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Research on fostering learning about percentages within intelligent tutoring systems (ITSs) is limited. Additionally, there is a lack of data‐driven approaches for improving the design of ITS to facilitate learning about percentages. To address these gaps, we first investigated whether students' understanding of basic mathematical skills (eg, arithmetic, measurement units and geometry) and fractions within an ITS predicts their understanding of percentages. We then applied a psychological network analysis to evaluate interdependencies within the data on 44 subtopics of basic mathematical concepts, fractions and percentages. We leveraged a large‐scale dataset consisting of 2798 students using the ITS bettermarks and working on approximately 4.1 million mathematical problems. We found that advanced arithmetic, measurement units, geometry and fraction understanding significantly predicted percentage understanding. Closer inspection indicated that percentage understanding was best predicted by problems sharing similar features, such as fraction word problems and fraction/natural number multiplication/division problems. Our findings suggest that practitioners and software developers may consider revising specific subtopics which share features with percentage problems for students struggling with percentages. More broadly, our study demonstrates how evaluating interdependencies between subtopics covered within an ITS as a data‐driven approach can provide practical insights for improving the design of ITSs. Practitioner notes What is already known about this topic Longitudinal studies showed that basic mathematical skills predict fraction understanding. There is only limited evidence on whether similar predictions can be observed for percentage understanding—in general and within intelligent tutoring systems. Process data from such intelligent tutoring systems can be leveraged to pursue both educational research questions and optimizing digital learning software. Problems involving percentages typically are word problems requiring multiplications and/or divisions. What this paper adds Similar to the case of fractions, students' performance on advanced arithmetic, measurement units and geometry significantly predicted performance with percentages. Students' performance with fractions also predicted performance with percentages significantly. A psychological network analysis was applied to evaluate specific interdependencies between a range of subtopics (eg, Multiplying and dividing fractions, Adding and subtracting fractions and Calculating with percentages). Fraction word problems and fraction problems involving multiplication/division turned out to be the best predictors of understanding percentages. Implications for practice and/or policy When facing difficulties with percentages, revision of previous mathematical concepts sharing similar features (eg, fraction word problems, fraction/natural number multiplication/division problems) may be advised. Software developers may consider implementing such data‐driven revision recommendations for students facing difficulties within intelligent tutor systems. Psychological network analysis can be utilized as a learning analytics method for easy‐to‐access visualizations illustrating relationships between a large range of different subtopics. What is already known about this topic Longitudinal studies showed that basic mathematical skills predict fraction understanding. There is only limited evidence on whether similar predictions can be observed for percentage understanding—in general and within intelligent tutoring systems. Process data from such intelligent tutoring systems can be leveraged to pursue both educational research questions and optimizing digital learning software. Problems involving percentages typically are word problems requiring multiplications and/or divisions. What this paper adds Similar to the case of fractions, students' performance on advanced arithmetic, measurement units and geometry significantly predicted performance with percentages. Students' performance with fractions also predicted performance with percentages significantly. A psychological network analysis was applied to evaluate specific interdependencies between a range of subtopics (eg, Multiplying and dividing fractions, Adding and subtracting fractions and Calculating with percentages). Fraction word problems and fraction problems involving multiplication/division turned out to be the best predictors of understanding percentages. Implications for practice and/or policy When facing difficulties with percentages, revision of previous mathematical concepts sharing similar features (eg, fraction word problems, fraction/natural number multiplication/division problems) may be advised. Software developers may consider implementing such data‐driven revision recommendations for students facing difficulties within intelligent tutor systems. Psychological network analysis can be utilized as a learning analytics method for easy‐to‐access visualizations illustrating relationships between a large range of different subtopics. [ABSTRACT FROM AUTHOR]

Previous studies have often demonstrated that educational television can have a positive effect on learning outcomes in low‐income countries when delivered in controlled settings. However, existing research in low‐resource contexts has scarcely considered the association between child outcomes and viewing in usual environments (ie, at their home, a friend's home or a relative's home). This lack of research is striking, as evidence from controlled settings might provide limited information on the effects of normal television exposure. This paper, therefore, investigates the relationship between normal exposure to a popular Tanzania‐produced cartoon, Ubongo Kids and mathematics capability, as represented by plausible values derived from an item response theory model applied to children's test responses. Cross‐sectional investigation of a sample of 38 682 Tanzanian children suggested normal educational television exposure to be significantly associated with mathematics capability, when controlling for age, sex, school enrolment, Kiswahili attainment and household fixed effects. While cross‐sectional results are not necessarily causal, the findings in this paper broadly correspond with those from previous designs using repeated observations. What is more, considering association results alongside cost and viewership estimates suggests television‐based interventions to be highly cost effective. Practitioner NotesWhat is already known about this topic National data for Tanzania suggests the country to have both low levels of mathematics proficiency and considerable access to television technology.Educational television‐based interventions might, therefore, be worthy of consideration by educational policymakers, especially given that studies conducted in controlled settings indicate that television can deliver learning benefits.There is, however, little evidence concerning educational television exposure outside of controlled settings. Only one such study in a low‐income context that concerned the association between learning outcomes and viewing among primary‐age children has been identified.What this paper adds This paper addresses this dearth of research by investigating the association between normal exposure to a Tanzanian cartoon, Ubongo Kids and mathematics capability, as derived from an item response theory model applied to the test responses of 38 682 children.Cross‐sectional findings suggest the association between normal television exposure and mathematics capability to be significant.Further, a cost‐effectiveness comparison with alternate interventions in comparable contexts indicates that educational television is highly cost‐effective.Implications for practice and/or policy The findings presented in this paper concerning educational television viewership in usual environments act to triangulate those from prior research conducted in controlled settings. As such, policymakers in low‐income contexts now possess more convincing evidence on the potential influence of educational television interventions.Additionally, the cost‐effectiveness comparison made suggests that educational television should be considered a viable option by policymakers seeking to address learning outcomes with limited resources. [ABSTRACT FROM AUTHOR]

Natural language helps express mathematical thinking and contexts. Conventional mathematical notation (CMN) best suits expressions and equations. Each is essential; each also has limitations, especially for learners. Our research studies how programming can be a advantageous third language that can also help restore mathematical connections that are hidden by topic‐centred curricula. Restoring opportunities for surprise and delight reclaims mathematics' creative nature. Studies of children's use of language in mathematics and their programming behaviours guide our iterative design/redesign of mathematical microworlds in which students, ages 7–11, use programming in their regular school lessons as a language for learning mathematics. Though driven by mathematics, not coding, the microworlds develop the programming over time so that it continues to support children's developing mathematical ideas. This paper briefly describes microworlds EDC has tested with well over 400 7‐to‐8‐year‐olds in school, and others tested (or about to be tested) with over 200 8‐to‐11‐year‐olds. Our challenge was to satisfy schools' topical orientation and fit easily within regular classroom study but use and foreshadow other mathematical learning to remove the siloes. The design/redesign research and evaluation is exploratory, without formal methodology. We are also more formally studying effects on children's learning. That ongoing study is not reported here. Practitioner notesWhat is already known Active learning—doing—supports learning.Collaborative learning—doing together—supports learning.Classroom discourse—focused, relevant discussion, not just listening—supports learning.Clear articulation of one's thinking, even just to oneself, helps develop that thinking.What this paper adds The common languages we use for classroom mathematics—natural language for conveying the meaning and context of mathematical situations and for explaining our reasoning; and the formal (written) language of conventional mathematical notation, the symbols we use in mathematical expressions and equations—are both essential but each presents hurdles that necessitate the other. Yet, even together, they are insufficient especially for young learners.Programming, appropriately designed and used, can be the third language that both reduces barriers and provides the missing expressive and creative capabilities children need.Appropriate design for use in regular mathematics classrooms requires making key mathematical content obvious, strong and the 'driver' of the activities, and requires reducing tech 'overhead' to near zero.Continued usefulness across the grades requires developing children's sophistication and knowledge with the language; the powerful ways that children rapidly acquire facility with (natural) language provides guidance for ways they can learn a formal language as well.Implications for policy and/or practice Mathematics teaching can take advantage of the ways children learn through experimentation and attention to the results, and of the ways children use their language brain even for mathematics.In particular, programming—in microworlds driven by the mathematical content, designed to minimise distraction and overhead, open to exploration and discovery en route to focused aims, and in which children self‐evaluate—can allow clear articulation of thought, experimentation with immediate feedback.As it aids the mathematics, it also builds computational thinking and satisfies schools' increasing concerns to broaden access to ideas of computer science. [ABSTRACT FROM AUTHOR]

Educational applications (apps) are ubiquitous within children's learning environments and emerging evidence has demonstrated their efficacy. However, it remains unclear what the active ingredients (ie, mechanisms), or combination of ingredients, of successful maths apps are. The current study developed a new, open‐access, three‐step framework for assessing the educational value of maths apps, comprised of type of app, mathematical content and app design features. When applied to a selection of available maths apps previously evaluated with children in the first 3 years of school (the final sample included 23 apps), results showed that practice‐based apps were the most common app type tested (n = 15). Basic number skills, such as number representation and relationships, were the most common area of mathematics targeted by apps (n = 21). A follow‐up qualitative comparative analysis showed observed learning outcomes with maths apps were enhanced when apps combined the following: a scaffolded and personalised learning journey (programmatic levelling) and explanations of why answers were right or wrong (explanatory feedback), as well as praise, such as 'Great job!' (motivational feedback). This novel evidence stresses the significance of feedback and levelling design features that teaching practitioners and other stakeholders should consider when deciding which apps to use with young children. Directions for future research are discussed. Practitioner notesWhat is already known about this topic Educational apps have been shown to support maths attainment in the first 3 years of school.Several existing frameworks have attempted to assess the educational value of some of these maths apps.Emerging experimental evidence also demonstrates the benefits of specific app design features, including feedback and levelling.What this paper adds Practice‐based maths apps are the most common type of app previously evaluated with young children.These evaluated maths apps have mostly focused on basic number skills.The combination of explanatory and motivational feedback, with programmatic levelling (either dynamic or static), was a necessary condition for enhancing learning outcomes with maths apps.Implications for practice and policy The inclusion of feedback and levelling in maths apps should be considered by app developers when designing apps, and by educational practitioners and parents when deciding which apps to use with their children.Further consideration is also needed for the development of educational apps that include a broad range of maths skills. [ABSTRACT FROM AUTHOR]

This study analyses the potential of a learning analytics (LA) based formative assessment to construct personalised teaching sequences in Mathematics for 5th‐grade primary school students. A total of 127 students from Spanish public schools participated in the study. The quasi‐experimental study was conducted over the course of six sessions, in which both control and experimental groups participated in a teaching sequence based on mathematical problems. In each session, both groups used audience response systems to record their responses to mathematical tasks about fractions. After each session, students from the control group were given generic homework on fractions—the same activities for all the participants—while students from the experimental group were given a personalised set of activities. The provision of personalised homework was based on the students' errors detected from the use of the LA‐based formative assessment. After the intervention, the results indicate a higher student level of understanding of the concept of fractions in the experimental group compared to the control group. Related to motivational dimensions, results indicated that instruction using audience response systems has a positive effect compared to regular mathematics classes. Practitioner notesWhat is already known about this topic Developing an understanding of fractions is one of the most challenging concepts in elementary mathematics and a solid predictor of future achievements in mathematics.Learning analytics (LA) has the potential to provide quality, functional data for assessing and supporting learners' difficulties.Audience response systems (ARS) are one of the most practical ways to collect data for LA in classroom environments.There is a scarcity of field research implementations on LA mediated by ARS in real contexts of elementary school classrooms.What this paper adds Empirical evidence about how LA‐based formative assessments can enable personalised homework to support student understanding of fractions.Personalised homework based on an LA‐based formative assessment improves the students' comprehension of fractions.Using ARS for the teaching of fractions has a positive effect in terms of student motivation.Implications for practice and/or policy Teachers should be given LA/ARS tools that allow them to quickly provide students with personalised mathematical instruction.Researchers should continue exploring these potentially beneficial educational implementations in other areas. [ABSTRACT FROM AUTHOR]

Although the educational potential of social media has been widely acknowledged, it remains unclear whether social media use might present opportunities for the development of math identity. This study drew on the socialization framework of math identity to examine the relationships between social media use for math learning, bicultural identity integration, ethnic‐math beliefs and math identity among ethnic minority high school students in China. Structural equation modelling results showed that (a) social media use was positively related to math identity; (b) high bicultural identity integration was positively associated with math identity, while biased ethnic‐math beliefs were negatively related to math identity and (c) social media use suppressed the socialization process of math identity, weakening the maladaptive roles of low bicultural identity integration and biased ethnic‐math beliefs in shaping math identity. Our findings highlight the beneficial role of social media use in student math learning. Theoretical and practical implications are discussed. Practitioner notesWhat is already known about this topicSocial media use for learning is associated with students' academic motivation, engagement and academic achievement.Social media use may have affordances for identity development, especially for ethnic minorities.The formation of ethnic minority students' math identity is intertwined with their math and ethnic socialization.What this paper addsSocial media use for math learning was directly and positively related to ethnic minorities' math identity.This study quantitatively confirmed the associations of bicultural identity integration and ethnic‐math beliefs with math identity.Social media use suppressed the relations of bicultural identity integration and ethnic‐math beliefs with math identity.Implications for practice and/or policyPromoting social media use for math learning benefits ethnic minority students' math identity.Social media use for math learning could alleviate the maladaptive role of low bicultural identity integration and biased ethnic‐math beliefs in math identity development.Ethnic minority students' math identity socialization processes merit attention. [ABSTRACT FROM AUTHOR]

The authors discuss three reasons that motivated them to propose and oversee the preparation of this special section of the journal. Topics include factor that led to the eventual recognition and appreciation of what has been called the situated cognition or situative perspective, status of the circular expectations in many nations for primary and secondary schools, and computer science and mathematics as two fields that are known to lack diversity in who participates professionally.