Modeling with Mathematics John A. Pelesko and Michelle Cirillo ...

Modeling with MathematicsJohn A. Pelesko and Michelle CirilloDepartment of Mathematical Sciences, University of DelawareOver ten years ago, the National Council of Teachers of Mathematics included modelingas an important element of their Algebra, Geometry, and Representation standards in the (2000)Principles and Standards for School Mathematics. The authors recommended that students in allgrades use mathematical models to represent and understand quantitative relationships, to solvegeometric problems, and to interpret physical, social, and mathematical phenomena (NCTM,1990). Modeling has been incorporated even more prevalently into the Common Core StateStandards in Mathematics (CCSS-M; National Governors Association Center for Best Practices& Council of Chief State School Officers, 2010) with modeling being both one of the eightStandards for Mathematical Practice as well as an important content standard at every grade levelfrom Kindergarten through High School. Using modeling, mathematically proficient studentsshould be able to “apply the mathematics they know to solve problems arising in everyday life,society, and the workplace” (p. 7). More specifically, the document states:Mathematically proficient students who can apply what they know are comfortablemaking assumptions and approximations to simplify a complicated situation, realizingthat these may need revision later. They are able to identify important quantities in apractical situation and map their relationships using such tools as diagrams, two-waytables, graphs, flowcharts, and formulas. They can analyze those relationshipsmathematically to draw conclusions. They routinely interpret their mathematical resultsin the context of the situation and they reflect on whether the results make sense, possiblyimproving the model if it has not served its purpose. (p. 7)The ability to model with mathematics is considered a practice that mathematics educatorsshould seek to develop in their students. As teachers, we need to support our students indeveloping the Model with Mathematics practice, one of the eight practices which rest onimportant processes and proficiencies with longstanding importance in mathematics education(CCSS-M, 2010).In this seminar, we take a “hands-on” approach to the subject of mathematical modeling. Thegoal is to engage participants in the entire process: observation, experiment, construction of amodel, analysis of a model, and connecting mathematical understanding with understanding ofthe natural world. Participants will make use of our experimental laboratory, the MEC Lab, andcarry out simple experiments, gather data, and build models. Computational investigations ofmathematical models will also occur, using such tools as Maple, Mathematica, GeometersSketchpad, and Matlab.During the seminar, our focus will be on how mathematics can be used as a way ofunderstanding the natural world. Mathematically, our tools will range from sequences of naturalnumbers, to systems of equations, functions, and elements of calculus. Fellows at all levels arewelcome and encouraged to join this seminar. Each Fellow will be encouraged to develop handsonactivities that can be taken back to the classroom and used to teach mathematical modeling.

Fellows who are not mathematics teachers, but who teach science at any level, are also welcomeand encouraged to join this seminar. Such Fellows will be encouraged to take current scienceclassroom activities and integrate mathematics into them.ReferencesNational Council of Teachers of Mathematics. (2000). Principles and standards for schoolmathematics. Reston, VA: Author.National Governors Association Center for Best Practices & Council of Chief State SchoolOfficers. (2010). Common core state standards for mathematics. Retrieved fromCommon Core State Standards website: http://www.corestandards.org/thestandards/mathematics