This study aims to determine the proof schemes used by primary education teacher candidates when solving a given problem and in their instructional explanations. Having a qualitative nature, the study utilized data collected from 277 third-year teacher candidates studying at the primary education department of the education faculty of a state…

In this paper, we identify various forms of geometric work carried out by student teachers who were asked to perform a geometric task for the estimation of a land area. The theory of Mathematical Working Spaces is used to analyze and characterize the work produced. This study provides evidence that students developed forms of geometric work that…

In this paper, Harel and Sowder's proof schemes of taxonomy were applied for identifying eighth grade students' learning of proof and proofing. This study aimed to examine what kind of proof schemes are used in geometry and measurement learning areas and student's skills in giving proof and their opinions about proof. Qualitative methods were…

Proof plays many important roles in mathematics. Proofs should do more than simply verify that a statement is true; instead, a proof should also explain why a statement is true and enrich both the author's and the readers' understanding of the statement and important mathematical ideas within it. Common practice in high school geometry classrooms…

This article discusses funky protractor tasks, which are designed to provide opportunities for students to reason about protractors and angle measure. These tasks afforded opportunities for students to think critically about angular measurement tools, which supported the teachers with valuable insights into students' developing conceptions of…

This study aimed to document pre-service elementary teachers' (PSTs'), who are going to teach K-5, ability to construct as well as evaluate justifications varied in terms of levels of sophistication. Additionally, this study aimed to investigate how PSTs' knowledge of content in which they were being asked to prove influenced their ability to…

The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of teaching early math to children ages 3 to 6. The guide provides practical, clear information on critical topics related to teaching early math and is based on the best available evidence as judged by the authors. The guide…

For a given initial speed of water from a spigot or jet, what angle of the jet will maximize the visual impact of the water spray in the fountain? This paper focuses on fountains whose spigots are arranged in circular fashion, and couches the measurement of the visual impact in terms of the surface area and the volume under the fountain's natural…

After a test is developed, most content validation analyses shift from ascertaining domain definition to studying domain representation and relevance because the domain is assumed to be set once a test exists. We present an approach that allows for the examination of alternative domain structures based on extant test items. In our example based on…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

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…