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Juraj Hromkovic; Regula Lacher – Informatics in Education, 2025
The design of algorithms is one of the hardest topics of high school computer science. This is mainly due to the universality of algorithms as solution methods that guarantee the calculation of a correct solution for all potentially infinitely many instances of an algorithmic problem. The goal of this paper is to present a comprehensible and…
Descriptors: Algorithms, Computer Science Education, High School Students, Teaching Methods
Servant-Miklos, Virginie F. C. – Advances in Health Sciences Education, 2019
This paper sheds light on an intellectual dispute on the purpose of problem-based learning that took place in the 1970s between two major figures in the history of PBL: Howard S Barrows from McMaster University and Henk Schmidt from Maastricht University. Using historical evidence from archive materials, oral history accounts and contemporary…
Descriptors: Problem Solving, Problem Based Learning, Educational History, Cognitive Psychology
Robert J. Sternberg – Roeper Review, 2024
The kind of transactional, or tit-for-tat giftedness that so many programs identify and develop will not help to create a better world. Yet, if anyone is in a position to create a better world, it is our gifted young people. In this article, roles are presented that can be used to create change in the world. Some of these roles, when applied…
Descriptors: Transformative Learning, Academically Gifted, Activism, Social Change
Schreiner, Claudia; Wiesner, Christian – European Educational Researcher, 2023
In the context of a rapid digital transformation, digital competence is now regarded as a fourth cultural skill complementing reading, writing, and arithmetic. We argue that a well-structured and sound competence model is needed as a shared foundation for learning, teaching, pedagogical diagnostics and evaluative schemes in the school system.…
Descriptors: Computation, Thinking Skills, Digital Literacy, Competence
Sternberg, Robert J.; Glaveanu, Vlad; Karami, Sareh; Kaufman, James C.; Phillipson, Shane N.; Preiss, David D. – Journal of Intelligence, 2021
A deeper understanding of the processes leading to problem framing and behind finding solutions to problems should help explain variability in the quality of the solutions to those problems. Using Sternberg's WICS model as the conceptual basis of problem solving, this article discusses the relations between creative, analytical, practical, and…
Descriptors: Intelligence, Creative Thinking, Logical Thinking, Cognitive Processes
Sandefur, James; Manaster, Alfred B. – ZDM: Mathematics Education, 2022
Recursive reasoning is a powerful tool used extensively in problem solving. For us, recursive reasoning includes iteration, sequences, difference equations, discrete dynamical systems, pattern identification, and mathematical induction; all of these can represent how things change, but in discrete jumps. Given the school mathematics curriculum's…
Descriptors: Abstract Reasoning, Problem Solving, Mathematical Logic, Logical Thinking
Stephan, Michelle L.; Reinke, Luke T.; Cline, Julie K. – Mathematics Teacher: Learning and Teaching PK-12, 2020
Teachers readily welcome instructional materials that situate mathematics in the real world because they provide the relevance of mathematics to students who genuinely seek the answer to the question, "When are we ever going to use math in real life?" Although using the real world as a motivational hook is often effective for engagement,…
Descriptors: Mathematics Instruction, Instructional Materials, Relevance (Education), Middle School Teachers
Daily, Sara – International Journal of the Whole Child, 2021
"Productive Struggle" refers to a strategy that gives students an opportunity to increase their background mathematical knowledge. Productive Struggle helps students connect key concepts, determine how and where an error occurs, and supports students in figuring out how to use their own thinking and reasoning skills to correct an error.…
Descriptors: Elementary School Mathematics, Mathematics Instruction, Teaching Methods, Mathematical Concepts
Star, Jon R.; Jeon, Soobin; Comeford, Rebecca; Clark, Patricia; Rittle-Johnson, Bethany; Durkin, Kelley – Mathematics Teacher: Learning and Teaching PK-12, 2021
Comparison is a powerful and important way that we learn. To support teachers in the use of comparison in their instruction, the authors developed an instructional routine called compare and discuss multiple strategies (CDMS). Similar to other instructional routines, CDMS is a structured, specific, repeatable minilesson that teachers can use to…
Descriptors: Mathematics Instruction, Teaching Methods, Discussion (Teaching Technique), Mathematical Logic
Joyce Vogel; Dan Bouhnik – European Journal of Education, 2024
Introduction to Computer Science is traditionally the first course that all computer science and software engineering majors take. The course introduces many problem-solving techniques which can be challenging for many freshman students. In order to mitigate some of the issues of this course, we, at the Higher Education Institute, introduced a new…
Descriptors: Computer Science Education, Introductory Courses, Awards, Problem Based Learning
Bishop, Jessica Pierson; Lamb, Lisa L.; Whitacre, Ian; Philipp, Randolph A.; Schappelle, Bonnie P. – Mathematics Teacher: Learning and Teaching PK-12, 2022
In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems…
Descriptors: Thinking Skills, Problem Solving, Mathematics Instruction, Logical Thinking
Roy, George J.; Eli, Jennifer A.; Hendrix, Leslie; Graul, LuAnn – Mathematics Teaching in the Middle School, 2018
Students who are adept in modeling with mathematics have the capability to use mathematics in situations that arise in everyday life. The German Tank problem described in this article created the expectation that student reasoning was rooted in logical deductions (NCTM 2000). By engaging in this problem, students grappled with challenging…
Descriptors: Mathematics Instruction, Word Problems (Mathematics), Problem Solving, Mathematical Logic
Symons, Duncan; Holton, Derek – Australian Primary Mathematics Classroom, 2020
Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.
Descriptors: Mathematical Logic, Logical Thinking, Mathematics Instruction, Elementary School Mathematics
Lim, Kien H. – Mathematics Teacher: Learning and Teaching PK-12, 2020
The hammer-and-nail phenomenon highlights human tendency to approach a problem using a tool with which one is familiar instead of analyzing the problem. Pedagogical suggestions are offered to help students minimize their mathematical impulsivity, cultivate an analytic disposition, and develop conceptual understanding.
Descriptors: Mathematics Instruction, Problem Solving, Teaching Methods, Cognitive Processes
Hobbs, Elizabeth; Schisler, Laura; Pressley, Hugh; Smith, Walter – Technology and Engineering Teacher, 2021
Picture students huddled around a 3D printer in a middle school classroom. They gaze at the object being printed, and exclamations of, "Where is that flag from?" "What does that symbol mean?" and "Oh; I didn't think of that!" can be heard. These examples of observation, curiosity, and critical thinking are the elusive…
Descriptors: Computer Peripherals, Printing, Student Projects, Global Approach