Research Alignment

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dummify™ does not introduce a new theory of learning.

It names and organizes patterns that already appear across decades of research in mathematics education, learning science, and cognitive psychology — particularly research showing that understanding forms through structure, representation, and relational sense-making before procedural fluency.

The site itself is designed to be usable without reference to research.
This page exists for educators, parents, and readers who want to see where these ideas already appear in established work.

The sources below are not prerequisites.
They are points of alignment.

Research consistently shows that focusing on learning progression and conceptual structure — rather than steps alone — supports deeper understanding and transfer.

This aligns with dummify™’s emphasis on orienting to what kind of task this is before attempting to solve it.

A substantial body of work highlights the role of visual structure, diagrams, and representations in forming mathematical meaning prior to symbolic notation.

This supports the Math Ladder sequence, where representation stabilizes understanding before symbols compress it.

Research in algebra instruction emphasizes relational reasoning — understanding how quantities depend on and constrain one another — before symbolic manipulation.

This aligns with dummify™’s framing of algebra as maintaining relationships while values change, rather than as letter-based computation.

Studies show that when learners become confused, returning to conceptual anchors — visual fields, relationships, or context — can restore understanding more effectively than repeating procedures.

This mirrors the instruction to return to the lowest rung of the Math Ladder that still makes sense.

Research on mathematical thinking challenges speed-based models of competence and emphasizes sense-making, reflection, and meaning over time.

This aligns with the recognition that many learners understand deeply — but not sequentially.

A selection of research that reflects these alignments includes work by:

• Suh & Seshaiyer — learning progressions over procedures
   
• Rivera — visually oriented mathematics curricula
   
• Presmeg — visualization and mathematical understanding
   
• Gurganus — relational approaches to algebra
   
• Schoenfeld — sense-making over speed
   
• Danquah; Bustang et al.; Lei & Xin — conceptual-first and reorientation strategies
   

(Full references available upon request.)