This paper provides evidence on how elementary school students from a Mexican public school move from using an operational sense, expressed in computational strategies, to a kind of relational thinking based on structure sense ideas and expressed by number decomposition. Even though the results are somewhat preliminary, they illustrate how…

Being able to effectively interpret students' thinking and respond effectively in the moment are important skills that preservice teachers (PSTs) need to learn. This study zooms in on 14 PSTs' planning, teaching, and reflections involved in number string lessons, and investigates to what extent PSTs anticipate their students' strategies and…

Although students' invented strategies typically prove to be effective in the improvement of students' mathematical understanding, little is known about how preservice teachers interpret and respond to student-invented strategies on whole number multiplication. This study investigated the nature of 25 preservice teachers' interpretations of and…

Fifteen elementary and secondary teacher candidates solved sixteen integer addition and subtraction problems during think-aloud interviews. Investigators further probed participants' solution strategies as well as what they noticed first when starting a new problem. Task analyses of participants' solutions led to the creation of two distinct maps…

Literature at national and international levels argues the importance of including mental computation in a mathematics curriculum that promotes number sense. However, mental computation does not feature in importance in the current Queensland mathematics syllabus documents. Hopefully, with the writing of a new mathematics syllabus, mental…

Four preschool children with developmental delays were taught to name the numerical value of sets of geometric figures, the corresponding numeral, the corresponding number word, and the corresponding Roman numeral. Half of the stimuli were taught with instructive feedback and the other half without, as two conditions were established: the future…

This paper discusses the question, what kinds of learning and new knowledge about content and children's thinking can an innovative curriculum program motivate? Discussion is restricted to whole number operations and how changing knowledge, beliefs, and practice as both an individual and collective problem might be conceived. To the extent that…

This study addressed the problem of promoting generalization of knowledge in people with mental handicaps, by presenting an approach based on the idea that certain cognitive representations of strategies and related concepts are common to solving a wide variety of problems. The surface context of these problems may vary considerably, but all will…

This paper reports on a study of seventh grade students (N=4) who attend a rural K-12 school. Students participated in a 5-week teaching experiment designed to build on their existing knowledge of the unit concept and extend it to the rational number operations of multiplication and division. Data collected comes in the form of videotapes,…

To isolate the process deficits underlying a specific learning disability in mathematics achievement, 77 academically normal and 46 learning disabled (LD) students in second, fourth or sixth grade were presented 140 simple addition problems using a true-false reaction time verification paradigm. (The problems were on a video screen controlled by…