Why Malcolm Knowles’s Five Assumptions of Learners Matter

Oct. 20, 2022 / Frameworks & methodologies , Learning-experience design , Strategy

alt=

At Maestro, we’ve spent countless hours thinking about learning and what creates meaningful, memorable learning experiences. From this we’ve developed our four Learning Principles , each influenced by theories, studies, and concepts found throughout learning history and in the industry today.

Meet Malcolm Knowles, an educator who was passionate about adult learners and what makes them unique. Let’s get to know Knowles along with his five assumptions of adult learners, and how to implement them into your next course strategy.

Who was Dr. Malcolm Knowles?

Malcolm Shepherd Knowles (1913–1997) was a prolific American educator well known for popularizing the term andragogy for adult education. In 1935, Knowles began working under Eduard C. Linderman, another educator who was part of the revitalization of andragogy as a concept, and continued his pursuit of mastering the art of teaching adults in both formal and informal settings.

Knowles spent his career theorizing about how older people approach learning in a way that’s unique compared to children, and from this, he developed five assumptions about adult learners.

To better understand Malcolm Knowles’ definition of andragogy, let’s look into these assumptions and why they’re important for anyone creating learning for adults.

What Is Adult Learning Theory? And How to Use It to Get Better Learning Outcomes

Malcolm Knowles’ theory: Five assumptions of adult learners

1. self-concept: adults become more self-directed as they mature.

The first of Knowles’ assumptions is this: as adults move throughout life, they become more independent and self-directed. Adult learners want to have ownership over their learning journey. This is why learning experience platforms (LXPs) and the advancement of eLearning have been huge in the learning industry—these tools allow adult learners to take ownership of what they learn and how they learn it.

It can be easy to make assumptions about what learners might need—especially from the position of leadership, which might not be as connected to the day-to-day work of the employees who actually need the training. Instead, consider giving your learners some freedom to make their own choices in their learning journey, whether that’s by allowing them to choose their learning paths or how they receive their information.

2. Learner experience: Adults bring a wealth of experience to the learning process

The second assumption Malcolm Knowles made is about the learner experience. Unlike children who are frequently learning things for the first time without previous experience, adult learners bring the richness of past education, jobs, and life events to learning experiences. Basically, don’t assume your learners are beginners without first understanding the knowledge they bring to the table .

Even if the concepts and skills you’re introducing are new, remember that adult learners may have skills and lived experiences that they can reference to enrich their own process of discovery and growth. Finding ways to integrate this with discussion groups and debriefs can be an effective way to help your learners feel like you see the value they bring, too.

3. Readiness to learn: Adults want to learn things that help them accomplish relevant tasks

You might’ve heard that adults care a lot about the “why” behind learning, and that’s where Knowles’ next assumption about “readiness to learn” comes in. Unlike children, who absorb everything they can as they grow up, adult learners are more selective with what information they take in. Common questions you might hear learners ask include, “How will this help me?” or, “What’s really in it for me?”

This is why the planning stage of any eLearning course or training is pivotal: you need to make it clear from the beginning what your learners are taking away from it and why that matters . Develop activities in your courses that mimic real-world job scenarios, include interactive elements, and make sure that what learners walk away with is applicable to their everyday job role experience.

4. Orientation to learning: Adult learners want to solve problems

Similar to readiness to learn, Malcolm Knowles spoke of adult learner orientation, noting that adults move away from subject-based learning, which centers around simply knowing about a concept, towards problem-based learning, which focuses on knowledge that tangibly contributes to problem solving.

Scenario-based learning can be incredible for teaching your adult learners problem-solving skills while avoiding costly mistakes on the job. See how this style of learning can engage learners and help them perform better in their roles.

5. Motivation to learn: Adults rely on internal rather than external motivation

Finally, Knowles made an assumption about adult motivation to learn. While children have external sources of motivation to learn—including parents, teachers, or the societal push for higher education—once learners become adults, they no longer have those same external motivators. They get replaced by internal motivators, which are individual to each learner. 

Internal motivations for learners could be to get a raise or promotion, to improve their skills in a relevant area, or to improve their life both in and outside of the workplace. It’s important that companies spend time understanding what motivates their learners so that these motivators can be part of what shapes the learning development process.

How you approach adult learners will determine your success

With a new understanding of Malcolm Knowles’ concept of andragogy, think about applying these assumptions before your next course or training. At the end of the day, your learners want to feel that you believe in their talent, trust them to do well, and want to invest in their future. By applying Malcolm Knowles’s assumptions, you’ll be on your way to doing all three.

Keep learning about how to create great experiences for adult learners.

Learn how the Tell, Show, Do, Review approach to learning creates more-effective experiences.

Training the next generation of crypto traders

Our experiential, consumer-grade crypto learning academy is designed to deliver a comprehensive introduction to crypto trading for OKX’s 20 million users.

VetBloom A blockchain-based credentialing platform for veterinary specialties

Acist medical systems lifelike 3d product training to guide service techs on the job, best western hotels & resorts helping transform brand culture with fresh, energizing ilt.

  • The Simplest Way to Avoid the Research Fail of the Yellow Walkman
  • 5 Sets of Tried-and-True Resources for Instructional Designers
  • Are You Skipping the Validation Step? Why Piloting Your Learning Matters

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • View all journals
  • Explore content
  • About the journal
  • Publish with us
  • Sign up for alerts
  • Published: 04 June 2018

Collaborative problem-solving education for the twenty-first-century workforce

  • Stephen M. Fiore 1 ,
  • Arthur Graesser 2 &
  • Samuel Greiff 3  

Nature Human Behaviour volume  2 ,  pages 367–369 ( 2018 ) Cite this article

1611 Accesses

57 Citations

30 Altmetric

Metrics details

The complex research, policy and industrial challenges of the twenty-first century require collaborative problem solving. Assessments suggest that, globally, many graduates lack necessary competencies. There is a pressing need, therefore, to improve and expand teaching of collaborative problem solving in our education systems.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Pre-service teachers becoming researchers: the role of professional learning groups in creating a community of inquiry

  • Sandris Zeivots
  • , John Douglas Buchanan
  •  &  Kimberley Pressick-Kilborn

The Australian Educational Researcher Open Access 20 January 2023

Access options

Access Nature and 54 other Nature Portfolio journals

Get Nature+, our best-value online-access subscription

24,99 € / 30 days

cancel any time

Subscribe to this journal

Receive 12 digital issues and online access to articles

111,21 € per year

only 9,27 € per issue

Rent or buy this article

Prices vary by article type

Prices may be subject to local taxes which are calculated during checkout

Fiore, S. M. et al. Collaborative Problem Solving: Considerations for the National Assessment of Educational Progress (National Center for Educational Statistics, United States Department of Education, Washington DC, 2017).

Graesser, A. C. et al. in Assessment and Teaching of 21st Century Skills. Research and Applications (eds Care, E., Griffin, P. & Wilson, M.) Ch. 5 (Springer International Publishing, Cham, 2018); https://doi.org/10.1007/978-3-319-65368-6_5 .

PISA 2015 Results (Volume V): Collaborative Problem Solving (Organization for Economic Cooperation and Development, 2017); https://doi.org/10.1787/9789264285521-en

National Academies of Sciences, Engineering, and Medicine Education for Life and Work: Transferable Knowledge and Skills in the 21st Century (National Academies Press, Washington DC, 2012); https://doi.org/10.17226/13398

National Research Council Enhancing the Effectiveness of Team Science (National Academies Press, Washington DC, 2015); https://doi.org/10.17226/19007

The Royal Society Assessing Experimental Science in 11–18 Education: New Research Directions (Royal Society Press, 2016); https://royalsociety.org/~/media/events/2016/10/education-conference-report-12-october-2016.pdf

Hart Research Associates Falling Short? College Learning and Career Success (Association of American Colleges and Universities, 2015).

Critical Skills Survey (American Management Association, 2012); https://www.amanet.org/uploaded/2012-Critical-Skills-Survey.pdf

National Academies of Sciences, Engineering, and Medicine Building America’s Skilled Technical Workforce (National Academies Press, Washington DC, 2017); https://doi.org/10.17226/23472

Weinberger, C. J. Rev. Econ. Stat. 96 , 849–861 (2014).

Article   Google Scholar  

Download references

Author information

Authors and affiliations.

University of Central Florida, Orlando, FL, USA

Stephen M. Fiore

University of Memphis, Memphis, TN, USA

Arthur Graesser

University of Luxembourg, Luxembourg City, Luxembourg

Samuel Greiff

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Stephen M. Fiore .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article.

Fiore, S.M., Graesser, A. & Greiff, S. Collaborative problem-solving education for the twenty-first-century workforce. Nat Hum Behav 2 , 367–369 (2018). https://doi.org/10.1038/s41562-018-0363-y

Download citation

Published : 04 June 2018

Issue Date : June 2018

DOI : https://doi.org/10.1038/s41562-018-0363-y

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

Improving collaborative problem-solving skills via automated feedback and scaffolding: a quasi-experimental study with cpscoach 2.0.

  • Sidney K. D’Mello
  • Nicholas Duran
  • Angela E. B. Stewart

User Modeling and User-Adapted Interaction (2024)

  • John Douglas Buchanan
  • Kimberley Pressick-Kilborn

The Australian Educational Researcher (2023)

Exploring the effects of role scripts and goal-orientation scripts in collaborative problem-solving learning

Education and Information Technologies (2023)

Integrating a collaboration script and group awareness to support group regulation and emotions towards collaborative problem solving

  • Matias Rojas
  • Miguel Nussbaum
  • Danilo Alvares

International Journal of Computer-Supported Collaborative Learning (2022)

Multimodal modeling of collaborative problem-solving facets in triads

  • Zachary Keirn

User Modeling and User-Adapted Interaction (2021)

Quick links

  • Explore articles by subject
  • Guide to authors
  • Editorial policies

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

problem solving training was developed on the assumption that

  • Reference Manager
  • Simple TEXT file

People also looked at

Original research article, the effect of a training program based on mathematical problem-solving strategies on critical thinking among seventh-grade students.

problem solving training was developed on the assumption that

  • 1 Department of Curricula and Methods of Teaching Mathematics, Princess Alia University College, Al-Balqa Applied University, As-Salt, Jordan
  • 2 Department of Special Education, Princess Alia University College, Al-Balqa Applied University, As-Salt, Jordan

The present study aimed at investigating the effect of a training program based on mathematical problem-solving strategies on critical thinking skills among seventh-grade students in King Abdullah II schools of Excellence. The study adopted the quasi-experimental research approach. The participants of the study comprised of 29 male seventh graders. The participants were randomly distributed into a control group ( n = 14) and an interventional group ( n = 15). The study adopted the critical thinking skills test (75 items). The tests consisted of five subtests (identifying assumptions, deduction, conclusion, interpretation, and discussion). The interventional training program was a group of training situations complementary to the official curriculum. These situations were based on the strategy of building an organized list or a table, the strategy of finding a pattern, trial and error strategy, the strategy of using an equation or a law, the strategy of building a model or a diagram, the strategy of solving an easier problem, deletion strategy, go backward strategy, and logical justification strategy. The results showed that there were significant statistical differences in the critical thinking post-test scores between the control group ( M = 26.5714, SD = 3.95580) and the interventional group ( M = 43.6667, SD = 4.68534, t = 10.640, p = 0.000). The study concluded that the training program based on solving mathematical problems is an effective interventional tool to improve the seventh graders’ critical thinking skills. The study recommends reviewing the content of the curricula designed for the elementary stage in Jordan and including drills related to solving mathematical problems that aim to improve critical thinking skills of the elementary stage students.

Introduction

Learning has become a priority on the list of all countries that want to progress, as well as developed countries that want to continue to grow and progress, and learning is what leads to real progress and not formality ( Mounier-Jack et al., 2017 ), leads to more experiences, mastery and advanced skills and helps in facing the challenges and expanding knowledge of this changing era ( Hodges et al., 2020 ). Thus, researchers and educators have a heavy burden in searching for everything new to give the character of mastery to learning and make it more flexible, interesting, productive, and attractive to the student, so that the student is more receptive and involved in it ( Post, 2020 ).

Mathematical problems are considered a fertile field for training in various ways of thinking ( Shahrill et al., 2018 ). Mathematical problems involve an inferential construction that starts from the introductions of valid postulates and derives the results from them using the rules of logic, and this is considered a basis for logical thinking ( Hoogland et al., 2018 ). Mathematical problems in terms of their material and issues are characterized by being logical and objective, which makes them a good mediator to develop creative thinking and problem-solving skills, this confirms that mathematics is rich in mathematical situations and exercises, which makes students able to distinguish between the elements of the situation, perceive the relationship, planning, and acquire mathematical insight and deep understanding ( Hidajat and Sa’dijah, 2019 ).

Problem-solving and mathematical problem-solving are closely related to thinking skills, especially critical thinking that helps students test evidences, explain contradictions, make judgments, reach appropriate solutions, analyze data, and deal with them with depth, breadth and logic ( Simamora and Saragih, 2019 ). Critical thinking and problem-solving include an aspect of creativity because each of them can lead to ideas that may be unusual or unexpected and useful at the same time ( Shanta and Wells, 2020 ). The development of any skill needs the development of the other skills because critical thinking is a special class of problem-solving behavior ( Alcantara and Bacsa, 2017 ).

Several studies have recommended the adoption of teaching strategies that focus on bringing about integration between problem-solving and thinking skills by presenting situations in which possible alternatives are presented, allegations are presented and debated by presenting arguments, decisions are taken and judged ( Kum et al., 2019 ; Samawi et al., 2019 ; Simamora and Saragih, 2019 ). In the same context, the National Council of Teachers of Mathematics (NCTM) recommended the adoption of teaching strategies that employ interactive activities based on a dialog between the instructor and students and between the students themselves and that are built by presenting new situations to students ( Joung and Byun, 2021 ).

Among the goals mentioned in the curricula of the primary and secondary stages in Jordan was to develop student’s ability to think logically and prove, and to acquire positive trends toward inquiry, innovation, and research. In addition, educational psychologists focus a lot on the study of cognitive methods and strategies for problem-solving as one of the most important components of thinking necessary for learning and education ( Momany et al., 2017 ).

Those who follow the results of the studies that dealt with mathematical thinking find that the students’ level of mathematical thinking is below standard, and teachers of basic and intermediate stages in Jordan do not direct their teaching toward an interest in mathematical thinking that is educationally acceptable in general, which calls for an interest in solving mathematical problems and their programs provided to students ( Mubark, 2012 ; Aljaberi, 2014 ; Star, 2018 ).

There is no doubt that the call for interest in mathematical issues and their programs presented to students necessarily leads to an investigation of their attitudes toward this subject and requires their research, in many years, as there is a belief by educators that the student’s attitudes toward mathematics in general, and mathematical issues in particular, affect the extent of his/her acceptance concepts and experiences, as well as affecting the extent of the student’s familiarity with its utilization ( Mairing, 2017 ). Therefore, it is necessary to do everything necessary to develop the student’s positive attitudes toward the mathematical issues he/she is learning, as well as improve the negative attitudes toward them as well.

Kenedi et al. (2019) suggest that solving mathematical problem can help students improve their analytical abilities, and use these abilities in different situations, as well as help them learn mathematical facts, skills, concepts, principles, and the interrelationships between them, understand issues in a deeper way, and retain information for a longer period and improve students’ motivation toward learning, and make it more fun and exciting for them.

Therefore, those interested in teaching mathematics advocate that all students experience problem-solving as part of their school mathematics. Problem-solving is the essence and soul of mathematics, and it is an important part of the work of mathematicians. Hence, students could better learn about the nature of mathematics and the activities of mathematicians by solving mathematical problems.

The Study Problem and Its Hypotheses

Jordanian students suffer from weakness in mathematics in general, and in particular solving the mathematical question. One of the indicators of this is the results of the Program for International Students Assessment (PISA) administered to primary 10th grade students. Jordan was ranked 61 out of 65 countries with an achievement below the international average ( Ababneh et al., 2016 ). In terms of students’ performance in mathematics, Jordan was ranked in 2012 in terms of the “Trends in International Mathematics and Science Study” (TIMSS) test, in which the eighth grade students participated in 2011 ( Ashraf, 2018 ). The report issued by the “International Association for the Evaluation of Educational Achievement” (IEA) stated that the performance of Jordanian students in mathematics ranked 2 out of 13 participating countries, with an average below the mean ( Abu Tayeh et al., 2018 ).

In light of what has been reviewed about the reality of the performance of Jordanian students in international and national tests in mathematics, and from the standpoint of seeking improvement and development in the processes of learning and education and upgrading to the stage of global competition in the knowledge society, keeping pace with the rapid technological development, facing the challenges of the present and future possibilities, and to develop thinking skills and problem-solving that are the ultimate goal of learning and teaching, the need has arisen to employ teaching strategies that enable students to reach higher stages in thinking and develop their ability to solve problems in a social, interactive, and cooperative context. The “National Center for Human Resource Development” (NCHRD) in Jordan conducted a national study that aimed to identify the extent to which teachers activate interactive teaching strategies in the classroom. The results showed that 2.16% of teachers only employ those strategies ( Bawaneh and Moumene, 2021 ). Therefore, the study problem can be identified by addressing the following main question:

What is the effect of a training program based on mathematical problem-solving strategies on critical thinking among seventh-grade male students in King Abdullah II Schools of Excellence?

Previous Literature Studies

Simbolon et al. (2017) carried out a study that sought to investigate the effect of an electronic problem-solving training program based on using Macromedia Flash on the eighth grade students’ critical thinking skills. The study adopted the experimental research approach through recruiting 25 eighth grade students. The results of the study showed that teachers were able to manage the problem-solving learning strategies through the use of Macromedia Flash. In addition, the results showed that the electronic training program significantly improved students’ critical thinking skills.

Jarbou (2014) conducted a study aimed at identifying the effect of reciprocal teaching on the development of mathematical thinking and attitudes toward mathematics among the eighth grade students in Gaza City, Palestine. The participants were (60) students, who were assigned into two groups: an experimental number of (30) students who were taught by the method of reciprocal teaching, and a control and the number of its members (30) students who were taught in the usual way. A mathematical reasoning test and an attitude scale were used. The findings indicated that “there were statistically significant differences between the mean scores of the experimental and control groups for the test of mathematical thinking in favor of the experimental group that was taught using the reciprocal teaching.”

Al-Btoush and Al-Darabkeh (2017) performed a study that sought to investigate the effect of a training program based on solving future problems on the critical thinking skills among gifted students at “King Abdullah II for Excellence School.” The study adopted the quasi-experimental research approach. The study sample consisted of 55 students who were distributed into an experimental group ( n = 28) and a control group ( n = 27). The training program was constructed based on the curricula syllabuses and focused on future problem-solving. The results of the study showed that there were significant statistical differences at a significance level of (α ≤ 0.05) between the controlled group and the experimental group in favor of the latter in all critical thinking skills due to the adopted training program based on solving future problems.

In addition, as indicated in Yana’s (2004) study, which aimed to investigate the impact of the future problem-solving strategy on the development of positive thinking skills and self-concept among a sample of university students at New York University, the study sample consisted of 72 students randomly assigned to two experimental and controlled groups, each of 36 students. The experimental group received a total of 22 training sessions on the program of solving future problems for a period of 1 month. The results of the study showed that there was a statistically significant improvement in positive thinking skills among the experimental group subjects compared to their peers in the controlled group.

Study Hypotheses

This study sought to test the following hypothesis—there are statistically significant differences in the critical thinking skills at the level (α = 0.05) between the mean scores of seventh-grade male students in the interventional and controlled groups due to the electronic training program based on mathematical problem-solving strategies.

The Importance of the Study and Its Justification

The theoretical importance of this study is that it may pave the way for new studies addressing the impact of mathematical problem-solving on critical thinking skills, especially in light of the significant lack of local and regional studies that have dealt with this topic.

In terms of practical importance, this study provides teachers with a learning and teaching strategy that is used to help students understand and solve the mathematical issue in a social context shaded by an atmosphere of democracy, communication, and cooperative work, in which thinking skills are developed and monitored, and in line with global trends in the development of learning and teaching processes. This is done under the umbrella of the constructive approach that takes into account individual differences and developmental requirements of students, through the application of the electronic training program that contains a large number of activities, in addition to the issues of critical thinking that have been raised in each educational session. This study may also benefit curriculum developers in terms of designing educational activities in books and instructional guides that develop communication and thinking skills, justification, and problem-solving.

Definitions in the Study

Critical thinking.

It is a precise intellectual process, through which concepts are developed, information obtained and evaluated, whether that information obtained through observation, thinking, experience, inference and others, and assessing its accuracy, consistency, clarity, relevance, and safety ( Akramova, 2017 ).

Critical Thinking Skills

The mental activities you use to process information, make connections, make decisions, create new ideas, and analyze and evaluate information, beliefs, or knowledge ( Kovic, 2016 ).

Problem-Solving

It is a thinking process that an individual uses through knowledge, experiences and experiences to change an unfamiliar situation in order to solve the ambiguity that the situation requires ( Van Aken and Berends, 2018 ).

Methodology

Design of the study.

The present study adopted a quasi-experimental study that involves the recruitment of an interventional group and a controlled group of seventh-grade male students.

Participants of the Study

The study participants were seventh-grade male students, consisting of 29 students, in the first semester of the years 2020–2021 in “King Abdullah II Schools of Excellence” in Madaba Governorate. The students were randomly distributed into two groups, one of which was the interventional group of 15 male students, whose students were electronically trained in a program based on strategies to solve the mathematical problem and the controlled group of 14 male students, which was taught in the traditional method.

Data Collection Measures

To test the study hypothesis and achieve its objectives, the study adopted the critical thinking skills developed by Abdul-Salam and Mamdouh (1982) . The critical thinking skills test was validated in the original study. However, the test was re-validated in a more recent study by Abu Mehadi and Darwish (2011) . The internal consistency validation results showed that the correlation coefficient values for the test domains with the whole test were as follows: identifying assumptions (0.431), interpretation (0.519), discussion (0.598), deduction (0.646), and conclusion (0.565), and all of them were significant at a significance level of (α = 0.01). In addition, Abu Mehadi and Darwish (2011) ensured the reliability of critical thinking skills by using both the Split-Half method and Cronbach’s alpha method. The reliability coefficient values using the Split-Half method were as follows: identifying assumptions (0.657), interpretation (0.743), discussion (0.592), deduction (0.604), and conclusion (0.699), and (0.774) for the whole critical thinking skills test. On the other hand, the values of Cronbach’s alpha coefficient were as follows: identifying assumptions (0.622), interpretation (0.772), discussion (0.692), deduction (0.657), and conclusion (0.532), and (0.724) for the whole critical thinking skills test.

Description of the Test

The critical thinking skills test consisted of five subtests, they were:

1. The first test/Identifying assumptions: It contains 15 questions, and for each question three hypotheses are proposed, to which it is answered by either mentioned or not.

2. The second test/interpretation: It also consists of 15 questions, and for each question two results are proposed to answer the question, to which it is answered either mentioned or not.

3. The third test/discussion: It also consists of 15 questions, and each question has two suggested answers; either strong or weak.

4. The fourth test/deduction: It also consists of 15 questions, and each question has two results to which it is answered correctly or incorrectly.

5. Fifth test/conclusion: It also consists of 15 questions, and each question has five proposed conclusions to answer the question, to which it is answered completely honest, possibly true, incomplete data, possibly false, and completely false.

Therefore, the critical thinking skills consisted of 75 questions, distributed over five subtests.

Test Scoring

The key to the critical thinking test is used, and the key is a piece of cardboard that matches the area designated for the answer on the answer sheet. This key is punched in places for the correct answer so that it is easy to know the correct answer through this key. Each correct answer is given a score of 1, whereas the incorrect answer was given a score of zero.

Validity and Reliability of the Critical Thinking Test

Researchers conducted a test on a sample of seventh-grade male students ( n = 15), with the aim of verifying the validity of the critical thinking test for administration in the Jordanian environment by calculating its validity and reliability through appropriate statistical methods.

Internal Consistency Validity

Researchers calculated correlation coefficients between the degree of each domain and the total degree of the test. Table 1 shows the correlation of the score for each dimension and the overall score for the critical thinking test.

www.frontiersin.org

Table 1. Correlation coefficients for each subtest in the critical thinking skills.

The results showed that there was a significant correlation between each subtest of critical thinking skills at a significance level of α ≤ 0.05 as the correlation coefficients ranged between 0.548 and 0.640. In addition, the item total correlation was found to be 0.606 at a significance level of α ≤ 0.05. To ensure the internal consistency of critical thinking skills tests, the corrected-item correlation coefficients were ensured to be higher than 0.3 for all the test items.

Cronbach’s Alpha Reliability Test

Researchers ensured the reliability of the critical thinking test by calculating the Cronbach’s alpha coefficient for each subtest and for the whole test ( Table 2 ).

www.frontiersin.org

Table 2. “Cronbach’s alpha coefficients” for sub-tests and the whole critical thinking test.

The results showed that the values of Cronbach’s alpha coefficient for the subtests and the whole test of critical thinking ranged between 0.643 and 0.811 and were all statistically significant at the significance level of α ≤ 0.05. A Cronbach’s alpha drop analysis was performed to check for the items that reduce the reliability of the critical thinking skills test. For the interpretation domain, item 7 was found to reduce the test reliability as the deletion of this item increased the reliability to 0.760, whereas the deletion of item 9 reduced the test reliability as the deletion of this item increased the reliability to 0.763. In addition, items 3 and 5 in the conclusion domain were found to reduce the test reliability as the deletion of these items increased the test reliability to 0.761 and 0.759, respectively. However, those items were not deleted as the test reliability is still higher than 0.7, which is acceptable value for educational research ( Taber, 2018 ).

A valid and reliable critical thinking test was applied before and after the designed electronic training program described below.

Description of the Training Program

The training program is a group of training situations independent of the curriculum, which aims to develop critical thinking skills among seventh-grade male students. The researchers prepared this, and applied it to the study sample between August and October 2021, and the training program was prepared through the following steps.

• Reviewing the theoretical literature on how to prepare and design training programs for elementary school students ( Csíkos et al., 2012 ; Nadler and Nadler, 2012 ; Siagan et al., 2019 ; Ahdhianto et al., 2020 ; Bakkar, 2021 ). These studies provided an overview of the methodological steps in designing training programs for school students, setting objectives, content of training programs, and monitoring the outcome of the training programs.

• Reviewing previous studies that focused on problem-solving strategies for elementary school students ( Arikan and Ünal, 2015 ; Al-Khateeb, 2018 ; Khoiriyah and Husamah, 2018 ). These studies highlighted the problem-solving strategies and skills needed for the elementary stage students. For example, Al-Khateeb (2018) analyzed the problem-solving skills needed by seventh-grade students in Jordan.

• Preparing the primary version of the training program and presenting it to eight experts from the faculty members in Jordanian universities to verify the psychometric properties of the program’s validity, and appropriate modifications were made in light of the referees’ opinions from the methodological, theoretical, and linguistic aspects.

The program is based on problem-solving strategies, namely:

- The strategy of building an organized list or a table, in which the student’s thinking about the problem is organized by placing the given data in an organized manner in the form of a list, and this allows the students to review what they have done, and determine what is the important step that they need to take to complete the solution to the problem. In this strategy, a table that contains the data given in the problem is made in a specific order. This arrangement helps the student find missing data and clarifies the relationships between them, which leads to the ease of understanding of the relationship between the data and what is required to reach the solution.

- The strategy of finding a pattern : Finding a pattern is a strategy for students to find patterns in the data. To solve a problem, students look for repeating items, numbers, or a series of events.

- Trial and error strategy : It is simply the application of possible processes to the information given within the problem, and some students with little experience in solving problems resort to it. Through this strategy, the student guesses all the possible possibilities to solve the problem, and then examines and tests the validity of these possibilities to solve this problem, by trying each possibility separately until the possibility is selected.

- The strategy of using an equation or a law : It is one of the most powerful strategies, so that many problems can be solved through this strategy, and its use is frequent, making it the first strategy that comes to mind when we want to solve a problem. The student translates the verbal problem into a mathematical sentence and then solves the mathematical sentence to find the value or values of the unknown, which represents the solution to the problem.

- The strategy of drawing a model or diagram : The drawing strategy is one of the effective strategies for solving mathematical problems, and it is used when there is a possibility to represent the problem with a drawing or an illustrative chart. Thus, the information and relationships involved in the problem become clearer to students, which helps them to understand the problem. Thus, rather than requiring drawings to be detailed and accurate, devising an appropriate plan to solve them, they are just illustrations that may be drawn directly without using engineering tools and without considering actual measurements.

- The strategy of solving an easier problem : Through this strategy, a similar related problem is solved. The problem is simplified by using numbers that are smaller or easier to calculate, and the problem may be simplified by temporarily omitting some conditions. Also, simplifying the problem may be through studying special cases and then trying to benefit from solving these special cases in solving the original problem. This strategy can be used in combination with other strategies to solve the problem. In other words, it may be a helpful step to solve the problem.

- Go backward strategy : This strategy was applied when the problem involves a series of successive calculations for a number and these calculations are given the final output, and it is required to find the value of a number in one of the calculations at the beginning of the problem, which may be difficult to calculate if we start from the data. Usually, students—in this type of problem—have a difficulty in forming algebraic equations or in using forward working strategies in general.

- Logical justification strategy : This strategy is often included in most problem-solving strategies. It is also used to solve problems and logical issues, and is often used to solve engineering exercises to determine the links and relationships between the data given in the problem and the realization of these relationships, to take logically justified steps in order to solve the problem and to solve problems through this strategy. A matrix or table to facilitate the justification process, especially in the primary stage, which may include other strategies, and focus on justifying the steps verbally in sequence.

The program was electronically delivered through the Microsoft Teams program, where the delivery of the program lasted for 3 weeks, with an average of four training sessions per week—each session is an hour long.

Statistical Processing

Researchers used the Statistical Package of Social Sciences (SPSS, v. 26.0, IBM Corporation) to process the scores of the critical thinking skills. The descriptive statistics “frequencies, percentages, mean, and SD” were used to describe participants’ characteristics. In addition, the independent sample t -test was performed to identify “the significant statistical differences between the controlled group and the Interventional group in the scores of the pre and post critical thinking skills.”

A total of 29 seventh-grade male students participated in this study. To determine the appropriate statistical tests, researchers explored the normality of the participants’ scores on both critical thinking pre- and post-test. The results presented in Table 3 represent the Shapiro–Wilk normality test results. The results showed that the data are normally distributed as there was no significant deviation of the sample mean scores ( M ) from the population mean scores (μ), which is evidenced by the values of the Shapiro–Wilk tests shown in Table 3 . To ensure meeting the assumptions of parametric tests, the Levene’s test of equality of error variances was used and revealed that there was no significant difference from an equality of variance across various conditions of the experiment ( F = 0.536, p = 0.946). Based on these results, parametric tests were used to analyze the study findings.

www.frontiersin.org

Table 3. Shapiro–Wilk normality test results.

The results shown in Table 4 represent the baseline scores of the critical thinking pre-test. The results showed that there was no significant statistical difference in the identifying assumptions pre-test between the control group ( M = 4.4286, SD = 0.75593) and the interventional group ( M = 4.4667, SD = 0.91548, t = 0.122, p = 0.904). In addition, the results showed no significant statistical differences in the interpretation pre-test between the controlled group ( M = 6.4286, SD = 1.78516) and the interventional group ( M = 6.4000, SD = 1.45406, t = −0.047, p = 0.963).

www.frontiersin.org

Table 4. Independent sample t -test for critical thinking pre-tests.

Moreover, the results indicated that there were no significant differences in the discussion pre-test between the controlled group ( M = 5.5000, SD = 2.13937) and the interventional group ( M = 5.5333, SD = 1.99523, t = 0.043, p = 0.966). In addition, the results revealed that there were no significant statistical differences in the deduction pre-test between the controlled group ( M = 5.2857, SD = 1.26665) and the interventional group ( M = 5.9333, SD = 1.38701, t = 1.310, p = 0.201).

With regard to the conclusion pre-test, the results showed that there were no significant statistical differences between the controlled group ( M = 4.2857, SD = 1.20439) and the interventional group ( M = 4.3333, SD = 0.81650, t = 0.124, p = 0.901).

In total, the results showed that there were no significant statistical differences in the critical thinking pre-test between the controlled group ( M = 25.9286, SD = 3.19770) and the interventional group ( M = 26.6667, SD = 3.88526, t = 0.560, p = 0.583).

The results shown in Table 5 represent the independent samples t -test scores of the critical thinking post-test. The results showed that there was a significant statistical difference in identifying assumption post-test between the controlled group ( M = 4.9286, SD = 1.63915) and the interventional group ( M = 9.3333, SD = 1.29099, t = 8.002, p = 0.000). In addition, the results revealed significant statistical differences in the interpretation post-test between the controlled group ( M = 6.4286, SD = 1.82775) and the interventional group ( M = 11.1333, SD = 1.29099, t = 6.690, p = 0.000).

www.frontiersin.org

Table 5. Independent sample t -test for the critical thinking post-test.

Moreover, the results showed that there was a significant difference in the discussion post-test between the controlled group ( M = 5.8571, SD = 1.95555) and the interventional group ( M = 11.0000, SD = 1.55839, t = 7.797, p = 0.000). In addition, the findings showed that there were significant statistical differences in the deduction post-test between the controlled group ( M = 5.4286, SD = 1.34246) and the interventional group ( M = 7.8000, SD = 2.51282, t = 3.199, p = 0.004).

With regard to the conclusion post-test, the results showed that there were no significant statistical differences between the controlled group ( M = 3.9286, SD = 0.91687) and the interventional group ( M = 4.4000, SD = 1.88225, t = 0.866, p = 0.404). In total, the results showed that there were significant statistical differences in the critical thinking post-test between the controlled group ( M = 26.5714, SD = 3.95580) and the interventional group ( M = 43.6667, SD = 4.68534, t = 10.640, p = 0.000).

To investigate the direction of significant statistical differences, a one-way analysis of variance (ANOVA) was performed ( Table 6 ). The results showed that there was a significant statistical difference [ F (27, 1) = 65.100, p ≤ 0.05], [ F (27, 1) = 44.541, p ≤ 0.05], [ F (27, 1) = 61.72, p ≤ 0.05], [ F (27, 1) = 9.832, p ≤ 0.05] in terms of identifying assumptions, interpretation, discussion, and deduction, respectively, between the controlled group and the interventional group in favor of the interventional group.

www.frontiersin.org

Table 6. Analysis of variance (ANOVA) results of the critical thinking post-test.

In addition, the results showed that there were no significant differences [ F (27, 1) = 0.718, p = 0.404] in the conclusion post-test between the controlled group and the interventional group in favor of the Interventional group.

Finally, the findings indicated that there were significant statistical differences [ F (27, 1) = 111.871, p ≤ 0.05] in the critical thinking post-test between the controlled group and the Interventional group in favor of the latter one.

Discussion and Conclusion

This study sought to investigate the effects of a training program based on solving mathematical problem strategies on critical thinking among seventh-grade male students in the “King Abdullah II Schools of Excellence.” The results showed statistically significant variations in the critical thinking post-test between the controlled group and the interventional group in favor of the interventional group, which was referred to the designed training program. This result might be referred to the adopted mathematical problem-solving strategies in the training program, which were the strategy of building an organized list or a table, the strategy of finding a pattern, trial and error strategy, the strategy of using an equation or a law, the strategy of building a model or a diagram, the strategy of solving an easier problem, deletion strategy, go backward strategy, and logical justification strategy. These strategies were reported to significantly increase students’ motivation, engagement, and desire to learning ( Beal and Stevens, 2007 ; Gök and Sýlay, 2010 ; Fukuzawa et al., 2017 ).

Furthermore, considering that education is fundamentally a thinking process, these adopted strategies were reported to enhance critical thinking skills among students by transforming the process of knowledge acquisition from an inactive process to a mental activity that leads to a better mastery of the cognitive content and a deeper understanding of it ( Bashith and Amin, 2017 ; Miterianifa et al., 2019 ; Fadilla et al., 2021 ). These results are consistent with the findings reported by Yana (2004) and Al-Btoush and Al-Darabkeh (2017) who reported the effectiveness of problem-solving strategies in improving thinking skills among elementary stage students. However, the contexts of the studies are somehow different due to differences in the population and the thinking skills investigated.

However, the results of this study showed that there were no significant differences in the conclusion skills between the controlled and interventional group. This could refer to that building conclusions is one of the basic order cognitive processes that require generating and predicting new ideas, and the issue needs extensive training and development of student skills, which cannot be achieved through a single training program. In addition, Al-Kahloot (2013) also reported that conclusion skills were the most available critical thinking skills in elementary stage curricula, which might point to the lack of students’ training and background knowledge of the conclusion skills. This could significantly affected the performance of seventh-grade male students in critical thinking skills in the conclusion domain.

The findings of the present study could be limited by a number of limitations, including a relatively low sample size, the adopted strategies to build the training program, and the psychometric properties of the critical thinking skills test. The inclusion of a larger sample size might significantly more accurate and reliable findings, in addition to building a training program based on the strategies retrieved through the analyses of the elementary stage curricula and diversifying the contents of the critical thinking test would significantly improve the quality of the findings. Moreover, a significant limitation of the present study is that it is limited to male students and should be extended to both men and women to provide more valid and reliable results.

The present study reported the effect of a training program based on solving mathematical problems on the improvement of critical thinking skills of seventh-grade male students in “King Abdullah II Schools of Excellence.” Based on the results reported above, the present study recommends conducting further studies addressing the effect of both educational and training programs based on solving mathematical problems and assessing their effect on improving critical thinking skills among elementary stage students in general, and seventh-grade male students in particular.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Ethics Statement

The studies involving human participants were reviewed and approved by Institutional Review Board (IRB) at Al-Balqa’ Applied University. The patients/participants provided their written informed consent to participate in this study.

Author Contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work, and approved it for publication.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Ababneh, E., Al-Tweissi, A., and Abulibdeh, K. (2016). TIMSS and PISA impact–the case of Jordan. Res. Papers Educ. 31, 542–555. doi: 10.1080/02671522.2016.1225350

CrossRef Full Text | Google Scholar

Abdul-Salam, F., and Mamdouh, S. (1982). Critical Thinking Test Handbook “Educational and Psychological Research Center. Mecca: Faculty of Education, Umm Al-Qura University.

Google Scholar

Abu Mehadi, S. A., and Darwish, A. H. (2011). Critical Thinking Skills Included in the Physics Curriculum for the Secondary Stage and the Extent to Which Students Acquire Them Ph. D, Thesis.

Abu Tayeh, K., and Al-Rsa’i, M. S. & Al-Shugairat, M. F. (2018). The reasons for the decline of the results of jordanian students in” TIMSS 2015”. Int. J. Instru. 11, 325-338.

Ahdhianto, E., Marsigit, H., Haryanto, H., and Nurfauzi, Y. (2020). Improving fifth-grade students’ mathematical problem-solving and critical thinking skills using problem-based learning. Univ. J. Educ. Res. 8, 2012–2021. doi: 10.13189/ujer.2020.080539

Akramova, G. R. (2017). Modern approaches to development critical thinking of students. Eastern Eur. Sci. J. 7, 2056–5852.

Al-Btoush, M. A., and Al-Darabkeh, M. M. (2017). The effect of a training program based on future problem-solving strategy in developing critical thinking skills among gifted students in Jordan. Educ. Psychol. Stud. J. Faculty Educ. Zagazig. 94, 93–121.

Alcantara, E. C., and Bacsa, J. M. P. (2017). Critical thinking and problem solving skills in mathematics of grade-7 public secondary students. Asia Pacific J. Multidisciplinary Res. 5, 21-27.

Aljaberi, N. M. (2014). Pre-service elementary school teachers’ level of mathematical thinking and their attitudes toward mathematics. J. Educ. Hum. Dev. 3, 181–195.

Al-Kahloot, K. (2013). The Degree of Inclusion of the Critical Thinking Skills in Elementary Stage Curricula Ph. D, Thesis. Faculty of Education, Islamic University in Gaza.

Al-Khateeb, M. (2018). The effect of teaching mathematical problems solving through using mobile learning on the seventh grade students’ ability to solve them in Jordan. Int. J. Interact. Mob. Technol. 12, 178–191. doi: 10.3991/ijim.v12i3.8713

Arikan, E. E., and Ünal, H. (2015). Investigation of problem-solving and problem-posing abilities of seventh-grade students. Educ. Sci. Theory Pract. 15, 1403–1416.

Ashraf, K. A. (2018). The relationship between Jordanian students’ 21st century skills (Cs21) and academic achievement in science. J. Turkish Sci. Educ. 15, 82-94.

Bakkar, M. L. (2021). The effect of using the differentiated education strategy in teaching mathematics to develop the mathematical problem solving skills of secondary school students. Educ. J. Adult Educ. 3, 53–89.

Bashith, A., and Amin, S. (2017). The effect of problem based learning on EFL students’ critical thinking skill and learning outcome. Al Ta Lim J. 24, 93–102. doi: 10.15548/jt.v0i0.271

Bawaneh, A. K., and Moumene, A. B. (2021). Science teachers’ employment of alternative assessments for gauging students’ learning. Islamic Univ. J. Educ. Psychol. Stud. 29, 36–59.

Beal, C. R., and Stevens, R. H. (2007). “Student motivation and performance in scientific problem solving simulations,” in Proceedings of the 2007 Conference on Artificial Intelligence in Education: Building Technology Rich Learning Contexts That Work. doi: 10.3390/s22010389

PubMed Abstract | CrossRef Full Text | Google Scholar

Csíkos, C., Szitányi, J., and Kelemen, R. (2012). The effects of using drawings in developing young children’s mathematical word problem solving: a design experiment with third-grade hungarian students. Educ. Stud. Math. 81, 47–65. doi: 10.1007/s10649-011-9360-z

Fadilla, N., Nurlaela, L., Rijanto, T., Ariyanto, S. R., Rahmah, L., and Huda, S. (2021). Effect of problem-based learning on critical thinking skills. J. Phys. Conf. Ser. 1810:012060.

Fukuzawa, S., Boyd, C., and Cahn, J. (2017). Student motivation in response to problem-based learning. Collected Essays Learn. Teach. 10, 175–188. doi: 10.22329/celt.v10i0.4748

Gök, T., and Sýlay, I. (2010). The effects of problem solving strategies on students’ achievement, attitude and motivation. Latin Am. J. Phys. Educ. 4:2.

Hidajat, F. A., and Sa’dijah, C. (2019). Exploration of students’ arguments to identify perplexity from reflective process on mathematical problems. Int. J. Instru. 12, 573–586. doi: 10.29333/iji.2019.12236a

Hodges, C., Moore, S., Lockee, B., Trust, T., and Bond, A. (2020). The difference between emergency remote teaching and online learning. Educ. Rev. 27, 1–12. doi: 10.5688/ajpe8142

Hoogland, K., de Koning, J., Bakker, A., Pepin, B. E., and Gravemeijer, K. (2018). Changing representation in contextual mathematical problems from descriptive to depictive: the effect on students’ performance. Stud. Educ. Evalu. 58, 122–131. doi: 10.1016/j.stueduc.2018.06.004

Jarbou, I. (2014). The Effectiveness of Employing the Reciprocal Teaching Strategy in Developing Thinking in Mathematics and the Direction Towards it Among the Eighth Grade Students in Gaza Ph. D, Thesis.

Joung, E., and Byun, J. (2021). Content analysis of digital mathematics games based on the NCTM content and process standards: an exploratory study. Sch. Sci. Math. 121, 127–142. doi: 10.1111/ssm.12452

Kenedi, A. K., Helsa, Y., Ariani, Y., Zainil, M., and Hendri, S. (2019). Mathematical connection of elementary school students to solve mathematical problems. J. Math. Educ. 10, 69–80. doi: 10.22342/jme.10.1.5416.69-80

Khoiriyah, A. J., and Husamah, H. (2018). Problem-based learning: creative thinking skills, problem-solving skills, and learning outcome of seventh grade students. JPBI (Jurnal Pendidikan Biologi Indonesia) 4, 151–160.

Kovic, M. (2016). A generalized definition of critical thinking. Swiss Skeptics Dis. Paper Ser. 1, 1–31.

Kum, R., Seo, I. S., Kim, T. H., Hahn, S. W., and Kim, M. S. (2019). The effects of creative teaching technique applied to nursing major curriculum on critical thinking disposition, problem solving process, and self-leadership. J. Korea Conv. Soc. 10, 373–382.

Mairing, J. P. (2017). Thinking process of naive problem solvers to solve mathematical problems. Int. Educ. Stud. 10, 1–11. doi: 10.5539/ies.v10n1p1

Miterianifa, Trisnayanti, Y., Khoiri, A., and Ayu, H. D. (2019). Meta-analysis: the effect of problem-based learning on students’ critical thinking skills. AIP Conf. Proc. 2194:020064.

Momany, M. A., Khasawneh, O., and Alrefaie, A. (2017). The implications of idealism as an educational philosophy in jordanians’ elementary curriculum stage as perceived by teachers. J. Al Quds Open Univ. Res. Stud. 42, 9–21. doi: 10.12816/0043014

Mounier-Jack, S., Mayhew, S. H., and Mays, N. (2017). Integrated care: learning between high-income, and low-and middle-income country health systems. Health Policy Plan. 32, iv6–iv12. doi: 10.1093/heapol/czx039

Mubark, M. (2012). Gender differences in mathematical thinking and mathematical achievement in jordanian 6th grade. Int. J. Arts Sci. 5:523.

Nadler, Z., and Nadler, L. (2012). Designing Training Programs. Milton Park: Routledge.

Post, D. (2020). After progress. Comparat. Educ. Rev. 64, 563–576.

Samawi, F. S., Al-Fayez, M. Q., and Aladwan, S. K. (2019). The level of mathematical thinking and its relationship to critical thinking and achievement in mathematics among gifted students in King abdullah II schools of excellence, jordan. Dirasat Educ. Sci. 46:70.

Shahrill, M., Putri, R. I. I., and Zulkardi, and Prahmana, R. C. I. (2018). Processes involved in solving mathematical problems. AIP Conf. Proc. 1952:020019.

Shanta, S., and Wells, J. G. (2020). T/E design based learning: assessing student critical thinking and problem solving abilities. Int. J. Technol. Des. Educ. 2020, 1–19.

Siagan, M. V., Saragih, S., and Sinaga, B. (2019). Development of learning materials oriented on problem-based learning model to improve students’ mathematical problem solving ability and metacognition ability. Int. Electron. J. Math. Educ. 14, 331–340.

Simamora, R. E., and Saragih, S. (2019). Improving students’ mathematical problem solving ability and self-efficacy through guided discovery learning in local culture context. Int. Electron. J. Math. Educ. 14, 61-72.

Simbolon, M., Surya, E., and Syahputra, E. (2017). The efforts to improving the mathematical critical thinking student’s ability through problem solving learning strategy by using macromedia flash. Am. J. Educ. Res. 5, 725-731.

Star, K. M. (2018). The level of mathematical thinking and its relation to achievement in mathematics among students in the tenth grade of basic education in Jordan. Math. Educ. Egyp. Assoc. Math. Educ. 21:10.

Taber, K. S. (2018). The use of cronbach’s alpha when developing and reporting research instruments in science education. Res. Sci. Educ. 48, 1273–1296. doi: 10.1007/s11165-016-9602-2

Van Aken, J. E., and Berends, H. (2018). Problem Solving in Organizations. Cambridge: Cambridge university press.

Yana, S. (2004). The Impact of Problem Solving on the Development of Positive Thinking Abilities Among a Sample of Students at the University of New York. New York: University of New York.

Keywords : mathematical problem-solving, critical thinking, King Abdullah II Schools of Excellence, seventh grade, Jordan

Citation: Alfayez MQE, Aladwan SQA and Shaheen HR’A (2022) The Effect of a Training Program Based on Mathematical Problem-Solving Strategies on Critical Thinking Among Seventh-Grade Students. Front. Educ. 7:870524. doi: 10.3389/feduc.2022.870524

Received: 07 February 2022; Accepted: 21 March 2022; Published: 18 April 2022.

Reviewed by:

Copyright © 2022 Alfayez, Aladwan and Shaheen. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Mona Qutaifan Ershed Alfayez, [email protected]

Book cover

International Conference on Knowledge Engineering and Knowledge Management

EKAW 1996: Advances in Knowledge Acquisition pp 1–16 Cite as

Assumptions of problem-solving methods

Theoretical and General Issues

  • Richard Benjamins 1 &
  • Christine Pierret-Golbreich 2  
  • Conference paper
  • First Online: 01 January 2005

197 Accesses

18 Citations

Part of the Lecture Notes in Computer Science book series (LNAI,volume 1076)

Assumptions of problem-solving methods refer to necessary applicability conditions of problem-solving methods, indicating that a problem-solving method is only applicable to realize a task, if the assumptions are met. In principle, such assumptions may refer to any kind of condition involved in a problem-solving method's applicability, including its required domain knowledge. In this paper, we propose a conceptual organization for assumptions of problem-solving methods and suggest a formal language to describe them. For illustration we take examples from the Propose & Revise problem-solving method and from diagnosis.

  • Domain Knowledge
  • Logical Combination
  • Proof Obligation
  • Knowledge Engineer

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Richard Benjamins is supported by the Netherlands Computer Science Research Foundation with financial support from the Netherlands Organization for Scientific Research (NWO). The work has partly been supported by the HCM program, financed by the CEC.

This is a preview of subscription content, log in via an institution .

Unable to display preview.  Download preview PDF.

A. Aamodt, B. Benus, C. Duursma, C. Tomlinson, R. Schrooten, and W. Van de Velde. Task features and their use in commonkads. Technical Report KADS-II/T1.5/VUB/TR/014/1.0, Free University of Brussels & University of Amsterdam & Lloyd's Register, 1992.

Google Scholar  

J. M. Akkermans, B. J. Wielinga, and A. Th. Schreiber. Steps in constructing problem-solving methods. In B. R. Gaines and M. A. Musen, editors, Proceedings of the 8th Banff Knowledge Acquisition for Knowledge-Based Systems Workshop . Volume 2: Shareable and Reusable Problem-Solving Methods , pages 29–1–29–21, Alberta, Canada, January 30–February 4 1994. SRDG Publications, University of Calgary.

V. R. Benjamins. Problem Solving Methods for Diagnosis . PhD thesis, University of Amsterdam, Amsterdam, The Netherlands, 1993.

V. R. Benjamins. Problem-solving methods for diagnosis and their role in knowledge acquisition. International Journal of Expert Systems: Research and Applications , 8(2):93–120, 1995.

B. Chandrasekaran. Design problem solving: A task analysis. AI Magazine , 11:59–71, 1990.

B. Chandrasekaran, T. R. Johnson, and J. W. Smith. Task-structure analysis for knowledge modeling. Communications of the ACM , 35(9):124–137, 1992.

L. Console and P. Torasso. Integrating models of the correct behaviour into abductive diagnosis. In L. C. Aiello, editor, Proc. ECAI-90 , pages 160–166, London, 1990. ECCAI, Pitman.

D. Fensel. Assumptions and limitations of a problem-solving method: A case study. In B. R. Gaines and M. A. Musen, editors, Proceedings of the 8th Banff Knowledge Acquisition for Knowledge-Based Systems Workshop , Alberta, Canada, 1995. SRDG Publications, University of Calgary.

D. Fensel, R. Straatman, and F. van Harmelen. The mincer metaphor: a new view on problem-solving methods for knowledge-based systems. Technical report, SWI, University of Amsterdam, Amsterdam, 1995.

J.H Gennari, S.W Tu, T.E Rotenfluh, and M.A. Musen. Mapping domains to methods in support of reuse. International Journal of Human-Computer Studies , 41:399–424, 1994.

C. Pierret-Golbreich. TASK model: a framework for the design of models of expertise and their operationalization. In B. R. Gaines and M. A. Musen, editors, Proceedings of the 8th Banff Knowledge Acquisition for Knowledge-Based Systems Workshop , pages 37.1–37.22. SRDG Publications, University of Calgary, 1994.

C. Pierret-Golbreich. Modular and reusable specifications in knowledge engineering: Formal specification of goals and their development. In Workshop on Knowledge Engineering Methods and Languages (KEML) , 1996.

C. Pierret-Golbreich and I. De Louis. Task: Task centered representation for expert systems at the knowledge level. In Proc. of the 8th AISB-conference . Springer-Verlag, 1991.

C. Pierret-Golbreich and X. Talon. An algebraic specification of the dynamic behavior of knowledge-based systems. In B. R. Gaines and M. A. Musen, editors, Proceedings of the 9th Banff Knowledge Acquisition for Knowledge-Based Systems Workshop , Alberta, Canada, 1995. SRDG Publications, University of Calgary.

A.R. Puerta, J. Egar, S. Tu, and M. Musen. A multiple-method shell for the automatic generation of knowledge acquisition tools. Knowledge Acquisition , 4:171–196, 1992.

William F. Punch and B. Chandrasekaran. An investigation of the roles of problem-solving methods in diagnosis. In Proc. of the Tenth International Workshop: Expert Systems and their Applications , pages 25–36, Avignon, France, 1990. EC2.

M. Reinders and B. Bredeweg. Strategic reasoning as a reflective task. In Proceedings of IMSA-92 , pages 159–163, 1992.

M. Schmidt-Schauß. Computational Aspects of an Order-Sorted Logic with Term Declarations . Springer-Verlag, Berlin, Germany, 1989. Lecture Notes in Artificial Intelligence No. 395.

L. Steels. Components of expertise. AI Magazine , 11(2):28–49, Summer 1990.

A. ten Teije and F. van Harmelen. An extended spectrum of logical definitions for diagnostic systems. In Proceedings of DX-94 Fifth International Workshop on Principles of Diagnosis , 1994.

A. ten Teije and F. van Harmelen. An extended spectrum of logical definitions for diagnostic systems. Computational Intelligence , 1995. Submitted.

G. van Heijst. The Role of Ontologies in Knowledge Engineering . PhD thesis, University of Amsterdam, May 1995.

K. van Marcke. A generic tutoring environment. In L. C. Aiello, editor, Proc. of the Ninth European Conference on Artificial Intelligence , pages 655–660, London, UK, 1990. Pitman.

J. Vanwelkenhuysen and P. Rademakers. Mapping knowledge-level analysis onto a computational framework. In L. Aiello, editor, Proc. ECAI-90 , pages 681–686, London, 1990. Pitman.

B. J. Wielinga, W. Van de Velde, A. Th. Schreiber, and J. M. Akkermans. The Common KADS framework for knowledge modelling. In B. R. Gaines, M. A. Musen, and J. H. Boose, editors, Proc. 7th Banff Knowledge Acquisition Workshop , volume 2, pages 31.1–31.29. SRDG Publications, University of Calgary, Alberta, Canada, 1992.

G. Yost. Configuring elevator systems. Technical report, Digital Equipment Corporation, 111 Locke Drive (LMO2/K11), Marlboro MA 02172, 1992.

Z. Zdrahal and E. Motta. An in-depth analysis of propose & revise problem solving methods. In B. R. Gaines and M. A. Musen, editors, Proceedings of the 9th Banff Knowledge Acquisition for Knowledge-Based Systems Workshop , Alberta, Canada, 1995. SRDG Publications, University of Calgary.

Download references

Author information

Authors and affiliations.

SWI, University of Amsterdam, Roetersstraat 15, NL-1018, WB Amsterdam, The Netherlands

Richard Benjamins

LRI, University of Paris-Sud, Bâtiment 490, 91405, Orsay Cedex, France

Christine Pierret-Golbreich

You can also search for this author in PubMed   Google Scholar

Editor information

Rights and permissions.

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper.

Benjamins, R., Pierret-Golbreich, C. (1996). Assumptions of problem-solving methods. In: Shadbolt, N., O'Hara, K., Schreiber, G. (eds) Advances in Knowledge Acquisition. EKAW 1996. Lecture Notes in Computer Science, vol 1076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61273-4_1

Download citation

DOI : https://doi.org/10.1007/3-540-61273-4_1

Published : 01 June 2005

Publisher Name : Springer, Berlin, Heidelberg

Print ISBN : 978-3-540-61273-5

Online ISBN : 978-3-540-68391-9

eBook Packages : Springer Book Archive

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Publish with us

Policies and ethics

  • Find a journal
  • Track your research

IMAGES

  1. what is problem solving steps process & techniques asq

    problem solving training was developed on the assumption that

  2. Master Your Problem Solving and Decision Making Skills

    problem solving training was developed on the assumption that

  3. Problem Solving Training Course Material By Oak Innovation

    problem solving training was developed on the assumption that

  4. 7 steps to master problem solving methodology

    problem solving training was developed on the assumption that

  5. 7 Steps to Improve Your Problem Solving Skills

    problem solving training was developed on the assumption that

  6. Speculative model of creative problem-solving training differentiating

    problem solving training was developed on the assumption that

VIDEO

  1. Daily Training Problem Solving

  2. Relatives Reactionat my IIT Result| #iit #jee2024 #jee2025

  3. Reliability Over Effectiveness

  4. Problem Solving Training 2024 Part 2

  5. The problem observed by Stanford lecturer

  6. Reliability & consistency!🧼✨

COMMENTS

  1. Problem-Solving Training

    The therapist will introduce a problem solving technique (Goldfried & Davison, 1976???) that involves the following five steps: (i) defining the problem, (ii)collecting information about the problem, (iii)generating different solutions, (iv) listing advantages and disadvantages for each solution, and (v) implementing and evaluating the solution.

  2. Why Malcolm Knowles's Five Assumptions of Learners Matter

    1. Self-concept: Adults become more self-directed as they mature The first of Knowles' assumptions is this: as adults move throughout life, they become more independent and self-directed. Adult learners want to have ownership over their learning journey.

  3. PDF THE PURSUIT OF ACTUAL PROBLEM SOLVING BEHAVIOR: AN ...

    The most commonly used problem-solving training model was developed by D'Zurilla and Goldfried (1971). The model appears to have face validity because it is based on the process used by "normal" individuals when they attempt to solve complex, difficult, or unique situations.

  4. PDF The Problem with Problem-Solving Training in Industry

    Abstract: This paper challenges the inherent assumptions reflected in the design and administration of the current problem-solving training model using evidence from empirical research, understanding of the realities of worker's knowledge, skill and ability; the realities of their work environment; and the strong theoretical base within the ad...

  5. PDF Learning, Teaching and Designing Problem Solving: An Assessment

    problem-solving methods developed in the 1960's. He concurs with the argument that problem solving is not a general, context-free skill. Instead, it is clear that problem-solving is a context-bound skill, in which experts synthesize their rich declarative knowledge to generate a dynamically changing, personal, working mental model of the

  6. The Influence of Attitudes and Beliefs on the Problem-Solving Performance

    The problem-solving performance of primary school students depend on their attitudes and beliefs. As it is not easy to change attitudes, we aimed to change the relationship between problem-solving performance and attitudes with a training program. The training was based on the assumption that self-generated external representations support the problem-solving process. Furthermore, we assumed ...

  7. The Pursuit of Actual Problem-Solving Behavior: An Opportunity for

    The generalization of trained verbal problem-solving skills to overt performance has been difficult to demonstrate and assess (Tisdelle & St. Lawrence, 1986). The few studies that have attempted to assess actual problem-solving behavior have used analogues or simulation situations. The most commonly used problem-solving training model was developed by D'Zurilla and Goldfried (1971). The ...

  8. PDF Problem Solving, Reasoning, and Analytical Thinking in a Classroom

    teach these vital problem-solving, reasoning, and thinking skills to children much younger than college students. At any given time, the Morningside Academy population may include students with special needs. Experts in the eld of teaching problem solving and thinking skills have remarked that certain procedures are reserved for students of ...

  9. Theory of Problem Solving

    The on-going consideration of the influences acting in time and their control is an assumption for successful problem solving process in those situations. The dynamics does not have to be in the context of problem solving understood as negative, it can operate also positively, and e.g. previously unsolvable problem suddenly becomes solvable. 2.

  10. Problem-Solving Theory: The Task-Centred Model

    General Overview. The task-centred model is a problem-solving, empirically based, short-term practice model. It was developed by social work educators Bill Reid and Laura Epstein and was intended for practice with various client populations, including clients from historically oppressed, diverse backgrounds.An underlying premise of the task-centred model is that life circumstances inevitably ...

  11. Training team problem solving skills: an event-based approach

    Abstract. Training problem solving teams presents a unique set of challenges to instructional designers. Given the criticality of teams to the performance of many organizations, it is important to develop training systems to support coordination and problem solving. While recent technological advancements, such as computer-based performance ...

  12. Collaborative problem-solving education for the twenty-first-century

    The complex research, policy and industrial challenges of the twenty-first century require collaborative problem solving. Assessments suggest that, globally, many graduates lack necessary ...

  13. PDF Facilitating Representation Change in Insight Problems Through Training

    Training involves teaching the problem solver a specific or general heuristic or procedure or the like that is intended to be recalled subsequently and improve unsupported problem solving. This differs from studies that pro-vide a hint with no teaching at the beginning of each problem or sometimes at an impasse during problem solving.1

  14. PDF The effects of problem-solving training on two problem-solving tasks

    Goldfried (1971) have proposed a five-stage model for training in problem- solving skills: (a) general orientation; (b) pr blem d finition and formula- tion; (c) generation of alternatives; (d) deci making; ion and (e) verification of problem solution. There are several skills or behaviors associated with each stage of their model.

  15. The Andragogy Approach: Knowles' Adult Learning Theory Principles in

    (Knowles, 1980). It was coined from the Greek andr + agogy which literally means "leading men." Practitioners and proponents emphasize the critical role of adult learners in their own education. This is because, for many adults, higher education is to be competent and competitive in their personal and specific endeavors.

  16. What you train is what you get? Task requirements and training methods

    The computer-based simulation ColorSim, which was developed for this experimental study, was used in three different variants. It is based on the work by Funke (1993) and simulates a small chemical plant that produces colors for subsequent processing and treatment, such as the dyeing of fabrics (for details, see Kluge, in press).ColorSim is a scenario for training, acquiring, and applying ...

  17. The Effect of a Training Program Based on Mathematical Problem-Solving

    The present study aimed at investigating the effect of a training program based on mathematical problem-solving strategies on critical thinking skills among seventh-grade students in King Abdullah II schools of Excellence. The study adopted the quasi-experimental research approach. The participants of the study comprised of 29 male seventh graders. The participants were randomly distributed ...

  18. CES Foundation Module 2 Lesson 5 Problem Solving Post Test

    What decision-making step is the mission statement developed. Step 2: Mission Analysis. What step in the Army problem solving is the key to making the rest of the process go smoothly. Developing criteria. What is a structured process that is best used for situations when operational planning is not appropriate. Army Problem-Solving Process.

  19. Creative Problem-Solving

    The creative problem-solving process Footnote 1 is a systematic approach to problem-solving that was first proposed by Alex Osborn in 1953 in his landmark book Applied Imagination.The approach went through several refinements over a period of five years. Osborn began with a seven-step model that reflected the creative process (orientation, preparation, analysis, hypothesis, incubation ...

  20. Chapter 10

    15. In cognitive behavioral group therapy. A. some research shows that this approach is effective for treating a wide range of emotional and behavioral problems. B. the group leader assumes a blank screen demeanor so as to enhance transference feelings of the members. C. the assumption is that a therapeutic atmosphere is both necessary and ...

  21. Analyzing the effects of the problem solving approach to the

    Further, Laal and Ghodsi (2012) emphasize in their review that learners involved in collaborative learning develop valuable problem solving skills. Problem solving skills refer to the ability of an individual to find meaningful solutions to solve problems using effective and timely strategies (Karabacak, Nalbant, & Topçuoğlu, 2015).

  22. BUS 201 Practice Flashcards

    a. it often results from the assumption that other members will pick up the slack. b. the amount of social loafing depends in part on the group leader's awareness of it. c. how much of a problem social loafing is depends in part on the nature of the task. d. it is often a problem in very small groups. e. some members put forth less effort in a ...

  23. Assumptions of problem-solving methods

    18 Citations Part of the Lecture Notes in Computer Science book series (LNAI,volume 1076) Abstract Assumptions of problem-solving methods refer to necessary applicability conditions of problem-solving methods, indicating that a problem-solving method is only applicable to realize a task, if the assumptions are met.