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In this paper, we continue describing the project and the experimentation of "Ricerca Operativa Applicazioni Reali" (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools, introduced. ROAR is composed of three teaching units, addressed to Grades 10, 11, and 12, respectively, having the main aim to improve students' interest, motivation, and skills related to Science, Technology, Engineering, and Mathematics disciplines by integrating mathematics and computer science through operations research. In a previous paper, we reported on the design and implementation of the first unit, started in Spring 2021 at the scientific high school IIS Antonietti in Iseo (Brescia, Italy), in a Grade-10 class. Here, we focus on the second unit, carried out in Winter/Spring 2022 with the same students, now in a Grade-11 class. In particular, we describe objectives, prerequisites, topics and methods, the organization of the lectures, digital technologies used, and a challenging final project. Moreover, we analyze the feedback from students and teachers involved in the experimentation.

A critical part of supporting the development of students' algorithmic thinking is understanding the challenges that emerge when students engage with algorithmatizing tasks--tasks that require the creation of an algorithm. Knowledge of these challenges can serve as a basis upon which educators can build effective strategies for enhancing students' algorithmic thinking skills. This paper presents three illustrative cases of emergent challenges evident as students grapple with the process of creating an algorithm. The first challenge highlights discrepancies between the method with which students solve a problem and the algorithm they create, and claim would, when implemented, solve the same problem. The second challenge pertains to the persistence of students' normatively incorrect algorithms, despite going through multiple iterations of testing and revising. Finally, the third challenge concerns issues around the use of test problems for supporting students in their creation of generalized algorithms. These three challenges are discussed using student data (illustrative cases) from three different mathematical algorithmatizing tasks. Suggestions are put forth for addressing some of these challenges, with a particular emphasis on practical pedagogical suggestions for cultivating students' mathematical thinking in the context of algorithmatizing tasks.

Computational thinking (CT) is an important 21st-century skill. This paper aims at investigating predictors of CT self-efficacy among high-school students. The hypothesized predictors are grouped into three areas: (1) student characteristics, (2) home environment, and (3) learning opportunities. CT self-efficacy is measured with the Computational Thinking Scales (CTS) that comprises five dimensions: creativity, algorithmic thinking, cooperativity, critical thinking, and problem solving. N = 202 high-school students act as the sample, linear regression as the analysis method. The best prediction is possible for algorithmic thinking (R[superscript 2] = 0.511). For cooperativity, the explanatory power of our model it is weak (R[superscript 2] = 0.146). Across all five CTS dimensions, CT self-concept is the best predictor for CT self-efficacy. [For the full proceedings, see ED636095.]

This paper reviews algorithmic or artificial intelligence (AI) bias in education technology, especially through the lenses of speculative fiction, speculative and liberatory design. It discusses the causes of the bias and reviews literature on various ways that algorithmic/AI bias manifests in education and in communities that are underrepresented in EdTech software development. While other recent work has responded to mainstream or private sector technology development, this review looks elsewhere where practitioners, artists, and activists engage underrepresented communities in brainstorming processes to identify and solve tough challenges. Their creative work includes films, toolkits, applications, prototypes and other physical artifacts, and other future-facing ideas that can provide guideposts for private sector development. Acknowledging the gaps in what has been studied, this paper proposes a different approach that includes speculative and liberatory design thinking, which can help developers better understand the educational and personal contexts of underrepresented groups. Early efforts to advocate for fairness and equity in AI and EdTech by groups such as the Algorithmic Justice League, the EdTech Equity Project, and EdSAFE AI Alliance is also explored.

This paper presents an application of the Kalman filter in signal processing in instrumentation systems when the conditions of the environment generate a large amount of interference for the acquisition of signals from measurement systems. The unwanted interferences make important use of the instrumentation system resources and do not represent useful information under any aspect. A simulation is presented using the Matlab tool, which remarkably facilitates the information processing so that the corresponding actions are taken according to the information obtained, taking advantage of the current resources offered by the embedded systems and the required measurements are obtained with enough accuracy.

This paper analyses how pre-service teachers approach the notion of the infinite limit of a sequence from two perspectives: Specialized Content Knowledge and Advanced Mathematical Thinking. The aim of this study is to identify the difficulties associated with this notion and to classify them. In order to achieve this, an exploratory qualitative approach was applied using a sample of 12 future teachers. Among the results, we can affirm that pre-service teachers mainly use algorithmic procedures to solve tasks in which this type of limit is implicit, although they would consider a resolution that specifically involves the notion with an intuitive approach if they had to explain it to their students.

This study explores student flexibility in mathematics by examining the relationship between accuracy and strategy use for solving arithmetic and algebra problems. Core to procedural flexibility is the ability to select and accurately execute the most appropriate strategy for a given problem. Yet the relationship between strategy selection and accurate execution is nuanced and poorly understood. In this paper, this relationship was examined in the context of an assessment where students were asked to complete the same problem twice using different approaches. In particular, we explored (a) the extent to which students were more accurate when selecting standard or better-than-standard strategies, (b) whether this accuracy-strategy use relationship differed depending on whether the student solved a problem for the first time or the second time, and (c) the extent to which students were more accurate when solving algebraic versus arithmetic problems. Our results indicate significant associations between accuracy and all of these aspects--we found differences in accuracy based on strategy, problem type, and a significant interaction effect between strategy and assessment part. These findings have important implications both for researchers investigating procedural flexibility as well as secondary mathematics educators who seek to promote this capacity among their students.

The aim of this paper is to present a teaching proposal for the theoretical part relating to the first- and second-order linear difference equations with constant coefficients suitable for the first-year students at various types of universities. In contradistinction to the methods often applied (memorization of algorithms without a proper conceptual understanding), we provide an alternative methodological way-out for lecturers that is partially based on posing suitable questions and constructing the knowledge. Our approach is therefore characterized by the minimal input knowledge imposed on students. In fact, we assume that students are acquainted only with the summation of terms of geometric sequences and with solving linear and quadratic equations.

We introduce "Ricerca Operativa Applicazioni Reali" (ROAR; in English, "Real Applications of Operations Research"), a three-year project for higher secondary schools. Its main aim is to improve students' interest, motivation, and skills related to Science, Technology, Engineering, and Mathematics disciplines by integrating mathematics and computer science through operations research. ROAR offers examples and problems closely connected with students' everyday life or with the industrial reality, balancing mathematical modeling and algorithmics. The project is composed of three teaching units, addressed to grades 10, 11, and 12. The implementation of the first teaching unit took place in Spring 2021 at the scientific high school IIS Antonietti in Iseo (Brescia, Italy). In particular, in this paper, we provide a full description of this first teaching unit in terms of objectives, prerequisites, topics and methods, organization of the lectures, and digital technologies used. Moreover, we analyze the feedback received from students and teachers involved in the experimentation, and we discuss advantages and disadvantages related to distance learning that we had to adopt because of the COVID-19 pandemic.

The simple vehicle routing problem (VRP) is a common topic of discussion in introductory operations research/management science courses. The VRP can be framed in a variety of ways, and it can be difficult to solve to optimality. For solution purposes, introductory textbooks demonstrate how Excel's Evolutionary Solver (ES) add-in produces a routing. The ES utilizes a genetic algorithm with a heuristic stopping rule to produce a routing that is not guaranteed to be optimal. Beyond pointing out that search controls, such as maximum execution time, may be extended and followed by restart(s) of ES, textbook treatments do not offer alternative ways to continue the search for a possibly better routing. In this paper, a suite of ways is presented in which students may investigate beyond what ES produces or any other optimality-uncertain VRP solution method. The suite includes perturbation methods and other ways that function within an Excel spreadsheet environment that is popular with students and textbook writers. Because there is no demonstrable feature that confirms optimality, the student problem Solver must settle for a 'best found' result as unsettling as it may be. The incertitude is addressed.