There is increasing concern among educators, parents, and the public worldwide that technology might be impeding students' ability to think mathematically. A recent UK survey reported by The Guardian found that secondary school teachers observed pupils using artificial intelligence losing their critical thinking skills. Two-thirds of the teachers reported noticing this decline among children who no longer feel the need to spell out words because of voice-to-text technology. “Students are losing core skills—thinking, creativity, writing, even how to have a conversation,” one teacher told the National Education Union poll. This situation in the UK mirrors what is happening in Ghana.

Walk into any Ghanaian secondary school classroom today, and you will see students reaching for calculators to solve problems that previous generations handled mentally. Observe a child shopping — they will pull out a phone to calculate change rather than do simple mental arithmetic. These observations raise a genuine concern: is the very tool designed to assist students’ learning actually hindering the development of essential mathematical thinking skills? This question deserves careful consideration, especially as Ghana advances its digital transformation in education. However, to answer it honestly, we must first recognise that the relationship between technology and mathematical thinking is far more complex than it appears.

A Historical Perspective: Technology Has Always Been Present

Let us begin by questioning the notion of a "pure" era of mathematical thought untouched by technology. The slide rule, which served engineers and scientists for generations, was a top-notch tool in its time. Logarithm tables simplified complex calculations into easy-to-use reference guides. The abacus, thousands of years old, remains a highly developed calculating tool. Counting boards with jetons—physical tokens moved across marked surfaces—made place value and arithmetic operations visible and tangible. Mesopotamian accountants used clay tokens as early as 4000 BCE. The Inca recorded numbers using knotted quipu cords. The Japanese and Koreans calculated with sangi rods. Mathematics has always been shaped by technology. Among these historical tools, several merit particular attention for what they reveal about the relationship between tools and thinking.

Napier's rods (or Napier's bones), invented by the Scottish mathematician John Napier in 1617, are an early example of technology designed to aid mathematical calculation. These were physical devices—usually made of ivory, wood, or metal—inscribed with multiplication tables in a cleverly arranged grid. To multiply, a student would select rods representing the digits of the number being multiplied, place them side by side, read across the rows to find partial products, and then add them to reach the final result. The rods displayed multiplication facts openly—the 7×8=56 was visible to all, not hidden inside a microchip. The student needed to understand place value to align the digits correctly. They also needed to know when and why to add the partial products. Furthermore, they had to estimate whether the final answer was reasonable. The rods made the distributive property visible and tangible; a learner could literally see how 432 × 5 breaks down into (400 × 5) + (30 × 5) + (2 × 5).

The geoboard, invented in the 1950s by Egyptian mathematician Caleb Gattegno, is deceptively simple: a flat board with pegs arranged in a grid, on which students stretch rubber bands to form geometric shapes. Yet this humble tool embodies deep mathematical thinking. When a student stretches a rubber band around pegs to create a square, they are not merely seeing a square — they are experiencing its properties. The right angles become tangible. The equal sides are visible and verifiable. Area becomes something you can count by the squares enclosed. Perimeter becomes something you can trace with your finger. The geoboard makes abstract geometric concepts concrete in a way that even sophisticated dynamic software struggles to match. It demands active participation — you cannot passively experience a geoboard.

The protractor has a rich history spanning abstract mathematics, applied sciences, and education. Students using protractors must understand the concepts of angles, estimation, and accuracy—the tool reveals rather than conceals. Graph paper, now so common that we forget it is a form of technology, was promoted by mathematician Eliakim Hastings Moore (1862–1932) in the early twentieth century as part of a 'lab method' of teaching mathematics, making calculations easier and demonstrating the links between abstract principles and real-world applications. Geometric models—physical three-dimensional objects—enabled students to see and handle abstract forms. Cube root blocks facilitated understanding of root extraction through physical manipulation.

What is instructive about all these historical tools is not just their existence but also how they functioned and what they required of their users. They were not passive answer-makers. They were active partners in thought. They were transparent — users could see how they worked because the mechanisms were visible and the operations demanded active participation. The tool acted as a thinking aid, not a thinking replacement.

Modern tools often behave differently. They act as "black boxes," where students input numbers and receive answers without understanding the underlying process. A calculator does not show its workings. A math app does not explain why the answer is correct. This contrast—transparency versus opacity, active versus passive involvement—lies at the heart of concerns about technology and mathematical thinking.