Middle school students' patterning performance on semi-free generalization tasks

F.D. Rivera, Joanne Rossi Becker
2016 Journal of Mathematical Behavior  
This longitudinal study empirically addresses the issue of structure construction and justification among a class of US seventh and eighth-grade Algebra 1 students (mean age of 12.5 years) in the context of novel semi-free pattern generalization (PG) tasks before and after a teaching experiment that emphasized a multiplicative thinking approach to patterns. We compared the students' PG responses before and after the experiment and found that (1) one source of variability in their abduced
more » ... ral processing was in part due to an initial conceptual preference toward thinking either in parts or in wholes and (2) a multiplicative understanding of structures significantly aided them in PG conversion (e.g., from the visual to the alphanumeric) and processing (e.g., from nonstandard to standard function-based formulas). Our findings provide both necessary and sufficient conditions for constructing, establishing, and justifying valid structures in the case of (semi-) free figural patterning tasks. or not exhibit the structure. For example, Fig. 2 shows three different but equivalent studentgenerated structures for the Squares Tiles Pattern in Fig. 1 . Che (age 12 years): "W = 4n + 4. So there's like 4 squares and then you add 4 to each one [corner]
doi:10.1016/j.jmathb.2016.05.002 fatcat:d6vi7nneynenji66gnrwzohybi