Critical moments: pre-service mathematics teachers’ narrative arcs and mathematical orientations over 20 years

This study explores narratives about critical moments in mathematics learning written by K-8 pre-service teachers’ (PSTs) in the United States over a 20-year period. These critical moments, such as a single memorable task, course, test, or comment from a teacher, had a powerful and sustained impact on PSTs’ mathematics identities, which they carried with them as they entered the teaching profession. We classified narratives using McCulloch et al. (Sch Sci Math 113(8):380–389, 2013) and Drake’s (J Math Teach Educ 9(6):579–608, 2006) categories and found a potentially new category, Taking the Reins. We also classified PSTs’ mathematics orientations as either relational (oriented toward creative problem solving and conceptual understanding) or instrumental (enacting rote procedures without meaning) (Skemp in Math Teach 77(1):20–26, 1976). Many PSTs identified a causal relationship between their mathematics orientations and narrative arcs: relational learning opportunities encouraged positive narratives, while instrumental learning opportunities either resulted in negative narrative arcs or positive but fragile mathematics identities that crumbled under minor stress. We found little variation over time in the nature and prevalence of the narrative arcs and mathematics orientations, suggesting that any changes in mathematics teaching practices over time were not reflected in students’ learning experiences.

     

A LONGITUDINAL STUDY OF THE DEVELOPMENT OF MATHEMATICS STRATEGIES AND UNDERLYING COUNTING SCHEMES

The purpose of this study was to determine whether patterns of strategy use in second, third and fourth grade children’s arithmetic supported Steffe’s model of numerical development. In addition to student-generated strategies, we looked at commonly taught algorithms not considered in Steffe’s model to determine whether these algorithms reflected underlying schemes. 206 children were assessed on their strategy use while solving arithmetic problems in the second grade, the third grade and again in the fourth grade. Factor analyses indicated some support for Steffe’s model, but there were exceptions. Not all children progressed in their number knowledge and strategies as a function of schooling and schooling appeared to affect the types of strategies children use independent of underlying schemes.     

正义、美德与教育（英文）

如果说正义是人类道德交往的基本法则或者维度,那么这也似乎适用于一些教育问题。简而言之,我们需要教育孩子和年轻人正义和公平。然而,这并不是可以仅通过教授正义的理论就能够实现的。因为,正如这篇文章所揭示的那样,这些理论通常涉及到维护正义的准则,即在有些情况下,公民个体不能总是做到如其所期待的那样正义与公平。所以,正义教育更多的是培养正义的美德。从这点出发,本文致力于探究如何借助富有想象力的文学作品来培养正义的美德。     

Exploring elementary students’ perceptions of disabilities using children's literature

The portrayal of characters in children's literature can be a very powerful influence on young children. Teachers have a responsibility to expose children to characters of all types, including those with disabilities. The goal of this study was to explore how third and fourth grade students responded to characters with disabilities in children's books. We read a total of 12 books that included characters with disabilities to students in two third‐grade and one fourth‐grade class at three elementary schools. We video‐recorded discussions about the books and identified the following four themes, all of which related to influences on students’ responses to the character with a disability: (a) societal messages, (b) academic responses, (c) teacher influence and (d) portrayal of disability. We recommend that teachers carefully select books featuring characters with disabilities based on the way the disability is portrayed in the book, and, after the read‐aloud, use questioning strategies that encourage students to make thoughtful, deep comments rather than giving ‘expected’ responses.     

The dynamic impact characteristics of tennis balls with tennis rackets

Abstract

The dynamic properties of six types of tennis balls were measured using a force platform and high-speed digital video images of ball impacts on rigidly clamped tennis rackets. It was found that the coefficient of restitution reduced with velocity for impacts on a rigid surface or with a rigidly clamped tennis racket. Pressurized balls had the highest coefficient of restitution, which decreased by 20% when punctured. Pressureless balls had a coefficient of restitution approaching that of a punctured ball at high speeds. The dynamic stiffness of the ball or the ball-racket system increased with velocity and pressurized balls had the highest stiffness, which decreased by 35% when punctured. The characteristics of pressureless balls were shown to be similar to those of punctured balls at high velocity and it was found that lowering the string tension produced a smaller range of stiffness or coefficient of restitution. It was hypothesized that players might consider high ball stiffness to imply a high coefficient of restitution. Plots of coefficient of restitution versus stiffness confirmed the relationship and it was found that, generally, pressurized balls had a higher coefficient of restitution and stiffness than pressureless balls. The players might perceive these parameters through a combination of sound, vibration and perception of ball speed off the racket.