Exploring academic and cognitive skills impacting retention and acquisition of word-problem knowledge gained during or after intervention

In the present study, we investigated the impact of a word-problem intervention in retention and acquisition of knowledge after the intervention ended. We based analyses upon Grade 4 students experiencing mathematics difficulty (average age at pretest = 8.77) who received one of two variants of a word-problem intervention (with [n = 111] vs. without [n = 110] embedded pre-algebraic reasoning instruction) and students within a business-as-usual condition (BaU [n = 127]) separately. Findings revealed that students who received the intervention not only tended to retain less, but they also showed more active knowledge acquisition after the intervention ended. Furthermore, word-problem intervention altered the contributions of some prior knowledge and skills on both retention and acquisition.

A Synthesis of the Conceptualization and Measurement of Implementation Fidelity in Mathematics Intervention Research

In intervention studies, high rates of implementation fidelity are important markers of a study's success; however, the definition of implementation fidelity is both complex and dynamic. In this synthesis, we examined the dimensions of implementation fidelity measured and reported in 99 studies in which researchers utilized a mathematics intervention for elementary students (i.e., Grades 1-5). We examined implementation fidelity following recommendations made by Dane and Schneider (1998), O'Donnell (2008), and DeFouw et al. (2009) to capture a comprehensive representation of the implementation fidelity data collected and reported within mathematics intervention studies. We organized our conceptualization of implementation fidelity into four overarching categories and nine dimensions within those categories: intervention design (i.e., theories of change and logistics), fidelity of implementor (i.e., adherence, quality of delivery, dosage, and implementor knowledge or experience), student engagement, and treatment analysis (i.e., treatment differentiation and analysis of implementation fidelity). Overall, findings indicate many author teams reported adherence data and dosage data, but significantly fewer studies reported quality of delivery data, student engagement data, or treatment differentiation data. In addition, author teams were more likely to report at least one form of logistics, such as implementor support, than theories of change. Implications for research and practice are discussed.

Applying an Individual Word-Problem Intervention to a Small-Group Setting: A Pilot Study's Evidence of Improved Word-Problem Performance for Students Experiencing Mathematics Difficulty

The purpose of this pilot study was to determine whether positive results from a word-problem intervention implemented one-to-one contributed to similar outcomes when implemented in small groups of three to four students. Third-grade students experiencing mathematics difficulty (N = 76) were randomly assigned to word-problem intervention (n = 56) or business-as-usual comparison (n = 20). Intervention occurred for 13 weeks, 3 times per week, 30 min per session. Multilevel models revealed the intervention condition significantly outperformed the BaU on a proximal word-problem outcome, corroborating results from our prior individual intervention. When comparing student performance in the individual versus small-group intervention, findings suggest students received added benefit from the individual intervention. The word-problem intervention successfully translated to a small-group setting, which holds important implications for educators working with students in supplemental, targeted, or Tier 2 mathematics intervention settings.

Integrating numerical cognition research and mathematics education to strengthen the teaching and learning of early number

BACKGROUND

Research into numerical cognition has contributed to a large body of knowledge on how children learn and perform mathematics. This knowledge has the potential to inform mathematics education. Unfortunately, numerical cognition research and mathematics education remain disconnected from one another, lacking the proper infrastructure to allow for productive and meaningful exchange between disciplines. The present study was designed to address this gap.

AIM

This study reports on the design, implementation, and effects of a 16-week (25-hour) mathematics Professional Development (PD) model for Kindergarten to Grade 3 educators and their students. A central goal of the PD was to better integrate numerical cognition research and mathematics education.

SAMPLE

A total of 45 K-3 educators and 180 of their students participated.

METHODS

To test the reproducibility and replicability of the model, the study was carried out across two different sites, over a two-year period, and involved a combination of two different study designs: a quasi-experimental pre-post-research design and a within-group crossover intervention design.

RESULT

The results of the first implementation (Year 1), indicated that compared to a control group, both teachers and students benefited from the intervention. Teachers demonstrated gains on both a self-report measure and a test of numerical cognition knowledge, while students demonstrated gains in number line estimation, arithmetic, and numeration. In Year 2, teachers in the intervention group demonstrated greater improvements than the control group on the self-report measure, but not the test of numerical cognition knowledge. At the student level, there was some evidence of gains in numeration.

CONCLUSION

The current PD model is a promising approach to better integrate research and practice. However, more research is needed to determine in which school contexts the model is most effective.