Lexical acquisition in elementary science classes

The purpose of this study was to further researchers' understanding of lexical acquisition in the beginning primary schoolchild by investigating word learning in small-group elementary science classes. Two experiments were conducted to examine the role of semantic scaffolding (e.g., use of synonymous terms) and physical scaffolding (e.g., pointing to referents) in children's acquisition of novel property terms. Children's lexical knowledge was assessed using multiple tasks (naming, comprehension, and definitional). Children struggled to acquire meanings of adjectives without semantic or physical scaffolding (Experiment 1), but they were successful in acquiring extensive lexical knowledge when offered semantic scaffolding (Experiment 2). Experiment 2 also shows that semantic scaffolding used in combination with physical scaffolding helped children acquire novel adjectives and that children who correctly named pictures of adjectives had acquired definitions

K-8 Pre-service Teachers’ Algebraic Thinking: Exploring the Habit of Mind Building Rules to Represent Functions

In this study, through the lens of the algebraic habit of mind Building Rules to Represent Functions, we examined 18 pre-service middle school teachers\u27 ability to use algebraic thinking to solve problems. The data revealed that pre-service teachers\u27 ability to use different features of the habit of mind Building Rules to Represent Functions varied across the features. Significant correlations existed between 8 pairs of the features. The ability to justify a rule was the weakest of the seven features and it was correlated with the ability to chunk information. Implications for mathematics teacher education are discussed

Learning by Seeing by Doing: Arithmetic Word Problems

Learning by doing in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children\u27s ability to see significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children\u27s ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children\u27s own word problems; play with dynamically linked representations with attention to children\u27s prior connections; and systematic problem variation based on empirically determined level of difficulty

Exploring the Relationship between K-8 Prospective Teachers’ Algebraic Thinking Proficiency and the Questions They Pose during Diagnostic Algebraic Thinking Interviews

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. In contrast, prospective teachers with higher algebraic thinking proficiency were able to pose probing questions to investigate student thinking or help students clarify their thinking. However, less than half of their questions were of this probing type. These results suggest that prospective teachers’ algebraic thinking proficiency is related to the types of questions they ask to explore the algebraic thinking of students. Implications for mathematics teacher education are discussed

Preservice elementary school teachers' knowledge of fractions: a mirror of students' knowledge?

This research analyses preservice teachers' knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed literature regarding students' knowledge of fractions. We did so because assessments of required content knowledge for teaching require review of the students' understanding to determine the mathematics difficulties encountered by students. The preservice teachers were tested on their conceptual and procedural knowledge of fractions, and on their ability in explaining the rationale for a procedure or the conceptual meaning. The results revealed that preservice teachers' knowledge of fractions indeed is limited and that last-year preservice teachers did not perform better than first-year preservice teachers. This research is situated within the broader domain of mathematical knowledge for teaching and suggests ways to improve instruction and student learning

Beyond the Spoken Word: Examining the Nature of Teacher Gesturing in the Context of an Elementary Engineering Curriculum for English-Learner Students

Our research team performed an exploratory analysis of teacher gesturing via a case study of an elementary teacher. We focused on gesturing, a practice found to support both bilingual English learner students’ linguistic development and mathematics achievement, during the teacher’s engineering and science lessons. The research team systematically analyzed teacher video data using McNeill’s gestural dimensions framework and found variation of gesturing types and rates when comparing engineering and baseline science lessons. Additionally, specific types of teacher-gestures appear to be associated with either behavioral or classroom management practices, procedural instructions, and discussion facilitation. We suggest that teacher-gestures such as these have the potential to facilitate bilingual English learners’ language acquisition, while also developing their STEM literacy in general and engineering capacity in particular. Further exploration of teacher-gestures in elementary engineering curricula could lead to an integrated STEM pedagogy that incorporates gesturing as a fundamental teaching strategy, bridging STEM instruction with linguistically responsive instructional practices.Educatio

Subtraction involving negative numbers: Connecting to whole number reasoning

In this article, we explore how students attempt to bridge from their whole number reasoning to integer reasoning as they solve subtraction problems involving negative numbers. Based on interviews with students ranging from first graders to preservice teachers, we identify two overarching strategies: making connections to known problem types and leveraging conceptions of subtraction. Their initial connections suggest that rather than identifying the best instructional models to teach integer concepts, we should focus on identifying integer instructional models that build on the potentially productive connections that students’ already make; we propose an example of one such form of instruction

Affordances of spreadsheets in mathematical investigation: Potentialities for learning

This article, is concerned with the ways learning is shaped when mathematics problems are investigated in spreadsheet environments. It considers how the opportunities and constraints the digital media affords influenced the decisions the students made, and the direction of their enquiry pathway. How might the leraning trajectory unfold, and the learning process and mathematical understanding emerge? Will the spreadsheet, as the pedagogical medium, evoke learning in a distinctive manner? The article reports on an aspect of an ongoing study involving students as they engage mathematical investigative tasks through digital media, the spreadsheet in particular. In considers the affordances of this learning environment for primary-aged students

Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem

Previous research has documented that preservice teachers (PSTs) struggle with under- standing fraction concepts and operations, and misconceptions often stem from their understanding of the referent whole. This study expands research on PSTs’ understanding of wholes by investigating pictorial strategies that 85 PSTs constructed for a multistep fraction task in a multiplicative context. The results show that many PSTs were able to construct valid pictorial strategies, and the strategies were widely diverse with respect to how they made sense of an unknown referent whole of a fraction in multiple steps, how they represented the wholes in their drawings, in which order they did multiple steps, and which type of model they used (area or set). Based on their wide range of pictorial strategies, we discuss potential benefits of PSTs’ construction of their own representations for a word problem in developing problem solving skills