We present our analysis of 254 Calculus I final exams from U.S. colleges and universities to identify features of assessment items that necessitate qualitatively distinct ways of understanding and reasoning. We explore salient features of exemplary tasks from our data set to reveal distinctions between exam items made apparent by our analytical…

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…

The research aimed to analyze the students' abilities in solving realistic mathematics problems using "What-If"-Ethnomathematics Instruments with content focused on plane and space materials. The "What-If"-Ethnomathematics instruments are instruments that enable educators to analyze various errors and obstacles experienced by…

Mathematics teaching and learning goes beyond computations and procedures; it rather includes complex problem-solving and critical thinking. Kilpatrick, Swafford, and Findell (2001) identify five mathematical competencies that are present in mathematics learning: conceptual understanding, procedural fluency, adaptive reasoning, strategic…

Problem solving is at the heart of mathematics, and is known to support learning for a diverse range of children. However, challenges can be encountered when teaching mathematics through problem solving. This article provides insights from research literature into: (1) the nature of the challenges; and (2) some ways that problem solving can be…

Science, technology, engineering, and mathematics (STEM) education is an emerging initiative in Australia, particularly in primary schools. This qualitative research aimed to understand Year 4 students' involvement in an integrated STEM education unit that focused on science concepts (e.g., states of matter, testing properties of materials) and…

This article shows how to modify classroom evaluation items to avoid four potential difficulties that limit a teacher's insight into students' mathematical understanding by addressing these issues: (1) poor choice of numbers; (2) implausible or inappropriate contexts; (3) inclusion of graphics that do not help make learning visible; and…

The purpose of this article is to explore student-generated connections among counting problems. The literature indicates that such problems pose difficulties for students, who struggle to detect common structures and identify models of underlying problem types. A case study is presented here, in which students elaborate upon connections they make…

This study examines how students solve problems that involve the concept of absolute value. One hundred seventeen students participated in the first (written) part of the study, 24 students participated in the second part (interview). Particular attention was paid to the actual process of problem solving and to the students' ability to establish…

In the 21st century, a deep understanding of mathematics, and the ability to apply that understanding, is more important than it has ever been. In Montgomery County (Maryland) Public Schools (MCPS), and across the country, mathematics instruction is changing to provide students with the skills and knowledge they need for success in college and the…

Since teachers always teach area and perimeter together--and they are both introduced soon after the definition of a rectangle--it is not surprising that students mix up the notions of area and perimeter. Changing the investigation on maximising the area of a fixed perimeter from the traditional, but boring, "Sheep pens" to the much more…

The purpose of this study was to explore the utility of a dynamic assessment (DA) of algebraic learning in predicting third graders' development of mathematics word-problem difficulty. In the fall, 122 third-grade students were assessed on a test of math word-problem skill and DA of algebraic learning. In the spring, they were assessed on…

Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method.…

With the current focus in mathematics education on the importance of developing students' conceptual understanding, fluency with the language of mathematics, critical thinking, and working mathematically, teachers are constantly expected to design challenging and investigative tasks that can engage and motivate students in their learning of…

Based on the efforts to infuse engineering practices within the technology education curriculum it is appropriate to now investigate how technology education teachers are assessing engineering design activities within their classrooms. This descriptive study drew a full sample of high school technology teachers from the current International…