I had the privilege to take a “History of the K-16 Mathematics Course” from Dr. Sharon Senk at Michigan State University. I loved the opportunities I had to dig into old mathematics textbooks – it’s amazing how many are available digitally through Google Scholar or other resources.
I argue that looking back at old textbooks helps me in thinking about mathematics education by broadening my perspective on what “traditional” means, how often the goals of textbook authors have changed, and giving me some additional support when I talk to parents and preservice teachers about why they need to learn “new-fangled” methods for understanding basic arithmetic operations.
I like to pull out some images I found in Swetz (1995), showing that multiple methods of multiplication (yes, even the “new-fangled” methods like the lattice method) were included in textbooks as early as the 13th century:
I like looking in old textbooks because they also help by allowing me to “rediscover” old methods or strategies that fell into disuse, and yet could be used to help students choose from additional methods, find methods that make more sense to them, and accept that mathematics isn’t a set of rigid procedures invented by a group of old math teachers somewhere, but that creativity can enter the mix – students can come up with their own strategies!
After looking at these methods, I also found this site that gives many other strategies for mulitplying:
Swetz, F. (1995). To know and to teach: mathematical pedagogy from a historical context. Educational Studies in Mathematics, 29(1), 73-88.