In this research we investigate how mathematics teachers, as graduate students, estimate the value of π by exploring the problem of squaring the circle using digital technology. Initially, we mention some aspects of teaching and learning of calculus in the literature, emphasizing studies that use the notion of humans-with-media to highlight the role of technology in mathematical thinking and knowledge production. Insights on the history of mathematics in calculus are also discussed. We developed a qualitative study based on three different solutions created by groups of teachers using the software GeoGebra and Microsoft Excel. All the teachers’ solutions improved the approximation (8/9)² \(\approx\) π/4, by determining p and q for (p/q)² \(\approx\) π/4. The first two solutions with GeoGebra emphasized experimentation and visualization, improving the approximation from one to three decimal places. The third solution with Excel pointed out the elaboration of a formula and improved it up to six decimal places. We emphasize how media shaped the strategies and solutions of the groups. Based on these solutions, we explore an approach for cubing the sphere, discussing approximations for π, highlighting the role of media in enhancing conceptual complexity in the solution of mathematical problems. The nature of the strategies for solving a problem is discussed, especially regarding different ways of thinking-with-technology developed by collectives of teachers-with-media. Although we acknowledge an alternative design for the proposed task, the exploration of problems using aspects of the history of mathematics contributes to the state of the art concerning the studies in calculus developed by the Research Group on Technology, other Media, and Mathematics Education in Brazil.

在这项研究中，我们研究作为研究生的数学老师如何通过探索使用数字技术对圆进行平方的问题来估计π的值。最初，我们在文献中提到微积分的教学和学习的某些方面，着重强调了使用以媒体为人的概念来强调技术在数学思维和知识生产中的作用的研究。还讨论了微积分中数学史的见解。我们基于教师小组使用软件GeoGebra和Microsoft Excel创建的三种不同解决方案进行了定性研究。通过确定p和q，所有教师的解决方案都提高了近似（8/9）² \（\ approx \） π/ 4。对于（p / q）² \（\ approx \） π/ 4。GeoGebra的前两个解决方案着重于实验和可视化，将近似值从小数点后一位提高到了三位。Excel的第三个解决方案指出了公式的详细说明，并将其改进到了小数点后六位。我们强调媒体如何塑造群体的策略和解决方案。基于这些解决方案，我们探索了一种对球体求立方的方法讨论了π的近似值，强调了媒体在解决数学问题中提高概念复杂性方面的作用。讨论了解决问题的策略的性质，特别是与媒体老师的集体开发的不同的技术思维方式。尽管我们认可拟议任务的替代设计，但利用数学历史方面的问题探索有助于促进巴西技术，其他媒体和数学教育研究小组开发的微积分研究的最新发展。