Articles about Mathematics Education
Constructing a Personal Understanding of Mathematics, Mark Ellis
| This article is a reflection on my own development as a teacher of mathematics, focusing particularly on the ways in which "teaching for understanding" led me to realize both my students' abilities to form insights about mathematics and my own limited (procedural) knowledge of mathematics. |
| This inquiry raises questions about the manner in which the No Child Left Behind Act aims to improve mathematics education through continued reliance on standardized testing and mandated use of scientifically based teaching practices. Specifically, it is argued that this approach is tied to assumptions about intellectual ability and achievement that precipitated the dividing practices used to justify differential access to mathematics learning almost a century ago. An examination of so-called objective and scientific approaches to school mathematics suggests the need for more earnest reflection about the particular path toward educational progress privileged by this legislation. |
Reframing Problems in Secondary Education [edited journal issue], Mark Ellis, Maria Grant, and Laura Haniford
| There is little disagreement that secondary education in the United States can and must be improved, with much attention given to analyses of outcomes ranging from dropout rates to academic achievement to international measures of literacy. The perspectives offered by the authors of the manuscripts in this guest edited issue of The High School Journal call into question the way in which problems in secondary education are defined or framed. ... Typically in the field of education, the gaps that are examined arise from fixed vantage points—in essence, the same perspectives that framed problems in education 30 or more years ago are still used today. ...Often missing from these perspectives—both teachers’ and administrators’—is a full examination of how the problems themselves have come to be identified. Exacerbating this concern is the realization that these historical perspectives tend to frame problems in ways that blame student characteristics and backgrounds for poor performance while ignoring factors such as opportunities to learn and access to information. |
The Paradigm Shift in Mathematics Education, Mark Ellis and Robert Berry, III
| This article represents a historical-theoretical examination of school mathematics practices in the United States. We argue that is has been only recently (since the 1990s) that serious efforts to reform teaching practices have emerged. Specifically, we point to the ways in which recent reforms have put concerns about equity and students' sense-making in mathematics in the forefront and the implications this has for how we prepare teachers of mathematics. |
Convergence of Observer Ratings and Student Perceptions of Reform Practices in Sixth-grade Mathematics Classrooms (draft version here), Mark Ellis, Carol Malloy, Judith Meece, and Patricia Sylvester
| As part of a research
project examining relationships between instructional practices and student
cognitive and social outcomes in middle-school mathematics classes, external
observers and students reported perceptions of teachers’ instructional
practices. The extent to which students in classrooms identified by external
raters as reform-oriented actually perceive instruction in ways aligned with
reform principles has not been established. A 25-item observation protocol
aligned with the reform practices called for in the Standards of the National
Council of Teachers of Mathematics (NCTM) was used to develop a quantitative
profile of instructional practices across two lessons in each of 28 classes of
15 participating teachers. Students in each of the observed classes completed a
49-item survey of their perceptions of instructional practices. As items for
both the observation protocol and Student Survey were designed to measure
alignment with the same dimensions of reform practice, the convergence of these
two data sets was examined as a means to confirm the observation ratings. The
findings show moderately strong correlations between ratings of external
observers and perceptions of sixth-grade students across three dimensions
(pedagogy, tasks and mathematical interactions) of reform-oriented teacher
practice in mathematics classrooms. Implications of these findings for future
research are discussed. |
Mathematics Placement and the Transition to Middle School, Patrick Akos, Marie Shoffner, and Mark Ellis
|
The transition to middle
school has been a frequent research topic in recent years. The findings have
highlighted both the significant risk and opportunity for school counselor
intervention in the transition. One particularly important component of the
multifaceted transition is course placement. The importance and influence of
mathematics and mathematics placement and the role of the school counselor
in this process are outlined. Specifically, pilot data that underscore the
importance of school counselor collaboration with parents and mathematics
faculty are presented. |
How and Why Do Teacher Credentials Matter for Student Achievement? Charles Clotfelter, Helen Ladd, and Jacob Vigdor
| "This paper explores the relationship between teacher characteristics and credentials, and student achievement. The authors conclude that, taken together, the various teacher credentials exhibit quite large effects on math achievement, whether compared to the effects of changes in class size or to the effects of socio-economic characteristics of students." |