The Humanistic Mathematics Network defines two different approaches to the term “Humanistic Mathematics” which include a cloud of ideas around the notion of teaching mathematics humanistically, or “teaching as if students mattered,” and another cloud of ideas around the notion of mathematics as a humanistic discipline, or “mathematics as a human endeavor.” We present a unit plan on the topic of numbers and operations which includes elements of both notions. The unit is designed to teach as if students mattered by implementing research from educational and sociological disciplines and is designed to show mathematics as a human endeavor by implementation of historical research. We present different methods and ideas associated with numbers, and operations on those numbers used by past cultures, as well as unique and creative methods used by present day cultures in the hopes of promoting a deeper understanding of number and number flexibility. We then challenge the students to do research into the mathematics used by people from their own culture and then work in groups to creatively develop their own system of numbers, symbols and corresponding operations.
Education Visual learners represent approximately 65 percent of the population and visual aids in the classroom improve learning by up to 400 percent (Statistics on Visual Learners, 2012, 11). “Research has shown that visual learning theory is especially appropriate to the attainment of mathematics skills for a wide range of learners” (Murphy, 2013). Motivated by these statistics, all lessons in this unit will be presented visually. Comprehensive research studies determine that students “need to be engaged in a broad form of mathematics-using and applying methods, and representing and communicating ideas”
(Boaler, p. 83). By presenting mathematical number systems of past cultures, students will see mathematics as form of communication of ideas as well as a method by which particular cultures accomplished day to day realistic activities. Using mathematics to model real-world activity is a Standard for Mathematical Practice within the Common Core Standards for Mathematics (Common Core Standards, 2014). As students are presented with modern number systems such as binary and hexadecimal, they will see the real-world application to the computer age. A lesson on “tropical math” will also be presented as an additional method of using mathematics to represent and communicate ideas (Speyer, 2009).
History of Math Looking at math from a historical perspective shows, not only where math has been, but also how it came to be. The number
system developed by the Babylonians, a base 60 system, still influences our lives today (Berlinghoff, 2004). Our clocks use 60 minutes to denote an hour and 60 seconds to denote a minute. The Mayans also developed extensive numeracy. The Mayan system made use of groups of single digits followed by groups of 5. These were combined into vertical groups of 20 (except at the beginning when they used 18) (Ascher, 1991). Both of these groups used math for everyday activities as well as for leisure activities.
Historical perspectives on mathematics may be used to inform students about the different ways mathematics is used in their everyday life. It also presents the fact that mathematics has been a part of humanity for centuries. The two cultures, Babylonian and Mayan both illuminate that numbers do not have to look the way we typically see them. They may be represented with different bases, written in different ways, and with different symbols. This lesson can easily dovetail into a discussion about modern number systems, such as binary and hexadecimal which are cornerstones of the modern high-tech society.
Sociology ( this is my part !!)
The culminating activity of our project is to have the students work in groups to create a number system (numbers, symbols, and two operations). To optimize the performance of the group, the discipline of sociology will inform our practice in designing the groups. The following strategies will be used:
We will ensure that the groups we design are mixed-ability groups because we want students to learn, communicate, and respect each other (Boaler, 2008). We must also take into consideration that different genders learn math differently ( Boaler, 2008). By prompting the students to research the mathematics background of their own culture we hope to develop in the students a positive cultural and social identity. A positive cultural identity can be fostered by the students reading the world “without losing sight of their cultural community as a source of knowing, understanding, and taking action” (Murrell, p. 38).
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