Different tools.
Different ways to see.
Compare how each system represents numbers and supports a teaching task. No one layout establishes better learning on its own.
This is a broad introductory selection, not an exhaustive catalogue. Product variants differ. These articles distinguish documented features, our practical analysis, provider claims and research findings.
Montessori golden beads and bead frames
Quantity before notation
Representation and evidenceJapanese soroban
One five-bead and four unit-beads
Representation and evidenceChinese suanpan
Two upper beads and five lower beads
Representation and evidenceRussian schoty / tchoty
Equal-value counters on horizontal rods
Representation and evidenceSchool counting frames
Rows for counting and grouping
Representation and evidenceRekenrek / number rack
Seeing groups of five and ten
Representation and evidenceBase-ten blocks / number pieces
Groups you can join and split
Representation and evidenceCuisenaire rods
Length and the chosen whole
Representation and evidenceNumber lines and ten-frames
Position and part–whole models
Representation and evidenceDigital abacus and mental calculation
A screen model and a training programme
What does research tell us?
A 2013 meta-analysis included 55 studies and 7,237 learners. It found aggregate benefits of concrete manipulatives over abstract-symbol-only instruction, with outcomes varying by instructional and methodological factors. It does not show that every tool works equally well or that TUA is effective.
Teaching through reasoning
Pearson describes Van de Walle, Karp and Bay-Williams’ Teaching Developmentally as using problem-based activities and learners’ reasoning. This is a teaching approach, not a competing product. TUA’s questions, predictions and checking activities are a design alignment, not an endorsement or validated implementation of that book.