Abstracting Sequences: Reasoning That Is a Key to Academic Achievement

Abstract

The ability to understand sequences of items may be an important cognitive ability. To test this proposition, 8 first-grade children from each of 36 classes were randomly assigned to four conditions. Some were taught sequences that represented increasing or decreasing values, or were symmetrical, or were rotations of an object through 6 or 8 positions. Control children received equal numbers of sessions on mathematics, reading, or social studies. Instruction was conducted three times weekly in 15-min sessions for seven months. In May, the children taught sequences applied their understanding to novel sequences, and scored as well or better on three standardized reading tests as the control children. They outscored all children on tests of mathematics concepts, and scored better than control children on some mathematics scales. These findings indicate that developing an understanding of sequences is a form of abstraction, probably involving fluid reasoning, that provides a foundation for academic achievement in early education.

Empirical Studies of Patterning

“…Finally Pasnak et al (2015) replicated the study of Kidd et al (2014) and partially replicated the results. The children taught either complex patterns or reading outscored the other control children on the TERA and TOWRE reading tests, but not on the GORT.…”

“…Identifying a pattern rule via induction and applying it via deduction to a new pattern which could be solved by the same rule could be the central mechanisms involved in patterning. Pasnak et al (2015) suggested that in addition to Gf, two other CHC components, Gq (quantitative reasoning) and Grw (a component of reading ability) are likely to be involved in understanding complex patterns, given the impact of instruction on such patterns on early mathematics and reading. If this suggestion is correct, the mechanisms involved would be three components of the CHC, currently the most widely accepted theory of intelligence.…”

The Effects of in-class tutoring of Kindergarteners on Patterning, Reading, or Mathematics

“…The patterning instruction was modeled after the interventions employed by Kidd et al (2013), Kidd et al (2014) and Pasnak, et al (2015). The children worked on completing, filling in, reproducing and creating patterns of numbers, shapes, or letters, rotations of an object and objects.…”

“…After four months of this parallel instruction on either patterns or academic subject matter, the children taught patterning outscored the others on Diagnostic Achievement Battery measures of mathematics and written language. More recently, researchers have compared first grade children randomly assigned to receive thrice weekly instruction for approximately five months on either complex patterns similar to those Hendricks et al (2006) employed, mathematics, reading, or social studies (Kidd, et al 2013;Kidd, et al 2014;Pasnak, et al 2015). Although results varied somewhat across experiments and tests, the children taught patterning scored as well or better on two standardized tests of mathematics than those taught mathematics or social studies.…”

“…Such a design would allow comparison of equal investments of time and resources in these subject matters, and hence show whether patterning instruction deserves the time spent on it in kindergarten curricula, or whether the time could be better devoted to additional time spent on literacy or mathematics. Accordingly, an experiment was designed similar to those of Kidd et al (2013), Kidd et al (2014), and Pasnak, et al (2015). Kindergarten children from the same school and classrooms were randomly assigned to receive 15-minute sessions of instruction on either patterns, reading, mathematics or social studies (control).…”