Have you been following our video series on the Standards for Mathematical Practice? If not, you can catch up with our posts on Mathematical Practice #1, Mathematical Practice #2, and Mathematical Practice #3. Today we are discussing Mathematical Practice #4: Model with mathematics.
There are multiple parts to each practice. The parts help students develop the habit of mind that is the main practice. Remember that the practices are defined as ways to help students become mathematically proficient. As we look at each practice, think of ways we can help students to take ownership of these practices.
In the fourth video, students are learning how to use data displays to make decisions about real life situations. The Essential Question asks: “How can you display data in a way that helps you make decisions?”
Observe how the teacher makes a connection to real life, thus providing meaning to the mathematics being taught. Notice how she validates each student’s choice for graphing data but asks the student to justify whether or not his/her decision makes sense. When students begin to work on problems in their groups, they will be able to use these strategies, thereby building their proficiency.
Mathematical Practice #4: Model with mathematics.
• Mathematically proficient (MP) students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.
• MP students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.
• MP students are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas.
• MP students can analyze relationships mathematically to draw conclusions.
• MP students routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
As you look at your classroom, you probably see students with varying degrees of expertise in this practice. Our job, as educators, is to help students develop a habit of mind that helps them naturally think before they begin to model mathematics. Ask yourself:
Do you give students the opportunity to discuss the connections between math and everyday life?
Are students comfortable making suggestions regardless of their accuracy?
Do students understand the importance of data displays?
As students take ownership of their learning and develop expertise using the mathematical practices, the content standards (knowledge, skills and understandings, procedural skills and fluency, and application and problem solving) will make sense, allowing students to achieve success in mathematics.