Building a Bridge for Inclusive Assessment of Newly-Arrived Migrants' Knowledge in Science and Mathematics

The Erasmus+/KA3 project Augmented Assessment “Assessing newly arrived migrants' knowledge in Science and Math using augmented teaching material” aims to address the gap that exists in assessing newly arrived migrant students' prior knowledge in the fields of science and mathematics caused by the linguistic obstacle between them and the teachers. To address this gap, the project will develop the Augmented Assessment Library as well as a teachers' training course focusing on inclusive assessment and augmented reality. The chapter outlines the theoretical orientations of the project (augmented assessment bridges) and discusses the elements that comprise them focusing on the connections among inclusive pedagogy, visual representations in science and math education, multimodality, and augmented reality. It also describes the pedagogical framework underpinning the design of the Augmented Assessment Training Course as well as the main innovation of the project which is the Augmented Assessment Library and its pedagogical value for assessment.

SMIS: A Stepwise Multiple Integration Solver Using a CAS

Multiple Integration is a very important topic in different applications in Engineering and other Sciences. Using numerical software to get an approximation to the solution is a normal procedure. Another approach is working in an algebraic form to obtain an exact solution or to get general solutions depending on different parameters. Computer Algebra Systems (CAS) are needed for this last approach. In this paper, we introduce SMIS, a new stepwise solver for multiple integration developed in a CAS. The two main objectives of SMIS are: (1) to increase the capabilities of CAS to help the user to deal with this topic and (2) to be used in Math Education providing an important tool for helping with the teaching and learning process of this topic. SMIS can provide just the final solution or an optional stepwise solution (even including some theoretical comments). The optional stepwise solutions provided by SMIS are of great help for (2). Although SMIS has been developed in the specific CAS Derive, since the code is provided, it can be easily migrated to any CAS which deals with integrals and text management that allow us to display comments for intermediate steps.

Sustainable Math Education of Female Students during a Pandemic: Online versus Face-to-Face Instruction

The present study was driven by the assumption that a key feature of sustainable education is its ability to preserve standards of quality even amid unforeseen, potentially disruptive events. It asked whether students’ academic success in math general education courses differed between synchronous online (during the COVID-19 pandemic) and face-to-face (before the pandemic), under the ancillary assumption that computational competency, a pillar of sustainable education, shapes enduring success in a variety of professional fields. As the early identification of at-risk students and ensuing remedial interventions can bring about academic success, the study also investigated the predictive validity of students’ initial performance in online and face-to-face math courses. Two general education courses (introductory calculus and statistics), taught by the same instructor, were selected. Class grades did not differ between instructional modes, thereby providing no evidence for the widespread concern that the switch to the online mode had damaged learning. Yet, during the semester, test and homework performance were differentially sensitive to modes of instruction. Furthermore, both test and homework performance during the first half of the semester predicted class grades in online courses, whereas only test performance predicted class grades in face-to-face courses. These results suggest that sustainable math education in times of crisis is feasible and that educators’ consideration of the differential predictive value of test and homework performance may aid its attainment.

Effects of a videogame in math performance and anxiety in primary school

The present paper describes the design and evaluation of a videogame developed to support math education and overcome math anxiety (MA) at the primary school level. The game narrative is based on the history of math. The player travels back on time and meets on-player characters such as Pythagoras of Samos and Ada Lovelace, learning about how math was used during their times. The player is invited to play a minigame where the concepts shared by the characters are used as a strategy to win. The game’s evaluation consisted of a pre and post-testing study that measured students’ math performance and MA levels. The experiment also included a group interview to collect students’ perceptions about the game. The experiment lasted five weeks, and 88 students from three primary schools played the game on weekly sessions 45-60 minutes long. Statistical analysis suggested the game significantly improves students’ math performance. However, the results indicated that female students from one of the classrooms had higher MA levels after playing the game. In addition, qualitative data shows students had a high level of engagement with the gameplay.

An Automatic Optimal Course Recommendation Method for Online Math Education Platforms Based on Bayesian Model

Online education platforms inject new vitality into the field of education, and greatly improves the accessibility to high-quality education resources. However, the current online education platforms do not support independent course selection based on personal preferences. To solve this problem, this paper designs an automatic recommendation method of optimal courses for online math education platforms based on Bayesian model. The results show that the Bayesian model can simulate the causal relationship between real-world affairs by building a graphic model based on the graph theory and the probability theory; the model can effectively merge priori and posteriori information, and encode the causality between knowledge points; the model clearly outshines user-based collaborative filtering model, term-based collaborative filtering model, and SlopeOne model, and achieves a stable accuracy rate in automatic recommendation of courses. The research provides an empirical evidence to the improvement and innovation of professional online math course platforms.

Three addend addition: Who goes out of order and why?

Single-digit, three addend sums of the type a + b + c offer a rich opportunity to directly observe the range of strategies that different participants may use because they afford the possibility of measuring a partial sum (i.e., a + b or a + c or b + c). For example, while computing the sum 9 + 7 + 1, do participants go in order by first adding 9 + 7 and then adding 1, or do they incur the cost of going out of order by adding 9 + 1 in order to obtain the partial sum of 10, which makes the subsequent addition of 7 less effortful? Informed by findings in simple and complex arithmetic, we investigated the problem types and participant characteristics that can predict out of order switching behavior in such three-addend sums. To test our hypotheses, we tasked participants, first in an online study, and then in an in-person study to complete 120 single-digit, three addend problems. We found that participants switched the order of addition to prioritize efficiency gains in contexts in which the partial sum addends were small or equal to each other, or when doing so led to a partial sum of 10, or led to a partial sum that is equal to the third remaining integer. Response latency data confirmed that participants were deriving efficiencies in the manner we expected. Related to individual differences, our findings showed that participants with higher levels of math education were most likely to seek efficiency benefits whenever they were on offer.

Causal pathways from fractions to algebra: Integrating psychology and math education perspectives

Algebra knowledge is an important gatekeeper to educational and economic opportunity. Both math education researchers and psychologists have shown that fractions may be a key to this gate (e.g., Hackenberg, 2013; Siegler et al., 2012). However, psychological and educational research on the fractions-algebra association has been disconnected, with separate frameworks, definitions, and designs. This integrative review synthesizes evidence from both disciplines about how and why fractions knowledge leads to stronger algebra knowledge. I suggest that the strength of causal evidence is limited by idiosyncratic measurement, limited longitudinal research, and imprecise definitions. I also review six plausible fractions-to-algebra mechanisms, which future research should empirically test. Throughout, I argue that more nuanced understanding of the fractions-algebra association will require interdisciplinary teams. Finally, I propose an integrative conceptual model of how fractions knowledge may lead to success in algebra and suggest new directions for collaborative investigation to inform developmental theory and educational practice.