Multiplicative reasoning as articulated through scheme theory suggests that students improve the sophistication of their reasoning as they are able to coordinate additional levels of units, often described through students' use of schemes and operation at particular multiplicative concepts. Theoretical descriptions of the second and third…

When implemented correctly, feedback from assessments can result in students reflecting and rethinking their mathematics, while increasing their effort and motivation. This article explores a formative assessment technique for use in the first few minutes of each class. Readers will find out how they can use the QuickQuiz (QQ) to drive…

This article provides a detailed description of three factors (specification of the ability distribution, numerical integration, and frame of reference for the item parameter estimates) that might affect the item parameter estimation of the three-parameter logistic model, and compares five item calibration methods, which are combinations of the…

We present a novel application of a generalized item response tree model to investigate test takers' answer change behavior. The model allows us to simultaneously model the observed patterns of the initial and final responses after an answer change as a function of a set of latent traits and item parameters. The proposed application is illustrated…

Ferris wheel is one amusement playground that resembles a giant spinning wheel. Many students are familiar with the Ferris wheel in the mini version of it at night market festivals. This is the potential for learning mathematics. Furthermore, there is a mathematical learning approach called Indonesian Realistic Mathematics Education (IRME) where…

The present study was conducted to compare the performances of high-achieving sixth grade students on written computation, symbolic representation, and pictorial representation tests. The study enrolled 107 sixth-grade students in three schools. Data were analyzed by using the Kruskal Wallis and Mann Whitney-U Tests and interviews were conducted…

Stopping rules for fixed-form tests with graduated item difficulty are intended to stop administration of a test at the point where students are sufficiently unlikely to provide a correct response following a pattern of incorrect responses. Although widely employed in fixed-form tests in education, little research has been done to empirically…

The study aimed to determine the extent of associations of physics, mathematics, and between physics and mathematics based on the results of the 2007, 2011, and 2015 Trends in Mathematics and Science Survey achievement tests. Utilizing educational data mining and correlational data analysis (significance set at [alpha] = 0.05), this study's…

The objective of this study is to explore the effect of the Big Math for Little Kids Program (BMKL) on the mathematical development of bilingual preschool children. For this purpose, an experimental design with pre-test/post-test with control group was employed. A total of 60 children from Diyarbakir were included in the research sample. Of these,…

Purpose: Cross-cultural comparisons based on ordinal Likert-type rating scales have been threatened by response style which is systematic tendencies to respond to items regardless of the item content. So, this study aimed to investigate the effect of extreme response style and acquisance response style on TIMSS 2015 data. Method: The sample of…

How should schools assign students to more rigorous math courses so as best to help their academic outcomes? We identify several hundred California middle schools that used 7th-grade test scores to place students into 8th-grade algebra courses and use a regression discontinuity design to estimate average impacts and heterogeneity across schools.…

In South Africa, differential performance in school mathematics with respect to social class remains an enduring concern as reflected in national and international large-scale assessments. The article examines the implications of evaluation for orientations to mathematics in a school populated by learners from upper-middle-class or elite…

Item nonresponses are prevalent in standardized testing. They happen either when students fail to reach the end of a test due to a time limit or quitting, or when students choose to omit some items strategically. Oftentimes, item nonresponses are nonrandom, and hence, the missing data mechanism needs to be properly modeled. In this paper, we…

The authors present the results of quantitative data and student feedback from a two-year study of the effects of a new assessment model called "mastery-based testing." In mastery-based testing, students are given problems in which they can only receive full credit for the problem after they demonstrate mastery of the objective being…

It is important for teachers to be able to accurately assess students' performance. Such judgments can be influenced by characteristics of the student Südkamp et al. (J Educ Psychol 104:743-762, 2012. 10.1037/a0027627). Besides students' actual performance, students' group characteristics (e.g., gender or immigration background) may effect…