Disciplinary Literacy in Mathematics
Disciplinary literacy in math relates to the why, the when, and the how of mathematics.
Students need to understand why algorithms work, for example. Why do we borrow when doing subtraction? Why does cross multiplication work? Why does long division work? Developing conceptual understanding of these methods is important because it builds students' problem solving skills, and their abilities to solve problems in areas where an algorithm isn't known.
Knowing when to use a particular method for solving a problem is also important - if students properly apply problem solving techniques to situations where those techniques are critical, they have far more opportunity to experience success than a student who cannot apply conceptual understanding or appropriate algorithms to a problem.
Finally, knowing how to apply the right problem solving technique is necessary to arrive at the correct solution. Here are three examples of skills related to math literacy:
Problem Solving and Perseverance: The problem solving process involves connecting the dots between sequential steps of solving a problem - considering multiple pathways to solving a problem, being able to eliminate pathways that don't apply, and correctly identifying a successful sequence for solving. Perseverance is critical throughout this process, otherwise the problem solving process reaches a dead end.
Reasoning and Explaining: It is important for students to be able to justify their reasoning to themselves and others. If a solution cannot be justified, it may not be a correct solution, and it will be difficult for students to use that technique to solve other problems down the road. Further, explaining the reasoning behind a solution is an important skill not only for problem solving in math but in the working world.
Generalizing and Seeing Structure: Being able to generalize a solution enables students to use solving techniques across different problems, and seeing structure in mathematics allows students to solve problems even when an algorithm for solving may not be know.
Students need to understand why algorithms work, for example. Why do we borrow when doing subtraction? Why does cross multiplication work? Why does long division work? Developing conceptual understanding of these methods is important because it builds students' problem solving skills, and their abilities to solve problems in areas where an algorithm isn't known.
Knowing when to use a particular method for solving a problem is also important - if students properly apply problem solving techniques to situations where those techniques are critical, they have far more opportunity to experience success than a student who cannot apply conceptual understanding or appropriate algorithms to a problem.
Finally, knowing how to apply the right problem solving technique is necessary to arrive at the correct solution. Here are three examples of skills related to math literacy:
Problem Solving and Perseverance: The problem solving process involves connecting the dots between sequential steps of solving a problem - considering multiple pathways to solving a problem, being able to eliminate pathways that don't apply, and correctly identifying a successful sequence for solving. Perseverance is critical throughout this process, otherwise the problem solving process reaches a dead end.
Reasoning and Explaining: It is important for students to be able to justify their reasoning to themselves and others. If a solution cannot be justified, it may not be a correct solution, and it will be difficult for students to use that technique to solve other problems down the road. Further, explaining the reasoning behind a solution is an important skill not only for problem solving in math but in the working world.
Generalizing and Seeing Structure: Being able to generalize a solution enables students to use solving techniques across different problems, and seeing structure in mathematics allows students to solve problems even when an algorithm for solving may not be know.
Dear Ken,
ReplyDeleteThank you for sharing your clearly written blog post about mathematical literacy. I really like the way you started out by explaining the importance of students being able to understand the why, when and how of math. This makes total sense to me.
Thank you, too, for sharing 3 important skills that students need to be successful in your discipline:
*Problem Solving and Perseverance (you've talked about this important skill)
*Reasoning and Explaining
*Generalizing and Seeing Structure
For each of these skills you did a great job of sharing, in detail, the reasons that these skills are necessary in math.
I appreciate your thoughtful insights, Ken! It is a pleasure to get to work with you, again.
Sincerely, Julie Elvin
I like that you mentioned seeing structure. This is so crucial to mathematics, but also can be overlooked. I also loved your explanation for perseverance - "being able to eliminate pathways that don't apply, and correctly identifying a successful sequence for solving" was super well put. Also, I like that you chose a text with mathematical problems as well as a text about a mathematics class. I hadn't really thought of using a syllabus or a course overview as a mathematical text but now that seems totally obvious!
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