Prior learning provides the basis for new learning. Mathematics educators employ formative assessment to "elicit" and "use" student thinking as the foundation of their instruction. Yet, information can be elicited and used in a variety of ways, so not all formative assessment is equally "formative." This means that…

Early math ability is one of the best predictors of children's math and reading skills into late elementary school. Children with stronger math proficiency in elementary school, in turn, are more likely to graduate from high school and attend college. However, early math skills have not historically been a major focus of instruction in preschool…

Creative imagination and memorization are complementary abilities in learning mathematics (Vygotsky, J Russian East Eur Psychol 42(1):7-97, 2004). These complementary abilities engage "movement" in learning mathematics among "realities" (e.g., personal and social experience, emotion, and cultural practices) (see also Dewey,…

Challenges with numerical proficiency at an early age can lead to substantial gaps in learning and are associated with detrimental long-term outcomes. In addition, students with emotional-behavioral disorders (EBD) can have some of the most challenging behavioral and academic needs to address. The purpose of this study was to identify the effects…

The narrative permeating higher education institutions globally is the assimilation of advancing information and communications technology into mainstream Mathematics Education. In this paper we report on a mixed mode case study which explored possible mathematical gaps that created barrier/s when engineering students (n=162) worked with the…

Mathematics course in vocational high school education is significant worldwide to equip vocational students with the technical and personal skills that are required for the effective workforce as discussed in the context of Science, Technology, Engineering and Mathematics (STEM) education. The present research sets out to investigate Turkish…

The primary objective of this study was to examine the effects of the Cogmed training program on working memory among youths 7 to 13 years old, with attention deficit/hyperactivity disorder (ADHD) type and comorbidity controlled for. A secondary objective was to examine the generalization of effects to ADHD symptoms, nonverbal reasoning,…

In this longitudinal study, we track student answers to a question from the Calculus Concept Inventory (CCI) pre- and post-instruction in Calculus I as well as an analogous question in the next semester framed in the context of Aerospace Engineering or Chemical Engineering. Nearly 88% of the students who answered the post-CCI question correctly…

Different cross-domain trajectories in the development of students' ability self-concepts (ASCs) and their intrinsic valuing of math and language arts were examined in a cross-sequential study spanning Grades 1 through 12 (n = 1,069). Growth mixture modeling analyses identified a "Moderate Math Decline/Stable High Language Arts" class…

Like many math educators, I have spent much of my career bound to traditional methods of instruction and assessment. In recent years, motivated by a growing understanding that such approaches may not result in equitable or inclusive classroom environments, my teaching philosophy has shifted radically. In this article, I describe how I transformed…

The purpose of this study was to examine the effectiveness of video-based mathematics instruction for seven middle school students with specific learning disability (SLD), using an augmented reality-based training package. The dependent variable was the percentage of steps students performed correctly to solve each type of mathematics problem. The…

Following recent increases in the diversity of students, technologies, pedagogies and environments, New Zealand classrooms are sites of growing complexity. Tasked with covering a broad range of disciplines within each school day, opportunities for subject integration are of increasing value to busy teachers. Developing upon a previous piece of…

Mathematical difficulties have been distinguished as mathematics learning disability (MLD) and persistent low achievement (LA). Based on 1,880 Finnish children who were followed from kindergarten (age 6) to fourth grade, this study examined the early risk factors for MLD and LA. Distinct groups of MLD (6.0% of the sample) and LA (25.7%) children…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

Numeracy has increasingly become a topic of importance and concern in our contemporary society. Student success in numeracy is influenced by the positive attitudes and values they hold about mathematics. This outreach project sought to foster the development of such attitudes and values through the design, implementation, and evaluation of a…