Math Principle 5: Use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
This principle is pretty straightforward....if you expect that students will be able to use the tools necessary for any math operation, they need time and practice using them. All tools, no matter how simple they may appear, need practice. Students can not be expected to use any of the measurement tools necessary to problem solve unless they have first hand knowledge of how everything works. Even a tool as simple as a ruler needs explicit instruction and follow up practice.
Once again as I read into these practices, I see how Inquiry Based learning helps our students to apply and use the skills they need to be proficient mathematicians. I think next year is looking like an exciting year for math!!
This principle is pretty straightforward....if you expect that students will be able to use the tools necessary for any math operation, they need time and practice using them. All tools, no matter how simple they may appear, need practice. Students can not be expected to use any of the measurement tools necessary to problem solve unless they have first hand knowledge of how everything works. Even a tool as simple as a ruler needs explicit instruction and follow up practice.
Once again as I read into these practices, I see how Inquiry Based learning helps our students to apply and use the skills they need to be proficient mathematicians. I think next year is looking like an exciting year for math!!
As I read through your explanations of each of these principals, I say to myself "well, duh!" These principals just make sense. I am so happy that someone (actually a group of someones) has actually taken the time to analyze what skills every mathematician use and translated them into skills al our students need to master.
ReplyDeleteAlso, thank you Diane for taking the time to read, analyze, and explain these principals. I agree, this is going to be an exciting year for math!
This standard makes me think of two things. The first is how hard Kim works at ordering and organizing manipulatives for us. We have what I consider a ton of resources. The second is how much fun it will be to bring in real math tools to solve the real life application problems the other standards refer to. I agree these all take specific instruction, modeling, and practice. Science and SS are also going to fit right into all the real life applications. Oh yea ELA will also be the basis for all this with information, research, and reporting results. I love connections!
ReplyDeleteI, too feel that we are lucky to have the resources at our fingertips. I think the difference for most is going to be the shift in thinking from using or looking at these tools or manipulatives as a way to support understanding to a way to build capacity and understanding. It is a shift in pedagogy. I feel that we, as educators, need to experience learning this way in order to be able to truly teach this way. I think we will all need to support each other as we try to dig deeper and build depth in our students' math understanding.
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