The following set of resources offer some good ideas to start approaching mathematics teaching conceptually by eliciting and building from students' thinking:

Diagnostic Teaching for Grades 6 and 7 (set of 12 problems and accompanying teacher materials)

How Do My Students Think? Diagnosing Student Thinking (research-based guide for teachers)

Learning from Mistakes and Misconceptions PD (slides and guide)

Gaps and Misconceptions in Maths (focuses on subtraction, division, and fractions)

Mathematics Assessment Probes (first chapter of

*Uncovering Student Thinking in Mathematics, Grades K-5*)

*Uncovering Student Thinking About Mathematics in the Common Core, Grades 6-12*(free sample chapters)

Chelsea Diagnostic Mathematics Tests (scanned versions of a book of diagnostic assessment from 1984)

Eliciting Mathematics Misconceptions (blog with two videos about fraction misconceptions)