A challenge for prospective teachers (PTs) is to determine what students know about a topic through asking appropriate questions and being thoughtful about the wording of these questions so as to capture and reframe students' spontaneous mathematical thinking and eventually unriddle the fuzzy boundary of students' complex thinking. This study…

Manipulatives support students with and without disabilities in mathematics. However, as students age, concrete manipulatives can be limiting and potentially not age appropriate (Satsangi, 2015). An alternative is virtual manipulatives, including app-based manipulatives. This study compared the use of app-based manipulatives to concrete…

This study aims to investigate the mathematical word problem-solving skills of preschool children 5-6 ages. To achieve this objective, the data were collected in four preschools (n = 162). A mathematical word problem test was used as data collection tools. In this study, it was found that the children's skills at solving mathematical word problems…

The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting the postsecondary success of students majoring in STEM fields. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. The present study…

We present a research report on addition and subtraction conducted with Down syndrome students between the ages of 12 and 31. We interviewed a group of students with Down syndrome who executed algorithms and solved problems using specific materials and paper and pencil. The results show that students with Down syndrome progress through the same…

Background: Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students' strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other…

Explores mathematical methods children use to find answers for themselves. Describes some methods used for multiplication and subtraction problems. (YP)

Investigated whether children who reflected the structure of word problems with their concrete models were successful in learning to symbolically represent problems with structure-based open number sentences. Forty-five first graders were taught to write canonical and noncanonical open number sentences. (Author/YP)

This paper looks at the issue of mathematics learning from a developmental perspective. It begins by focusing on the importance for teachers of understanding how mathematical thinking develops. The New Zealand Number Framework is used as an example of a developmental progression that is of particular relevance to the teaching of mathematics. The…

Children begin school with the ability to use their informal and implicit conceptual knowledge to guide their problem solving, but shift to the use of superficial strategies in their attempts to solve word problems as they progress through school. This paper describes a study designed to investigate the effects of an instructional sequence that…