Broadening the horizons of research on discovery-based learning

In reviewing the six articles within this Instructional Science special issue, we are reminded of Schoenfeld’s (Educ Res 45(2):105–111, 2016) review of American Educational Research Association president-authored papers for the centennial celebration of AERA. There, he succinctly unveiled the content focus of AERA research in the first half of the twentieth century: “there is content to be mastered; it is the schools’ job to help students master it” (p. 106). Yet, like Schoenfeld says, “A century later, we hear the echoes of this functionality in the calls for ‘21st-century skills,’” (p. 106), and the “skills” of the twentieth and twenty-first century would hardly know each other. Twentieth century skills, as represented in the accounts from past AERA presidents, were product-oriented, like accurate copying and precise handwriting. Twenty-first century skills are focused on creativity, ingenuity, critical thinking, and the like. In our primary research space, mathematics education, problem solving, sense making, and conceptual understanding dominates in the twenty-first century, whereas procedures dominated teaching and learning mathematics in the twentieth century.     

Beginning the cycle of equitable teaching: The pivotal role of cooperating teachers

Cooperating teachers are prominent people in influencing the next generation of teachers because they interact daily with student teachers. This paper discusses the impact of gender-sensitive cooperating teachers on student teachers' teaching strategies, questioning patterns and interactions during their teaching practicum. Student teachers working with these gender-sensitive cooperating teachers were more equitable in their questioning patterns and more likely to ask students (of both genders) higher-order questions than their peers. Concord High School Caesar Rodney High School Glasgow High School Middletown High School Hanby Middle School     

Teaching creativity with computers

Some criticize computer use because computers — by their nature mechanistic and algorithmic — support only uncreative thinking and production. However, adults increasingly view computers as valuable tools of creative production. Educational research indicates that there is no single “effect” of the computer on creativity; technology can support either uncreative drill or creative production. Research also provides strong evidence that certain computer environments, such as Logo, word processing, and design tools, hold the potential for the computer's facilitation of creativity. There is equally strong evidence that the curriculum in which computer programs are embedded and the teacher who chooses, uses, and infuses these programs, are essential elements in realizing the full potential of technology.     

Students' Development of Strategies for Turn and Angle Measure

We studied a group of fourth grade students identified by their classroom teachers as having above average ability in mathematics who were participating in pull-out enrichment sessions. We sought to test, using observational and microgenetic methods, hypotheses regarding students' measurement strategies that have been generated post hoc by other research teams. These above-average mathematics students did not show initial difficulties with turn commands previously reported in mixed populations. They created strategies to accurately determine the correct direction of turn and to estimate the amount of turn. They did follow a similar developmental order as students in previous work: They synthesized and integrated two schemes, turn as body movement and turn as number. Analyses extending this work revealed a process of psychological curtailment in which students gradually replace full rotations of their bodies with smaller rotations of an arm, hand, or finger.This revised version was published online in September 2005 with corrections to the Cover Date.     

Effects of tactile stimulation on the initiation and maintenance of the following response in Japanese quail (Coturnix coturnix japonica)

Effects of tactile contact with an imprinting stimulus object on the initiation and maintenance of the following response in neonatal Japanese quail,Coturnix coturnix japonica, were examined. Tactile contact with an imprinting stimulus object was permitted during a preexposure period and/or during a following test. Results indicated that following was stronger when tactile contact was permitted during either the preexposure or test periods than when such contact was not given. Following occurred sooner when contact was permitted during the preexposure period than during following only, or when no contact was permitted. The greatest strength of following occurred when tactile stimulation was permitted during both preexposure and testing periods. It was concluded that the results support the hypothesis that tactile stimulation can facilitate both the initiation and maintenance of following behavior, and this is interpreted as being consistent with Schneirla’s (1965) theory.     

Spatial ability,visual imagery,and mathematical performance

116 Foundation Year Engineering Students, at the University of Technology, Lae, Papua New Guinea, were given a battery of mathematical and spatial tests; in addition, their preferred modes of processing mathematical information were determined by means of an instrument recently developed in Australia by Suwarsono.Correlational analysis revealed that students who preferred to process mathematical information by verbal-logical means tended to outperform more visual students on mathematical tests. Multiple regression and factor analyses pointed to the existence of a distinct cognitive trait associated with the processing of mathematical information. Also, spatial ability and knowledge of spatial conventions had less influence on mathematical performance than could have been expected from recent relevant literature.     

Early mathematics assessment: validation of the short form of a prekindergarten and kindergarten mathematics measure

In recent years, there has been increased interest in improving early mathematics curricula and instruction. Subsequently, there has also been a rise in demand for better early mathematics assessments, as most current measures are limited in their content and/or their sensitivity to detect differences in early mathematics development among young children. In this article, using data from two large samples of diverse populations of prekindergarten and kindergarten children, we provide evidence regarding the psychometric validity of a new theory-based early mathematics assessment. The new measure is the short form of a longer, validated measure. Our results suggest the short form assessment is valid for assessing prekindergarten and kindergarten children’s numeracy and geometry skills and is sensitive to differences in early mathematics development among young children.