The main purposes of this study were to test the effects of teaching at-risk 4th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3 conditions: a control group and 2 variants of a multi-component fraction…

The field of EDM has focused more on modeling student knowledge than on investigating what sequences of different activity types achieve good learning outcomes. In this paper we consider three activity types, targeting sense-making, induction and refinement, and fluency building. We investigate what mix of the three types might be most effective…

A new generation of students should learn from e-materials on tablets, notebooks and smart phones. This consequently means that teachers must be competent to teach new literacies, needed for reading/learning from PDF texts, hypertexts and/or World Wide Web. The presented research investigated future teachers' metacognitive awareness in the process…

Most students always lack of experience and perceive difficult regarding problem posing. The study hypothesized that worked examples may have benefits for supporting students' problem posing activities. A quasi-experiment was conducted in the context of a business mathematics course for examining the effects of integrating worked examples into…

Understanding of measuring time has difficulty for children because it is intangible. Standard units often used directly by teacher for learning time measurement. Many researches involved games in designing learning material to facilitate fun and meaningful learning for children. For this reason, learning of time measurement that connects with…

Global education is the backbone of balanced teaching. This is also applicable in the second language teaching domain where its application could result in enhancing global awareness and the linguistic competence of learners. It is, however, important to consider the platform of teaching English to speakers of other languages where the…

Open-ended questions, as discussed in this article, are questions that can be solved or explained in a variety of ways, that focus on conceptual aspects of mathematics, and that have the potential to expose students' understanding and misconceptions. When working with teachers who are using open-ended questions with their students for the…

The primary school mathematics curriculum in Ireland is based upon a constructivist philosophy of learning. As constructivism is a theory of learning and not teaching, implementing a constructivist approach in the classroom requires teachers to identify the implications and applications of constructivist philosophy for teaching. In this research,…

Science is a complex process, and we must not teach our students overly simplified versions of "the" scientific method. We propose that students can uncover the complex realities of scientific thinking by exploring the similarities and differences between solving the familiar crossword puzzles and scientific "puzzles."…

General education placement of students with autism spectrum disorders (ASD) has increased at a rate faster than all other disability categories combined. As more children are diagnosed with ASD and expected to meet the same academic standards as their neurotypical peers, there is a demand for effective educational strategies. Using a…

This article shows how to modify classroom evaluation items to avoid four potential difficulties that limit a teacher's insight into students' mathematical understanding by addressing these issues: (1) poor choice of numbers; (2) implausible or inappropriate contexts; (3) inclusion of graphics that do not help make learning visible; and…

A problem-solving capstone course for mathematics and mathematics education majors can help majors synthesize material learned in the major, create a basis for lifelong learning in the discipline, develop confidence, and promote interest in graduate study. Such a course may also play a role in departmental assessment of the major. This article…

The purposes of this study are to (1) understand how elementary school students use writing to reflect their learning and problem solving in mathematics; and (2) to explore how teachers adapt their instructional approaches based upon reflection on students' writing. This qualitative exploratory study spanned six weeks and included 18…

This research study was specifically concerned with the development, testing, and revision to an instructional theory for studying the mathematical concepts of equivalence and equation solving with multiple representations and multiple tools. Following a design research approach, a collaborative teaching experiment was conducted with a ninth-grade…

This article argues for a shift in how researchers discuss and examine students' uses of representations during their calculus problem solving. An extension of Zazkis, Dubinsky, and Dautermann's (1996) Visualization/Analysis-framework to include physical modes of reasoning is proposed. An example that details how transitions between visual,…