Let's explore how assembly trajectories can help organize the design of a curriculum for teaching generalized same/different responding that spans non-arbitrary to arbitrary (verbally entailed only) relations:
Terms – micro-level assembly, meso-level assembly, macro-level assembly, entailment, combinatorial entailment, transformation of function, contextual scalability, mathetics, world line.
Note 1: The equivalences of terms between AT and RFT will be discussed below. The details of the application of AT empirical methods and maths to the further understanding RFT processes and mechanisms will be discussed in a later blog.
Note 2: Note 1 implies that the details of the functional evolution of emergent verbal behavior structures and the blending and separation of proximal and spactial-temporal distal causal relations within and between these structures will be discussed in a later blog. The following is illustrative.
Review
Complexity and Compositionality. AT proposes that complex structures and scale level dynamics can be modeled by the sequence and number of steps required to assemble a relational world line (i.e., the temporal trace of the assembly over time). The HDML model of RFT illustrates that relational frames and networks of frames are complex, multi-component assemblies involving bidirectional, combinatorial, transformation of function, and contextually controlled relations. By analyzing the many compositional complexities of relational frames and networks, we can better understand how these frames are constructed and how they function.
Potential Micro-Level (Non-Arbitrary) Transitional and Emergent Relations
Matching simple visual patterns, such as sorting objects by color or shape. Resulting in the learner easily identify that a red block is the same as another red block and different from a blue block. This level of Mathetics focuses on establishing a generalized repertoire of same/different responding based on high and low concentrations of shared stimulus features.
- Operants - sampling
- Observer repertoire
- Visual regard of others, events, objects
- Visual tracking of others, events, objects
- Auditory regard of others, events, objects
- Auditory tracking of others, events, objects
- Observer repertoire
- Discriminated Operants - sampling
- Listener repertoire
- Observer repertoire
- MTS identical objects
- MTS similar objects
- For example, vary in size, slant, shape, spacing
- MTS simulacra
- Gradual reduction of shared common stimulus features
- MTS “not” same objects
- Learner must respond away from an attractor, that shares a mecommon stimulus features with the sample, and toward a distractor that shares a minimum of common stimulus features.
- MTS “not” similar objects
- MTS “not” simulacra objects
- MTS identical objects
Meso-Level (Transitional Phase and Emergent) Relations
The learner is taught to match objects across dimensions (e.g., 2D v. 3D) within groups, to match objects within groups, to apply same/different responding across groups of objects, etc.
- Arbitrary relations taught – “Cat” in the presence of a picture, figurine or real cat. “Animal” in the presence of each of a variety of pictured, modeled or real animals.
- Simultaneous and dynamic inculcation of arbitrary and non-arbitrary responding within and across socially maintained groups of objects.
Macro-Level (Arbitrary Transitional and Emergent Relations)
Instruction contains high volume of verbally entailed Prime/Prompt/Fade instructions and labeling of "same" and "different" relations that have few or no non-arbitrary referents. Following instruction the Learner can react to, mand, tact and intraverbally respond as both a listener and speaker to these relations, like understanding that the word "cat" refers to the word “feline” when taught that “A lion is a feline” and then asked “Name another feline” or “How are a lion and a cat the same/different?” or “What is the same between ‘joy’ and ‘happiness’?”
Example of Emergent Mathematical Competency
Non-Arbitrary Relations. The learner is taught basic counting and number enumeration, recognition and application. For example, to tact the cardinal number “three” when shown three apples or three oranges. Also, able to match quantities visually without any verbal mediation.
Meso-Level Relations. The learner correctly responds via tact, mand, intraverbal and auto-clitic repertoires in relation to mathematical symbols and operations. For example, intraverbally tacting that the symbol "3" represents the same quantity as three physical objects or tacting that 2 + 2 is the same as 4, is the same as 7 – 3, is the same as 16/4, is the same as … .
Macro-Level Relations. The Learner evolves more abstract mathematical verbal behavior under the control of concepts and terminology, such as responding the same to "addition" as to "sum" and "plus." Learners begin to apply these verbal relations to verbal conditionals and equivalencies. For example, recognizing that the phrase "combine these groups" entails the same operation as "add these numbers." Learners begin to demonstrate that they can generalize the concept of sameness and difference across various mathematical contexts without instruction or external reinforcement.