We are interested in inspecting the foundations beneath claims that are commonly made within math education discourse, particularly if the claim is associated with recommendations that math education experts might make to practitioners. What follows are just candidate claims that might be inspected; we do not endorse any of these claims as necessarily true.
Many of the claims can be phrased in the following form, drawing upon constructs just below...
"Mathematics teaching that consistently features <PARTICULAR INSTRUCTIONAL FEATURE> will positively impact <PARTICULAR STUDENT OUTCOME>."
Cognitively-Demanding Tasks
Opportunities for Productive Struggle
Mathematical Discussions
Collaborative Learning
Multiple Representations
Opportunities for Student Agency
Responsive Teaching / Teacher Noticing
Contextualized Tasks / Concrete Fading
Conceptual Development Before Procedures
Digital Technology / Calculators
Design Based on Learning Trajectories
Homework
Learning
Achievement
Conceptual Understanding
Procedural Understanding
Transfer
Attitudes Toward Math
Sense of Belonging
Agency
Identity Formation
Critical Consciousness
High levels of teachers' mathematical content knowledge positively impacts <PARTICULAR STUDENT OUTCOME>.
Reform-oriented math curricula positively impact <PARTICULAR STUDENT OUTCOMES>.
Dialogic instructional models (incorporating many particular instructional features into a coherent vision) positively impacts <PARTICULAR STUDENT OUTCOMES>.
Formal teacher education programs lead to teachers who employ instructional practices that are more effective than those who did not attend formal teacher education programs (or, perhaps the instructional practices are equally effective but those from formal teacher education programs are more likely to remain in the profession).
The Inspecting Foundations project team is being formed. Future versions of this site will share the claims we are inspecting, the evidence we uncover, and our assessments of the strength of that evidence.