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.

     

Scholars committed to opportunities in psychological education: a training and mentoring program for future psychologists of color

ABSTRACT

Although strides towards inclusivity and racial equality have been made in graduate education, many barriers to graduate education remain for racial/ethnic minorities. In response, we created Scholars Committed to Opportunities in Psychological Education (SCOPE), a mentor-based program for racial/ethnic minority undergraduates. 63 racial/ethnic minority undergraduates completed the SCOPE curricula and pre- and post-program questionnaires regarding graduate school application knowledge, application confidence, stress, self-efficacy, and SCOPE program satisfaction. Mentors completed a training and questionnaires in one SCOPE cohort. Knowledge about the GRE, the application process, and application confidence increased, and stress decreased, following SCOPE. The result of this work is a portable mentoring program that can be used across disciplines and demographics to increase inclusivity and equality.     

Group-based intervention on attention and executive functions in the school context

The objective of the study was to examine the effects of a group-based behavioural, cognitive and skills training intervention (Maltti) provided in schools for elementary school pupils with attention and executive function (EF) deficits. The treatment effects were identified by comparing an intervention group (n = 46) with a waitlist control group (n = 26). Specific effects of the intervention on behavioural deficits in attention and EF in a classroom setting as well as on academic skills were examined. Our analysis indicated that significant intervention effects could be found in the behavioural manifestation of attentional and executive skills in the classroom setting among children (n = 30) who were evaluated as having moderate symptoms in the pre-intervention assessment. Positive effects of the intervention were also observed in arithmetic and reading skills. The severity level of pre-intervention attention and EF deficits did not moderate the results observed in the academic skills tests. The results of this study suggest that a combination of behavioural, cognitive and skills training methods applied in a school context can be effective in reducing attention and EF problems and enhancing the academic performance of children with attention and EF deficits.     

Evaluation practices for college students with LD

To examine current practices in the use of psychoeducational evaluations for service delivery, we surveyed 91 service providers to college students with learning disabilities. The three purposes of the survey were to determine (a) whether service delivery decisions are based on information from psychoeducational evaluations, (b) which sections of the psychoeducational report are most useful in making service delivery decisions, and (c) the respondents' satisfaction with the tests and measurements for service delivery. The findings supported the common belief that data from psychoeducational evaluations serve as the primary basis for both eligibility and specific accommodation determinations. Respondents reported that all sections of the psychoeducational evaluation written report were useful, with the least useful section being test scores and the most useful being the summary of cognitive strengths and weaknesses. However, the section used most often for service delivery decisions was the professional's recommendations.     

Foundational issues in evolution education

There is a great need for effective evolution education. This paper reviews some of the evidence that demonstrates that need and analyzes some of the foundational semantic, epistemological, and philosophical issues involved. This analysis is used to provide a functional understanding of the distinction between science and non-science. Special emphasis is placed the scientific meaning of the terms theory, hypothesis, fact, proof, evidence, and truth, focusing on the difference between religious belief and acceptance of a scientific theory. Science is viewed as theologically neutral and as not mutually exclusive from religion. Finally, a number of practical recommendations to the classroom biology teacher are presented.     

Early Childhood Services in Ireland

This paper gives background information on early childhood services in Ireland and presents the results of a survey of the preschool experiences of 1065 children. The results of the survey suggest that the majority of children experienced some form of early childhood service before starting school. The most common service was a playgroup although a significant proportion of the children had experienced home‐based care with a relative or family day care provider. The implications of the findings for the development of a policy on early childhood services are discussed.     

Crazy Children, Fantastical Theories, and the Many Uses of Metaphysics

Woolley rightly challenges the incredible idea, held by some adults, that it is children who are peculiarly "fantastical" in their thinking. However, Woolley expresses little appreciation for "fantastical thinking" as it underlies the capacity for both grand delusions and amazing insights. In reducing "fantastical thinking" to conceptual error, she overlooks the mythical underpinning of her own theorizing and neglects the many constructive roles of "fantastical thinking" in development.     

A theory for decoupling lossless coupled tapered lines with applications to directional couplers

A simple theory is presented for decoupling a pair of lossless coupled nonuniform transmission lines (CNUTL), with a common return and supporting TEM waves, into two lossless nonuniform transmission lines (NUTL). This theory is independent of the port terminations, symmetry conditions, etc. The method directly relates the line parameters of the lossless CNUTL's to those of the decoupled lines and vice versa; further, the matrix parameters of the CNUTL's as a four-port are explicitly expressed in terms of those of the decoupled lines as two-ports. This theory is then utilized to study the applications of CNUTL's as directional couplers.It is shown that for CNUTL's to behave as a codirectional coupler, each of the decoupled lines should be a proportional line, while for contradirectional coupler action, the two decoupled lines have to be duals of each other. The coupling response of the codirectional coupler is found to be periodic, while the phase shift between coupled and transmitted signals varies linearly with frequency. The coupling response of various contradirectional couplers with smooth transition at one of the ends, for which the decoupled lines are “basic NUTL's with hyperbolic solutions”, are studied in detail. It is shown that all these couplers have a high-pass response and that the CNUTL's with “hyperbolic cosine squared lines” as decoupled lines have the best response of all the CNUTL's considered.     

Sum and product separabilities of multivariable functions and applications

Necessary and sufficient conditions for reducibility of certain classes of multivariable polynomials are considered. The special case when a polynomial in that class can be factored into a finite product of single variable polynomials is investigated. A set of necessary and sufficient conditions for decomposing a multivariable p.r.f. into a sum of single variable p.r.f.'s is given. Examples to illustrate applications of sum and product separabilities of functions are given.