Teaching the partial products algorithm with the concrete representational abstract sequence and the strategic instruction model

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning provides the foundation for advanced mathematics and algebraic reasoning. For students who struggle in mathematics, instruction in multiplication algorithms should ensure conceptual understanding so that students have a foundation for success in advanced mathematics. The concrete representational abstract (CRA) sequence addresses conceptual understanding and the strategic instruction model (SIM) supports procedural knowledge. The current pilot study combined these methods to teach elementary students the partial products algorithm. Twelve students in grades four and five participated in the study, receiving instruction from teachers in their school during an intervention period. Within a pre-experimental design, using pre- and postintervention data, students showed a significant change in performance. The article will describe and show how teachers implemented the CRA-SIM interventions and discuss implications for practice.     

Reflections on Transformative Experiences with Mathematical Inquiry: The Case of Christine

Abstract

We present a first-hand, longer-term account of one student’s (Christine’s) experiences in and after a mathematics inquiry course. In this course, students actively posed problems, conducted their own mathematical explorations, and wrote journal entries about their experiences. During the course, Christine found that inquiry helped her develop mathematical content knowledge and a deeper understanding of the nature of research. After the course, Christine became a mathematics education faculty member in a mathematics department and reports that the course impacted the way she teaches mathematics. This provides an illustrative case of the potential long-lasting benefits of an inquiry course.     

Students’ views of assessment in project-led engineering education: findings from a case study in Portugal

According to the demands of the Bologna process, new educational methods and strategies are needed in order to enhance student-centred learning. Project work is one of those approaches. This paper aims to evaluate the impact of project-led education (PLE) on students’ learning processes and outcomes, within the context of a first-year engineering programme. It explores students’ perceptions about assessment procedures and processes. Data collection was based on individual surveys at the end and the beginning of each PLE edition and through focus groups, after a period of six months. Findings are presented according to emerging themes from the data analysis, focusing mainly on students’ perspectives of learning and assessment, the role of formative and summative assessments in PLE and their impact on learning. Implications for improving assessment practices are discussed.     

Education,age and skills: An analysis using PIAAC data

The main aim of this article is to analyse the change of adult skills, as captured by cognitive skills assessed in PIAAC, across age cohorts, taking into account that the quality of schooling may change from one cohort to another. We estimate a model that relates numeracy and literacy skills to age, schooling, gender and variables related to both family background and labour market performance. The specification allows us to control for changes in the efficiency of the transformation of schooling into skills when drawing age‐skill profiles. Our results show that the effect of ageing on skills, once isolated from cohort effects related to schooling, decreases monotonically across consecutive cohorts. The change of the efficiency of the transformation of schooling into both numeracy and literacy skills shows a remarkably similar pattern. Nonetheless, this change differs substantially between education levels, with the efficiency of the transformation of schooling into skills showing a steadier profile for intermediate than for higher education. Finally, empirical evidence is provided for the decomposition of the differences in the skill levels of the older vs. the prime age generations. The results suggest that the progressive expansion of schooling across younger generations partially offsets the negative effect of the irrepressible ageing of society on skills.     

Meaning in life and school guidance programs: Adolescents’ voices from Hong Kong

International Journal for Educational and Vocational Guidance - This study provides insights into how Chinese adolescents in Hong Kong interpret the concept of “meaning in life.” Data...     

Generic tendencies in majority and non‐majority supreme court opinions: The case of justice Douglas

Using a sample of Supreme Court Justice William O. Douglas' Supreme Court opinons as the data base, this study investigated the question of whether majority or non‐majority status constitutes a variable sufficiently strong to predict the rhetorical quality of the opinion. The three traditional schools of legal philosophy, Natural Law, Legal Positivism, and Legal Realism, provided the basis of three hypothetical rhetorical genres which were found to be present in statistically similar frequencies in all opinion types. These findings (1) call into question the conventional wisdom that majority and dissenting opinions represent different rhetorical sub‐species, and (2) suggest that a more fruitful avenue of analysis looks to the generic architechtonics of Supreme Court opinions rather than to the relatively more superficial dimension of stylistics.