While proof has been studied from different perspectives in the mathematics education literature for decades, students continue to struggle to build proof comprehension. Complicating this, the manner in which proof comprehension is assessed largely remains to be the definition-theorem-proof format in which students are asked to reproduce proofs or…

This paper describes a study that used a novel method to investigate conceptual difficulties with mathematical induction among two groups of undergraduate students: students who had received university-level instruction in formal mathematical induction, and students who had not been exposed to formal mathematical induction at the university level.…

This article illustrates and differentiates the unique role cognitive interviews and think-aloud interviews play in developing and validating assessments. Specifically, we describe the use of (a) cognitive interviews to gather empirical evidence to support claims about the intended construct being measured and (b) think-aloud interviews to gather…

This article provides a critical evaluation of a technique of analysis, the "Social Activity Method," recently offered by Dowling (2013) as a "gift" to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between "expression" and "content") instead of a finer…

Previous research has documented schemes and operations that undergird students' understanding of fractions. This prior research was based, in large part, on small-group teaching experiments. However, written assessments are needed in order for teachers and researchers to assess students' ways of operating on a whole-class scale. In this study,…

Recent studies indicate that students in the United States are not achieving sufficient mathematics skills to meet the demands required of them within and outside of school. Among the keys to preventing mathematics difficulties are to identify and intervene with those students who may be most at risk for later failure, monitoring their progress as…

Four alternate versions of a 15-item general outcome measure (GOM) of mathematics conceptual understanding and applications were developed and administered to 117 eighth-graders. Results were correlated with scores on state multiple-choice mathematics achievement tests. Correlations ranged from .81 to .87 with no significant differences, offering…

This publication contains Arizona public schools' academic standards for grade 3. The contents of this document include the following: (1) The Arts Standard 2006--Grade 3; (2) Comprehensive Health Education/Physical Activity Standards 1997--Foundations (Grades 1-3); (3) Foreign and Native Language Standards 1997--Foundations (Grades 1-3); (4)…

This publication contains an updated academic standards of Arizona public schools for grade 5. The contents of this document include the following: (1) The Arts Standard 2006--Grade 5; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Foundations (Grades…

This publication contains an updated academic standards of Arizona public schools for grade 6. The contents of this document include the following: (1) The Arts Standard 2006--Grade 6; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades…

This publication contains the updated academic standards of Arizona for Grade 8. The contents of this document include the following: (1) The Arts Standard 2006--Grade 8; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades 4-8); (4) Reading…

This publication contains Arizona public schools' updated academic standards for high school. The contents of this document contain: (1) The Arts Standard 2006--High School; (2) Comprehensive Health Education/Physical Activity Standards 1997--Proficiency and Distinction (Grades 9-12); (3) Foreign and Native Language Standards 1997--Proficiency and…

This document contains the Arizona academic standards for Grade 7. The following 11 standards are reviewed: (1) The Arts Standard 2006 --Grade 7; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades 4-8); (4) Reading Standard Articulated by…

This publication contains Arizona public schools' academic standards for kindergarten. The contents of this document include the following: (1) The Arts Standard 2006--Kindergarten; (2) Comprehensive Health Education/Physical Activity Standards 1997--Readiness (Kindergarten); (3) Foreign and Native Language Standards 1997--Readiness…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…