Introduction
Often, mathematics concepts are taught in a very dry, algorithm centered way; take number a and number b and do some operation with them, and the result is number c. The focus on the algorithm removes the mathematics concept from the real world, and forces students into a position where they have no way of relating the operations that they are learning to their lives or experiences. This can be difficult for many students, and especially students with dyscalculia. The goal of this project is to take a mathematical operation, in this case division, and embed it into a realistic narrative, to not only introduce the concept in a creative way but also create a context for the operation and help students build conceptual models of the operation.
For students with dyscalculia, learning division the way it is traditionally taught, with an emphasis on numbers, symbols, and "equal groups", poses multiple challenges. Many students with dyscalculia have difficulty recognizing numbers and symbols, and associating meaning with those symbols. The symbol manipulation that is often used in division lessons may have no meaning for them because they are unable to translate between the numerals and symbols and conceptual quantities (see Dana Caffee-Glenn's site for more). The "equal groups" strategy may not be effective because it is often taught without any strategies to help students think about making equal sized groups. Many students with dyscalculia have either very poor or nonexistent strategies for comparing different quantities. Lastly, many students with dyscalculia have had many negative experiences with learning new math concepts, and may be anxious or fearful when new concepts are introduced(see Sonia Salgado's site for more).
This lesson addresses the issues found in traditional division instruction by completely changing the format in which division is presented, and shifting the focus from algorithms to real world conceptual understanding. This is done by placing the lesson in the context of a narrative, in this case the story of "Division Farm". Many students with dyscalculia have strengths in the areas of language and literacy (see Miriam Manglani's site for more) and this lesson seeks to leverage those strengths for a number of reasons. The first reason is based on the affective response students may have when presented with new mathematics concepts. In presenting a math concept through a story, this lesson is trying to alleviate the negative affective response many students have by using a medium that is familiar and comfortable to students, and one in which they feel confident. Second, the story, and the imagery from the story, will set the stage for the following activities that will use the same visual representation. The goal is to address students' recognition weaknesses by removing the emphasis on numbers and symbols and instead using real world objects to present the concept. Lastly, placing mathematics concepts in real world situations, and shifting the emphasis from the numbers involved to the application of the concept will help students develop strategies for thinking about division that are not based on symbol manipulation.
While this lesson was designed specifically with students with dyscalculia in mind, this lesson will help all students in a diverse classroom. Many students, not just students with dyscalculia, struggle to make connections between the algorithms they are learning in class and the real world concepts they represent. Helping students build conceptual models of division will help all students gain a deeper understanding of the concepts, and help them draw connections between what they learn in the classroom and their real-world experiences.