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.

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.

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).

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.

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.

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.

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.