Note: this guest post is part of an Independent Study the author is completing under the direction of Bernard K. Means.
By Al Pajak
Professional Development Facilitator, Arizona Science Center
Ph.D. Candidate, Prescott College, Prescott, Arizona
Although history encompasses elements of science, technology, engineering, and math, education silos these subjects. With STEM Integration, a holistic approach unites these subjects creating a complete experience for students. While browsing Thingiverse for ideas, I discovered the models for sheep astragalus, which are durable ankle bones that support the weight of the animal by connecting the tibia, a long bone in the lower leg, to the foot stabilizing the ankle during movement. As it turns out, the astragali of the Artiodactyls, the cloven hooved family of animals that include sheep, cows, camels, and pigs, is a dense four sided grooved bone. These became early dice for the Romans, Greeks, and Mongolians. In a game called Astragali, you roll the bones and score points based on the manner in which the bones land. Figure 1 illustrates the simplified rules of play. Misha Tikh (2015), who scanned the bones and shared the files, explains that each bone has four unique sides with unequal probability of landing on one of the sides, which contrasts to modern dice that have an equal probability. There are many different rules for the game, which still played in parts of the world today (Tikh, 2015).
In an effort to integrate STEM and history, I recently introduced students to the Astragali dice. In the classroom, students first considered how the bones function in the animal through models of legs. The Idaho Virtualization Laboratory provides an excellent sheep skeleton on Sketchfab.com (https://skfb.ly/6sWtn) that allows exploration of leg bones. Once they locate the astragalus on the sheep, they are introduced to the game. As they play the game, the students collect data on the number of times the bones land on a side. By graphing the results, the students build an understanding of probability. Next, students roll and graph the occurrence of the sides for modern dice and compare the results. Students may recognize the limitations of using astragalus bones and suggest modification of the rules of play. In Figure 2, for example, the three point “Back” and four point “Belly” sides occur more frequently than the one point “Chios” side. Most students predict that the “Chios” side will have the highest frequency based on the point value. This figure also illustrates that each side of modern dice has a similar frequency. With combined class data, this becomes even more apparent.
As an extension to this activity, students can compare astragali from other mammals. There are similarities between members of the same taxonomic family. Sketchfab.com has a good selection of scanned anatomical specimens, including mastodons, ground sloths, horses, artiodactyls, and primates. Some can be downloaded while others can be viewed and compared virtually. I placed the examples in a Sketchfab collection, which can be found through this link: https://skfb.ly/6x7WI
Link to printable rule cards: http://bit.ly/AstaragaliRules – after Tikh (2015).
Thingiverse File for the Astragali: https://www.thingiverse.com/thing:1036458 Creative Commons Attribution Non-Commercial License.
Kowalski, S. 2007. Roman Board Games – Tali and Tropa (Retreived From http://www.aerobiologicalengineering.com/wxk116/Roman/BoardGames/tali.html)
Pajak, A. 2018. Astragali and Tali Lesson Plan. Copyright Arizona Science Center. http://bit.ly/Astragoli.
Tikh, M. 2015, Knucklebone Dice (Retrieved from Thingiverse https://www.thingiverse.com/thing:1036458). Creative Commons Attribution.