This report provides an overview of the development, implementation, and psychometric properties of a student mathematics interview designed to assess first- and second-grade student achievement and thinking processes. The student interview was conducted with 622 first- or second-grade students in 22 schools located in two public school districts…

Formative assessment involves the gathering of information that can guide the teaching of individual or groups of children. This approach requires a sound understanding of children's thinking and learning, as well as an effective method for gaining the information. We propose that formative assessment should employ a version of clinical…

This study investigated longitudinal pathways leading from early spatial skills in first-grade girls to their fifth-grade analytical math reasoning abilities (N = 138). First-grade assessments included spatial skills, verbal skills, addition/subtraction skills, and frequency of choice of a decomposition or retrieval strategy on the…

The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

Understanding logical necessity is an important component of proof and reasoning for teachers of grades K-8. The ability to determine exactly where young students' arguments are faulty offers teachers the chance to give youngsters feedback as they progress toward writing mathematically valid deductive proofs. As defined, logical necessity is the…

Meaning and importance of proof in mathematics and education increases gradually. Therefore levels of doing proof, proof-related opinions and perceptions of the teachers and pre-service teachers who will train the students in future are of importance. Accordingly, this study aims to determine the proof-related opinions of pre-service elementary…

In this study we investigated relationships between convergent and divergent thinking with an emphasis on fluency, originality, flexibility and elaboration in the mathematical domain. A related purpose was to examine relationships between problem types in mathematical tasks. The math section of a performance-based assessment was used to assess 857…

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)…