As part of CTL’s book study for the Focus in High School Mathematics Reasoning & Sense Making (FOCUS), this is the sixth in the series of those blog posts. Last time we looked at what the authors suggested for those Reasoning Habits that assists students in understanding and using the mathematics needed for the 21st century – in other words, a way of thinking about the mathematical situation/problem. Let’s stay within the convenes of Chapter 2 and explore the mathematical process of modeling that embodies each of those Reasoning Habits.
Within the structure for thinking about the mathematics: analyzing the problem, implementing a strategy, seeking and using connections, and reflecting on a solution, I believe that mathematical modeling fits within each of those structures/processes of thinking. Additionally, mathematical modeling is also one of the eight Standards for Mathematical Practice from the Common Core State Standards(CCSS) for Mathematics.
The mathematical modeling process that the authors use is in Figure 2.2 on Page 13. It takes the mathematical modeling cycle from the real-world situation to the mathematical model including assumptions to the mathematical conclusions to the real-world situation and then repeats the process.
Let’s connect that process to the reasoning habits and mathematical modeling from FOCUS to mathematical modeling from the CCSS. Please note that these connections are not mutually exclusive thus lots of overlapping and connecting.
| FOCUS Reasoning Habits | FOCUS Mathematical Modeling | CCSS Mathematical Modeling |
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| Analyzing the Problem: Figuring out the problem on my own; Asking what does the problem say. Exploring with various models; Asking– how do you know, why will this work. |
Connecting the real-world problem to past experiences; | Using prior knowledge; Use assumptions and approximations to simplify a complicated situation; |
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| Implementing a Strategy | Combining various mathematical ideas; Building a model that includes the assumptions of the problem |
Using prior knowledge to solve the real world problem; Identifying important quantities in a practical situation and map their relationships using such tools as diagrams, 2-by-2 tables, graphs, flowcharts and formulas. |
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| Seeking & using connections | Determining results for solving the real-word situation; Drawing conclusions; Interpreting results; |
Describe the situation using mathematical formulas, functions, graphs, pictures, other rules; Drawing conclusions from analyzing relationships; |
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| Reflecting on a solution | Interpreting results; Repeating the reasoning process. |
Check to see if an answer makes sense within the context of a situation and change the model when needed. |
The Kentucky Department of Education, Kentucky Committee for Mathematics Achievement , and the Kentucky Council of Teachers of Mathematics have developed a series of podcast that provide instructional prototypes of the CCSS Mathematical Practices. I have posted the podcast for mathematical modeling – see what you think.
For the other podcast, go to http://www.kctm.org/ they are available through ITunes. Download ITunes and search for KY Core Academic Standards. For more information on the Kentucky Committee for Mathematics Achievement visit their forum.
See what you think and join us in the next blog post for the book study.