The best math teachers know what works because they've spent careers figuring out what moves make students think rather than just answer. That same knowledge lives in decades of research in cognitive science, math ed and teacher ed, in the work of organizations like NCTM, the National Academies, and the American Statistical Association. We founded Wren to make it more accessible and actionable — not as a document teachers read once, but embedded in every activity they run and every teaching move it supports.
Research Themes
These are the bodies of evidence that shape how Wren activities are designed and what teacher moves they include.
High-Leverage Instructional Practices
Certain teaching moves have an outsized effect on what students learn — not just what they cover. Ball & Forzani (2009) call these high-leverage practices: moves that are fundamental to effective instruction regardless of content area. Hiebert & Grouws (2007) identify two classroom features that consistently predict learning across otherwise different pedagogical approaches: explicit attention to concepts, and students engaging with important mathematics at the edge of their current understanding. Wren instructional routines are built around both.
Productive Struggle and Learning from Errors
Students who work through problems before receiving instruction develop deeper conceptual understanding than those who are taught the method first — even when the initial attempts fail. Kapur's research on productive failure (2008, 2014, 2015) shows that the struggle itself is where much of the learning happens. Separately, Booth and colleagues (2013) found that middle schoolers who studied and explained common errors improved their algebra performance more than those who only saw correct solutions. Test It, Tune It and Learn from Mistakes are grounded in this evidence.
Mathematical Discourse and Argumentation
When students explain their thinking, argue for a position, and engage with someone else's reasoning, they develop understanding that procedural practice alone doesn't produce. Hiebert & Wearne (1993) documented the specific moves that distinguish meaning-focused instruction: shifting from product questions ("what's the answer?") to process questions ("how did you get there?"). Smith & Stein's five practices (2018) provide the framework for making those discussions productive rather than merely active. Decide & Defend, Always, Sometimes, Never, and Rank and Reason are built from this work.
Multiple Representations
Moving fluidly between graphs, tables, equations, and verbal descriptions is one of the most reliable indicators of mathematical understanding. Goldin & Shteingold (2001) showed that different representations highlight different features of mathematical relationships — and that students need explicit practice moving between them, not just working within a single mode. Graph-Table-Equation, Graph Sort, and Fit or Misfit develop this translational fluency directly.
Comparison and Contrasting Cases
Examining multiple related examples helps students extract underlying structure in ways that single examples can't. Schwartz & Bransford (1998) showed that analyzing contrasting cases creates what they call "a time for telling" — students become ready to understand distinctions they would otherwise miss. Graph Sort, Which One Doesn't Belong, and Rank and Reason are designed around this mechanism.
Metacognition and Self-Regulated Learning
Students who develop awareness of their own problem-solving strategies — not just fluency with procedures — perform better and transfer their knowledge more reliably. Schoenfeld's foundational work (1992/2016) and Zimmerman's framework for self-regulation (2002) inform how Wren activities prompt students to reflect on their own reasoning process, not just their answers. Test It, Tune It and Learn from Mistakes develop this directly.
How Professional Learning Actually Works
Research on sustained professional development is consistent: two days in August doesn't change how teachers teach. Change requires repeated cycles of learning, practice, reflection, and community (National Academies, 2018; Lemov et al., 2012). This is why Wren is designed as a practice-building system, not a content library: the instructional routines, the moves embedded in each one, and the community are all part of the same mechanism.