Learning Landscape in Gamification: The Need for a Methodological Protocol in Research Applications.

In education, the term "gamification" refers to of the use of game-design elements and gaming experiences in the learning processes to enhance learners' motivation and engagement. Despite researchers' efforts to evaluate the impact of gamification in educational settings, several methodological drawbacks are still present. Indeed, the number of studies with high methodological rigor is reduced and, consequently, so are the reliability of results. In this work, we identified the key concepts explaining the methodological issues in the use of gamification in learning and education, and we exploited the controverses identified in the extant literature. Our final goal was to set up a checklist protocol that will facilitate the design of more rigorous studies in the gamified-learning framework. The checklist suggests potential moderators explaining the link between gamification, learning, and education identified by recent reviews, systematic reviews, and meta-analyses: study design, theory foundations, personalization, motivation and engagement, game elements, game design, and learning outcomes.

Identification and evaluation of technology trends in K-12 education from 2011 to 2021.

Educational technologies have captured the attention of researchers, policy makers, and parents. Each year, considerable effort and money are invested into new technologies, hoping to find the next effective learning tool. However, technology changes rapidly and little attention is paid to the changes after they occur. This paper provides an overall picture of the changing trends in educational technology by analyzing the Horizon Reports' predictions of the most influential educational technologies from 2011 to 2021, identifying larger trends across these yearly predictions, and by using bibliometric analysis to evaluate the accuracy of the identified trends. The results suggest that mobile and analytics technologies trended consistently across the period, there was a trend towards maker technologies and games in the early part of the decade, and emerging technologies (e.g., VR, AI) are predicted to trend in the future. Overall, the specific technologies focused on by the HRs' predictions and by educational researchers' publications seem to coincide with the availability of consumer grade technologies, suggesting that the marketplace and technology industry is driving trends (cf., pedagogy or theory).

Children's understanding of multiplication and division: Insights from a pooled analysis of seven studies conducted across 7 years.

Research suggests that children's conceptual understanding of multiplication and division is weak and that it remains poor well into the later elementary school years. Further, children's understanding of fundamental concepts such as inversion and associativity does not improve as they progress from grades 6 to 8. Instead, some children simply possess strong understanding while others do not. Other studies have identified an increase across these grades. The present investigation analyses data from seven studies of Grade 6 (n = 226), Grade 7 (n = 221), and Grade 8 (n = 216) children's three-term problem-solving (e.g., 3 × 24 ÷ 24 and 3 × 24 ÷ 6) and provides a unified account of multiplication and division understanding, one in which grade differences and individual variability coexist and are moderated by sex. Statement of contribution What is already known on this subject? Children's conceptual understanding of multiplication and division is weak and it is unclear whether it increases across the key grades of 6-8. Understanding of the inversion and associativity concepts is characterized by high individual variability, but grade and sex have never been found to be a contributing factor. What does this study add? A meta-analysis of seven data sets (n = 643) indicates that grade differences and individual variability coexist and are moderated by sex. Understanding increases across grade only for boys, but an equal number of boys and girls are in the top 10% of conceptual problem-solvers.

Children's understanding of additive concepts.

Most research on children's arithmetic concepts is based on one concept at a time, limiting the conclusions that can be made about how children's conceptual knowledge of arithmetic develops. This study examined six arithmetic concepts (identity, negation, commutativity, equivalence, inversion, and addition and subtraction associativity) in Grades 3, 4, and 5. Identity (a-0=a) and negation (a-a=0) were well understood, followed by moderate understanding of commutativity (a+b=b+a) and inversion (a+b-b=a), with weak understanding of equivalence (a+b+c=a+[b+c]) and associativity (a+b-c=[b-c]+a). Understanding increased across grade only for commutativity and equivalence. Four clusters were found: The Weak Concept cluster understood only identity and negation; the Two-Term Concept cluster also understood commutativity; the Inversion Concept cluster understood identity, negation, and inversion; and the Strong Concept cluster had the strongest understanding of all of the concepts. Grade 3 students tended to be in the Weak and Inversion Concept clusters, Grade 4 students were equally likely to be in any of the clusters, and Grade 5 students were most likely to be in the Two-Term and Strong Concept clusters. The findings of this study highlight that conclusions about the development of arithmetic concepts are highly dependent on which concepts are being assessed and underscore the need for multiple concepts to be investigated at the same time.

The relationship between adults' conceptual understanding of inversion and associativity.

Children's understanding of the mathematical concepts of inversion and associativity are positively related, as measured by the use of conceptually based shortcut strategies on 3-term inversion problems (i.e., a + b - b, d x e / e) and associativity problems (i.e., a + b - c, d x e / f; Robinson & Dubé, 2009; Robinson & Ninowski, 2003). Individuals who use the inversion shortcut (e.g., 3) are more likely to use the associativity strategy (e.g., 3 x 12 / 4. 12 / 4 = 3, 3 x 3 = 9), which is almost never used by an individual who does not also use the inversion shortcut (Robinson & Dubé, 2009). One possible reason for this relationship is that directing attention to the right-most operation during problem solving may be required to prime the conceptually based shortcut strategies for both problem types. This study investigated the relationship between adults' understanding of inversion and associativity. Adults (N = 42) solved inversion and associativity problems in 1 of 2 conditions. The participants were either presented with the left-most operation and then the whole problem or presented with the right-most operation and then the whole problem. A positive relationship between the use of the conceptually based strategies was found, and it was strikingly similar to the relationship found in childhood. There was evidence that the presentation of the right-most operation first primed the inversion shortcut.

A microgenetic study of the multiplication and division inversion concept.

This microgenetic study investigated the discovery and development of the multiplication and division concept of inversion. Little is known about multiplicative concepts relative to additive concepts, including the inversion concept. Grade 6 participants (mean age = 11 years 6 months) solved multiplication and division inversion problems (e.g., d x e/e) for several weeks. In the final week they solved inversion, modified inversion (e.g., e x d/e), and lure problems (e.g., d/e x d) to investigate transfer of knowledge. Despite years of formal arithmetic instruction and repeated exposure to inversion problems, over a third of the participants failed to discover the inversion-based shortcut whereas another third used the shortcut almost exclusively. Almost all participants had difficulty appropriately generalising the inversion concept. Current theories of mathematical understanding may need to be modified to include the developmental complexities of multiplicative concepts.

Children's understanding of addition and subtraction concepts.

After the onset of formal schooling, little is known about the development of children's understanding of the arithmetic concepts of inversion and associativity. On problems of the form a+b-b (e.g., 3+26-26), if children understand the inversion concept (i.e., that addition and subtraction are inverse operations), then no calculations are needed to solve the problem. On problems of the form a+b-c (e.g., 3+27-23), if children understand the associativity concept (i.e., that the addition and subtraction can be solved in any order), then the second part of the problem can be solved first. Children in Grades 2, 3, and 4 solved both types of problems and then were given a demonstration of how to apply both concepts. Approval of each concept and preference of a conceptual approach versus an algorithmic approach were measured. Few grade differences were found on either task. Conceptual understanding was greater for inversion than for associativity on both tasks. Clusters of participants in all grades showed that some had strong understanding of both concepts, some had strong understanding of the inversion concept only, and others had weak understanding of both concepts. The findings highlight the lack of developmental increases and the large individual differences in conceptual understanding on two arithmetic concepts during the early school years.

A microgenetic study of simple division.

How simple division strategies develop over a short period of time was examined with a microgenetic study. Grade 5 students (mean age = 10 years, 3 months) solved simple division problems in 8 weekly sessions. Performance improved with faster and more accurate responses across the study. Consistent with R. S. Siegler's (1996) overlapping waves model, strategies varied in their use. Direct retrieval increased, retrieval of multiplication facts remained steady, and addition facts, derived facts, and special tricks marginally decreased. Consistent with previous research, multiplication fact retrieval was the most common strategy, although it was slower and more error prone than direct retrieval. Strategy variability within and across individuals was striking across all of the sessions and underscores Siegler's (1996) assertion that development is in a constant transitional state.