Reasoning as an Associative Process: II. “Direction” in Problem Solving as a Function of Prior Reinforcement of Relevant Responses

1956 ◽  
Vol 2 (3) ◽  
pp. 501-507 ◽  
Author(s):  
Abe J. Judson ◽  
Charles N. Cofer ◽  
Sidney Gelfand
Keyword(s):  
Problem Solving ◽  
Problem Solution ◽  
Complex Response ◽  
Associative Process ◽  
Response Systems ◽  
Verbal Problem ◽  
A Chain ◽  
Set Up

Several studies are described in which relevant patterns of verbal associations, set up by learning in the first stage of the experiment, are shown to be associated with the frequencies of certain types of solution in the Maier two string and hat rack problems. It is also shown, in the case of a simple verbal problem, that problem solution requiring choice of members of a chain of free associations is affected by prior reinforcement of one member of the chain. These investigations are interpreted as giving support to and indicating the fruitfulness of a conception of set or direction in problem solving as consisting of complex response systems or habit families.

Reasoning as an Associative Process: I. “Direction” in a Simple Verbal Problem

1956 ◽  
Vol 2 (3) ◽  
pp. 469-476 ◽  
Author(s):  
Abe J. Judson ◽  
Charles N. Cofer
Keyword(s):  
Problem Solving ◽  
Classification Problems ◽  
Associative Process ◽  
Response Systems ◽  
Verbal Problem

Two investigations are described in which series of verbal classification problems were used to study two hypotheses concerning the nature of set or direction in problem solving. The evidence is considered to support the hypotheses, which state that direction is a function of priority of stimulus activation of response systems under certain conditions and of activation of strong and pervasive response systems previously acquired by Ss under other conditions.

scholarly journals Different Perspectives on Success in Solving Stand-Alone Problems by 14 to 15-Year-Old Students / Različite prespektive o uspješnosti 14 i 15-godišnjaka u rješavanju izoliranoga problema

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Nives Baranović ◽  
Branka Antunović-Piton
Keyword(s):  
Elementary Schools ◽  
Problem Solving ◽  
Secondary School ◽  
Mathematical Task ◽  
Mathematical Concepts ◽  
Urban Elementary Schools ◽  
8Th Grade ◽  
Verbal Problem ◽  
Set Up ◽  
Problem Solving Process

The paper defines a special type of problem tasks and considers its didactic potential, as well as the success of students in solving the selected problem. The research instrument used is a geometrical task from the National Secondary School Leaving Exam in Croatia (State Matura). The geometrical task is presented in three versions: as a verbal problem, as a verbal problem with a corresponding image and as a problem in context. The material analysed in the present paper was collected from 182 students in 7th and 8th grade of Croatian urban elementary schools. The didactic potential is considered from the aspect of use of mathematical concepts and connections. The success of students in problem-solving is considered from the aspect of implementation of the problem-solving process and producing correct answers, depending on the manner in which the tasks are set up. The results show that the stand-alone problem, as a special type of problem task, has considerable didactic potential. However, the students’ skills of discovering and connecting mathematical concepts and their properties are underdeveloped. In addition, the manner in which the tasks are set up considerably affects the process of solving the task and consequently the success of that process. Based on the results of the research, proposals are given for application of stand-alone problems in teaching mathematics.Key words: isolated problem; mathematical task; problem solving; problem evaluation.  --- U radu se definira posebna vrsta problemskoga zadatka te se razmatra njegov didaktički potencijal kao i uspješnost učenika u rješavanju odabranoga problema. Instrument istraživanja je geometrijski zadatak s državne mature koji se postavlja u tri inačice: kao tekstualni problem, kao tekstualni problem uz odgovarajuću sliku te kao zadatak u kontekstu. U istraživanju je sudjelovalo 182 učenika 7. i 8. razreda hrvatskih gradskih osnovnih škola. Didaktički potencijal razmatra se s aspekta iskoristivosti matematičkih koncepata i veza, a uspješnost učenika u rješavanju problema razmatra se s aspekta provedbe procesa rješavanja i otkrivanja točnoga rješenja ovisno o načinu postavljanja zadatka. Rezultati pokazuju da promatrani problem kao posebna vrsta problemskoga zadatka ima veliki didaktički potencijal, ali da učenici imaju nedovoljno razvijene vještine otkrivanja i povezivanja matematičkih koncepata i njihovih svojstava. Osim toga, način postavljanja zadatka značajno utječe na proces rješavanja, a posljedično i na uspješnost određivanja rješenja. Na temelju rezultata daju se prijedlozi primjene opisane vrste problema u nastavi Matematike.Ključne riječi: izolirani problem; matematički zadatak; rješavanje problema; vrednovanje problema

In Search of Somatic Precursors of Spontaneous Insight

2018 ◽  
Vol 32 (3) ◽  
pp. 97-105 ◽  
Author(s):  
Wangbing Shen ◽  
Yuan Yuan ◽  
Chaoying Tang ◽  
Chunhua Shi ◽  
Chang Liu ◽  
...  
Keyword(s):  
Problem Solving ◽  
Direct Evidence ◽  
Electrodermal Activity ◽  
Cardiovascular Responses ◽  
Solution Time ◽  
Problem Solution ◽  
Insight Problem ◽  
Creative Insight ◽  
Insight Problem Solving ◽  
Analytic Problem

Abstract. A considerable number of behavioral and neuroscientific studies on insight problem solving have revealed behavioral and neural correlates of the dynamic insight process; however, somatic correlates, particularly somatic precursors of creative insight, remain undetermined. To characterize the somatic precursor of spontaneous insight, 22 healthy volunteers were recruited to solve the compound remote associate (CRA) task in which a problem can be solved by either an insight or an analytic strategy. The participants’ peripheral nervous activities, particularly electrodermal and cardiovascular responses, were continuously monitored and separately measured. The results revealed a greater skin conductance magnitude for insight trials than for non-insight trials in the 4-s time span prior to problem solutions and two marginally significant correlations between pre-solution heart rate variability (HRV) and the solution time of insight trials. Our findings provide the first direct evidence that spontaneous insight in problem solving is a somatically peculiar process that is distinct from the stepwise process of analytic problem solving and can be represented by a special somatic precursor, which is a stronger pre-solution electrodermal activity and a correlation between problem solution time and certain HRV indicators such as the root mean square successive difference (RMSSD).

Sharing of Knowledge and Problem Solving When Teammates Have Diverse Hearing Status

2021 ◽  
pp. 104649642110102
Author(s):  
Michael Stinson ◽  
Lisa B. Elliot ◽  
Carol Marchetti ◽  
Daniel J. Devor ◽  
Joan R. Rentsch
Keyword(s):  
Problem Solving ◽  
Hard Of Hearing ◽  
The Other ◽  
Postsecondary Students ◽  
Problem Solution ◽  
Group Problem ◽  
Team Members ◽  
Group Problem Solving ◽  
Complete Problem ◽  
Hearing Status

This study examined knowledge sharing and problem solving in teams that included teammates who were deaf or hard of hearing (DHH). Eighteen teams of four students were comprised of either all deaf or hard of hearing (DHH), all hearing, or two DHH and two hearing postsecondary students who participated in group problem-solving. Successful problem solution, recall, and recognition of knowledge shared by team members were assessed. Hearing teams shared the most team knowledge and achieved the most complete problem solutions, followed by the mixed DHH/hearing teams. DHH teams did not perform as well as the other two types of teams.

scholarly journals German Teacher Educators' Conceptions About Teaching Problem Solving in Mathematics Classroom - an Obstalce to a Large-Scale Dissemination?!

2018 ◽  
Vol 12 (2) ◽  
pp. 77-97
Author(s):  
Ana Kuzle
Keyword(s):  
Professional Development ◽  
Problem Solving ◽  
Mathematics Teacher ◽  
Large Scale ◽  
Teacher Educators ◽  
Mathematics Classroom ◽  
Research Report ◽  
Mathematics Teacher Educators ◽  
Set Up ◽  
Teaching Problem

Problem solving in Germany has roots in mathematics and psychology but it found its way to schools and classrooms, especially through German Kultusministerkonferenz, which represents all government departments of education. For the problem solving standard to get implemented in schools, a large scale dissemination through continuous professional development is very much needed, as the current mathematics teachers are not qualified to do so. As a consequence, one organ in Germany focuses on setting up courses for teacher educators who can “multiply” what they have learned and set up their own professional development courses for teachers. However, before attaining to this work, it is crucial to have an understanding what conceptions about teaching problem solving in mathematics classroom mathematics teacher educators hold. In this research report, I focus on mathematics teacher educators’ conceptions about problem solving standard and their effects regarding a large-scale dissemination.

scholarly journals Adaptabilidade de Objetos de Aprendizagem usando Calibragem e Sequenciamento Adaptativo de Exercícios

2018 ◽  
Vol 26 (1) ◽  
pp. 70
Author(s):  
Rômulo César Silva ◽  
Alexandre Ibrahim Direne ◽  
Diego Marczal ◽  
Ana Carla Borille ◽  
Paulo Ricardo Bittencourt Guimarães ◽  
...  
Keyword(s):  
Problem Solving ◽  
Empirical Study ◽  
Cognitive Skills ◽  
Learning Objects ◽  
Skill Level ◽  
Problem Solution ◽  
Algebraic Expressions ◽  
Student Skill ◽  
Definition Of ◽  
Two Parameters

The work approaches theoretical and implementation issues of a framework for creating and executing Learning Objects (LOs) where problem-solving tasks are ordered according to the matching of two parameters, both calculated automatically: (1) student skill level and (2) problem solution difficulty. They are formally defined as algebraic expressions. The definition of skill level is achieved through a rating-based measure that resembles the ones of game mastery scales, while the solution difficulty is based on mistakes and successes of learners to deal with the problem. An empirical study based on existing students data demonstrated the suitability of the formulas. Besides, the motivational aspects of learning are considered in depth. In this sense, it is important to propose activities according to the student’s level of expertise, which is achieved through presenting students with exercises that are compatible with the difficulty degree of their cognitive skills. Also, the results of an experiment conducted with four highschool classes using the framework for the domain of logarithmic properties are presented.

Studies of Verbal Problem Solving. 2. Prediction of Performance from Sentence-Processing Scores

1978 ◽  
Author(s):  
Nicholas A. Bond ◽  
Donald McGregor ◽  
Kathy Schmidt ◽  
Mary Lattimore ◽  
Joseph W. Rigney
Keyword(s):  
Problem Solving ◽  
Sentence Processing ◽  
Verbal Problem

Discovering mathematical knowledge by students as the way to successful learning of mathematics

2020 ◽  
pp. 317-332
Author(s):  
Anna Rybak
Keyword(s):  
Problem Solving ◽  
Mathematics Teaching ◽  
Theoretical Background ◽  
Mathematics Problem Solving ◽  
Whole Process ◽  
Learning Mathematics ◽  
Creative Learning ◽  
Set Up ◽  
The University

Students in many countries have problems learning mathematics. Many students do not like mathematics. It is also a problem for teachers. The question has to be answered: Why does math education cause so many problems? We have set up the Centre for Creative Learning of Mathematics at the University of Bialystok (Poland). It is a place where we try to create appropriate athmosphere and circumstances for students of all ages to become active discoverers of mathematics, not just passive recipients of knowledge from books or teachers. As a theoretical background we took ideas from Tamás Varga, Zofia Krygowska, the theory of constructivism, the strategy of functional mathematics teaching and problem-solving method. Lessons and workshops for students in our Centre are based on the combination of the following ideas: The participants solve practical or theoretical problems (problem solving method) and carry out concrete, representative and abstract activities (strategy of functional mathematics teaching by Z. Krygowska) which help them discover and formulate knowledge (constructivism). The whole process corresponds very well to some of T. Varga's important ideas or his conviction of the main objectives of mathematics teaching: Students explore the knowledge themselves and think independently. The subject of mathematics is transformed into a thought formulation process in which students turn from the role of passive recipients to the active knowledge creation. Classification: A80. Keywords: T. Varga, Z. Krygowska, constructivism, strategy of functional teaching of mathematics, problem solving method, creative learning

Good Old-Fashioned AI and Genetic Algorithms: An Exercise in Translation Scholarship

2005 ◽  
Author(s):  
Herbert A. Simon
Keyword(s):  
Problem Solving ◽  
Theorem Proving ◽  
Mathematical Expression ◽  
Electrical Circuit ◽  
Problem Solution ◽  
Problem Statement ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Problem Solving Process

In both the GA and GOFAI traditions, invention or design tasks are viewed as instances of problem solving. To invent or design is to describe an object that performs, in a range of environments, some desired function or serves some intended purpose; the process of arriving at the description is a problem-solving process. In problem solving, the desired object is characterized in two different ways. The problem statement or goal statement characterizes it as an object that satisfies certain criteria of structure and/or performance. The problem solution describes in concrete terms an object that satisfies these criteria. The problem statement specifies what needs to be done; the problem solution describes how to do it [9]. This distinction between the desired object and the achieved object, between problem statement and problem solution, is absolutely fundamental to the idea of solving a problem, for it resolves the paradox of Plato's Meno: How do we recognize the solution of a problem unless we already knew it in advance? The simple answer to Plato is that, although the problem statement does not define a solution, it contains the criteria for recognizing a solution, if and when found. Knowing and being able to apply the recognition test is not equivalent to knowing the solution. Being able to determine, for any given electrical circuit, whether it would operate, to a sufficiently good approximation, as a low-pass filter does not imply that one knows a design for a circuit that meets this condition. In asserting that we do not know the solution in advance, we must be careful to state accurately what the problem is. In theorem proving, for example, we may know, to the last detail, the expression we are trying to prove; what we do not know is what proof (what sequence of expressions, each following inferentially from the set of its predecessors) will terminate in the specified one. Wiles knew well the mathematical expression that is Fermat's last theorem; he spent seven years or more finding its proof. In the domain of theorem proving, the proof is the problem solution and the recognition criteria are the tests that determine whether each step in the proof follows from its predecessors and whether the proof terminates in the desired theorem.

Sign in / Sign up

Export Citation Format

Share Document