Tales from three countries: reflections during COVID-19 for mathematical education in the future.

How can school mathematics prepare citizens for a democratic society? Answers to this question are not static; they change as society and its problems change. The SARS-CoV-2 pandemic with its corresponding disease COVID-19 presents such a problem: what is needed to navigate this complex situation that involves, among other things, mathematics? Using the essay genre, we use three narratives from three countries-Italy, the USA (California), and Germany-to reflect on the goals of teaching mathematics during this crisis and examine aspects of each country's standards for mathematics education. These three stories are framed by the authors' backgrounds, experiences, interests, their country's situation, and response to the pandemic. We first present the three narratives and then examine common issues across them that might provide insights beyond this current crisis, for preparing students to become active citizens. In particular, we focus on three issues: (1) developing a positive mindset toward mathematics to engage with and reflect on real-world problems, (2) improving interdisciplinary connections to the sciences to better understand how science professional practices and insights are similar or different from everyday practices, and (3) considering interpersonal and collective matters beyond the individual.

How dogs scan familiar and inverted faces: an eye movement study.

Faces play an important role in communication and identity recognition in social animals. Domestic dogs often respond to human facial cues, but their face processing is weakly understood. In this study, facial inversion effect (deficits in face processing when the image is turned upside down) and responses to personal familiarity were tested using eye movement tracking. A total of 23 pet dogs and eight kennel dogs were compared to establish the effects of life experiences on their scanning behavior. All dogs preferred conspecific faces and showed great interest in the eye area, suggesting that they perceived images representing faces. Dogs fixated at the upright faces as long as the inverted faces, but the eye area of upright faces gathered longer total duration and greater relative fixation duration than the eye area of inverted stimuli, regardless of the species (dog or human) shown in the image. Personally, familiar faces and eyes attracted more fixations than the strange ones, suggesting that dogs are likely to recognize conspecific and human faces in photographs. The results imply that face scanning in dogs is guided not only by the physical properties of images, but also by semantic factors. In conclusion, in a free-viewing task, dogs seem to target their fixations at naturally salient and familiar items. Facial images were generally more attractive for pet dogs than kennel dogs, but living environment did not affect conspecific preference or inversion and familiarity responses, suggesting that the basic mechanisms of face processing in dogs could be hardwired or might develop under limited exposure.

Visual event-related potentials of dogs: a non-invasive electroencephalography study.

Previously, social and cognitive abilities of dogs have been studied within behavioral experiments, but the neural processing underlying the cognitive events remains to be clarified. Here, we employed completely non-invasive scalp-electroencephalography in studying the neural correlates of the visual cognition of dogs. We measured visual event-related potentials (ERPs) of eight dogs while they observed images of dog and human faces presented on a computer screen. The dogs were trained to lie still with positive operant conditioning, and they were neither mechanically restrained nor sedated during the measurements. The ERPs corresponding to early visual processing of dogs were detectable at 75-100 ms from the stimulus onset in individual dogs, and the group-level data of the 8 dogs differed significantly from zero bilaterally at around 75 ms at the most posterior sensors. Additionally, we detected differences between the responses to human and dog faces in the posterior sensors at 75-100 ms and in the anterior sensors at 350-400 ms. To our knowledge, this is the first illustration of completely non-invasively measured visual brain responses both in individual dogs and within a group-level study, using ecologically valid visual stimuli. The results of the present study validate the feasibility of non-invasive ERP measurements in studies with dogs, and the study is expected to pave the way for further neurocognitive studies in dogs.

Landmarks in nature to support wayfinding: the effects of seasons and experimental methods.

Landmarks constitute an essential basis for a structural understanding of the spatial environment. Therefore, they are crucial factors in external spatial representations such as maps and verbal route descriptions, which are used to support wayfinding. However, selecting landmarks for these representations is a difficult task, for which an understanding of how people perceive and remember landmarks in the environment is needed. We investigated the ways in which people perceive and remember landmarks in nature using the thinking aloud and sketch map methods during both the summer and the winter seasons. We examined the differences between methods to identify those landmarks that should be selected for external spatial representations, such as maps or route descriptions, in varying conditions. We found differences in the use of landmarks both in terms of the methods and also between the different seasons. In particular, the participants used passage and tree-related landmarks at significantly different frequencies with the thinking aloud and sketch map methods. The results are likely to reflect the different roles of the landmark groups when using the two methods, but also the differences in counting landmarks when using both methods. Seasonal differences in the use of landmarks occurred only with the thinking aloud method. Sketch maps were drawn similarly in summertime and wintertime; the participants remembered and selected landmarks similarly independent of the differences in their perceptions of the environment due to the season. The achieved results may guide the planning of external spatial representations within the context of wayfinding as well as when planning further experimental studies.

Sign Language in Light of Mathematics Education: An Exploration Within Semiotic and Embodiment Theories of Learning Mathematics.

Research rarely focuses on how deaf and hard of hearing (DHH) students address mathematical ideas. Complexities involved in using sign language (SL) in mathematics classrooms include not just challenges, but opportunities that accompany mathematics learning in this gestural-somatic medium. The authors consider DHH students primarily as learners of mathematics, and their SL use as a special case of language in the mathematics classroom. More specifically, using SL in teaching and learning mathematics is explored within semiotic and embodiment perspectives to gain a better understanding of how using SL affects the development, conceptualization, and representation of mathematical meaning. The theoretical discussion employs examples from the authors' work and research on geometry, arithmetic, and fraction concepts with Deaf German and Austrian learners and experts. The examples inform the context of mathematics teaching and learning more generally by illuminating SL features that distinguish mathematics learning for DHH learners.

Event-related potential (ERP) responses to violations of inflectional and derivational rules of Finnish.

Event-related potentials (ERP) were used to investigate the electrophysiological correlates of inflectional and derivational morphology. The participants were presented with visual sentences containing critical words in which either inflectional, derivational or both rules (combined violation) of Finnish were violated. Inflectional anomalies violated a number agreement of a noun with a previous auxiliary word. Derivational violations included a word-internal selectional restriction violation, i.e., a root and suffix category violation. Combined violations contained both a number and a category violation. The phonemic length of the critical words was controlled. Inflectional violations elicited a bilateral negative effect in the 450-550 ms time window, which was interpreted as an anterior negativity (AN) effect. Inflectional violations also elicited a late positivity (P600) effect. Derivational violations elicited an N400-like negativity effect, followed by the P600 effect. The P600 effects in the derivational and inflectional violation conditions summated linearly in the combined violation condition. The results are discussed with respect to the hypothesis that inflectional and derivational processes are independent and elicited in parallel in the online language comprehension.

Brain oscillatory EEG event-related desynchronization (ERD) and -sychronization (ERS) responses during an auditory memory task are altered in children with epilepsy.

PURPOSE: Children with epilepsy are in risk for cognitive impairment, but reliable methods, other than neuropsychological testing, to verify such a decline are few. The purpose of this study was to assess the effect of infrequent seizures on cognitive skills in children with non-symptomatic focal epilepsy taking antiepileptic medication but still having infrequent seizures. METHODS: EEG (electroencephalogram) brain electric oscillatory responses of the 4-6Hz, 6-8Hz, 8-10Hz and 10-12Hz EEG frequency bands were studied. These responses, assessed by means of the event-related desynchronization (ERD) and synchronization (ERS) method, were recorded in 6 children with epilepsy (mean age 11.3 years) and in 11 control children (mean age 12 years) while they performed an auditory memory task. All subjects also underwent a comprehensive neuropsychological test battery. RESULTS: The differences in the 4-6Hz ERD/ERS responses between encoding and recognition were smaller in the children with epilepsy as compared to those of the control children. In the 6-8Hz frequency band, the responses of the two groups dissociated most notably in the frontal electrodes. No statistically significant differences in the alpha frequency range (8-12Hz) were observed between the groups. CONCLUSIONS: Significant alterations in the lower EEG frequency (4-8Hz) ERD/ERS responses in children with epilepsy during auditory memory processing, as compared to age-matched, healthy children may suggest that seizures affect memory and underlying brain processes, indexed also by poorer performance particularly in neuropsychological subtests related to language functions.

Brain oscillatory responses during the different stages of an auditory memory search task in children.

We assessed brain oscillatory responses of the 4-30 Hz electroencephalographic frequency bands in children (mean age 13 years) during the different stages of an auditory memory search, namely the encoding of four words and recognition of the positive and negative probe words. In children, theta (approximately 4-6 Hz) electroencephalographic responses during recognition were of greater magnitude than those during encoding and alpha (approximately 8-12 Hz) event-related synchronization responses during encoding increased with increasing memory load. During recognition, greater magnitude alpha and beta (>12 Hz) event-related desynchronization responses were observed during the presentation of the positive probe as compared with the negative. Complex patterns of theta, alpha and beta frequency brain oscillatory responses during auditory information processing are present already in children of age approximately 13 years.

Brain oscillatory 4-30 Hz responses during a visual n-back memory task with varying memory load.

Brain oscillatory responses of 4-30 Hz EEG frequencies elicited during the performance of a visual n-back task were examined in 36 adult volunteers. Event-related desynchronization (ERD) and event-related synchronization (ERS) responses were examined separately for targets and non-targets in four different memory load conditions (0-, 1-, 2- and 3-back). The presentation of all stimuli in all memory load conditions elicited long-lasting theta frequency (approximately 4-6 Hz) ERS responses which were of greater magnitude for the target stimuli as compared to the non-target stimuli. Alpha frequency range (approximately 8-12 Hz) ERD responses were observed in all memory load conditions for both targets and non-targets. The duration of these alpha ERD responses increased with increasing memory load and reaction time. In all memory load conditions, early appearing beta rhythm (approximately 14-30 Hz) ERD responses were elicited, and with increasing memory load, these beta ERD responses became longer in duration. Additionally, beta ERS responses were observed in the 0- and 1-back memory load conditions. The current results reveal a complex interplay between brain oscillations at different frequencies during a cognitive task performance.

Electrophysiological correlates of memory processing in early Finnish-Swedish bilinguals.

Event-related desynchronization (ERD) and event-related synchronization (ERS) of the 1-30 EEG frequencies were studied in eight early Finnish-Swedish bilinguals during an auditory bilingual Sternberg memory task using Finnish-Swedish cognates as stimuli. Only subtle differences between languages were expected, since cognates have been assumed to have shared conceptual representations in the bilingual memory. Encoding elicited theta and alpha frequency ERS and beta frequency ERD responses in both languages. Retrieval elicited theta ERS and alpha and beta ERD responses. Some statistically significant differences between encoding and retrieval in Finnish versus Swedish emerged: greater theta and alpha ERS responses were observed during encoding in Swedish than during encoding in Finnish. During between-language retrieval, later-appearing theta ERS and alpha ERD responses were elicited as compared to within-language retrieval. These delayed oscillatory responses might reflect the involvement of central executive attentional functions in relation to language switching.

Nasal Oxytocin Treatment Biases Dogs' Visual Attention and Emotional Response toward Positive Human Facial Expressions.

The neuropeptide oxytocin plays a critical role in social behavior and emotion regulation in mammals. The aim of this study was to explore how nasal oxytocin administration affects gazing behavior during emotional perception in domestic dogs. Looking patterns of dogs, as a measure of voluntary attention, were recorded during the viewing of human facial expression photographs. The pupil diameters of dogs were also measured as a physiological index of emotional arousal. In a placebo-controlled within-subjects experimental design, 43 dogs, after having received either oxytocin or placebo (saline) nasal spray treatment, were presented with pictures of unfamiliar male human faces displaying either a happy or an angry expression. We found that, depending on the facial expression, the dogs' gaze patterns were affected selectively by oxytocin treatment. After receiving oxytocin, dogs fixated less often on the eye regions of angry faces and revisited (glanced back at) more often the eye regions of smiling (happy) faces than after the placebo treatment. Furthermore, following the oxytocin treatment dogs fixated and revisited the eyes of happy faces significantly more often than the eyes of angry faces. The analysis of dogs' pupil diameters during viewing of human facial expressions indicated that oxytocin may also have a modulatory effect on dogs' emotional arousal. While subjects' pupil sizes were significantly larger when viewing angry faces than happy faces in the control (placebo treatment) condition, oxytocin treatment not only eliminated this effect but caused an opposite pupil response. Overall, these findings suggest that nasal oxytocin administration selectively changes the allocation of attention and emotional arousal in domestic dogs. Oxytocin has the potential to decrease vigilance toward threatening social stimuli and increase the salience of positive social stimuli thus making eye gaze of friendly human faces more salient for dogs. Our study provides further support for the role of the oxytocinergic system in the social perception abilities of domestic dogs. We propose that oxytocin modulates fundamental emotional processing in dogs through a mechanism that may facilitate communication between humans and dogs.

Cognition- and memory-related ERD/ERS responses in the auditory stimulus modality.

In the year 1994, Krause et al. published an initial report of acoustically elicited electroencephalogram (EEG) event-related desynchronization (ERD)/ event-related synchronization (ERS) responses. Later, Krause et al. reported of distinct ERD/ERS responses during an auditory memory task: the encoding of acoustic material elicited alpha-frequency ERS whereas retrieval or recognition of the same stimulus material evoked alpha ERD. The research group of Krause and co-workers has published several reports on acoustically evoked ERD/ERS responses utilizing various cognitive tasks and diverse stimuli. Recently, also clinical studies have been initiated. This chapter reviews, summarizes, and discusses the findings on cognition- and memory-related ERD/ERS responses specifically in the auditory stimulus modality.

Modality matters: the effects of stimulus modality on the 4- to 30-Hz brain electric oscillations during a lexical decision task.

The aim of the current study was to assess modality-specific brain oscillatory responses during cognitive processing. Brain oscillatory ERD/ERS responses of the 4- to 30-Hz EEG frequency bands were examined during lexical decision where the task is to identify whether the presented stimulus is a word or a pseudoword. Seven subjects performed the task with visual stimuli and twelve subjects with auditory stimuli. Visual stimuli elicited greater theta ERS responses as compared to the auditory stimuli. Both stimulus modalities elicited alpha and beta frequency ERD, these being greater for the auditory stimuli. Auditory stimuli elicited also later emerging beta ERS responses, absent for the visual stimuli. The lexicality effects (words vs. pseudowords) were greater for the auditory than for the visual stimuli. When studying brain oscillatory correlates of cognitive processing, the stimulus modality matters. Some effects may arise and some vanish depending on in which modality a cognitive experiment is being conducted.

Event-related desynchronization/synchronization during an auditory-verbal working memory task in mild Parkinson's disease.

OBJECTIVE: Event-related desynchronization (ERD) and synchronization (ERS) were studied during an auditory-verbal working memory task in patients suffering from Parkinson's disease (PD). METHODS: PD patients (n=7, mean age 59) at a mild stage of the disease volunteered in the study. A group of healthy subjects (n=10, mean age 61) served as control group. ERD and ERS of the 1-25 Hz EEG frequencies were studied using wavelet transforms during memory encoding and retrieval. RESULTS: Both groups performed equally well on the memory task. Statistically significant differences in ERD/ERS responses were observed in posterior electrodes during encoding of the memory set due to the fact that alpha ( approximately 10-15 Hz) ERS was elicited in the controls, but not in the PD group. In broad frequency bands ( approximately 6-25 Hz) ERD responses were observed in both groups during memory retrieval. A pre-stimulus alpha ERS seen in the control group was absent in the PD group. CONCLUSIONS: The results of this preliminary study indicate that Parkinson's disease might affect brain oscillatory responses in the alpha frequency range in the encoding phase of auditory-verbal working memory. SIGNIFICANCE: The ERD/ERS patterns may reflect neurophysiological alterations in the processes underlying working memory deficits in PD.

Brain oscillatory 1-30 Hz EEG ERD/ERS responses during the different stages of an auditory memory search task.

Event-related desynchronization (ERD) and event-related synchronization (ERS) responses of 1-30 Hz EEG frequencies during the different stages of an auditory Sternberg memory task were examined. The ERD/ERS responses were examined separately for successive memory set items (four) and for the two recognition conditions (YES/NO). The presentation of the memory set elicited ERS responses in the theta and alpha frequencies, and also beta ERD responses. These ERD/ERS responses elicited during encoding were found to evolve with successive memory set item presentation. The ERD/ERS responses elicited during the presentation of the probe dissociated significantly between the two recognition conditions (YES/NO). When the probe was included in the memory set (YES condition), recognition elicited stronger alpha and beta frequency ERD responses as compared to the NO condition. The findings from the current study verify that alpha ERD/ERS responses robustly dissociate between auditory encoding and recognition. The increasing alpha ERS responses with increasing memory set item presentation during encoding may be correlates of the functioning phonological loop, active memory maintenance and/or attention. The alpha ERD responses during recognition are undoubtedly associated with auditory memory search processes and distinguish between previously presented versus not presented verbal material. We propose that alpha ERD/ERS responses reflect explicitly auditory memory processes, discriminating between auditory encoding and recognition. Theta ERS responses may be associated with working memory processes, and possibly more specifically with the functioning of the central executive. Beta ERD/ERS responses may reflect also cognitive and/or memory processing, rather than merely the activity of the motor cortices.

Mobile phone effects on children's event-related oscillatory EEG during an auditory memory task.

PURPOSE: To assess the effects of electromagnetic fields (EMF) emitted by mobile phones (MP) on the 1 - 20 Hz event-related brain oscillatory EEG (electroencephalogram) responses in children performing an auditory memory task (encoding and recognition). MATERIALS AND METHODS: EEG data were gathered while 15 subjects (age 10 - 14 years) performed an auditory memory task both with and without exposure to a digital 902 MHz MP in counterbalanced order. RESULTS: During memory encoding, the active MP modulated the event-related desynchronization/synchronization (ERD/ERS) responses in the approximately 4 - 8 Hz EEG frequencies. During recognition, the active MP transformed these brain oscillatory responses in the approximately 4 - 8 Hz and approximately 15 Hz frequencies. CONCLUSIONS: The current findings suggest that EMF emitted by mobile phones has effects on brain oscillatory responses during cognitive processing in children.

Brain oscillatory responses to an auditory-verbal working memory task in mild cognitive impairment and Alzheimer's disease.

We report preliminary findings on EEG oscillatory correlates of working memory in mild cognitive impairment (MCI) and Alzheimer's disease (AD). Event-related desynchronization (ERD) and synchronization (ERS) of the 1-20 Hz EEG frequencies were studied using wavelet transforms in elderly controls, MCI patients and mild probable AD patients performing an auditory-verbal Sternberg memory task. Behaviourally, the AD patients made more errors than the controls and the MCI group. Statistically significant differences during the encoding of the memory set were found between the controls and the MCI group, such that the latter group showed ERD in the approximately 10-20 Hz frequencies. The findings may reflect different, compensatory encoding strategies in MCI. During retrieval, the most obvious differences were observed between the controls and the AD group: the ERD in the approximately 7-17 Hz frequencies was absent in the AD group particularly in anterior and left temporal electrode locations. This finding might indicate that AD is associated with deficient lexical-semantic processing during the retrieval phase in working memory tasks. Future studies with larger patient groups are needed to establish the diagnostic value of ERD/ERS patterns in MCI and AD.

The impact of a multidisciplinary, integrated approach on improving the health and quality of care for individuals dealing with multiple chronic conditions.

This study examined the effects of using a multidisciplinary, integrated, whole-person, team advocate approach to educate and empower participants with multiple chronic illnesses and coordinate, monitor, and support their health care process. Individuals (N = 39) from Midwest hospitals participated and completed self-report instruments. Changes in participants' functioning were also measured with diagnostic measures completed by the team advocates. The results indicate that the participants' perceptions of physical functioning, physical well-being, control, self-efficacy, and life satisfaction increased. Additionally, health-related behavior changes were reported, and short-term costs were significantly lower than projected costs. Finally, the participants rated their health care services in the program as more effective than previous health care services.

Computer Enabled Neuroplasticity Treatment: A Clinical Trial of a Novel Design for Neurofeedback Therapy in Adult ADHD.

BACKGROUND: We report a randomized controlled clinical trial of neurofeedback therapy intervention for ADHD/ADD in adults. We focus on internal mechanics of neurofeedback learning, to elucidate the primary role of cortical self-regulation in neurofeedback. We report initial results; more extensive analysis will follow. METHODS: Trial has two phases: intervention and follow-up. The intervention consisted of neurofeedback treatment, including intake and outtake measurements, using a waiting-list control group. Treatment involved ~40 h-long sessions 2-5 times per week. Training involved either theta/beta or sensorimotor-rhythm regimes, adapted by adding a novel "inverse-training" condition to promote self-regulation. Follow-up (ongoing) will consist of self-report and executive function tests. SETTING: Intake and outtake measurements were conducted at University of Helsinki. Treatment was administered at partner clinic Mental Capital Care, Helsinki. RANDOMIZATION: We randomly allocated half the sample then adaptively allocated the remainder to minimize baseline differences in prognostic variables. BLINDING: Waiting-list control design meant trial was not blinded. PARTICIPANTS: Fifty-four adult Finnish participants (mean age 36 years; 29 females) were recruited after screening by psychiatric review. Forty-four had ADHD diagnoses, 10 had ADD. MEASUREMENTS: Symptoms were assessed by computerized attention test (T.O.V.A.) and self-report scales, at intake and outtake. Performance during neurofeedback trials was recorded. RESULTS: PARTICIPANTS were recruited and completed intake measurements during summer 2012, before assignment to treatment and control, September 2012. Outtake measurements ran April-August 2013. After dropouts, 23 treatment and 21 waiting-list participants remained for analysis. Initial analysis showed that, compared to waiting-list control, neurofeedback promoted improvement of self-reported ADHD symptoms, but did not show transfer of learning to T.O.V.A. Comprehensive analysis will be reported elsewhere. TRIAL REGISTRATION: "Computer Enabled Neuroplasticity Treatment (CENT)," ISRCTN13915109.

Dogs Evaluate Threatening Facial Expressions by Their Biological Validity--Evidence from Gazing Patterns.

Appropriate response to companions' emotional signals is important for all social creatures. The emotional expressions of humans and non-human animals have analogies in their form and function, suggesting shared evolutionary roots, but very little is known about how animals other than primates view and process facial expressions. In primates, threat-related facial expressions evoke exceptional viewing patterns compared with neutral or positive stimuli. Here, we explore if domestic dogs (Canis familiaris) have such an attentional bias toward threatening social stimuli and whether observed emotional expressions affect dogs' gaze fixation distribution among the facial features (eyes, midface and mouth). We recorded the voluntary eye gaze of 31 domestic dogs during viewing of facial photographs of humans and dogs with three emotional expressions (threatening, pleasant and neutral). We found that dogs' gaze fixations spread systematically among facial features. The distribution of fixations was altered by the seen expression, but eyes were the most probable targets of the first fixations and gathered longer looking durations than mouth regardless of the viewed expression. The examination of the inner facial features as a whole revealed more pronounced scanning differences among expressions. This suggests that dogs do not base their perception of facial expressions on the viewing of single structures, but the interpretation of the composition formed by eyes, midface and mouth. Dogs evaluated social threat rapidly and this evaluation led to attentional bias, which was dependent on the depicted species: threatening conspecifics' faces evoked heightened attention but threatening human faces instead an avoidance response. We propose that threatening signals carrying differential biological validity are processed via distinctive neurocognitive pathways. Both of these mechanisms may have an adaptive significance for domestic dogs. The findings provide a novel perspective on understanding the processing of emotional expressions and sensitivity to social threat in non-primates.