Tacoma Shuffle

1998 ◽  
Vol 91 (3) ◽  
pp. 212-216
Author(s):  
Lyman S. Holden ◽  
Loyce K. Holden
Keyword(s):  
Problem Solving ◽  
Mathematical Induction ◽  
Computer Application ◽  
Trial And Error ◽  
C Language ◽  
Key Concepts ◽  
Proof By Induction ◽  
Iterative Functions

The key concepts discussed in this article include problem-solving activities, mathematical induction, proof by induction, and use of the phrase “without loss of generality.” Several problem-solving tools are illustrated, such as trial and error, working backward, and seeing patterns. The computer application illustrates recursive and iterative functions using C language.

Alice in the Real World

2012 ◽  
Vol 17 (7) ◽  
pp. 410-416 ◽  
Author(s):  
Tom Parker
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematical Problem ◽  
Computer Application ◽  
Mathematical Problem Solving ◽  
The Real ◽  
Programming Knowledge

A computer application promotes programming knowledge and allows students to create their own worlds through mathematical problem solving.

An Experiment in Problem Solving

1951 ◽  
Vol 3 (4) ◽  
pp. 184-197 ◽  
Author(s):  
J. W. Whitfield
Keyword(s):  
Problem Solving ◽  
Experimental Work ◽  
Human Subjects ◽  
Qualitative Difference ◽  
Trial And Error ◽  
Qualitative Nature ◽  
The Individual

Trial-and-error problems are described in terms of “stimulus” difficulty, which is a measure of the number of possible modes of response left to the individual when all the information given is taken into account; and “phenomenal” difficulty, which is a measure derived from the individual's performance. An experiment is described in which three types of problem were presented to human subjects. In all three problems the stimulus difficulty was calculable, stage by stage, in the solution. The problems differed in this stimulus difficulty and also in the qualitative nature of the information provided—from unequivocal to conditional. It is shown that the qualitative difference of the nature of the information bears most relationship to phenomenal difficulty. Some observations are made on the modes of solution adopted, and further experimental work is suggested.

Arithmetic, philosophical issues in

2018 ◽  
Author(s):  
Michael Potter
Keyword(s):  
Natural Number ◽  
Decision Procedure ◽  
Mathematical Induction ◽  
Universal Quantifier ◽  
Number Concept ◽  
Special Character ◽  
The Status ◽  
Proof By Induction ◽  
Philosophy Of Arithmetic ◽  
Principle Of Mathematical Induction

The philosophy of arithmetic gains its special character from issues arising out of the status of the principle of mathematical induction. Indeed, it is just at the point where proof by induction enters that arithmetic stops being trivial. The propositions of elementary arithmetic – quantifier-free sentences such as ‘7+5=12’ – can be decided mechanically: once we know the rules for calculating, it is hard to see what mathematical interest can remain. As soon as we allow sentences with one universal quantifier, however – sentences of the form ‘(∀x)f(x)=0’ – we have no decision procedure either in principle or in practice, and can state some of the most profound and difficult problems in mathematics. (Goldbach’s conjecture that every even number greater than 2 is the sum of two primes, formulated in 1742 and still unsolved, is of this type.) It seems natural to regard as part of what we mean by natural numbers that they should obey the principle of induction. But this exhibits a form of circularity known as ‘impredicativity’: the statement of the principle involves quantification over properties of numbers, but to understand this quantification we must assume a prior grasp of the number concept, which it was our intention to define. It is nowadays a commonplace to draw a distinction between impredicative definitions, which are illegitimate, and impredicative specifications, which are not. The conclusion we should draw in this case is that the principle of induction on its own does not provide a non-circular route to an understanding of the natural number concept. We therefore need an independent argument. Four broad strategies have been attempted, which we shall consider in turn.

International Perspectives: The Triple Jump: A Potential Area for Problem Solving and Investigation

1998 ◽  
Vol 4 (2) ◽  
pp. 104-108
Author(s):  
Doug Clarke
Keyword(s):  
Problem Solving ◽  
Proportional Reasoning ◽  
International Perspectives ◽  
Key Concepts ◽  
Potential Area

Many teachers comment that interesting appucations of ratio are hard to find. Teachers also find that many students have difficulty with proportional reasoning in general, and ratio in particular. In this article, I talk through a process that led to the discovery of the role of ratios and percentages in discussions about triple jump performances, and to a range of tasks that provide important information about students' understanding of key concepts in mathematics.

Math and Mr. Men

2017 ◽  
Vol 24 (2) ◽  
pp. 82-83
Author(s):  
James Russo ◽  
Toby Russo
Keyword(s):  
Problem Solving ◽  
Mathematical Tasks ◽  
Acting Out ◽  
Trial And Error ◽  
Problem Solving Strategies ◽  
Concrete Materials

Read a Mr. Men story with your students, and tackle the associated mathematical tasks. Success with these tasks requires children to draw on a variety of problem-solving strategies, including drawing diagrams and pictures, creating tables, trial-and-error strategies (guess and check), modeling problems with concrete materials, and possibly even acting out the problems. Have fun!

Observational learning in the large-billed crow (Corvus macrorhynchos)

2011 ◽  
Vol 12 (2) ◽  
pp. 281-303 ◽  
Author(s):  
Ei-Ichi Izawa ◽  
Shigeru Watanabe
Keyword(s):  
Problem Solving ◽  
Observational Learning ◽  
Cognitive Abilities ◽  
Trial And Error ◽  
Imitative Learning ◽  
Subsequent Test ◽  
Corvus Macrorhynchos ◽  
Alternative Techniques ◽  
Learn Problem ◽  
Matching Techniques

Exploiting the skills of others enables individuals to reduce the risks and costs of resource innovation. Social corvids are known to possess sophisticated social and physical cognitive abilities. However, their capacity for imitative learning and its inter-individual transmission pattern remains mostly unexamined. Here we demonstrate the large-billed crows' ability to learn problem-solving techniques by observation and the dominance-dependent pattern in which this technique is transmitted. Crows were allowed to observe one of two box-opening behaviours performed by a dominant or subordinate demonstrator and then tested regarding action and technique. The observers successfully opened the box on their first attempts by using non-matching actions but matching techniques to those observed, suggesting emulation. In the subsequent test sessions, dominant observers (i.e. those dominant to the bird acting as demonstrator) consistently used the learned technique, whereas subordinates (i.e. those subordinate to the bird acting as demonstrator) learned alternative techniques by explorative trial and error. Our findings demonstrate crows' capacity to learn by observing behaviours and the effect of dominance on transmission patterns of behavioural skills. Keywords: social learning; imitation; emulation; affordance; culture; innovation

scholarly journals Learning Microbiology Through Cooperation: Designing Cooperative Learning Activities that Promote Interdependence, Interaction, and Accountability

2002 ◽  
Vol 3 (1) ◽  
pp. 26-36
Author(s):  
JANINE E. TREMPY ◽  
MONICA M. SKINNER ◽  
WILLIAM A. SIEBOLD
Keyword(s):  
Problem Solving ◽  
Cooperative Learning ◽  
Student Satisfaction ◽  
Learning Model ◽  
Learning Activities ◽  
Group Processing ◽  
Engineering And Technology ◽  
The World ◽  
Key Concepts ◽  
Individual Accountability

A microbiology course and its corresponding learning activities have been structured according to the Cooperative Learning Model. This course, The World According to Microbes , integrates science, math, engineering, and technology (SMET) majors and non-SMET majors into teams of students charged with problem solving activities that are microbial in origin. In this study we describe development of learning activities that utilize key components of Cooperative Learning—positive interdependence, promotive interaction, individual accountability, teamwork skills, and group processing. Assessments and evaluations over an 8-year period demonstrate high retention of key concepts in microbiology and high student satisfaction with the course.

scholarly journals Educating Students for a Complex Future: Why Integrating a Problem Analysis in Problem-Based Learning Has Something to Offer

2020 ◽  
Vol 14 (2) ◽  
Author(s):  
Anja Overgaard Thomassen ◽  
Diana Stentoft
Keyword(s):  
Higher Education ◽  
Problem Solving ◽  
Sustainable Development Goals ◽  
Problem Based Learning ◽  
Problem Analysis ◽  
Science And Society ◽  
Key Concepts ◽  
Development Goals ◽  
Face Complex ◽  
Learning Principles

The aim of this paper is to raise awareness of problem-based learning (PBL) and more specifically the problem analysis as a set of learning principles and practices offering the potential to bridge higher education to the complexities and uncertainties of science and society. Literature on PBL often argues that PBL supports education aimed at developing students’ competences in problem-solving. However, as we increasingly face complex and wicked problems, we cannot assume that problems can be solved based on existing methods and theories; the focus needs to shift from problem-solving to problem analysis and complexity navigation. This paper describes and discusses the need to focus on authenticity, exemplarity, and interdisciplinary as key educational concepts when developing competencies to analyze complex problems. In addressing these key concepts, the paper touches upon the didactical implications of problem analysis as the most important competence to achieve during higher education and as essential when moving beyond education and into a complex world where problems are always interrelated, as reflected in the UN’s Sustainable Development Goals.

scholarly journals PENERAPAN MODEL PEMBELAJARAN TERPADU TIPE NESTED DALAM PEMBELAJARAN PEMECAHAN MASALAH MATEMATIKA PADA MATERI INDUKSI MATEMATIKA

2020 ◽  
Vol 6 (2) ◽  
pp. 113
Author(s):  
Aan Armini
Keyword(s):  
Problem Solving ◽  
Positive Attitude ◽  
Mathematical Problem ◽  
Learning Model ◽  
Mathematical Induction ◽  
Mathematical Problem Solving ◽  
Integrated Learning ◽  
School Year ◽  
Post Test ◽  
Students Attitudes

Through classroom action research, researchers seek to improve students 'mathematical problem solving abilities on mathematical induction material by using nested integrated learning methods and explore students' attitudes towards the application of the given learning model. The study was conducted during two cycles which included four stages of learning, namely: planning, implementation, observation, and reflection. The study was conducted in the odd semester of the 2019/2020 school year involving 34 students of class XI MIPA-2 SMAN 1 Garawangi, Kuningan. There are 2 types of research instruments used, namely tests and questionnaires. Based on the test results, it can be seen that in the post-test, the N-Gain index obtained was 0.61 (moderate). Meanwhile, based on the results of the questionnaire, it can be seen that 100% of students show a positive attitude. Thus, it can be concluded that the nested type integrated learning model can improve students' mathematical problem solving abilities on mathematical induction material and get a good appreciation with the presence of a positive attitude shown by all participants.

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