John A. Dossey

Using Mathematical Competencies to Predict Item Difficulty in PISA: A MEG Study

This paper reports an analysis of features of mathematics assessment items developed for the OECD’s Programme for International Student Assessment survey (PISA) in relation to a set of six mathematical competencies. These competencies have underpinned the PISA mathematics framework since the inception of the PISA survey; they have been used to drive mathematics curriculum and assessment review and reform in several countries; and the results of the study are therefore likely to be of interest to the broad mathematics education community.

Limited microdiscectomy for lumbar disk herniation: a retrospective long-term outcome analysis.

Objective and Summary of Background Data: Surgical treatment of lumbar disk herniation is traditionally accomplished by removal of the extruded fragment as well as an aggressive decompression of the disk space. This retrospective study evaluates the long-term results of limited discectomy, otherwise known as fragmentectomy, for lumbar disk herniation using a minimally invasive technique. Although there are ample studies in literature regarding short-term outcome after limited microdiscectomy, there is a paucity of literature for long-term outcomes after fragmentectomy. We present long-term outcomes averaging 7 years after limited discectomy. Study Design and Methods: A total of 152 patients were operated on between January 1, 2001 and June 30, 2003 for single-level herniated lumbar disks. All patients had microsurgical fragmentectomy performed through a small skin incision off the midline using a tubeless retraction system. Fifty-four patients participated in the study, whereas 98 patients were lost to long-term follow-up. Long-term outcome was assessed by telephone survey or mail-in survey using the Oswestry Low Back Pain Disability Index and a patient outcome survey. After Institutional Review Board approval and patient consent, all 54 patients had a thorough chart review for evaluation of further lumbar surgeries. The mean long-term follow-up was 86.2 months (range, 72–104 mo) or about 7.2 years. Results: Forty-eight of the 54 patients (88.9%) reported an excellent (26 patients) or good (22 patients) long-term outcome with surgery. Long-term back and leg pain improvement was seen in 44 of 49 (89.8%) and 44 of 50 (88.0%) patients reporting back or leg pain, respectively. The mean Oswestry Disability Index for long-term follow-up was 8.89, indicating minimal disability. Same-level recurrences requiring reoperation were seen in 6 of the 54 patients who participated (11.1%) within the average 86.2-month follow-up. Four of 34 (11.85%) known contained herniations and 2 of 20 (10.0%) known extruded herniations presented for same-level surgical recurrence. All recurrences were successfully treated with reexploration and fragmentectomy. Two patients from the recurrence group and 1 from the original 54 progressed to need an arthrodesis at the initial operated level (5.6%). One patient in the same-level recurrence group and 2 patients from the original 54 developed an operative herniated disk at an adjacent level (5.6%). Conclusions: Our long-term outcome study shows that a minimally invasive approach to microdiscectomy with removal of the fragment only is an effective way to treat lumbar disk herniation. The rate of recurrence in our long-term study seems slightly higher compared with previously published studies, which generally had shorter follow-up periods. Long-term patient outcomes for back and leg pain were also very low. No appreciable difference in operative reherniation could be found with patients who had contained verses extruded fragments. It is difficult to predict from this study whether a simple fragmentectomy was the cause of the progression to further surgeries or whether this was the natural progression of a degenerative spine. Further prospective trials are necessary to fully understand the factors associated with limited microdiscectomy.

Implications of International Studies for National and Local Policy in Mathematics Education

This chapter examines large-scale comparative studies of mathematics education focussed on student achievement in an attempt to explain how such investigations influence the formation and implementation of policies affecting mathematics education. In doing so, we review the nature of comparative studies and policy research. Bennett’s (1991) formulation of policy development and implementation is used in examining national reactions to the results of international studies. Focus is given to the degree to which mathematics educators and others have played major roles in determining related policy outcomes affecting curriculum and the development and interpretations of the assessment instruments and processes themselves.

Issues in Mathematics Assessment in the United States

The results of comparative studies of United States students’ mathematical achievement (McKnight et al., 1987; Crosswhite et al., 1987; Dossey et al., 1988) in national and international arenas have heightened the United States’ awareness of the importance of mathematics as a tool for stability in an era of rapid change (MSEB, 1989a, 1989b; Adelman & Alsalam, 1988; Johnson & Packard, 1987). At the same time, mathematics educators and others set out to describe how the United States’ society might measure both the growth of mathematical ability in individuals and in the society itself (Alexander & James, 1988; Kulm, 1990; Raizen & Jones, 1985; Resnick, 1987; NCTM, 1989). These attempts also brought with them a number of reports dealing with the dangers of testing and the role testing might play in stratifying society (National Commission on Test and Public Policy, 1990).

PISA 2003—Mathematical Literacy and Learning in the Americas

The article provides an overview of the mathematics assessment program of the Organization for Economic Cooperation and Developments’ (OECD) Program for Student Assessment (PISA). As such, it provides a comparative view of the PISA results for Canada, Mexico, and the United States. It outlines the program, its frameworks, and competencies PISA uses to describe the achievement of 15-year-olds in over 40 countries participating in the PISA assessments. Particular attention is given to the PISA conception of mathematical literacy and cross-disciplinary problem-solving. These two areas were a focus of the 2003 assessment. In addition to a discussion of general results, two sample problems are presented, one from the mathematical literacy and one from cross-disciplinary problem-solving, along with detailed information about student performances in the items. The article concludes with a consideration of the lessons to be learned from the PISA study relative to the teaching and learning of mathematics.RésuméCet article trace les grandes lignes du programme PISA de l’OCDE (Organisation pour la coopération et le développement économique) pour ce qui est de l’évaluation des mathématiques. L’étude fournit ainsi des données comparatives sur les résultats du programme PISA au Canada, au Mexique et aux états-Unis. Elle définit les bases et le cadre du programme, ainsi que les compétences qui servent à décrire le niveau de compétences des étudiants de 15 ans, dans plus de 40 pays participant aux évaluations PISA. Une attention toute particulière a été accordée à l’alphabétisation mathématique et à la résolution de problèmes multidisciplinaires, deux aspects qui ont été l’objet de l’évaluation réalisée en 2003. Outre l’analyse générale des résultats, deux problèmes types sont présentés, l’un relevant de l’alphabétisation mathématique et l’autre de la résolution de problèmes multidisciplinaires, et des informations détaillées sur la performance des étudiants dans ces deux aspects sont fournies. L’article se termine par une réflexion sur les leçons à tirer du programme PISA en ce qui a trait à l’enseignement et à l’apprentissage des mathématiques.

Canadian and United States Students' Performances on the OECD's PISA 2012 Problem-Solving Assessment

This article presents an overview of the Organization for Economic Cooperation and Development’s (OECD) Programme for International Student Assessment (PISA) 2012 Problem-Solving assessment. The assessment examined the capabilities of 15-year-olds in 40 nations and four large international cities, as well as the Canadian Provinces, to solve a set of 16 problem units presented in contextualized situations. These units each had two or three tasks for students to solve. Students’ performances on these items served as a basis for developing the PISA score scale and the associated proficiency levels for each of the participating entities. Student performances on the PISA 2012 mathematics, reading, and science assessments provided an avenue to estimating student performances on the problem-solving assessment for students having similar score backgrounds in the three content areas. Student performances were also examined by item types and by differing problem situations. These latter two analyses provide interesting perspectives for comparing problem solving profiles across the participating entities. Finally, some conclusions are drawn concerning the study as a whole.RésuméCet article présente dans ses grandes lignes l’Évaluation PISA 2012 en résolution de problèmes, de l’OCDE. Cette évaluation analyse les compétences de jeunes de 15 ans dans 40 pays, 4 grandes villes internationales, et aussi dans les provinces canadiennes, pour résoudre une série de 16 unités de problèmes présentés en contexte. Chacune de ces unités comprenait 2 ou 3 tâches à faire résoudre par les élèves. Leurs performances dans chacune de ces tâches ont servi à mettre au point l’échelle de pointage du PISA et les niveaux de compétences liés à chacun des groupes participants. Les performances des étudiants à l’évaluation du PISA 2012 en mathématiques, en lecture, et en sciences ont ouvert une voie permettant d’estimer quelles seraient les performances en résolution de problèmes des élèves ayant obtenu des scores comparables dans les trois domaines de contenus. Les performances ont aussi été analysées par type d’élément et par type de situation problématique. Ces deux dernières analyses fournissent des perspectives intéressantes permettant de comparer différents profils de résolution de problèmes dans tous les groupes de participants. Enfin, nous tirons certaines conclusions au sujet de l’étude dans son ensemble.

Mathematics Achievement in U.S. High Schools from an International Perspective.

Performance of U.S. students on international tests of math ematics achievement continues to lag, say these authors, who review the results of a study conducted by the International Association for the Evaluation of Educational Achievement.

Concept Teaching Strategy Length

The development of a taxonomy of mathematical concept teaching moves by Henderson (1967) led to a group of studies examining the relative effectiveness of various permutations of the concept teaching moves in promoting student attainment of mathematical concepts (Dossey, 1976). The research has provided information about the use of example and nonexample moves, the effectiveness of various permutations of the moves, and the interactions between types of moves and types of concepts. Unfortunately, these studies have used concept teaching strategies of various lengths (5, 10, 12, 16, and 38 moves). Comparing their results becomes a questionable and hazardous activity.