reinforcement intervention was used to establish conditioned reinforcement for math.
Experiment II expanded the results of Experiment I in that participants’ rate of learning prior to and following the establishment of conditioned reinforcement was measured. The establishment of conditioned reinforcement for math using the individualized reinforcement intervention resulted in an educationally significant accelerated rate of learning math in pre-kindergarten students.
The importance of conditioning stimuli as reinforcers for observing and the effect of this conditioning on learning has been well documented in a series of verbal developmental studies (Buttigieg, 2015; Delgado, Greer, Speckman, & Goswami, 2009; Du, Broto & Greer, 2015; Greer & Han, 2015; Greer, Pistoljevic, Cahill, & Du, 2011; Maffei, Singer-Dudek, & Keohane; Tsai & Greer, 2006). Experiment II adds to this body of research. Like the participants in the present study, the above studies were conducted with preschool aged children. Each of the above studies used the stimulus-stimulus pairing procedure to establish conditioned reinforcement for: voices and faces (Greer et al., 2011; Maffei et al., 2014), two-dimensional and three-dimensional stimuli (Du et al., 2015, Greer & Han, 2015; Pereira-Delgado et al., 2009), and books (Buttigieg, 2015; Tsai & Greer, 2006). All of these participants acquired a verbal developmental cusp (Rosales-Ruiz & Baer, 1996) following the intervention. This means that the participants were now able to contact the environment in ways they previously could not. The results of these studies demonstrate that acquiring certain reinforcers also results in the acquisition of new cusps (Greer & Du, 2015). In addition to acquiring a verbal developmental cusp, conditioning stimuli as reinforcers for observing function to accelerate students’ rate of learning for listener programs,
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visual match to sample programs, and sight words respectively. The results of this study are consistent with the above studies in that conditioning stimuli as reinforcers, in this case math, led to an increase in participants’ rate of learning math.
The results of this study extended those of O’Rourke’s (2006) math conditioning study conducted with second and third grade students. While O’Rourke was successful in establishing conditioned reinforcement for math as a function of observational conditioning-by-denial, the participants’ rate of learning math only slightly improved for 3 out of 4 of the participants. The slight effects on rate of learning may be related to the discrepancy between the type of math that was conditioned as compared to the math learning used for the dependent variable. The
objectives used to test for changes in rate of learning were within the geometry domain while the math that was conditioned was within the numeracy domain. For this reason, units 11, 12, and 13 (geometry units) of the MEF-Math curriculum were omitted from Participant L’s rate of learning measures. All conditioning materials within Experiment I and math tasks in Experiment II were conducted with objectives within the numeracy domain in order to make accurate comparisons about the changes within participants’ rate of learning following the establishment of conditioned reinforcement for math.
Early math instruction greatly impacts students’ later math development. Research has shown that children are able to learn complex math (Ginsburg et al., 2008). Increasing students’ rate of learning will maximize instructional time and allow for high quality instruction on more complex mathematical skills. The participants in Experiment II were pre-kindergarten students who by the end of the study were either at the start or well into kindergarten math while still in the middle of their pre-kindergarten school year. The results of Experiment II not only show that students’ rate of learning increases as a function of conditioned reinforcement for math, but also
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that students are indeed able to acquire more complex math operations without sacrificing the students’ play time. In fact, many of the participants in Experiment I and II consider their math groups as play time following the establishment of conditioned reinforcement for math. Bridging the Gap- Low SES Students
Math achievement at the onset of kindergarten is the strongest predictor of future performance in math and reading. This means that at the pre-kindergarten level there may already be gaps between students who come from low socioeconomic homes and those that do not. “For these children especially, the long-term success of their learning and development requires high-quality experience during their early ‘years of promise’” (Clements & Sarama, 2014, p. 2). According to the National Math Panel (2008), the math gap between low-income and middle-income students increasingly expands throughout their school-aged years. The results of Experiment II demonstrate that students’ rate of learning accelerates by 1.5 to 2 times following the establishment of conditioned reinforcement for math. These low SES students who are deemed “at risk” would benefit from conditioned reinforcement for math as it would increase their rate of learning thus bridging the gap between themselves and their middle-class peers. While a relation between SES and the presence or absence of conditioned reinforcement for math was not investigated in Experiments I and II, the Brigance scores of the participants in both experiments varied across the physical, language, and cognitive domains. The variance in Brigance scores supports the notion that conditioned reinforcement for math can be established and would be beneficial for all students.
Limitations
The study is not without limitations. The textual responses in Experiment I and the units of MEF-Math in Experiment II were not counterbalanced, making it difficult to account for the
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difficulty of the sets or units. That is, the possible differences in difficulty were not controlled for. The units used prior to the establishment of conditioned reinforcement for math consisted of matching numbers to quantities, counting, and other basic foundational math skills. The MEF- Math units used for post-rate of learning measures consisted of arguably more complex math, including addition and subtraction, word problems, and finding the missing numbers within equations. From the students’ point of view, basic math skills may be just as difficult as addition and subtraction, however, addition and subtraction are indeed higher-level math skills that require multiple steps to complete compared to basic math that usually only requires one step. This means that following the establishment of conditioned reinforcement for math all six participants in Experiment II acquired more complex math objectives at a faster rate.
Another limitation was the rule-governed behavior of the participants in Experiment I as evidenced by their first phase of math during indirect probes of conditioned reinforcement. The participants in Experiment I have an instructional history of following directions and teacher presence functioning as instructional control. Therefore, when the performance task was presented to Participants I, T, and L they completed it without regard to whether they were receiving Play-Doh® or math as a consequence. By the second math phase, the participants responded directly to the contingency between their correct responses and how much Play-Doh® or math they received. Once they contacted the contingency, extinction effects were shown. This stimulus control was also apparent for Participant T and Participant L’s first direct reinforcement probe. Once the students were certain that they would not receive any consequence following direct probes, they very clearly selected Play-Doh® for the remaining four direct probes.
In addition to the math sets/units and the rule-governed behavior of the students, the lack of two -month follow-up probes for the participants in Experiment II is another limitation in this
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study. Follow-up probes would determine whether or not math remained a conditioned reinforcer after the intervention and could demonstrate whether or not the participants continued to acquire math objectives at an accelerated rate. However, anecdotally, the participants of Experiment II continue to request math instruction and tact math principles within the environment.
Future Research
The results of Experiment I and II demonstrate that it is possible to establish conditioned reinforcement for math for children as young as 4.4 years old and different conditioning
procedures are necessary for different students. Across both experiments, five participants required learn units, four required the stimulus-stimulus pairing procedure, and one participant required observational conditioning-by-denial. The results of Experiments I, II, and Buttigieg (2015) suggest that observational conditioning-by-denial would be most effective for the students who have more cusps and capabilities. This may be due to observational stimulus control. Students who do not have observational stimulus control may not attend to the confederate’s access to the target stimulus. Compared to learn unit instruction or the stimulus- stimulus pairing procedure, observational conditioning-by-denial is faster to implement. The unaddressed matter is whether the five participants who only required learn units or the four participants who required the stimulus-stimulus pairing in the present study would have acquired conditioned reinforcement for math faster if observational conditioning-by-denial was
implemented first. Another possibility would be to begin with learn unit instruction, since that alone is successful for some, followed by observational conditioning-by-denial, and then the stimulus-stimulus pairing procedure if necessary. In order to maximize instructional time, future research should investigate which procedure is most appropriate for which kids and whether
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there is a relation between the students’ rate of acquisition or other cusps and the procedure that was effective in establishing reinforcement value for math.
Establishing conditioned reinforcement for math may also have collateral effects on students’ reading objectives. Previous research has shown that children’s math skills predict their reading and math ability later in life (Claessens & Engel, 2013). Future research should examine the effects of the establishment of conditioned reinforcement for math using the individualized reinforcement intervention on students’ rate of learning both math and reading.
Conclusion
The results of Experiment I showed that the individualized reinforcement intervention, which includes the delivery of learn units, stimulus-stimulus pairing, and observational
conditioning-by-denial was effective in establishing conditioned reinforcement and preference for math over Play-Doh®. Experiment II replicated and extended upon Experiment I. Following the establishment of conditioned reinforcement for math, all six participants’ rate of learning significantly accelerated. Not only did math become a conditioned reinforcer, but participants were learning math 1.5-2 times as fast. There is still much that is unknown about the effects of establishing conditioned reinforcement for math – are there collateral effects on reading rate of learning and what is the relation between students’ cusps and capabilities and the specific procedure that is effective in establishing conditioned reinforcement for math? However, the present study offers the individualized reinforcement intervention as an effective means to establish conditioned reinforcement for math while also accelerating learning.
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92 Appendix A
94 Appendix B
96 Appendix C