Teaching Mathematics with Technology: Problem Solving with a Spreadsheet

1990 ◽  
Vol 38 (3) ◽  
pp. 52-56
Author(s):  
Karl Hoeffner ◽  
Monica Kendall ◽  
Cheryl Stellenwerf ◽  
Pixie Thames ◽  
Patricia Williams
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Thinking Skills ◽  
Teaching Mathematics ◽  
Higher Level Thinking ◽  
Use Of Technology ◽  
Electronic Spreadsheet ◽  
Valuable Role ◽  
Changing Society

As mathematics education adapts to the needs of a changing society, the use of technology becomes increasingly important. Technology can play a valuable role in developing problem-solving capabilities in students by freeing them from tedious computations. Thus, higher-level thinking skills can be emphasized. An electronic spreadsheet can calculate rapidly, generate data from which patterns can be found, show relationships between two or more variables, and investigate “what if?” questions with ease.

scholarly journals Um cenário de estudos envolvendo o ensino de Matemática através da Resolução de Problemas em periódicosA study scenario involving the teaching of mathematics through problem solving in journals

2020 ◽  
Vol 22 (2) ◽  
pp. 252-280
Author(s):  
Kaique Nascimento Martins ◽  
Jamille Vilas Bôas
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
The State ◽  
University Education ◽  
Teaching Mathematics ◽  
Mathematics Teaching And Learning ◽  
Teaching Of Mathematics

ResumoO presente estudo é uma pesquisa bibliográfica inspirada no Estado do Conhecimento, tendo como objetivo compreender focos temáticos nas produções acadêmicas que utilizam/abordam o ensino de matemática através da resolução de problemas. Para tanto, realizou-se um mapeamento das produções acadêmicas publicadas nos periódicos: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista e Educação Matemática Pesquisa, entre janeiro de 2011 e junho de 2019. De um modo geral, percebemos uma variedade de estudos contendo diferentes perspectivas discutidas e abordadas tanto na educação básica quanto no ensino superior.  A partir deste trabalho, é possível ampliar o entendimento sobre a temática, fortalecendo a ideia de que esta pode potencializar o processo de ensino e aprendizagem de matemática.Palavras-chave: Resolução de problemas, Mapeamento, Educação matemática.AbstractThe present study is a bibliographic research inspired by the state of knowledge, aiming to understand thematic focuses on academic productions that use/approach teaching mathematics through problem-solving. For this purpose, we mapped the academic productions published in journals: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista, and Educação Matemática Pesquisa, published between January 2011 and June 2019. We noticed a variety of studies containing different perspectives discussed and addressed both in basic and university education. From this work, it is possible to broaden the understanding of the theme, strengthening the idea that it can enhance the mathematics teaching and learning process.Keywords: Problem solving, Mapping, Mathematics education. ResumenEl presente estudio es una investigación bibliográfica inspirada en el estado del conocimiento, con el objetivo de comprender enfoques temáticos sobre producciones académicas que utilizan/abordan la enseñanza de las matemáticas a través de la resolución de problemas. Para ello, mapeamos las producciones académicas publicadas en las revistas: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista y Educação Matemática Pesquisa, publicadas entre enero de 2011 y junio de 2019. Notamos una variedad de estudios que contienen diferentes perspectivas discutidas y abordadas tanto en educación básica como en educación universitaria. A partir de este trabajo, es posible ampliar la comprensión del tema, fortaleciendo la idea de que puede potenciar el proceso de enseñanza y aprendizaje de las matemáticas.Palabras clave: Resolución de problemas, Mapeo, Educación matemática.

Crosscutting Concepts in Science Support Literacy and Writing

2019 ◽  
pp. 262-275
Author(s):  
Diana Loyd O'Neal
Keyword(s):  
Problem Solving ◽  
Social Studies ◽  
Research Problem ◽  
Thinking Skills ◽  
Content Areas ◽  
Higher Level Thinking ◽  
Teachers And Students ◽  
Primary Focus ◽  
Literacy And Writing ◽  
Crosscutting Concepts

The purpose of the chapter is to guide teachers in development of authentic and engaging lessons through multidisciplinary integration. As cross-curricular lessons are implemented, collaborative support between science, math, ELA, social studies, and related arts classes builds excitement for teachers and students. Students are challenged to take ownership of learning using higher-level thinking skills, creativity in design, and practicing 21st century skills such as collaboration, research, problem solving, and innovation. The chapter provides examples of integrative ideas and suggestions on how to begin developing multidisciplinary lessons. Although the primary focus relates to the crosscutting concepts in science with ELA expectations, the resources provided also include integrations for other content areas as well. The goal of the chapter is to provide models for the development of inquiry-based, authentic, and engaging opportunities for students to develop higher conceptual understanding and offer methods for applying their learning to real-world concepts.

Learner-Controlled Computing: A Description and Rationale

1975 ◽  
Vol 3 (3) ◽  
pp. 207-216 ◽  
Author(s):  
Stuart D. Milner
Keyword(s):  
Problem Solving ◽  
Learner Control ◽  
Thinking Skills ◽  
Cognitive Outcomes ◽  
Affective Outcomes ◽  
Self Confidence ◽  
Use Of Technology ◽  
Drill And Practice ◽  
It Controlling ◽  
Specific Learning

This paper discusses a use of technology in which the student controls the computer (e.g., computer programming) instead of it controlling the student (e.g., drill-and-practice). A description of the nature of this mode of computer use is provided, and some examples are given. A rationale for learner control is discussed in terms of cognitive and affective outcomes of computing. The cognitive outcomes include relatively specific learning and thinking skills and more general systematic methods of problem solving. Affective outcomes include self-confidence, curiosity and exploratory behaviors, and motivation.

scholarly journals Students’ visual thinking ability in solving the integral problem

2020 ◽  
Vol 5 (2) ◽  
pp. 175-186
Author(s):  
Ummu Sholihah ◽  
Maryono Maryono
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Essential Role ◽  
Thinking Skills ◽  
Specific Information ◽  
Visual Thinking ◽  
Graph Problems ◽  
Learning Mathematics ◽  
Thinking Ability ◽  
Technological Tools

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with technological tools, describing and communicating information and ideas, developing ideas, and understanding improvement. This research describes students’ visual thinking ability to solve integral problems. The approach used in this study was descriptive qualitative. The subjects in this study were three students from the Department of Mathematics Education at the State Islamic Institute of Tulungagung. The data were collected by using tests and interviews. The steps to analyze the data were categorization, reduction, exposure, interpretation, and conclusion. Based on the analysis of students’ visual thinking skills in solving integral problems, there were three levels of visual thinking: semi-local visual, local visual, and global visual. At the semi-local visual level, students could only understand algebraically, and they have not shown it graphically at all. Meanwhile, at the local visual level, they have already understood geometry as an alternative language and been able graphically represented problems or concepts, even though it was not perfectly done yet. While on a global visual level, they could perfectly visualize visual thinking indicators, understand algebra and geometry as alternative languages for problem-solving, extract specific information from diagrams, graph problems, and use them to solve problems perfectly.  

scholarly journals A Research on Mathematical Thinking Skills: Mathematical Thinking Skills of Athletes in Individual and Team Sports

2017 ◽  
Vol 5 (9) ◽  
pp. 133 ◽  
Author(s):  
Halil Onal ◽  
Mehmet Inan ◽  
Sinan Bozkurt
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Team Sports ◽  
Thinking Skills ◽  
Basketball Players ◽  
Problem Solving Skills ◽  
Higher Level Thinking ◽  
Individual Sports

The aim of this research is to examine the mathematical thinking skills of licensed athletes engaged in individual and team sports. The research is designed as a survey model. The sample of the research is composed of 59 female and 170 male licensed athletes (n = 229) and (aged 14 to 52) licensed who do the sports of shooting, billiards, archery, tennis, basketball, football, volleyball in various clubs in Turkey. The "Mathematical Thinking Scale" developed by Ersoy (2012) has been employed in the research. Individual sports athletes are more likely to have higher mathematical thinking scores than team athletes. In sports types; those who play billiards and archery have higher scores of mathematical thinking skills compared to other sports types. According to the type of sports the lowest scores of thinking skills were obtained by basketball players. These differences are valid for higher-level thinking tendencies, reasoning, mathematical thinking skills and problem-solving skills, which are sub-dimensions of the mathematical thinking scale.

Learning algebraic procedures through problem solving

2019 ◽  
pp. 61-69
Author(s):  
Alex Friedlander
Keyword(s):  
Problem Solving ◽  
Thinking Skills ◽  
Multiple Solution ◽  
Higher Level Thinking ◽  
Solution Methods ◽  
Solving Equations ◽  
Multiple Solution Methods ◽  
Equivalent Expressions

In this paper, I attempt to present several examples of tasks and some relevant findings that investigate the possibility of basing a part of the practice-oriented tasks on higher-level thinking skills, that are usually associated with processes of problem solving. The tasks presented and analysed here integrate problem solving-components – namely, reversed thinking, expressing and analysing patterns, and employing multiple solution methods, into the learning and practicing of algebraic procedures – such as creating equivalent expressions and solving equations.

Ideas

1993 ◽  
Vol 41 (4) ◽  
pp. 208-215
Author(s):  
Marcy Cook
Keyword(s):  
Problem Solving ◽  
Thinking Skills ◽  
Point Of View ◽  
Discrete Mathematics ◽  
Evaluation Standards ◽  
Analysis And Evaluation ◽  
Active Involvement ◽  
Problem Situations ◽  
Higher Level Thinking ◽  
Nonroutine Problems

The “IDEAS” section for this month focuses on combinations, an important part of discrete mathematics probability. from the point of view of the NCTM's Curriculum and Evaluation Standards (1989). As we continually strive to make mathematics an area for problem solving. we see the need to investigate questions from problem situations and to connect mathematics to the outside world. Students are encouraged to discover all the combinations for a given problem; they should experience estimating, eliminating, collecting data in an organized manner, and drawing conclusions. Active involvement with a set of crayons allows all students to attack nonroutine problems. Forming generalizations — or mathematical statements to explain the phenomena — can extend the upper-grade activities. The use of such higher-level-thinking skills as synthesis, analysis, and evaluation replaces working on tedious worksheets and memorizing rules and algorithms. Students explore relationships, discover ways to accomplish tasks, and make predictions about outcomes without being presented with prescribed formulas.

Assessment: Describing Student Performance Qualitatively

1996 ◽  
Vol 1 (10) ◽  
pp. 828-835
Author(s):  
Jinfa Cai ◽  
Maria E. Magone ◽  
Ning Wang ◽  
Suzanne Lane
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Student Performance ◽  
Conceptual Understanding ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Reasoning Problem ◽  
Mathematics Educators

The issue of linking testing with instructional practice is not new. In recent years, mathematics educators have been redefining the goals of mathematics education to include increased attention to problem solving and reasoning. For example, the National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991) and the National Research Council's Everybody Counts (1989) suggest an emphasis on reasoning, problem solving, conceptual understanding, and communicating mathematically.

How and wherer can a Mathematics Teacher Utilize his 33 Years of Teaching Experience? A Math Teacher about Teaching Mathematics-Excerpt from 33 Years of Teaching Experience

2019 ◽  
pp. 467-472
Author(s):  
Ildikó-Anna Pomuczné Nagy
Keyword(s):  
High School ◽  
Mathematics Education ◽  
Teacher Training ◽  
Problem Solving ◽  
Mathematics Teacher ◽  
Teaching Experience ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Years Of Teaching Experience ◽  
Textbook Writing

This paper shows how a mathematics teacher can utilize his teaching experience. I have been working as a mathematics and physics teacher in Hungary for 33 years. I have taught at various levels of the education system: at elementary school, high school, teacher training college, and in teacher training too, but at most time of my job I taught at high school. I am currently working on the series of a new mathematics textbook for 10 to 14-year-old students. It is based on the traditions of the Hungarian mathematics education, but using the opportunities offered by the 21st century, it also includes modern sample tasks that fit into the curriculum, for example Geogebra files, written by me. I would like to share how I use my teaching experience in textbook writing and how I focus primarily on the didactic aspects of teaching mathematics. I pursue my PhD research in the topic of problem-solving thinking, so I study the mathematical thinking of my students studying in different school types. In my lecture, I analyse different tasks by focusing on mathematical methodological aspects. For example I will tell that I believe it is advantageous to introduce mathematical definitions with examples which are astonishing for students in order to draw attention to maths as much as possible. I will give examples of how I build my experience into the textbook in order to make the system of mathematical concepts optimal for pupils. I would like it if give you an insight into a segment the current Hungarian mathematics education, the current teaching of problem-solving thinking and the different ways of students’ thinking.

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