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Introduction: Across the world, mathematical expressions are represented very differently in braille. The aim of this study was (1) to gain an overall insight in mathematical braille notations and (2) to investigate how mathematical braille notations support braille readers in reading and comprehending mathematical expressions. Method: Twenty teachers from sixteen countries (thirteen European Union, EU, and three non-EU) were asked to transform 21 mathematical expressions and equations into the mathematical braille notation currently used by their braille readers. Three mathematical expressions were selected, and the transformed expressions in the different braille notations were qualitatively compared at braille and mathematical structure level. Results: The results illustrated that most mathematical braille notations use mathematical structures that either support braille readers in getting an overview of an expression—for example, by announcing the start and end of a fraction—or facilitate communication between braille readers and people who can see. Discussion: The method of comparing transformed expressions at structure level can be extended to other types of mathematical expressions and other mathematical braille notations. Agreement on the structure of different mathematical expressions can be a first step towards a universal mathematical braille notation. Implications for Practitioners: Mathematics teachers should be aware of and use the strengths of the mathematical braille notation and try to compensate for weaknesses of the notation in the support of braille readers. © American Foundation for the Blind 2022.

In this review, we evaluate the claim that translanguaging in the classroom supports the development of the bilingual lexicon by enhancing cross-linguistic transfer. To address this issue, we integrate findings from psycholinguistics and educational sciences in order to identify how effective pedagogical practices for monolingual children can be extended to pedagogical practices for bilingual children. We show that both monolingual and bilingual children benefit from teaching strategies that strengthen the mental connections between semantically and phonologically related words, and that for bilingual children, these strategies should support both within- and cross-language connections. We argue that by stimulating the use of the home language in the classroom, translanguaging strategies like multilingual label quests and multilingual reading and writing can strengthen cross-language connections and, thereby, facilitate cross-linguistic lexical transfer. For closely related languages, stimulation of the home language has the additional benefit of implicitly facilitating the transfer of cognate vocabulary. Explicit instruction about cognates could further stimulate the development of cognate awareness, but whether it also enhances vocabulary learning is still an open question.

In March 2020, many schools worldwide were closed due to the COVID-19 pandemic. This closure confronted mathematics teachers with the challenging transition to emergency remote teaching (ERT). How did students experience ERT, and how did these experiences relate to context variables and to their teachers’ beliefs and practices? In particular, what didactic approaches and formative assessment practices did secondary mathematics students experience, and which beliefs did they hold concerning digital mathematics education? How were these student experiences and beliefs related to student context variables (gender, need to support family, personal home equipment), teacher beliefs, delivery modes, and student appreciation of mathematics? To investigate these issues, we set out online questionnaires for mathematics teachers and their students in Flanders—the Dutch-speaking part of Belgium—, Germany, and the Netherlands. Data consisted of completed questionnaires by 323 mathematics teachers and 2126 of their students. Results show that even though students preferred regular face-to-face teaching, they were content with the quality of their teachers’ distance mathematics teaching. Students reported that they were taught new topics often, but did not experience teachers initiating peer feedback. High student appreciation of mathematics, good home environment, and more synchronous delivery of ERT were related to ERT experiences and more positive beliefs concerning digital mathematics education. These findings have implications for ERT teaching strategies in future, as well as for hybrid teaching practices.

The COVID-19 pandemic has confronted mathematics teachers with the challenge of developing alternative teaching practices—in many cases at a distance through digital technology—because schools were closed. To investigate what distance practices in secondary mathematics education have emerged and how teachers experienced them, we set out online questionnaires in Flanders—the Dutch-speaking part of Belgium—, Germany, and the Netherlands. The questionnaire focused on teaching practices, teacher beliefs, didactics, and assessment. Data consisted of completed questionnaires by 1719 mathematics teachers. Results show that the use of video conferencing tools increased massively, while the use of mathematics-specific tools that teachers used before the lockdown reduced substantially. Further findings are that teachers' confidence in using digital technologies increased remarkably during the lockdown and that their experiences and beliefs only marginally impacted their distance learning practices. Also, we observed some differences between the three countries that might be explained by differences in educational policies and in technological facilities and support. For future research, it would be relevant to investigate long-term changes in teachers’ practices, as well as students’ views and experiences related to the teacher’s practices.

The process of thinking through the implications of the Anthropocene for the humanities, including history, is well under way. The time has come for historians of science to take stock of the situation in Anthropocene scholarship and collaboratively reflect on how we want to situate our field toward that scholarship. It will involve taking up such fundamental questions as why and how, as well as for and with whom, we do the history of science. This introduction to the Focus section “History of Science in the An-thropocene” presents the Anthropocene as both a challenge and an opportunity, opening up new avenues of research and widening spatial, temporal, and topical boundaries while giving rise to urgent problems, dilemmas, and choices that will need to be faced. The aim of this Focus section is to put these challenges and opportunities on the history of science’s agenda and, thereby, to start a discipline-wide dialogue.

We study the augmented reality sandbox (ARSB) as an embodied learning environment to foster meaning making in the context of bivariable calculus. We present the case of Tiago, a first-year bachelor chemistry student, performing a series of tasks based on embodied design, including perception-based, action-based and incorporation-based tasks. Tiago’s work demonstrates the affordances of the ARSB, e.g. to trace a height line and to manipulate plastic planes either with or without feedback from projected height lines. Tiago’s reasoning about mathematical concepts, e.g. the parameters in a plane equation and the gradient vector, is supported by perceptual structures that he discovers during these embodied tasks. We distinguished two ways in which ARSB affordances were used in the learning sequence. In perception-based and action-based tasks, the affordances of the ARSB were immediately available and intensively involved in the interaction. In incorporation tasks, on the contrary, a critical affordance was deliberately removed and the student was able to reproduce its functionality without technology.

Although reconsolidation-based interventions constitute a promising new avenue to treating fear and anxieties disorders, the success of the intervention is not guaranteed. The initiation of memory reconsolidation is dependent on whether a mismatch between the experienced and predicted outcome-a prediction error (PE)-occurs during fear memory reactivation. It remains, however, elusive whether any type of PE renders fear memories susceptible to reconsolidation disruption. Here, we investigated whether a value PE, elicited by an outcome that is better or worse than expected, is necessary to make fear memories susceptible to reconsolidation disruption or whether a model-based identity PE, i.e., a PE elicited by an outcome equally aversive but different than expected, would be sufficient. Blocking beta-adrenergic receptors with propranolol HCl after reactivation did, however, not reduce the expression of fear after either type of PE. Instead, we observed intact fear memory expression 24 h after reactivation in the value-, identity- and a no-PE control group. The present results do not corroborate our earlier findings of reconsolidation disruption and point towards challenges that the field is currently facing in observing evidence for memory reconsolidation at all. We provide potential explanations for the unexpected failure of replicating reconsolidation disruption and discuss future directions.

Graphs are ubiquitous. Many graphs, including histograms, bar charts, and stacked dotplots, have proven tricky to interpret. Students’ gaze data can indicate students’ interpretation strategies on these graphs. We therefore explore the question: In what way can machine learning quantify differences in students’ gaze data when interpreting two near-identical histograms with graph tasks in between? Our work provides evidence that using machine learning in conjunction with gaze data can provide insight into how students analyze and interpret graphs. This approach also sheds light on the ways in which students may better understand a graph after first being presented with other graph types, including dotplots. We conclude with a model that can accurately differentiate between the first and second time a student solved near-identical histogram tasks.

We investigated French primary school teachers’ assessment practice in mathematics. Using an online questionnaire on teachers’ background, teaching, and grading practice, we were able to determine assessment profiles of 604 primary school teachers. As evidenced by the teachers’ scores on the latent factors Assessment purposes, Assessment practices, and Differentiation, teachers with the profile of Enthusiastic assessors view assessment as more useful and use it more often to adapt their instruction than teachers with the profile of Unenthusiastic assessors. This can be useful for practice and sheds more light on French teachers’ assessment practices in mathematics. It is also interesting to compare the results of this survey with those from China and the Netherlands, as the differences reflect different assessment cultures and may shed light on some of the results of international large-scale assessments such as PISA.

As technologies that put the body at the center of mathematics learning enter formal and informal learning spaces, we still know little about the teaching methods educators can use to support students’ learning with these specialized systems. Drawing on ethnomethodology and conversation analysis (EMCA) and the Co-Operative Action framework, we present three multimodal ways that educators can be responsive to learners’ embodied ideas and help them transform sensorimotor patterns into mathematically significant perceptions. These techniques include (1) encouraging learners to use gesture to express and reflect on their ideas, (2) presenting multimodal candidate understandings to check comprehension of learners’ embodied ideas, and (3) co-constructing multimodally expressed embodied ideas with learners. We demonstrate how these techniques create opportunities for learning and discuss implications for a multimodal, embodied practice of responsive teaching.

ispartof: Educational Studies In Mathematics vol:104 issue:3 pages:299-311 ispartof: location:Netherlands status: published

There is increasing attention for interest as a powerful, complex, and integrative construct, ranging in appearance from entirely momentary states of interest to longer-term interest pursuits. Developmental models have shown how these situational interests can develop into individual interests over time. As such, these models have helped to integrate more or less separate research traditions and focus the attention of the field more on the developmental dynamics. This, however, also raises subsequent questions, one being how development can be understood in terms of interest structure. The developmental models seem to suggest that development occurs roughly along the line of six dimensions, which we summarize as the dimensions of historicity, value, agency, frequency, intensity, and mastery. Using an experience sampling method that was implemented in a smartphone application, we prompted 94 adolescents aged 13 to 16 (60% female) to rate each interest they experienced during two weeks on these six dimensions. A latent profile analysis on 1247 interests showed six distinct multidimensional patterns, indicating both a homogeneous and heterogeneous structure of interest. Four homogeneous patterns were indicated by more or less equal levels on all six dimensions in varying degrees, and contained 86% of the interests. Two heterogeneous patterns were found, describing variations of interest that are interpreted and discussed. These results endorse the complexity of the construct of interest and provide suggestions for identifying different manifestations of interest.