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At the Intersection of Derived Relations and Observational Learning: Teaching Fraction–Percentage Relations

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Abstract

Little research has examined the intersection of derived relations and observational learning, which may be an avenue by which an instructor can increase the total amount of learning while conserving instructional resources. In this study, we investigated this intersection in the context of teaching third-grade students fraction–pictogram–percentages equivalence classes. We taught participants two baseline relations and observed the emergence of all possible derived relations. Prior to training, the participants could sort percentage stimuli from least to greatest (comparative relations), but could not do this with fraction stimuli. Following the formation of equivalence classes, the participants could accurately sort fraction stimuli, thus demonstrating the transfer of function. Two additional participants observed the target participants undergo the training of baseline relations. The observing participants acquired baseline relations with no direct reinforcement, derived all relations, and demonstrated transfer of function. These findings suggest a novel way to incorporate equivalence-based instruction into classroom settings.

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References

  • Albers, A. E., & Greer, R. D. (1991). Is the three-term contingency trial a predictor of effective instruction? Journal of Behavioral Education, 1, 337–354.

    Article  Google Scholar 

  • Albright, L., Reeve, K. F., Reeve, S. A., & Kisamore, A. N. (2015). Teaching statistical variability with equivalence based instruction. Journal of Applied Behavior Analysis, 48, 883–894. https://doi.org/10.1002/jaba.249.

    Article  PubMed  Google Scholar 

  • Alegre, F., Moliner, L., Maroto, A., & Lorenzo-Valentin, G. (2018). Peer tutoring in mathematics in primary education: A systematic review. Educational Review. https://doi.org/10.1080/00131911.2018.1474176.

    Article  Google Scholar 

  • Berens, N. M., & Hayes, S. C. (2007). Arbitrary applicable comparative relations: Experimental evidence for a relational operant. Journal of Applied Behavior Analysis, 40, 45–71.

    Article  PubMed  PubMed Central  Google Scholar 

  • Bondy, A. S., & Frost, L. A. (1994). The picture exchange communication system. Focus on Autistic Behavior, 9, 1–19.

    Article  Google Scholar 

  • Brodsky, J., & Fienup, D. M. (2018). Sidman goes to college: A meta-analysis of equivalence-based instruction in higher education. Perspectives on Behavior Science, 14, 95–119. https://doi.org/10.1007/s40614-018-0150-0.

    Article  Google Scholar 

  • Bryne, B. L., Rehfeldt, R. A., & Aguirre, A. A. (2014). Evaluating the effectiveness of the stimulus pairing observation procedure and multiple exemplar instruction on tact and listener responses in children with autism. Analysis of Verbal Behavior, 30, 160–169.

    Article  Google Scholar 

  • Critchfield, T. S., & Twyman, J. S. (2014). Prospective instructional design: Establishing conditions for emergent learning. Journal of Cognitive Education and Psychology, 13, 201–217. https://doi.org/10.1891/1945-8959.13.2.201.

    Article  Google Scholar 

  • Curriculum Associates. (2014). i-Ready proven to predict. Retrieved from: http://www.curriculumassociates.com/products/iready/i-ready-predicts.aspx.

  • Delgado, J. A. P., & Greer, R. D. (2009). The effects of peer monitoring training on the emergence of the capability to learn from observing instruction received by peers. The Psychological Record, 59, 407–434. https://doi.org/10.1007/BF03395672.

    Article  Google Scholar 

  • Dymond, S., & Rehfeldt, R. A. (2000). Understanding complex behavior: The transformation of stimulus functions. The Behavior Analyst, 23, 239–254.

    Article  PubMed  PubMed Central  Google Scholar 

  • Fienup, D. M., Covey, D. P., & Critchfield, T. S. (2010). Teaching brain—Behavior relations economically with stimulus equivalence technology. Journal of Applied Behavior Analysis, 43, 19–33.

    Article  PubMed  PubMed Central  Google Scholar 

  • Fienup, D. M., & Critchfield, T. S. (2011). Transportability of equivalence-based programmed instruction: Efficacy and efficiency in a college classroom. Journal of Applied Behavior Analysis, 44, 435–450.

    Article  PubMed  PubMed Central  Google Scholar 

  • Fienup, D. M., Wright, N. A., & Fields, L. (2015). Optimizing equivalence-based instruction: Effects of training protocols on equivalence class formation. Journal of Applied Behavior Analysis, 48, 613–631. https://doi.org/10.1002/jaba.234.

    Article  PubMed  Google Scholar 

  • Greer, D. R. (2002). Designing teaching strategies: An applied behavior analysis systems approach. San Diego, CA: Academic Press.

    Google Scholar 

  • Greer, R. D., Dudek-Singer, J., & Gautreaux, G. (2006). Observational learning. International Journal of Psychology, 41, 486–499. https://doi.org/10.1080/00207590500492435.

    Article  Google Scholar 

  • Greer, R. D., Keohane, D., Meincke, K., Gautreaux, G., Chavez-Brown, M., Pereira, J., & Yuan, L. (2004). Key components of effective tutoring. In J. Moran & R. Malott, (Eds.), Evidence-Based Educational Practices. New York: Elsevier/Academic Press.

  • Greer, R. D., & Longano, J. (2010). A rose by naming: How we may learn how to do it. The Analysis of Verbal Behavior, 26, 73–106.

    Article  PubMed  PubMed Central  Google Scholar 

  • Greer, R. D., & Ross, D. E. (2008). Verbal behavior analysis: Inducing and expanding new verbal capabilities in children with language delays. Boston: Person Education Inc.

    Google Scholar 

  • Hayes, S. C., Barnes-Holmes, D., & Roche, B. (Eds.). (2002). Relational frame theory: A post-Skinnerian account of human language and cognition. New York: Kluwer.

    Google Scholar 

  • Hayes, S. C., Kohlenberg, B. S., & Hayes, L. J. (1991). The transfer of specific and general consequential functions through simple and conditional equivalence relations. Journal of the Experimental Analysis of Behavior, 56, 119–137.

    Article  PubMed  PubMed Central  Google Scholar 

  • Horne, P. J., & Lowe, C. F. (1996). On the origins of naming and other symbolic behavior. Journal of the Experimental Analysis of Behavior, 65, 185–241. https://doi.org/10.1901/jeab.1996.65-185.

    Article  PubMed  PubMed Central  Google Scholar 

  • Leader, G., & Barnes-Holmes, D. (2001). Establishing fraction–decimal equivalence using a respondent-type training procedure. The Psychological Record, 51, 151–165. https://doi.org/10.1007/BF03395391.

    Article  Google Scholar 

  • Lovett, S., Rehfeldt, R. A., Garcia, Y., & Dunning, J. (2011). Comparison of a stimulus equivalence protocol and traditional lecture for teaching single-subject designs. Journal of Applied Behavior Analysis, 44, 819–833.

    Article  PubMed  PubMed Central  Google Scholar 

  • Lowe, M. L., & Cuvo, A. J. (1976). Teaching coin summation to the mentally retarded. Journal of Applied Behavior Analysis, 9, 483–489.

    Article  PubMed  PubMed Central  Google Scholar 

  • Lynch, D. C., & Cuvo, A. J. (1995). Stimulus equivalence instruction of fraction–decimal relations. Journal of Applied Behavior Analysis, 28, 115–126.

    Article  PubMed  PubMed Central  Google Scholar 

  • Miguel, C. F. (2018). Problem-solving, bidirectional naming, and the development of verbal repertoires. Behavior Analysis: Research and Practice, 18, 340–353. https://doi.org/10.1037/bar0000110.

    Article  Google Scholar 

  • Murphy, C., Barnes-Holmes, D., & Barnes-Holmes, Y. (2005). Derived manding in children with autism: Synthesizing Skinner’s verbal behavior with relational frame theory. Journal of Applied Behavior Analysis, 38, 445–462.

    Article  PubMed  PubMed Central  Google Scholar 

  • Ninness, C., Barnes-Holmes, D., Rumph, R., McCuller, G., Ford, A. M., Payne, R., et al. (2006). Transformations of mathematical and stimulus functions. Journal of Applied Behavior Analysis, 39, 299–321.

    Article  PubMed  PubMed Central  Google Scholar 

  • Ninness, C., Dixon, M., Barnes-Holmes, D., Rehfeldt, R. A., Rumph, R., McCuller, G., et al. (2009). Constructing and deriving reciprocal trigonometric relations: A functional analytic approach. Journal of Applied Behavior Analysis, 42, 191–208.

    Article  PubMed  PubMed Central  Google Scholar 

  • Ramirez, J., & Rehfeldt, R. A. (2009). Observational learning and the emergence of symmetry relations in teaching Spanish vocabulary words to typically developing children. Journal of Applied Behavior Analysis, 42, 801–805.

    Article  PubMed  PubMed Central  Google Scholar 

  • Rehfeldt, R. A. (2011). Toward a technology of derived stimulus relations: An analysis of articles published in the journal of applied behavior analysis, 1992–2009. Journal of Applied Behavior Analysis, 44, 109–119. https://doi.org/10.1901/jaba.2011.44-109.

    Article  PubMed  PubMed Central  Google Scholar 

  • Rehfeldt, R. A., Latimore, D., & Stromer, R. (2003). Observational learning and the formation of classes of reading skills by individuals with autism and other developmental disabilities. Research in Developmental Disabilities, 24, 333–358.

    Article  PubMed  Google Scholar 

  • Rosales, R., & Rehfeldt, R. A. (2007). Contriving transitive conditioned establishing operations to establish derived manding skills in adults with severe developmental disabilities. Journal of Applied Behavior Analysis, 40, 105–121. https://doi.org/10.1901/jaba.2007.117-05.

    Article  PubMed  PubMed Central  Google Scholar 

  • Rothstein, M. B., & Gautreaux, G. G. (2007). The effects of a peer-yoked contingency on observational learning and the collateral emergence of naming. Journal of Early and Intensive Behavior Intervention, 4, 453–470. https://doi.org/10.1037/h0100384.

    Article  Google Scholar 

  • Sidman, M. (1994). Equivalence relations and behavior: A research story. Boston: Authors Cooperative.

    Google Scholar 

  • Singer-Dudek, J., Oblak, M., & Greer, R. D. (2011). Establishing books as conditioned reinforcers for preschool children as a function of an observational intervention. Journal of Applied Behavior Analysis, 44, 421–434. https://doi.org/10.1901/jaba.2011.44-421.

    Article  PubMed  PubMed Central  Google Scholar 

  • Stromer, R., Mackay, H. A., & Stoddard, L. T. (1992). Classroom applications of stimulus equivalence technology. Journal of Behavioral Education, 2, 225–256. https://doi.org/10.1007/BF00948817.

    Article  Google Scholar 

  • Taylor, I., & O’Reilly, M. F. (2000). Generalization of super market shopping skills for individuals with mild intellectual disabilities using stimulus equivalence training. Psychological Record, 50, 49–62. https://doi.org/10.1007/BF03395342.

    Article  Google Scholar 

  • Verales, A., & Fields, L. (2017). Equivalence based instruction by group based clicker training and sorting tests. The Psychological Record, 67, 71–80. https://doi.org/10.1007/s40732-016-0208-x.

    Article  Google Scholar 

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Correspondence to Daniel M. Fienup.

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This study was approved by the Institutional Review Board of the respective university. We obtained parent permission and child assent for each participant described in this manuscript.

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Verdun, V.R., Chiasson, B.A. & Fienup, D.M. At the Intersection of Derived Relations and Observational Learning: Teaching Fraction–Percentage Relations. J Behav Educ 29, 741–762 (2020). https://doi.org/10.1007/s10864-019-09343-8

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  • DOI: https://doi.org/10.1007/s10864-019-09343-8

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