Problem Solving and Computational Thinking in a Learning Environment (1212.0750v1)

Abstract: Computational thinking is a new problem soling method named for its extensive use of computer science techniques. It synthesizes critical thinking and existing knowledge and applies them in solving complex technological problems. The term was coined by J. Wing, but the relationship between computational and critical thinking, the two modes of thiking in solving problems, has not been yet learly established. This paper aims at shedding some light into this relationship. We also present two classroom experiments performed recently at the Graduate Technological Educational Institute of Patras in Greece. The results of these experiments give a strong indication that the use of computers as a tool for problem solving enchances the students' abilities in solving real world problems involving mathematical modelling. This is also crossed by earlier findings of other researchers for the problem solving process in general (not only for mathematical problems).

• The paper explores the relationship between critical thinking and computational thinking (CT) in problem-solving, defining CT as analytical thinking using mathematical and engineering principles.
• Classroom experiments showed that using computers as a tool significantly enhanced student performance in solving real-world mathematical problems compared to traditional methods (e.g., GPA improved from 2 to ~2.49 in one experiment).
• Authors conclude that while computers aid problem-solving, they don't replace foundational thinking skills, suggesting future math education should emphasize problem-solving and posing to foster creativity and other skills impatiently

This paper explores the relationship between critical thinking and computational thinking (CT) in problem-solving, and it presents classroom experiments on the use of computers as a tool for problem-solving.

The authors posit that problem-solving is a complex activity that uses cognitive or cognitive and physical means to overcome an obstacle and develop a better understanding of the world. They review the evolution of research on problem-solving in mathematics education, highlighting key periods and figures such as Polya and Schoenfeld. They mention that a problem consists of three states: the starting state, the goal state, and the obstacles.

The authors define critical thinking as the ability to transcend one's subjective self to arrive rationally at substantiated conclusions. They argue that critical thinking is a prerequisite for knowledge acquisition and application in problem-solving, but it is not sufficient for complex real-world technological problems, which also require CT. They describe CT as a type of analytical thinking that employs mathematical and engineering principles to solve complex problems within real-world constraints. They also present CT as a hybrid of abstract, logical, modeling, and constructive thinking [29].

The authors propose two models for problem-solving:

• A linear model where critical thinking, knowledge, and CT are sequential prerequisites for application.
• A 3-D model where these processes occur simultaneously, with the type of problem dictating the sequence of relationships.

They suggest that teaching practices should recognize the link between CT and critical thinking.

To explore the effect of computers in solving mathematical problems, the authors conducted classroom experiments at the Graduate Technological Educational Institute (TEI) of Patras, Greece, during the academic year 2011-2012. In the first experiment, 90 students of the School of Technological Applications were divided into control and experimental groups. The control group received lectures in the classical way, while the experimental group had part of their lectures and exercises in a computer laboratory using technological tools and mathematical software. At the end of the term, students took a final written examination with theoretical questions, exercises, and simplified real-world problems requiring mathematical modeling. The performance of the experimental group was significantly better in solving the problems (GPA1 = 2, GPA 2 ≈ 2.49). Here, GPA is calculated as

$$GPA = \frac{0 \cdot n_F + 1 \cdot n_D + 2 \cdot n_C + 3 \cdot n_B + 4 \cdot n_A}{n}$$,

where

$n$ is the total number of students, $n_A$, $n_B$, $n_C$, $n_D$, and $n_F$ denote the numbers of students getting the marks A, B, C, D, F respectively.

The same experiment was also performed under similar conditions with two groups of students of the School of Management and Economics of the TEI of Patras (100 students in each group). In this case, the performance of the first (control) group was found to be slightly better for the first part of the examination (questions and exercises), but the performance of the experimental group was found again to be better for the second part (problems).

The authors conclude that the use of computers as a tool for problem-solving enhances students' abilities to solve real-world mathematical problems. They caution against the illusion that computers can replace teachers, emphasizing the importance of learning to think rationally and creatively. They advocate for future mathematics teaching to focus on problem-solving and problem-posing to foster creativity, systematization, communication, argumentation, and teamwork.