Generalization of Academic Skills

Simple Generative Responding & Complex Generative Responding

Why are we here?

I attended the 50th annual convention for the Association of Applied Behavior Analysis International in Philadelphia. I was thankful to see Art Dowdy, who works at Temple University (R1 institution).

While at the conference, I enjoyed attending Symposium #203: Towards a Technology of Generalization: Simple Generative Responding With the Morningside Model of Generative Instruction. The following includes the list of presenters and the title of their presentations.

• Just Teach…Using the Competent Learner Model Curriculum to Develop Skills Versus Decelerating Undesirable Behaviors (Christina Lovaas & Kristina Zaccaria)

• Towards a Technology of Generalization: Morningside’s Five Ingredients for Guaranteeing Simple Generative Responding (Andrew Kieta & Kent Johnson)

• Towards a Technology of Generalization: Simple Generative Responding of Reading Skills to Real-World Contexts (Nicole Erickson, Andrew Kieta, Kent Johnson)

• Towards a Technology of Generalization: Simple Generative Responding of Persuasive Writing Skills to Real-World Challenges (Adam G. Stretz, Andrew Kieta, Kent Johnson)

The presentation jived with a lot of thinking I have been doing related to declarative math facts, procedural knowledge, and conceptual knowledge. I am thankful that Andrew Kieta was willing to share a slide deck (along with some additional resources) to help inform this post (and subsequent). I intend for this initial post to unpack concepts related to generalization with a follow-up post or two providing more detailed examples of what this *might* look like in practice.

Generalization

Baer, Wolf, and Risley (1968) provided seven dimensions of applied behavior analysis. One of the dimensions they included was generality, stating “A behavioral change may be said to have generality if it proves durable over time, if it appears in a wide variety of possible environments, or if it spreads to a wide variety of related behaviors” (p. 96). Stokes and Baer (1977) echoed this sentiment by stating, “A therapeutic behavioral change, to be effective, often (not always) must occur over time, persons, and settings, and the effects of the change sometimes should spread to a variety of related behaviors” (p. 350). So, what does this jawn mean - remember Art?

• If the behavior is present with the special education teacher, we’d want to see it present with the general education teacher

• If the behavior is present in school, we’d want to see it present at home

• If the behavior is present with one type of stimuli (e.g., 4 + 5 written horizontally), we’d want to see it present with different stimuli (e.g., 4 + 5 presented vertically)

• If the stimulus is provided, the student can provide multiple responses. For example, when presented with 4 x 3 the student can provide the responses of (a) 3 + 3 + 3 + 3 (4 groups of 3), (b) 12, (c) provide an example of this problem (4 tables with 3 students at each table), (d) provide a physical representation (e.g., array model).

• We’d want to see the behavior spread to related skills. For example, the student can use their knowledge of 4 + 5 when solving 24 + 15. Or the student can use their knowledge of 4 + 5 to solve the following 4 + 5 = ? + 2.

To summarize the previous conversation, in many spaces when people discuss the idea of generalization the conversation is simplified to

• stimulus-response is maintained across time - I use the term maintenance

• stimulus-response is consistent across people

• stimulus-response is consistent across settings

• stimulus generalization. The stimulus can vary slightly but the corresponding response is still provided

• response generalization. The stimulus is provided but varied responses are provided

Implicit versus Explicit View of Generalization

Here are some cliff notes.

Stokes and Baer (1977) highlighted that many theories (and attempts to promote) generalization at this point in history viewed the process as passive.

Stokes and Osnes (1989) outlined ways to promote generalization through a more active lens.

Twenty-six years after the Stokes and Baer (1977) article, Osnes and Lieblein (2003) concluded that more researchers were actively promoting generalization. However, the authors highlighted that the concept of promoting generalization was still very much stuck in theoretical conversations, and much more empirical evidence was needed to inform best practices.

To summarize, the field of applied behavior analysis has identified that for generalization to occur, an active approach likely is needed. In 2003, there was still a lot to uncover from an empirical lens.

Connection to Math Intervention

I find this conversation of particular interest when connecting it to the math intervention space. I hear lots of people advocating that they want to see students be creative when engaging with math, wrestle with rich math problems, and find ways to notice and use math in their everyday lives. These outcomes, theoretically, can all be couched as different examples of generalization within the framework explained above.

Morningside Model of Generative Instruction

It would be a failure on my part to not mention Morningside Academy (although I don’t want to derail our current conversation). For those interested, check out the following resources.

• Zach Groshell writing about his trip to Morningside

• Zach Groshell’s interview with Kent Johnson & Andrew Kieta

Within the Morningside Model of Generative Learning, 6 core components steer the ship (I am copying and pasting these from Andrew Kieta’s ABAI presentation, slides 3-4).

1. “First Things First”: Select curricula for instruction on the component behaviors that are deconstructed from today’s classroom holistic activities, and real-world composite repertoires. 

2. Homogeneously group learners for instruction. 

   1. Group students based on current knowledge NOT age/grade

3. Directly and explicitly teach components to accuracy with Mathetics. 

4. Schedule practice of components to fluency with celeration using Precision Teaching.

5. Application: Provide instruction and guided opportunities to practice direct application of previously taught skills and concepts to real-world circumstances. 

6. Adduction: Provide instruction and guided opportunities to engage in re-combinations of previously taught behavior in novel contexts.

An Active Description of Generalization

Application and adduction are specific descriptions of ways students can engage in generalization.

Application involves students using previous knowledge to engage in tasks with new antecedents, circumstances, and contexts. From our description of generalization above, this would include the following (a) stimulus-response is consistent across people; (b) stimulus-response is consistent across settings; and (c) stimulus generalization. The stimulus (antecedent) can vary slightly but the corresponding response is still provided.

To simplify application is “same behavior, new context” (Andrew Kieta, slide 8)

We can refer to this as simple generative responding

Let’s consider some examples of application within mathematics.

• Student demonstrates 1:1 correspondence in counting sets to 10 with manipulatives in class and then performs this skill with a collection of coins they find in their parent’s car.

• Student has engaged with a computer-based math fact intervention and then performs the skill at a similar level with a paper/pencil task.¹

• Student solves total word problems with varying situation contexts. The teacher presents word problems that vary slightly (e.g., using tables or graphs to display data; including irrelevant information) and the student solves them.²

Adduction involves students engaging in new combinations and blends of behavior in new antecedents, circumstances, and contexts.

To simplify adduction is “new behavior, new contexts” (Andrew Kieta, slide 8)

We can refer to this as complex generative responding

Let’s consider some examples of adduction within mathematics.

• The student demonstrates strong fluency in sums to 18. A cloze problem is presented, 10 + [ ] = 7 + 7 and the student correctly identifies 4 would complete the number sentence.

• The student is taught to solve 2-digit by 2-digit and 3-digit by 3-digit addition and subtraction problems, both with and without regrouping. In a word problem the student encounters a problem requiring 4-digit by 3-digit addition with regrouping and solves it correctly.

Takeaways and What’s Next

Key takeaways

1. Generalization is something that we must actively pursue versus just “hoping” it occurs

2. We should break down our goals of generalization as either application (simple generative responding) or adduction (complex generative responding). This will inform the types of instruction tactics we will need to use to support generalization.

What’s Next

1. Discussion of how to promote simple generative responding within the mathematics environment with examples across grade spans.

2. Discussion of how to promote complex generative responding within the mathematics environment with examples across grade spans.

1. I have received LOTS of questions about this recently. Fluency scores (i.e., digits correct per minute) from paper/pencil and computer or tablet may not be comparable. This can occur for many reasons. Two elements to consider are the student’s number writing fluency and their typing fluency. If these are vastly different you will observe differences in your estimatiton for student’s to generalize. Anecdotally, my son’s typing is highly inaccurate in comparison to his writing - thus his fluency (digits correct per minute) via paper/pencil is much higher than computer.

2. Schema instruction is widely discussed today but what gets lost in the shuffle is that there were slightly different approaches to the intervention. Schema-based instruction and schema broadening instruction differed slightly in there approach. Through a series of research studies, Lynn and Doug Fuchs investigated schema broadening instruction to identify how to support student transfer of additive word problem solving knowledge to novel problems. This would be an example of the research team aiming to promote generalization, specifically application.