowledge of the process from which the components related to the concept of problem, resolution process and disposition to face a problem emerge; and a pedagogical knowledge where we distinguish a component referring to learning and another to the teaching of problem solving. Our reflection confirms the idea that the different nature of a process such as problem solving, causes a knowledge that the models have omitted.doi: 10.30827/pna.v13i2.7876Scopus record and citations

scholarly journals Mathematics Teachers’ Perceptions about Problem-Solving: The case of Ghana

2019 ◽  
Vol 13 ◽  
pp. 1-18
Author(s):  
Ernest Ampadu
Keyword(s):  
Professional Development ◽  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
Junior High School ◽  
Teaching And Learning ◽  
Senior High School ◽  
Cape Coast ◽  
Problem Solving Skills ◽  
Problem Solving Strategies

Most students experience different levels of difficulties in learning mathematics. TIMSS results have shown that most students in Ghana do not perform well in higher level tasks designed to assess applications and non-routine problems. This study, therefore, aimed at examining Ghanaian Junior and Senior High School mathematics teachers problem-solving strategies and their professional development needs about problem-solving. 114 mathematics teachers from 28 Junior High School (JHS) and Senior High School (SHS) in the Cape Coast Metropolis took part in the study. Quantitative and qualitative data were collected using a semi-structured questionnaire. The results from the study show that although teachers appreciate the importance of problem-solving in improving mathematics teaching and learning, there has not been the needed problem-solving training to support teachers in this regard. The researcher, therefore, argue that despite the numerous advantages associated with problem-solving strategy of teaching and learning, continuous professional development training for teachers should be paramount in our quest for helping students develop problem solving skills. Ghanaian JHS and SHS students can be in a disadvantageous position as they compete with their peers from other countries in international comparison examinations if our teachers are not given the needed support to become proficient in the use of problem-solving strategies in the classrooms.

Technology Tips: A Mathematical Look at a Free Throw Using Technology

1996 ◽  
Vol 89 (9) ◽  
pp. 774-779
Author(s):  
Charles Vonder Embse ◽  
Arne Engebretsen
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematics Curriculum ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Free Throw ◽  
Problem Situations ◽  
Real World Problem

Technology can be used to promote students' understanding of mathematical concepts and problem-solving techniques. Its use also permits students' mathematical explorations prior to their formal development in the mathematics curriculum and in ways that can capture students' curiosity, imagination, and interest. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recommends that “[i]n grades 9–12, the mathematics curriculum should include the refinement and extension of methods of mathematical problem solving so that all students can … apply the process of mathematical modeling to real-world problem situations” (p. 137). Students empowered with technology have the opportunity to model real-world phenomena and visualize relationships found in the model while gaining ownership in the learning process.

Flying through Graphs: An Introduction to Graph Theory

2001 ◽  
Vol 94 (8) ◽  
pp. 680-688
Author(s):  
Amy Roth McDuffie
Keyword(s):  
Graph Theory ◽  
Problem Solving ◽  
Computer Technology ◽  
School Curriculum ◽  
Discrete Mathematics ◽  
National Council ◽  
High School Curriculum ◽  
Problem Situations ◽  
Education Community ◽  
Solution Methods

The mathematics education community has called for changes in the high school curriculum to increase the emphasis on meaningful problem solving and on topics in discrete mathematics (National Council of Teachers of Mathematics 1989, 1991, 2000). This recommendation resulted from changes in knowledge and revisions in problem-solving needs because of advances in such fields as information processing and computer technology. Including graph theory in the curriculum is one way to meet these goals. Graphs present an opportunity to model and analyze such problem situations as networks and circuits. This activity incorporates basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel.

scholarly journals Comparison of Traditional and ADRI Based Teaching Approaches in an Introductory Programming Course

10.28945/3793 ◽  
2017 ◽  
Vol 16 ◽  
pp. 267-283 ◽  
Author(s):  
Sohail Iqbal Malik ◽  
Jo Coldwell-Neilson
Keyword(s):  
Problem Solving ◽  
Focus Group ◽  
Teaching And Learning ◽  
Science Studies ◽  
Future Research ◽  
Learning Approach ◽  
Final Exam ◽  
Introductory Programming ◽  
Problem Solving Strategies ◽  
Programming Knowledge

Aim/Purpose: This study introduced a new teaching and learning approach based on an ADRI (Approach, Deployment, Result, Improvement) model in an introductory programming (IP) course. The effectiveness of the new teaching and learning process was determined by collecting feedback from the IP instructors and by analyzing the final exam grades of the course. Background: Learning to program is considered a difficult and challenging task for a considerable number of novice programmers. As a result, high failure and dropout rates are often reported in IP courses. Different studies have been conducted to investigate the issue. One of the reasons for this challenge is the multiple skills that students have to master in order to be able to build programs. These skills include programming knowledge and problem-solving strategies and being able to pay equal attention to these required skills in the IP course. Methodology: A focus group was conducted to obtain feedback from the IP instructors about the ADRI approach. The performance of the students who had completed the IP course before ADRI was compared with those who used the ADRI approach by undertaking a comparative analysis of their final exam grades. Contribution: The study demonstrates that the new teaching and learning approach based on the ADRI model encourages students to pay equal attention to programming knowledge and problem-solving strategies, discouraging programming shortcuts and reducing high attrition rates (failure and dropout) in the IP course. Findings: The results of the focus group show that the instructors preferred the ADRI approach compared to the traditional approach. The final exam grades show that the students performed better in semesters which offered the ADRI approach as compared to those semesters without this approach. Future Research: Future research will explore the ADRI approach in other fields of computer science studies, such as database and data structure, to determine if its impact has a wider application than just teaching introductory programming.

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