The result of simultaneously considering Stevin’s 1585 treatment of multiplying decimal fractions and PSMTs’ recollection of their learning and their beliefs about teaching the topic were significant for setting the context for the remainder of the “Using History” course. Indeed, investigating the development of school mathematics topics often taught as proceduralized content and devoid of their rich history would prove to challenge my PSMTs’ mathematical knowledge for teaching. Additionally, their beliefs about the benefits of alternative instructional methods (e.g., historical perspectives) were also challenged. I close with a few excerpts from student reflection journals after they completed the above task. (All excerpts are used with the express written permission of the student and all student names are pseudonyms.)

By using history, students can use the methods like Stevin’s decimals to help students to understand the method of multiplying decimal numbers together without getting confused with the decimal point. What I like about the Stevin decimal number is that it is broken down so that (0) is taking the place as the decimal point. This assignment we actually worked the problems that were even difficult for people in the past. I didn’t quite understand how multiplying decimals was a problem, so now I have a unique tool I can use to show my students how to multiply decimals.** ** This activity will benefit my students by grasping the concept of multiplying decimal numbers whenever they see one. (Shania, Fall 2007)

The history of mathematics has helped me understand notation better. I had never thought about where the notation we use came from because it had never been taught in any of my classes. It is fascinating to know that it wasn’t until the sixteenth century that a decimal fraction notation was invented. Simon Stevin in my opinion was a brilliant man who had the spirit to be a teacher. His invention was simple and easy to examine. I also liked the fact that he wrote his book in the language of the people and not “math language”. He worked not for fame but to inform the astrologers and land measurers of his day. I can definitely see myself incorporating this history in my classroom. Writing out the decimals as fractions 8 9/10 3/100 can help the students remember the names of the different place values. It can also be taught exponentially as 8(1/10)^0 for just the number 8. * *Another way this history can be incorporated is with the multiplication of decimals. If the tenths, hundredths, and thousandths place are clearly written above the digits they represent, it can help students keep their numbers in straight columns. (Daniel, Fall 2007)

My perspective on the article was that it was based on a very interesting and simple topic, decimals and their notation, but how could this possibly be interesting to read about? As I read on I realized that so much of mathematics is a process, not just an equation where you have to follow the “order of operations” to answer it correctly. Someone had to identify what a decimal was, how to determine if what you have just measured, calculated or discovered should be represented by a decimal. And if so, how do we write it? What impressed me most about Stevin’s notation was the fact that he did not just figure out a way to “separate” the numbers, but he also made it a system that allowed you to calculate a portion of that decimal number. He could have used pointless symbols to mark the various “places,” but instead he made this system that we can today use and check to make sure it was accurate. For students this could be very beneficial in breaking down the concept of a decimal and the value of each place. That is one thing that I feel most students struggle with at first, the concept of a decimal is easy, it is the true value that each number holds and the comparison of it to other values in various representations which is more difficult. I could see myself using Simon Stevin’s work to help students adjust to decimals and fractions and the values of each and how they are similar and different and maybe even where they lie on a number line. (Cassy, Fall 2007)