At the end of Primary 6, students in Singapore schools take a national examination, the Primary School Leaving Examination (PSLE). Society at large view the PSLE as a highstakes examination. In addition to out-of-class work assigned by mathematics teachers for students to prepare for the PSLE mathematics, parents may also draw on out-ofschool…

Measurement instruments of early childhood teachers' mathematical pedagogical content knowledge (MPCK) have to consider the special characteristics of early childhood teaching. Early childhood teaching includes some planned activities but in contrast to learning in school, it is often motivated and generated by situations which unfold…

This paper reports on a design-based implementation study of the use of a diagnostic classroom assessment tool framed on learning trajectories (LTs) for middle grades mathematics, where teachers and students are provided immediate data on students' progress along LTs. The study answers the question: "How can one characterize the challenges…

The National Assessment of Educational Progress (NAEP) is the only continuing and nationally representative measure of trends in academic achievement of U.S. elementary and secondary school students in various subjects. For more than four decades, NAEP assessments have been conducted periodically in reading, mathematics, science, writing, U.S.…

Learning or performance gains are often measured in improvements of test scores over time. However, learners may also answer questions incorrectly which they appeared to master previously, making claims about overall learning gains problematic. Using data from 1,211 grade 6 learners in the Umgungundlovu district in KwaZulu-Natal, we interrogated…

Validation efforts typically focus around what, exactly, is measured by an instrument(s), and whether what is measured corresponds to the theoretical domain(s) originally specified. The authors' goal for this article is to build instruments focused around measuring the mathematical knowledge used in teaching: not only the content that teachers…

Examined 6 widely used grade-8 standardized tests for content, required processes, and level to determine their alignment with the 5-8 NCTM "Curriculum and Evaluation Standards." Concluded that these tests inadequately covered the 5-8 standards. A follow-up study examined items from newly developed and foreign tests to demonstrate the…

In the spring of 1989, over 2,000 pairs of fourth- and eighth-grade students were assessed on their ability to apply mathematical and scientific concepts. The tests (administered in alternate years during the written assessments of the Massachusetts Educational Assessment Program) required students to apply what they knew about mathematics and…

"Informed math self-placement," a program implemented at American River College in Sacramento, California, to determine students' readiness for college-level math, has been in place for three years. This case study describes the development and implementation of math self-placement at American River. Math self-placement consists of a…