A Problem String is a powerful teaching tool based on the idea that learning mathematics is about constructing relationships and connections. It’s not the only thing that could happen in a math class, but I propose that it’s an important part.
A Problem String is a series of related problems purposefully sequenced to help students construct mathematical relationships so that powerful strategies become their natural instincts. This powerful teaching tool is designed to help students mentally construct mathematical relationships. In this mini-lesson structure, teachers and students interact to construct important mathematical strategies, models, and concepts.
“A problem string is a purposefully designed sequence of related problems that helps students mentally construct numerical relationships and nudges them toward a major, efficient strategy…
[P]roblem strings are not intended to be used all at once, handed out as worksheets, or used as independent work for students.
By using models and problem strings in a systematic way, with an eye toward the major, efficient strategies, we can help secondary students construct mental numerical relationships. For those students who come to us with some elementary work in numeracy, we can build on their current understanding and support their continued development, while at the same time helping those who lack that understanding gain the foundation they need. When we give secondary students this numerical power, we also help them engage in learning higher mathematics with more confidence and more success.”
Building Powerful Numeracy for Middle & High School Students, p. 10
The power of a Problem String lies in the carefully crafted conversation as students solve problems, one at a time, and the teacher makes student thinking visible and draws out important connections and relationships.
You can learn more about problem strings in episode #71 of my podcast. I also highly recommend you take my FREE ONLINE WORKSHOP Developing Mathematical Reasoning to better understand the importance of developing reasoning in students, how algorithms can hinder, and how Problem Strings can help.
For more algebra Problem Strings:
For numeracy Problem Strings:
And finally, be sure to check out these example videos of Problems Strings in real classrooms. See if they live up to the hype!