A Developing Approach to Studying Students’ Learning through Their Mathematical Activity

We discuss an emerging program of research on a particular aspect of mathematics learning, students’ learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning trajectories of students by specifying a series of conceptual steps through which students pass in the context of particular instructional approaches or learning environments. Generally missing from the literature is research that examines the process by which students progress from one of these conceptual steps to a subsequent one. We provide a conceptualization of a program of research designed to elucidate students’ learning processes and describe an emerging methodology for this work. We present data and analysis from an initial teaching experiment that illustrates the methodology and demonstrates the learning that can be fostered using the approach, the data that can be generated, and the analyses that can be done. The approach involves the use of a carefully designed sequence of mathematical tasks intended to promote particular activity that is expected to result in a new concept. Through analysis of students’ activity in the context of the task sequence, accounts of students’ learning processes are developed. Ultimately a large set of such accounts would allow for a cross-account analysis aimed at articulating mechanisms of learning.     

Dynamic Touch by Hand and Head During Walking: Protective Behavior for the Head?

We investigated perception of the extent of an object held in the hand or attached to the head during walking. Participants wielded an occluded, weighted rod by hand and by head and reported the perceived location of the rod end (relative to a virtual vertical line) while walking and while standing. There was an unexpected effect of body part on perceived location of the rod end. In particular, participants stood or walked so that the rod end was farther away from the vertical line when wielding with the head than wielding with the hand. It is possible that differences between the tasks and the relative costs of a collision influenced the locomotory behavior in each condition.     

Bantams (Gallus gallus domesticus) also perceive a reversed Zöllner illusion

Although pigeons have been shown to be susceptible to several size and length illusions, other avian species have not been tested intensively for illusory perception. Here we report how bantams perceive the Zöllner figure, in which parallel lines look nonparallel due to short crosshatches superimposed on the lines. Watanabe et al. (Cognition 119:137–141, 2011) showed that pigeons, like humans, perceived parallel lines as nonparallel but that the orientation of subjective convergence was opposite to that of humans. We trained three bantams to peck at the narrower (or wider) of the two gaps at the end of a pair of nonparallel lines. After adapting them to target lines with randomly oriented crosshatches (which result in no apparent illusion to humans), we tested the bantams’ responses on randomly inserted probe trials, in which crosshatches that should induce the standard Zöllner-like illusion for humans replaced the randomly oriented ones. The results suggested bantams, like pigeons, perceive a reversed Zöllner illusion.     

Retrospective perceptual distortion of position representation does not lead to delayed localization

Previous studies have reported retrospective influences of visual events that occur after target events. In the attentional attraction effect, a position cue presented after a target stimulus distorts the target’s position towards that of the cue. The present study explored the temporal relationship between stimulus presentation and reaction time (RT) in this effect in two experiments. Participants performed a speeded localization task on two vertical lines, the positions of which were to be distorted by an additional attentional cue. No significant difference in RTs was found between the conditions with simultaneous and delayed cues. RTRT was modulated by the perceived (rather than physical) alignment of the lines. In Experiment 2, we manipulated the strength of attentional capture by modulating the color relevance of the cue to the target. Trials with cues producing stronger attentional capture (with cues of a different color from the targets) were found to induce apparently stronger distortion effects. This result favors the notion that the observed repulsion and attraction effects are driven by attentional mechanisms. Overall, the results imply that the attentional shift induced by the cue might occur rapidly and complete before the establishment of conscious location representation of the cue and the target without affecting overall response time.     

Biological motion stimuli are attractive to medaka fish

In many social fish species, visual cues play an important role in inducing shoaling behaviour. The present study is the first to examine whether and how “biological motion” depicting a moving creature by means of only a small number of isolated points induces shoaling behaviour in fish. Medaka (Oryzias latipes) were used because they are known to have high visual acuity and exhibit a strong tendency to form shoals. In experiment 1, we found that the presentation of medaka biological motion resulted in heightened shoaling behaviour when compared with that of non-biological motion (depicted by a small number of points placed at fixed distances that moved at a constant speed in a constant direction). In experiment 2, it was indicated that medaka biological motion was more effective at inducing shoaling behaviour when compared with human biological motion. In experiment 3, it was demonstrated that shoaling behaviour was largely dependent on the smoothness of the biological motion. In experiment 4, we revealed that shoaling behaviour was maximised in normal speed group and decreased in faster- and slower-than-normal speed groups. In experiment 5, it was shown that shoaling behaviour was slightly reduced when a reversed movie was presented. These results suggest that motion information extracted from conspecifics was sufficient to induce shoaling behaviour in medaka and that deviation from normal and familiar motion impeded shoaling behaviour. The naturalness of motion may be responsible for the induction of shoaling behaviour.     

Effects of direct and averted gaze on the subsequent saccadic response

The saccadic latency to visual targets is susceptible to the properties of the currently fixated objects. For example, the disappearance of a fixation stimulus prior to presentation of a peripheral target shortens saccadic latencies (the gap effect). In the present study, we investigated the influences of a social signal from a facial fixation stimulus (i.e., gaze direction) on subsequent saccadic responses in the gap paradigm. In Experiment 1, a cartoon face with a direct or averted gaze was used as a fixation stimulus. The pupils of the face were unchanged (overlap), disappeared (gap), or were translated vertically to make or break eye contact (gaze shift). Participants were required to make a saccade toward a target to the left or the right of the fixation stimulus as quickly as possible. The results showed that the gaze direction influenced saccadic latencies only in the gaze shift condition, but not in the gap or overlap condition; the direct-to-averted gaze shift (i.e., breaking eye contact) yielded shorter saccadic latencies than did the averted-to-direct gaze shift (i.e., making eye contact). Further experiments revealed that this effect was eye contact specific (Exp. 2) and that the appearance of an eye gaze immediately before the saccade initiation also influenced the saccadic latency, depending on the gaze direction (Exp. 3). These results suggest that the latency of target-elicited saccades can be modulated not only by physical changes of the fixation stimulus, as has been seen in the conventional gap effect, but also by a social signal from the attended fixation stimulus.     

The Satisfaction with Life Scale in Adolescent Samples: Measurement Invariance across 24 Countries and Regions,Age, and Gender

Measurement of adolescent life satisfaction across cultures has not received much attention in previous empirical research. The present study evaluated measurement invariance of the Satisfaction with Life Scale (SWLS) among adolescents in 24 countries and regions (N = 22,710; age range = 13–19 years; 53% female). A single-factor model with residual covariance between a pair of items tapping past life satisfaction fitted well in 19 countries and regions and showed a partial metric invariance. In a subset of nine countries and regions, partial scalar invariance was supported. Partial metric invariance across all 24 countries and regions was achieved when custom model modifications in five countries and regions were included. Three SWLS items showed evidence of noninvariance across cultures. The measurement model was found to operate similarly across gender and age. Our findings suggest that caution is needed when using the SWLS for measuring life satisfaction among adolescents from different cultures.

     

Critical roles of mecamylamine-sensitive mushroom body neurons in insect olfactory learning

In insects, cholinergic neurons are thought to transmit olfactory conditioned stimulus (CS) to the sites for associating the CS with unconditioned stimulus (US), but the types of acetylcholine (ACh) receptor used by neurons participating in the association have not been determined. In cockroaches, a type of nicotinic ACh receptor specifically antagonized by mecamylamine (MEC) has been characterized. Here we investigated the roles of neurons possessing MEC-sensitive ACh receptors (MEC-sensitive neurons) in olfactory conditioning of salivation, monitored by changes in activities of salivary neurons, in cockroaches. Local and bilateral microinjection of MEC into each of the three olfactory centers, antennal lobes, calyces of the mushroom bodies and lateral protocerebra, impaired olfactory responses of salivary neurons, indicating that MEC-sensitive neurons in all olfactory centers participate in pathways mediating olfactory responses of salivary neurons. Conditioning of olfactory CS with sucrose US was impaired by injection of MEC into the antennal lobes or calyces, i.e., conditioned responses were absent even after recovery from MEC injection, suggesting that the CS-US association occurs in MEC-sensitive neurons in calyces (most probably Kenyon cells) or in neurons in downstream pathways. In contrast, conditioned responses appeared after recovery from MEC injection into the lateral protocerebra, suggesting that MEC-sensitive neurons in the lateral protocerebra are downstream of the association sites. Since lateral protocerebra are major termination areas of mushroom body efferent neurons, we suggest that input synapses of MEC-sensitive Kenyon cells, or their output synapses upon mushroom body efferent neurons, are the sites for CS-US association for conditioning of salivation.     

Do birds (pigeons and bantams) know how confident they are of their perceptual decisions?

Rhesus monkeys are known to recognize confidence about their immediate perceptual and cognitive decisions by using a betting procedure (Son and Kornell in The missing link in cognition: origins of self-reflective consciousness. Oxford University Press, New York, pp 296–320, 2005; Kornell et al. in Psychol Sci 18:64–71, 2007). In this report, we examined whether this ability is shared in two avian species (pigeons and bantams) in order to know how widespread this metacognitive ability is among animals. We trained pigeons and bantams to search for a differently colored disk (target) among others (distracters) displayed on a touch-sensitive monitor. In test, the subjects were required to choose one of two confidence icons, “risk” and “safe”, after the visual search. A peck at the “risk” icon after a correct response in the visual search (i.e., a peck at the target) was reinforced by food and light, while that after an incorrect response (i.e., a peck at a distracter) resulted in a timeout. A peck at the “safe” icon was always reinforced by food and light, or by light only, regardless of the visual search result. The percentages of “safe” choices after incorrect responses were higher than after correct responses in all six pigeons and two of three bantams. This behavior generalized to novel stimuli in some subjects, and even to a novel line-classification task in a pigeon. These results suggest that these two distantly related avian species have in common a metacognitive ability that allows them to recognize confidence about their immediate perceptual decisions.