Promoting Equity in Elementary School Mathematics

This chapter describes the frameworks of mathematics tasks, equity-based mathematics teaching practices, technological pedagogical and content knowledge (TPACK), and how they relate to teaching for equity in virtual learning environments (VLE). The frameworks are used to describe vignettes from VLEs with elementary school learners and elementary school teacher candidates (future teachers). Implications of these vignettes include a need for an empirically based trajectory related to equity-based teaching practices as well as a need to consider which technologies in a VLE can be used to effectively promote equity-based mathematics teaching practices.

Error Analysis of Students with Mathematics Learning Difficulties in Tibet

It has been reported that a noticeable high percentage (33%) of students with mathematics learning difficulties (MLD) in Tibet can partly be explained by the current state of mathematics teaching. This study investigated the errors the Tibetan seventh grade students (N = 30) with MLD made in mathematics tasks. A novel Mathematics Error Pattern Identification Test (MEPIT) was used, identifying eight different error types: visual-spatial, comprehension, transformation, relevance, fact, procedural, measurement, and presentation errors. The most frequent error types among Tibetan students found were fact and comprehension errors. Compared to boys, girls seemed to be more vulnerable to fact and relevance errors. No significant differences were found between students from rural and urban school, except rural school students made more comprehension errors. The novel measure of MEPIT could serve as a screening tool for Tibetan teachers to identify the errors students make in mathematics tasks, and to take these into consideration in their teaching to meet the learning needs of the students.

Shared Developmental Trajectories for Fractional Reasoning and Fine Motor Ability in 4 and 5 Year Olds

We investigated preschool-aged children’s understanding of early fractional tasks and how that performance correlates with fine motor skills and use of gestures while counting. Participants were 33 preschoolers aged 4 to 5 in two Southeastern public elementary schools. Children were tested individually in an interview-like setting. Mathematics tasks were presented in a paper and pencil format and the Grooved Pegboard test assessed fine motor skills. Finally, utilization of gestures was evaluated by taking a behavioral rating of the child’s hand morphology, accuracy of gestures, and synchrony of gestures and spoken word while performing a counting task. Results indicate that performance on fractional reasoning tasks significantly predicts both fine motor ability and accuracy of gestures.

The Dynamics of Inclusivity in Teaching and Assessing Mathematics for Lower Grade Learners

The chapter explores the diverse interpretations related to the learning of mathematics for learners at lower grade levels. At the core of understanding the dynamics of teaching and assessment of mathematics tasks for lower grade learners lie the general perceptions on the subject and how these have shaped educator and learner approaches to the subject as well as associated nuances of cognitive development. The chapter also explores how educators deal with inclusivity in the context of the curriculum and cognitive capabilities of learners in teaching and assessment. Different interpretations to assessments are also explored. A different approach to assessment that locates learners on a continuum of current proficiency is advocated. A flexible teaching philosophy is proposed which rather than cut the class into a pass/fail dichotomy, acknowledges each learner's right to progress in particular through the use of targeted teaching for challenged learners.

Redesigning Mathematics Tasks

This chapter presents how the results of an empirical research study conducted with in-service teachers can be used to enhance and strengthen the critical thinking skills of pre-service teachers. The chapter begins with a description of the study methodology and the task redesign process. Data is presented (often in the words of teachers themselves) that paint a compelling picture of the process in real-time. Limitations and potential drawbacks of its use are discussed along with possible design ideas that may better align the process with the specific needs of pre-service teachers and their professors. It is followed by a summary of how the task redesign process could be redesigned to be used more effectively with pre-service teachers as a way to increase critical thinking about the teaching of mathematics. Potential benefits, including an increased capacity for critical thinking, are offered along with additional research directions and an invitation for suggestions into improving the task redesign process.

Shared Developmental Trajectories for Fractional Reasoning and Fine Motor Ability in 4 and 5 Year-Olds

We investigated preschool-aged children’s understanding of early fractional tasks and how that performance correlates with fine motor skills and use of gestures while counting. Participants were 33 preschoolers aged 4 to 5 in two Southeastern public elementary schools. Children were tested individually in an interview-like setting. Mathematics tasks were presented in a paper and pencil format and the Grooved Pegboard test assessed fine motor skills. Finally, utilization of gestures was evaluated by taking a behavioral rating of the child’s hand morphology, accuracy of gestures, and synchrony of gestures and spoken word while performing a counting task. Results indicate performance on fractional reasoning tasks significantly predicts both fine motor ability and accuracy of gestures.