The development of the first computers in the mid-20th century was a watershed moment in the history of computational thinking. One of the earliest examples of computational thinking was the development of the first algorithms, which are sets of instructions used to perform specific tasks. These algorithms were used to solve mathematical problems and process data on early computers.
Similar to how computers process information, computational thinking is best defined as a problem-solving approach that involves breaking down complex problems into smaller, more manageable pieces and using logical reasoning and algorithms to solve them. Its role in the field of mathematics and education has been debated for quite some time now.
The process of computational thinking consists of 4 steps:
- Decomposition — Breaking down the problem into smaller, manageable parts
- Pattern recognition — Finding similarities within and between problems
- Abstraction — Focusing only on important aspects of the problem, ignoring irrelevant details
- Algorithm design — Developing a step-by-step solution to the problem
Owing to these 4 steps, computational thinking is now being applied to fields outside of computer science, such as education, where it is being used to teach problem-solving and critical thinking skills to students. Hence, the article below discusses the role of computational thinking in mathematics education.
Computational thinking and its applicability in the classroom
In mathematics education, computational thinking has been of great use in helping students understand and apply mathematical concepts in a variety of contexts. A study by Siri Krogh Nordby, suggested that computational thinking techniques like sequencing, looping, debugging, and several others, make it a natural fit for a subject like mathematics. It can be put to use, in elementary school, to teach students how to decompose numbers and understand place value. Students can use CT to break down a number into its individual digits and understand how each digit contributes to the overall value of the number. In high school, it can be used to teach students how to solve complex mathematical problems, such as solving systems of equations or understanding geometric proofs.
However, the technique is challenging for both students and teachers, thus, computational thinking can be considered a partial “bliss,”. For students, computational thinking can require a shift in the way that they approach math problems. Instead of simply memorizing formulas or procedures, students must learn to break down complex problems into smaller, more manageable pieces and use logical reasoning and algorithms to solve them. This can be challenging, especially for students who have not had prior experience with computational thinking.
For teachers, incorporating computational thinking into math instruction may also require a shift in their pedagogical approach. It may involve spending more time on problem-solving and critical thinking activities, and less time on rote memorization of formulas and procedures. Additionally, computational thinking may require more technological resources, such as computers and software, which may not be readily available in all classrooms.
How computational thinking plays a significant role in mathematics learning
Despite these challenges, the benefits of computational thinking in mathematics education make it worth pursuing.
1. Applicable to real-world situations
One of the key benefits of computational thinking in mathematics is that it allows students to apply their knowledge to real-world situations. By using computational thinking to analyze data and make predictions, students can gain a deeper understanding of how mathematical concepts apply to the world around them.
2. Helpful in abstract concepts
In addition, computational thinking can help students better understand and apply abstract mathematical concepts. Many mathematical concepts, such as algebra and geometry, can be difficult for students to grasp because they are abstract and not tied to concrete, real-world examples. By using computational thinking to approach these concepts, students can better understand how they can be applied to solve real-world problems, which can make the material more engaging and meaningful.
3. Fosters creativity
Computational thinking can be useful in mathematics education in several ways. One way is by providing a new way for students to approach mathematical concepts and problems. Instead of simply memorizing formulas or procedures, students can learn to think creatively and logically to solve problems in new and innovative ways. This can make math more reality-oriented and meaningful for students.
4. Boosts critical thinking
Another way that computational thinking can be useful in mathematics education is by helping students develop important problem-solving and critical thinking skills. By breaking down complex problems into smaller, more manageable pieces and using logical reasoning, looking for patterns, and using algorithms to solve them, students can learn to approach problems in a structured and systematic way. These skills are not only useful in math, but also in other subjects and in real-world situations.
Examples to illustrate the use of computational thinking in math classrooms
There are several strategies that teachers can use to incorporate computational thinking into their mathematics classrooms:
1. For Elementary School
- Decomposing numbers: Teachers can help students use CT to break down a number, such as 456, into its individual digits (4, 5, and 6) and understand how each digit contributes to the overall value of the number.
- Understanding place value: By using CT, teachers can help students understand the relationship between digits in a number and the place value of each digit. For example, students can use CT to understand that the 4 in 456 represents 400, the 5 represents 50 and the 6 represents 6.
- Counting and addition: Teachers can train students to use CT to understand how to count and add numbers. They can use algorithms to add numbers, such as starting at the ones place and moving to the tens place.
- Multiplication: Using CT to break down multiplication problems into smaller parts and understand how to use repeated addition to solve them, is another way teachers can use the approach in a mathematics class.
- Problem-solving: Students can use CT to solve word problems by breaking them down into smaller parts and understanding what information is needed to solve the problem.
2. For High School
- Solving systems of equations: In higher classes, teachers can teach students to use CT to solve systems of equations by breaking down the problem into smaller parts and using algorithms, such as elimination or substitution.
- Understanding geometric proofs: To understand the logic behind geometric proofs, CT can be employed. Students can be taught to break down the problem into smaller parts and understand the relationships between different geometric shapes and figures.
- Calculus: Students can use CT to understand the concepts of limits, derivatives, and integrals by breaking down the problem into smaller parts and using and applying algorithms.
- Discrete mathematics: Students can use CT to understand the concepts of logic, set theory, and number theory by abstracting, logical reasoning, and analyzing using algorithms.
- Data analysis: Students can use CT to understand how to collect and analyze data, such as by breaking down a large dataset into smaller parts and using algorithms to identify patterns or trends.
Computational thinking helps break down complex problems into smaller, more manageable parts and develop algorithms or step-by-step solutions. Overall, the use of computational thinking in a mathematics class can help students develop critical thinking and problem-solving skills, as well as a deeper understanding of mathematical concepts. It can also give students the opportunity to apply their knowledge in a practical, hands-on way.
- Nordby, S.K., Bjerke, A.H. & Mifsud, L. Computational Thinking in the Primary Mathematics Classroom: a Systematic Review. Digit Exp Math Educ 8, 27–49 (2022). https://doi.org/10.1007/s40751-022-00102-5.