Speakers in conversation typically repeat and modify earlier comments. In mathematics conversations, these repetitions, or poetic structures, can facilitate the collaborative discovery of mathematical relationships. A close analysis of 90 turns of an algebraic problem-solving conversation reveals eight types of poetic structures. This report…

Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…

Distinguishing between sources of variability in mathematics performance may contribute to a more comprehensive theory of mathematics skills. Research has examined student differences based upon scores on achievement tests, which provide overall proficiency, but may not provide the detailed information for identifying and remediating difficulties.…

The Real Engagement in Active Problem Solving (REAPS) model was developed in 2004 by C. June Maker and colleagues as an intervention for gifted students to develop creative problem solving ability through the use of real-world problems. The primary purpose of this study was to examine the effects of the REAPS model on developing students' general…

Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

In this study, we investigated how empirical indicators of test-taking engagement can be defined, empirically validated, and used to describe group differences in the context of the Programme of International Assessment of Adult Competences (PIAAC). The approach was to distinguish between disengaged and engaged response behavior by means of…

The aim of this study is to reveal the relationship between the secondary school students' attitudes towards the educational computer games, and their reflective thinking skills. As the model of the research, it's utilized from the correlational research model. The target population of the study consists of secondary school students that receive…

Many educational data mining studies have explored methods for discovering cognitive models and have emphasized improving prediction accuracy. Too few studies have "closed the loop" by applying discovered models toward improving instruction and testing whether proposed improvements achieve higher student outcomes. We claim that such…

This study aims to synthesize the research findings on the effects of K-12 invention education regarding creativity, attitudes toward invention, attitudes toward science, and tendency for technological problem solving in South Korea. Meta-analyses were conducted by calculating the effect size of 37 studies, including theses and journal papers…

While recognizing that instructional scaffolding in a whole-class context can engage students' learning as they move through individual zone of proximal developments (ZPDs), in this chapter, we argue that instructional scaffolding also can collectively engage a class through a shared ZPD when participant structures and discourse practices provide…

Purpose: This study aims to examine the roles of stories in the innovation process. Design/methodology/approach: An integrative literature review was used to identify and analyze studies that examined stories of innovation in various organizational settings. The conceptual framework of the review was based on three perspectives of organizational…

This article presents "The Two Children Problem," published by Martin Gardner, who wrote a famous and widely-read math puzzle column in the magazine "Scientific American," and a problem presented by puzzler Gary Foshee. This paper explains the paradox of Problems 2 and 3 and many other variations of the theme. Then the authors…

We investigated a new phenomenon that sheds light on age-related differences in strategy selection: the strategy repetition phenomenon (i.e., tendency to repeat the same strategy over consecutive items). Young and older adults had to provide the best estimates of multiplication problems like 47 × 86. They had to select the best of 2 rounding…

Students' judgments about "what counts" as mathematics in and out of school have important consequences for problem solving and transfer, yet our understanding of the source and nature of these judgments remains incomplete. Thirty-five sixth grade students participated in a study focused on what activities students judge as…

It has been noted elsewhere that an idea is acknowledged to be creative if it is novel, or surprising and adaptive. So how does that fit with education's desire to measure student performance against fixed, consistent and predicted learning outcomes? This study explores practical measures and theoretical constructs that address the dearth of…