Algebra Problem Strings

”A problem string is a purposeful sequence of related problems, designed to help students mentally construct mathematical relationships.  It is a powerful lesson structure during which teachers and students interact to construct important mathematical strategies, models, and concepts.  The power of a problem string lies in the carefully crafted conversation as students solve problems, one at a time, and the teacher models student thinking and draws out important connections and relationships.”

”Facilitating a problem string requires careful attention to the mathematics as well as the ability to really listen to students and model their thinking for all to see.  Thinking is often in development— not fully polished or formed and sometimes idiosyncratic or just tricky to understand.  Because we believe in a mathematical community that includes all learners, our role is to bring before the class what is helpful for development— whether it is clear, clean, and polished, or messy, incomplete, and developing, or even incorrect.  The goal is always to give students the chance to articulate their ideas and to see each others’ thinking— to give the class the chance to respond to, challenge, and make sense of someone else’s strategy or idea.”

“Our belief in problem strings stems partially from the idea that telling or showing students mathematics does not produce learning— and it fact, it never has.  Disrupting this pattern of ‘delivering’ or ‘showing’ students mathematics is a bold undertaking that will require planning, restraint, and real trust in students’ ability to think for themselves.  We must believe that our students are full of interesting mathematical ideas, insights, and questions— and that what they offer is enough to begin the work of formal algebra together.  Allowing students to solve problems any way they want, asking students to share their thinking, and pushing students to justify can be foreign, new, and unsettling.  And, downright fun.”