The Importance of Mathematical Practices

The Importance of Mathematical Practices



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• Standards for Mathematical practice –processes and proficiencies
• Habits of mind of the mathematically proficient student
• Description of modeling; applying mathematics outside the math classroom
• Using mathematics tools in flexible, sophisticated, and relevant ways across disciplines
• Technology, structure, and generalization

the standards have content standards and they also have standards for mathematical practice those standards are meant to capture the processes and proficiencies that we want students to have not just the knowledge and skills but also how they use those knowledge and skills they they capture the habits of mind or thinking skills that are specific to mathematics one of those skills is the ability to construct arguments and to reason and to think about why what you're doing works mathematically that's a very important part of the practice standard sis's students who are going to go on to whatever career they go on to I get a need to be able to use mathematics in that career they might just be using the mathematics in their daily life when they read the newspaper and see some complicated data display that they need to understand they're understand a claim that's being made on that data they might be going into a scientific or an engineering profession where they need higher levels of mathematics it doesn't really matter they need to be able to reason mathematically so that's a very important group of practice standards at the beginning there's also a practice standard about modeling modeling means taking a problem external to mathematics thinking of a mathematical description of that problem that you can manipulate mathematically coming to a mathematical solution and then interpreting that solution back again in terms of the real problem it's really the heart of what most students when they go on will be doing with mathematics namely using it to solve problems outside of mathematics modeling in the high school standards stresses that students have to be able to apply mathematics to real-world problems and problems arising outside of the mathematics classroom this was something we heard very strongly from the business community and representatives from Career and Technical Education who gave input into the standards but it's not enough for kids to be able to do math when they're asked to do a math problem the math problems that arise in everyday life aren't like word problems in books the boss doesn't come in to you and say Johnson two trains left two cities two different times when are they going to collide what happens is that you're faced with a messy situation you have to make assumptions you have to simplify you have to bring the tools you know to bear on the problem and analyze it and gain insight into it modeling and real-world applications in the standards are an important component of college and career readiness another important standard is the standard about technology the content standards themselves don't say much about technology because they're about mathematics technology can support students doing mathematics but technology shouldn't be doing the mathematics the kids should be doing the mathematics and the technology practice standard basically says that you should learn to be strategic and wise about when it's appropriate to use technology and also when it's not appropriate to use technology and how to interpret the results when you have the technological tool when you when you do use one there's a group of standards at the end about structure and generalization those standards are really the heart and soul of mathematics in some sense in the sense that when you look at a mathematical object you want to be able to see it as having meaning let's just see it as something you have to sort of poke with a stick and hope it turns into what you want so the standards about seeing mathematical structure and about generalizing are describing the sort of skills you want students to have as they work with mathematical expressions equations functions geometric constructions you want them to be able to see hidden structures transform those objects into things that have a purpose and they use that they can be put you

4 thoughts on “The Importance of Mathematical Practices”

  1. Thank you for pointing out the distinction between word problems and real world problem solving. Many educators tend to use these terms synonymously missing opportunities to engage students in everyday situations that we as adults take for granted.

  2. What is the purpose of these mathematical practices? Can they be in any way helpful? These standards are good habits of mind practiced by mathematicians and, to some degree, good students and teachers. For those that already have these habits, the practices are no news.The issue is that they are wrongly perceived as cause, when they are effect, consequence of understanding through PS. Important thing is that those that don't have that kind of understanding at least can get excited. Ridiculous!

  3. Thanks for these videos; they are helping me understand the new standards. You say that students should learn to use technology strategically, but that technology shouldn't "do the math." As a high school math teacher, I would love for the standards to be more specific about this. It is certainly not possible/necessary to do everything by hand anymore, but where do we draw the line? For example, should we still teach students to factor polynomials using the Rational Roots Theorem?
    Colleen

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