Personal Journey to Mathematical Modeling
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Mathematical Modeling:
Elements of a Dynamic Process: Life --> Math --> Life For additional information and resources to support teachers who wish to implement mathematical modeling in the classroom, select this link. START WITH LIFE. Life --> Math --> Life Establish real purpose. (LIFE) Start with the real-world: a situation to understand, a problem to solve, a decision to make, a product or process to improve or assess, a plan of action to develop, a prediction to consider, or a curiosity to resolve/pursue or pursue data to reveal a need to change. The ideas of "real" and "relevant" are important. Fantasy contexts can seem real to some students. Real situations may be irrelevant to young students. Situations can range from, "what is the best strategy to win this game?" or "what price should we charge?" or "which venue should we choose?" or "what is the most efficient system for delivering packages?" to social justice issues such as, "is a subgroup over-represented in remedial math classes?" to critical issues such as, "How do we best manage scarce resources such as water or food?" or "How do we prepare for natural disasters?" Focus the investigation. (LIFE) Decide which real-world factors and variables are important to the situation. May require simplification and preliminary assumptions. Some factors may be set aside and revisited later as needed. MATHEMATIZE Life --> Math --> Life Quantify/Represent/Mathematize (DO MATH) Which of the variables can be quantified or represented with mathematics? Create a mathematical model or models in the form of equations, graphs, tables, spreadsheets, diagrams, maps, flowcharts and/or pictures. Solve/Extrapolate (DO MATH) Apply mathematics to the model with the goal of solving the problem. May require the learning of new mathematics. RETURN TO LIFE Life --> Math --> Life Interpret (LIFE) Is the information provided by utilizing the model sufficient to recommend a solution path? Is the model adequate? Did more variables need to be considered with others discarded? Is there a need to start over? Closure (LIFE) • Act upon the results of the investigation • Recommend and defend a solution or pathway. • Report • Propose further exploration Process Notes: A shorthand for the modeling process: Life --> Math --> Life In real life the process is not necessarily linear as illustrated above. The situation and the process can be messy. In real situations it is typical to revisit assumptions or even the initial question itself. Sometimes a model needs to be revised or improved to provide a better solution. This may require learning new mathematics (how cool is that!). Without returning to life and resolving the initial problem: Life --> Math In this scenario the process uses life to motivate the learning of mathematics. (Not a terrible thing but not the purpose of mathematical modeling.) Many authentic/realistic textbook applications fit this scenario. Culturally-relevant Mathematics Mathematics can be a powerful tool for positive change! In some countries and classrooms, mathematical modeling is a vehicle for teachers and students to investigate issues related to social justice and equity and/or the lived experiences of the students. S Fo |
Connecting Life to Math to Life:
A Personal and Professional Journey Currently being edited. S |
