We present findings from an analysis of tests of teacher mathematical knowledge identified over a 20-year period of mathematics education literature. This analysis is part of a larger project aimed at developing a repository of instruments and their associated validity evidence for use in mathematics education. We report on how these tests are…

Mathematical language (or the content-specific words in mathematics) has repeatedly shown to be related to mathematical abilities in preschool and in the early grades of primary education. Research in this field has predominantly focused on young children's quantitative and spatial language. At the same time, recent research has discovered that…

Consequential validity (often referred to as "test fairness" in practice) is an essential aspect of educational measurement. This study evaluated the consequential validity of the Research-Based Early Mathematics Assessment (REMA). A sample of 627 children from PreK to second grade was collected using the short form of the REMA. We…

This study was carried out in order to determine how the 3rd grade students of the Department of Elementary Mathematics Education structured their "if and only if propositions". The data were obtained by examining the students' answers given to the midterm exam questions and discussing the solutions with the students in the classroom.…

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…

Children have mathematical understanding beginning from the early years of life. Mathematics education during these years has a significant effect on children's future lives. Play is a significant issue in children's lives and can be used as a way for teaching and learning. It presents a rich learning environment. In this study, therefore, we…

Research has shown that a profound place value understanding is crucial for success in learning mathematics. At the same time, a substantial number of students struggles with developing a sustainable place value understanding. In this regard, two aspects of the place value system appear especially relevant: First, the knowledge of the decimal…

Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., "add," "more," "triangle"). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary…

The development of proofs and argumentation is one of the major standards for mathematical practices in K-12 education that researchers and practitioners alike are continuing to improve. Further, the use of discourse is considered essential in the learning of mathematical concepts at these levels. However, K-12 educators continue to confound how…

The present paper studies the effects of lesson study as a sample of participative researches in classroom as well as Behrangi Education Management Model in courses by aiming at exploring and allowing students to use the indexes of course concepts as an effective model in learning. The research plan is pre-test, posttest with control group type.…

Scholars have long argued that individuals' beliefs influence their behaviors and the decisions they make throughout their lives. Focusing on beliefs as a cognitive construct, the purpose of this study was to identify several key beliefs about mathematics teaching and learning held by practicing elementary mathematics teachers. An iterative…

Scholars have long argued that individuals' beliefs influence their behaviors and the decisions they make throughout their lives. Focusing on beliefs as a cognitive construct, the purpose of this study was to identify several key beliefs about mathematics teaching and learning held by practicing elementary mathematics teachers. An iterative…

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…

Argumentation in mathematics teaching has potential to move students beyond tacit understanding of mathematical concepts and procedures towards articulation and justification of their ideas; a practice in which evidence is central. Design-based research was used to examine the nature of evidence used by a class of primary students through levels…

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…