The study set out to explore different mathematical difficulties among 877 second-grade children and to test the effect of memorization versus conceptual practices with number combinations. It used a latent profile analysis of baseline measurements of digit writing speed, number combination fluency, multidigit calculation, and number sense skills…

Word problems form an important part of the early grade mathematics curriculum in South Africa. Studies have shown that the relative difficulty of word problems differ: learners are more likely to solve certain types of word problems than others, with compare type problems being the most difficult. In order to help early grade learners understand…

The current paper overviews a nine-month PhD study that investigated the impact of learning mathematics through sequences of challenging tasks on the mathematical competence and attitudes of Year 2 students (n = 59). Adopting a Self-Determination Theory lens, a pragmatist paradigm and a mixed-method design, the study found that at all levels of…

Young children can struggle to learn difficult disciplinary content and important skills for practicing science. Problem-based learning (PBL) may be useful for addressing such difficulties, yet evidence to support its usefulness in elementary school-aged children is limited. We considered the role of a PBL unit in improving students' genetics…

Providing students the autonomy and choice to learn when productive struggle becomes unproductive is a core teaching belief in the author's classroom. The author teaches in a multiage classroom where he has 16 first- and second-grade students, ages 6, 7, and 8. Like other educators, he believes in the importance of productive struggle. The author…

Making accurate judgements and interpretations about student growth and progress in mathematics can be problematic when using open-ended assessments. This study reports on the development of a class-based assessment instrument and marking key designed to assess Year 2 students' mathematics competence to reflect their learning of mathematics…

Elementary school students struggle in interpreting the equal sign as a symbol denoting equivalence. Although many have advocated using a pan-balance scale to help students develop this understanding, less is known about what features associated with this model support learning. To attempt to control and examine these features, the investigators…

Process-oriented dynamic testing aims to investigate the processes children use to solve cognitive tasks, and evaluate changes in these processes as a result of training. For the current study, a dynamic complex figure task was constructed, using the graduated prompts approach, to investigate the processes involved in solving a complex figure task…

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…

Children in the elementary grades are expected to solve equations to demonstrate prealgebraic proficiency. Prealgebraic differences may emerge based equation type (i.e., standard vs. nonstandard), the operation shown or required for solution (i.e., addition or subtraction), and the position of the unknown. Prealgebraic differences may also be…

This report provides a description of the development process, field testing, and psychometric properties of a student mathematics test designed to assess grades K, 1, and 2 student abilities. The test was administered to 4,486 participating grade K, 1, and 2 students in 67 schools located in 10 public school districts in Florida during fall 2015.…

The purpose of the study was to examine differences in early numerical competencies, as well as subtraction skill, as a function of children's mathematics difficulty (MD) status: computational difficulty (CD), word problem-solving difficulty (PD), concurrent difficulty (CDPD), or neither difficulty (i.e., typically developing; TYP). Based on…

Teacher nominations of students are commonly used in gifted and talented identification systems to supplement psychometric measures of reasoning ability. In this study, second grade teachers were requested to nominate approximately one fourth of their students as having high learning potential in the year prior to the students' participation in a…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

Current assessment practices in the United States are not able to accurately capture the total linguistic, cognitive, and achievement abilities of bilingual learners. There are psychometric complexities involved when assessing and interpreting test results of bilingual students, which impact the validity of this practice. Further, the compromise…