Groupitizing reflects conceptual developments in math cognition and inequities in math achievement from childhood through adolescence.

Groupitizing – the ability to take advantage of grouping cues to rapidly enumerate sets that otherwise require serial counting – is linked to conceptual aspects of numbers (accessing the cardinality of subgroups) and math (combining the subgroups values) that rapidly emerge during the first years of schooling (Starkey & McCandliss, 2014). Little else is known about its broader role in mathematical development. This study followed the development of groupitizing skill from late childhood through early adolescence (N = 1,209), revealing a pattern of progressive development over these critical years for math achievement. Individual differences were highly predictive of global math achievement from 3rd to 8th grade, above and beyond socioeconomic and cognitive (domain-general and math-specific) predictors. Experimental manipulations of item grouping cues (number of subgroups, numerical composition of subgroups) lead to similar effects that manipulations of operands have on symbolic mathematical reasoning, corroborating the view that groupitizing draws upon the same conceptual processes as symbolic math even in the absence of well-learned symbolic retrieval cues. Finally, we show that groupitizing provides new cognitive insights into the nature of the socioeconomic status achievement gap, which cannot be fully explained by familiarity with specific symbolic math facts learned in school but rather suggest inequities in educational opportunities that promote flexible mastery of conceptual processes. Taken together, groupitizing – as a non-symbolic assessment of conceptual processes in mathematics – could be a critical tool in implicitly assessing math ability.

The Effects of a Multicomponent Motivational System Intervention Using Peer-Tutoring for Implementation on the Automation of Single-Digit Addition Tasks of Four Struggling Elementary Students

Derived math fact fluency becomes more imperative across all mathematical content areas during a students’ mathematics development. However, many of them struggle to automate the most basic math facts sufficiently and therefore are not able to deal with more complex mathematical problems. This leads to the fact that many of them are already left behind in the early years of their school careers whether they have diagnosed learning disabilities or not. In this single-case research project, we evaluated a peer-tutoring approach designed to extend the number of automated single-digit addition tasks for four struggling elementary students through a multicomponent motivational system including immediate correction of errors, graphical feedback on performance, positive reinforcement, direct instruction flashcards, and a racetrack game. A multiple-baseline design (ABE) across subjects was applied to assess the effects of the treatment. The results indicate significant and large effects of the intervention on the number of automated math facts for the participants. This substantiates the assumption that the math-fact recall performance of struggling students can be improved through the method of peer tutoring even with the limited resources available in everyday school life.

PENINGKATAN KETERAMPILAN BERPIKIR KRITIS DAN PEMAHAMAN KONSEP TRIGONOMETRI MELALUI PENERAPAN PROBLEM BASED LEARNING PADA SISWA SMA NEGERI 1 PANDAAN

The purpose is to increase critical thinking skills and conceptual understanding of mathematical trigonometric equations through problem-based learning model. The type of money research used is PTK with the subjects of all class XI MIA 3 students of SMA Negeri 1 Pandaan in the 2019/2019 academic year, totaling 35 students. The results showed that after the first cycle was implemented, 73.06% of students who think critically with sufficient qualifications were obtained, then increased in the second cycle with a result of 81.66%. The students’ conceptual understanding also increased where in the first cycle of 35 students only 6 students (17.14%), then increased in cycle II to 19 students (54.29%) with good qualification. It showed that the problem-based learning model can actually improve critical thinking skills and conceptual understanding because students are actively involved in collecting, studying, and discussing math facts related to the subject matter of trigonometric equations compared to before.

What counts? Sources of knowledge in children’s acquisition of the successor function

Although many US children can count sets by 4 years, it is not until 5½-6 years that they understand how counting relates to number - i.e., that adding 1 to a set necessitates counting up one number. This study examined two knowledge sources that 3½-6-year-olds (N = 136) may leverage to acquire this “successor function”: (1) mastery of productive rules governing count list generation; and (2) training with “+1” math facts. Both productive counting and “+1” math facts were related to understanding that adding 1 to sets entails counting up one number in the count list; however, even children with robust successor knowledge struggled with its arithmetic expression, suggesting they do not generalize the successor function from “+1” math facts.