Developing both conceptual and procedural knowledge is important for students' mathematics competence. This study examined whether U.S. Grade 9 general education mathematics teachers' self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders' algebra achievement…

This single-case study assessed the effectiveness of a mnemonic pegword strategy designed to enhance the multiplication fact fluency of three 6th-grade students who demonstrated persistent learning difficulties in mathematics. A nonconcurrent multiple baseline across subjects design was utilized, incorporating 3-5 baseline sessions followed by…

In this theoretical essay, I build on complexity theory and commognition to theorize the ways in which failure to teach/learn mathematics (FTLM) emerges through the dynamic interactions among teacher, learner, and curriculum demands. I focus on two main concepts of complexity theory: emergence in dynamic systems and attractor states (stable,…

This paper details a literature review of mathematics vocabulary intervention studies for students with mathematics difficulty. The primary aim was to identify instructional practices that support mathematics vocabulary development. We conducted a database search to identify mathematics intervention studies either focused exclusively on vocabulary…

This single-subject design study examines the effectiveness of a Tier 3 math intervention designed to address the academic challenges of three fifth-grade students not meeting minimum proficiency standards in long division. Using the self-regulated strategy development (SRSD) model, the intervention targeted procedural fluency and conceptual…

Fractions are a fundamental component of the school mathematics curriculum, and most students achieve proficiency in these concepts during their elementary education. However, a significant proportion of students still encounter challenges in this area even after entering secondary education, necessitating additional support to prevent further…

This study developed a teacher education program for teacher education students (TESs), incorporating collaborative inquiry and panoramic cameras to guide them in observing young students' learning performances during teaching, with the goals of enhancing instructional design capability for diagnosing student learning problems and investigating…

This pilot study examined the feasibility of using worked examples as a mechanism to improve verbal explanations of fractions concepts among Grade 5 students with mathematics difficulties in a small-scale randomized controlled trial (RCT) before scaling up to a large-scale RCT. Students (N = 49) were randomly assigned to a business-as-usual (BAU)…

Through a constructivist teaching experiment, we studied how a 6th-grade student (Adam, pseudonym) struggling in mathematics may reorganize his available additive scheme (count-up-to) into a more advanced scheme involving the decomposition of composite units (break-apart-make-ten, or BAMT). First, we posed a task that led us to infer Adam was yet…

This study examined how mathematics anxiety, trait emotional intelligence, and mathematics self-concept predict calculation fluency, numerical operations, and mathematical reasoning in students with and without mathematics learning difficulties (MLD). Participants (N = 326) were third- to fifth-grade students from China who completed standardized…

The present study used the Early Childhood Longitudinal Study, Kindergarten Class of 2011 (ECLS-K:2011) to examine the bidirectionality and co-occurrence between math achievement and behavioral outcomes of upper elementary school students. We analyzed the cross-lagged relations across four groups of students who had different initiating statuses…

The purpose of this study was to examine the effects of a number line intervention with supported self-explanation on student understanding of fraction magnitude and quality of explanation. Participants were three U.S. middle school students with significant behavior problems. Participants were given eight lessons containing explicit instruction…

This article reports on a project implemented to help middle school teachers provide evidence-based instruction and intervention to students with mathematics learning disabilities (MLD) and mathematics difficulties (MD). Multiple sources--interviews, surveys, and field notes from formal and informal observations--were used to gather data on…

The transition from arithmetic to algebra in middle school can be critical for students having persistent difficulties in mathematics. The leading perception in our project is that holistic relational thinking is an effective problem-solving tool in both arithmetic and algebra. We worked in collaboration with two teachers of special classes to…

Productive struggle is crucial to students' mathematics learning. However, it has proven difficult for teachers to sustain struggle when it is productive or make it so when it is not. Studies show that teachers may offer students support when their struggles are productive or even refrain from offering support when students' struggles are…