The Teaching of Heuristic Problem-Solving Strategies in Elementary Calculus

1974 ◽  
Vol 5 (1) ◽  
pp. 36-46
Author(s):  
John F. Lucas
Keyword(s):  
Problem Solving ◽  
Solution Process ◽  
Problem Solver ◽  
Thought Processes ◽  
Heuristic Strategies ◽  
Efficient Performance ◽  
Elementary Calculus ◽  
Problem Solving Strategies ◽  
Human Problem ◽  
Heuristic Problem Solving

Research in the area of computer simulation of human thought processes indicates that the solution of every problem involves the element of search in a space of many alternatives (Newell, Shaw, & Simon, 1958). For human problem solving, the space may conceivably include infinitely many alternatives; however, humans appear to exhibit more efficient performance than exhaustive scanning or purely random trial and error. Human problem solving is characterized by heuristic strategies. These higher-order processes (heuristics) guide the search, enabling the problem solver to select from a reduced set of alternatives and to order his solution process in a sequence of steps; they are tentative rules of thumb that are based on experience or plausible assumptions and that apply generally to problems (Pylyshyn, 1963).

scholarly journals Using process data to understand problem-solving strategies and processes for drag-and-drop items in a large-scale mathematics assessment

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Yang Jiang ◽  
Tao Gong ◽  
Luis E. Saldivia ◽  
Gabrielle Cayton-Hodges ◽  
Christopher Agard
Keyword(s):  
Problem Solving ◽  
Time Allocation ◽  
Large Scale ◽  
Solution Process ◽  
Process Data ◽  
Mathematics Assessments ◽  
Assessment Design ◽  
Eighth Grade Students ◽  
Problem Solving Strategies ◽  
Drag And Drop

AbstractIn 2017, the mathematics assessments that are part of the National Assessment of Educational Progress (NAEP) program underwent a transformation shifting the administration from paper-and-pencil formats to digitally-based assessments (DBA). This shift introduced new interactive item types that bring rich process data and tremendous opportunities to study the cognitive and behavioral processes that underlie test-takers’ performances in ways that are not otherwise possible with the response data alone. In this exploratory study, we investigated the problem-solving processes and strategies applied by the nation’s fourth and eighth graders by analyzing the process data collected during their interactions with two technology-enhanced drag-and-drop items (one item for each grade) included in the first digital operational administration of the NAEP’s mathematics assessments. Results from this research revealed how test-takers who achieved different levels of accuracy on the items engaged in various cognitive and metacognitive processes (e.g., in terms of their time allocation, answer change behaviors, and problem-solving strategies), providing insights into the common mathematical misconceptions that fourth- and eighth-grade students held and the steps where they may have struggled during their solution process. Implications of the findings for educational assessment design and limitations of this research are also discussed.

From the Editorial Panel: Fostering Flexible Mathematical Thinking

2012 ◽  
Vol 106 (4) ◽  
pp. 245
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Multiple Representations ◽  
Mathematical Understanding ◽  
Thought Processes ◽  
Problem Solving Strategies ◽  
Flexible Thinking ◽  
Thinking Differently ◽  
Ability And Willingness

Understanding and making connections is at the heart of flexible mathematical thinking. Flexible thinking is generally observed in students' ability and willingness to work with multiple representations, but it can also be seen in their facility in adapting problem-solving strategies when faced with novel situations, reversing thought processes, viewing notation as a process as well as an object, interpreting others' ideas, and posing problems. Although teachers may characterize flexible mathematical thinking differently according to context, we can probably all agree that providing students with opportunities to engage in flexible mathematical thinking is vital for fostering the kind of mathematical understanding that we want them to have

Metacognition of Problem-Solving Strategies in Brazil, India, and the United States

2007 ◽  
Vol 7 (1-2) ◽  
pp. 1-25 ◽  
Author(s):  
Brian Wiley ◽  
C. Dominik Güss
Keyword(s):  
United States ◽  
Problem Solving ◽  
The United States ◽  
Uncertainty Avoidance ◽  
Metacognitive Strategies ◽  
Thought Processes ◽  
Combination Strategy ◽  
Problem Solving Strategies ◽  
Production Strategy ◽  
The U.S

AbstractMetacognition, the observation of one's own thinking, is a key cognitive ability that allows humans to influence and restructure their own thought processes. The influence of culture on metacognitive strategies is a relatively new topic. Using Antonietti's, Ignazi's and Perego's questionnaire on metacognitive knowledge about problem-solving strategies (2000), five strategies in three life domains were assessed among student samples in Brazil, India, and the United States (N=317), regarding the frequency, facility, and efficacy of these strategies. To investigate cross-cultural similarities and differences in strategy use, nationality and uncertainty avoidance values were independent variables. Uncertainty avoidance was expected to lead to high frequency of decision strategies. However, results showed no effect of uncertainty avoidance on frequency, but an effect on facility of metacognitive strategies. Comparing the three cultural samples, all rated analogy as the most frequent strategy. Only in the U.S. sample, analogy was also rated as the most effective and easy to apply strategy. Every cultural group showed a different preference regarding what metacognitive strategy was most effective. Indian participants found the free production strategy to be more effective, and Indian and Brazilian participants found the combination strategy to be more effective compared to the U.S. participants. As key abilities for the five strategies, Indians rated speed, Brazilians rated synthesis, and U.S. participants rated critical thinking as more important than the other participants. These results reflect the embedded nature and functionality of problem solving strategies in specific cultural environments. The findings will be discussed referring to an eco-cultural framework.

Explicit Heuristic Training as a Variable in Problem-Solving Performance

1979 ◽  
Vol 10 (3) ◽  
pp. 173-187 ◽  
Author(s):  
Alan H. Schoenfeld
Keyword(s):  
Problem Solving ◽  
Explicit Instruction ◽  
The Other ◽  
Heuristic Strategies ◽  
Problem Solving Strategies ◽  
The Impact

This experiment examined the impact that explicit instruction in heuristic strategies, above and beyond problem-solving experience, has on students' problem-solving performance. Two groups of students received training in problem solving, spent the same amount of time working on the same problems, and saw identical problem solutions. But half the students were given a list of five problem-solving strategies and were shown explicitly how the strategies were used. The heuristics group significantly outperformed the other students on posttest problems that were similar to, but not isomorphic to, those used in the problem sets. This lends credence to the idea that explicit instruction in heuristics makes a difference--an idea further supported by the transcripts of students solving the problems out loud.

Simulation of Human Problem-Solving Method

SIMULATION ◽  
1964 ◽  
Vol 3 (2) ◽  
pp. 64-70
Author(s):  
D.L. Johnson ◽  
A.D.C. Holden
Keyword(s):  
Problem Solving ◽  
Digital Computer ◽  
Small Region ◽  
Exhaustive Search ◽  
Trial And Error ◽  
Thought Processes ◽  
Human Thought ◽  
Human Problem ◽  
At Will ◽  
Made In

One of the most intriguing and potentially important applications of the digital computer is in the simula tion of human thought processes. The objects of thought when suitably coded can be transformed, classified and stored within the computer at will. The predominant charactertistic of human thought processes is their generality. To make any progress in the simulation of such processes, it is first necessary to isolate a small region and examine it in isolation. As progress is made in one region, it can be ex panded and generalized to include a wider field, and it is likely that many of the methods used in a re stricted field will be susceptible to modification for use in a larger area. It is desirable to work initially in a region in which the relationships between the ob jects of thought are clearly defined. This report deals with the problem of finding se quences of transformations which constitute proofs of trigonometric identities. The method described need not be confined to this particular problem, but could easily be used in other fields if the allowable transformations are known. The behaviour of a ma chine which has been programmed to carry out this process is described in detail and its responses, when several identities were presented to it for proof, are given. No attempt is made to use the method of finding proofs by exhaustive search, even though in this case such a search is quite feasible, since the number of "basic" trigonometric transformations which can be applied to a given function is relatively small. It is considered here that such repetitive "trial and error" methods are less interesting than the methods which we shall discuss. It is desirable to decide on the best transformation for a particular problem by compar ing the characteristics of the problem with the prop erties of each transformation in such a way that the machine's performance will improve with experi ence. Exhaustive search methods become useless when the number of possible decisions at each step becomes large.

System Failures

2019 ◽  
pp. 91-112
Author(s):  
William B. Rouse
Keyword(s):  
Pattern Recognition ◽  
Problem Solving ◽  
Complex Systems ◽  
Mental Models ◽  
Social Phenomena ◽  
Team Coordination ◽  
System Failures ◽  
Operations And Maintenance ◽  
Problem Solving Strategies ◽  
Human Problem

This chapter focuses on the operations and maintenance of new product and service offerings once they have been deployed; in particular, it addresses dealing with system failures. Addressing system failures is an important aspect of operating and maintaining complex systems, particularly when laced with behavioral and social phenomena. Despite advances in technology and automation, humans will inevitably have roles in addressing failures when detection, diagnosis, and compensation cannot be automated. Human problem-solving involves a mix of pattern recognition and structural sleuthing based on mental models for taskwork and teamwork. Training and aiding can enhance human problem-solving performance by fostering problem-solving strategies and tactics, as well as team coordination.

scholarly journals PROBLEM SOLVING IN THE CONTEXT OF COMPUTATIONAL THINKING

2019 ◽  
Vol 8 (2) ◽  
pp. 109
Author(s):  
Swasti Maharani ◽  
Muhammad Noor Kholid ◽  
Lingga Nico Pradana ◽  
Toto Nusantara
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Planning Process ◽  
Solution Process ◽  
Computational Thinking ◽  
Problem Solver ◽  
Global Movement ◽  
Generalization Stage ◽  
Relationship Of ◽  
The Relationship

Computational thinking is needed in the 21st century, where we live in an era of digitalization. Also, there is a global movement to incorporate computational thinking into the education curriculum, especially Mathematics education. The different of this research with others is this research compares the Polya problem solving and computational thinking. This research was conducted to find out how the relationship/relationship of the Polya problem-solving with the steps of computational thinking. The method used in this research is descriptive qualitative. The subject of this study was mathematics education students. The results showed that the relationship between problem-solving and computational thinking of respondent when solving the problem is when defining the problem in the context of problem-solving, the respondent performs the stage of decomposition and abstraction in the context of computational thinking. During the planning process of the solution process, respondents carried out the generalization stage. When the scene is carrying out the plan and the problem solver to look back to evaluate the solution, the respondent performs the debugging and algorithmic steps.

Knowledge Representation in Human Problem Solving: Implications for Expert System Design

1988 ◽  
Vol 32 (5) ◽  
pp. 395-398 ◽  
Author(s):  
David C. Gibson ◽  
Gavriel Salvendy
Keyword(s):  
Expert System ◽  
Problem Solving ◽  
Knowledge Representation ◽  
Expert Systems ◽  
System Design ◽  
Problem Representation ◽  
Problem Solver ◽  
Problem Type ◽  
Type Transformation ◽  
Human Problem

The study focuses on the identification of the underlying representational properties of human problem solving and their application to expert systems. In this study the interaction between problem representation (procedural, conceptual, unstructured) and problem type (transformation, arrangement, inducing structure) was observed. The results of this study indicate partly that quantitative and qualitative differences in problem solving performance can be attributed to the form of knowledge representation employed by the problem solver. It is suggested that expert systems could be implemented with different shells or structures according to problem characteristics.

scholarly journals Heuristic: Its Influence to the Mathematics Anxiety and Coping Mechanism

2015 ◽  
Vol 2 ◽  
pp. 192-199
Author(s):  
Ma. Aletha V. Hobilla ◽  
Belinda M. Go
Keyword(s):  
Problem Solving ◽  
Mathematics Anxiety ◽  
Math Anxiety ◽  
Coping Mechanisms ◽  
Rank Test ◽  
Coping Mechanism ◽  
Heuristic Strategies ◽  
Significant Difference ◽  
Before And After ◽  
Problem Solving Strategies

This is a quantitative-qualitative study that aims to determine the influence of heuristic or problem-solving strategies (PS) to the mathematics anxiety of 97 or 87% of the Bachelor of Elementary Education (BEEd) second-year students of Western Visayas College of Science and Technology enrolled in the subject Problem Solving during the second semester, SY 2014-2015. It also aims to find out the coping mechanisms and perceived causes of mathematics anxiety of the participants. For the quantitative data, a one-group pretest-posttest design was used. The Mathematics Anxiety-Apprehension Survey (MAAS) was administered before the start of the intervention and at the end of the intervention. For the qualitative data, the participants were asked to write a journal on the perceived causes of their math anxiety and their coping mechanism. Personal interviews were conducted to participants with high math anxiety regarding their coping mechanisms. The statistical tools used were the mean, standard deviation, Wilcoxon Signed Rank test, and Kruskal-Wallis Test. The test in the hypothesis was set at .05 alpha level. Results showed that, as an entire group, and when grouped according to sections, the participants have “moderate” mathematics anxiety. Likewise, the participants have “moderate” mathematics anxiety before and after learning heuristic strategies. There is no significant difference in the level of mathematics anxiety when the participants were grouped according to sections and before and after learning heuristic strategies. The perceived causes of mathematics anxiety of the participants were mostly attributed to their bad experience with their teachers in basic education such as “terror” teachers, physical or verbal punishment, as well as time pressure during math examinations/quizzes. Another identified factor was the quality of teaching like teachers spoke too fast or spoke with a low voice. Some of the common coping mechanisms of the participants were “studying harder”, “utilizing problem-solving strategies or heuristics”, “ asking help from peers”, “listening attentively during class “, and “developing positive attitude” in mathematics.

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