Concrete Representational Abstract CRA Progression Lookup
Audit observed concrete, representational and abstract stages against a declared CRA progression. Learners may revisit representations; missing stages and inversions are observations, not mastery or efficacy judgments.
Description
Concrete, representational and abstract approaches connect physical examples, representations and symbolic reasoning.
Concrete, representational and abstract approaches connect physical examples, representations and symbolic reasoning.1
This audit compares observed stages with your declared order and reports coverage and local order inversions.
When to use Concrete Representational Abstract CRA Progression Lookup
Use this tool to review missing stages and local order inversions. Establish the learning task, observed evidence and applicable framework or policy edition.
How to use Concrete Representational Abstract CRA Progression Lookup and understand its results
- Establish the learning task, observed evidence and applicable framework or policy edition.
- Enter callerObservedCraStageIds, callerStageDeclaredOrder, using the field meanings and rules below, then run the tool.
- Read missingDeclaredStageIds, orderInversionIndices. Inspect nested result fields where present, and review unknown records separately from known matches.
- Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerObservedCraStageIds | Caller observed cra stage ids | list of string | Required |
| callerStageDeclaredOrder | Caller stage declared order | list of string | Required |
Require a nonempty unique nonblank declared stage list. An observed list can be empty; otherwise it must also be unique and nonblank. Every observed stage must belong to the declared list. Return declared stages absent from observations, in declared order, and zero-based observed positions whose declared rank is lower than the immediately previous observed rank. This is a local adjacent inversion check, not a count of all inverted pairs. Exact strings are matched without normalization.
missing=declared−observed; inversions={i≥1:declaredRank(observed_i)<declaredRank(observed_(i−1))} Use the matching field units and the exact boundary, ordering and reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| missingDeclaredStageIds | Missing declared stage ids | list of string |
| orderInversionIndices | Order inversion indices; zero-based positions in the relevant supplied record or adjacent-pair list | list of number |
{
"input": {
"callerObservedCraStageIds": [
"concrete",
"abstract"
],
"callerStageDeclaredOrder": [
"concrete",
"representational",
"abstract"
]
},
"output": {
"missingDeclaredStageIds": [
"representational"
],
"orderInversionIndices": []
}
}Limitations and assumptions
The declared sequence and its source edition are supplied inputs. Coverage does not measure mastery, consent, teaching quality or learning effect. Observed stages must be unique, so record separate cycles separately when the activity revisits a stage.
Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries; ordinary string lists allow at most 128 strings of 128 UTF-16 units each; numeric matrices allow at most 128 rows and 128 columns, subject to narrower requirements above.
Alternative or Complementary methods
For a related step, use Concrete Examples Abstract Concept Pairing Guide: Concrete examples can illustrate an abstract concept in several contexts. For a complementary comparison, use Phonics Scope Sequence Phoneme Grapheme Order Lookup: A phonics scope and sequence connects speech sounds with written representations in a chosen program and orthography.
References
Similar or alternative tools
- Concrete Examples Abstract Concept Pairing Guide
Concrete examples can illustrate an abstract concept in several contexts.
- Phonics Scope Sequence Phoneme Grapheme Order Lookup
A phonics scope and sequence connects speech sounds with written representations in a chosen program and orthography.