In this paper, a learning progression for geometric transformations is developed based on research that demonstrates the importance of viewing transformations as functions of the plane. The 5 levels of the progression reflect a student's evolving understanding of transformations as functions and their evolving understanding of the domain of these…

Evidence suggests the use of 'metacognitive strategies' -- which get pupils to think about their own learning -- can be worth the equivalent of an additional +7 months' progress when used well. However, while the potential impact of these approaches is very high, particularly for disadvantaged pupils, less is known about how to apply them…

Adoption of the Common Core State Standards present challenges to school districts, school administrators, and teachers. To assist in this endeavor, we present our work on unpacking the CCSS-M for the length, area, and volume Learning Trajectory (LT). The overarching theme of "genetic epistemology" and a five-characteristic framework…

Too often, teachers scratch their heads and ask, "What were my students thinking?" then answer, "I don't want to know." But teachers should want to know, and students should question their own thinking, as well. Critical thinking involves not just problem solving, creativity, analysis, and synthesis but also self-awareness of learning and learning…

This study focuses on teacher learning of student thinking through grading homework, assessing and analyzing misconceptions. The data were collected from 10 teachers at fifth-eighth grade levels in the USA. The results show that assessing and analyzing misconceptions from grading homework is an important approach to acquiring knowledge of…

In this paper we describe two episodes of instructional interaction, in which examples are used in order to help students face their misconceptions. We introduce the notions of pivotal example and bridging example and highlight their role in creating and resolving a cognitive conflict. We suggest that the convincing power of counterexamples…

The aim of this paper is to introduce to the education community to a newly developed "Learner Centred Learning-By-Designing Extended Cyberhunts" (LCLBDEC) strategy for teaching and learning in schools. The main focus of the strategy is to enable learners to become designers of an educational tool which assists them to learn during the…

The overall aim of this article is to analyze the relationships between the roles of assessment in pedagogy, the interactions between curriculum assessment and pedagogy, and the study of pupils' progression in learning. It is argued that well-grounded evidence of pupils' progressions in learning is crucial to the work of teachers, so that a method…

Within the field of education, there has been an increasing recognition of the importance of formative assessment and of structural knowledge. In an effort to fill needs in each of these areas, this article describes an innovative feedback strategy intended to improve students' structural knowledge. Twenty-four high school physics students were…

The aim of this study is to investigate Emiratii high school students' understandings of stoichiometry, their use of metacognitive strategies, and the influence of students' use of metacognitive strategies on their understandings of stoichiometry. Two instruments were used in this study, the first to measure students' understandings of…

We report a study of 10-14 year old children's use of additive strategies while solving ratio and proportion tasks. Rasch methodology was used to develop a diagnostic instrument that reveals children's misconceptions. Two versions of this instrument, one with "models" thought to facilitate proportional reasoning and one without were…

This book provides practical strategies and tools for assessing and teaching even the most hard to reach English language learners across the content areas. Syrja offers educators the latest information on working with ELLs (including using formative assessments) and provides a wealth of classroom-tested models and measures. These tools have…

This document is the fourth volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 42 research reports by presenters with last names beginning between Mul and Wu:…

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) Improving Decimal Number Conception by Transfer from Fractions to Decimals (Irita Peled and Juhaina Awawdy Shahbari); (2) The Development of Student Teachers' Efficacy Beliefs in Mathematics during…