In-service Secondary Teachers Research Articles

BEING SLOPPY ABOUT SLOPE: THE EFFECT OF CHANGING THE SCALE

What is the slope of a(linear) function? Due to the ubiquitous use of mathematical software, this seemingly simple question is shown to lead to some subtle issues that are not usually addressed in the school curriculum. In particular, we present evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale and angle. The confusion arises when some common but undeclared default assumptions, concerning the isomorphism between the algebraic and geometric systems, are undermined. The participants in the study were 11th-grade students, prospective and in-service secondary mathematics teachers, mathematics educators and mathematicians — a total of 124 people. All participants responded to a simple but non-standard task, concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches, which we have termed ‘analytic’ and ‘visual’, as well as some combinations of the two.

Keep Counting Those Boxes-There's More

Afamous, well-traveled, and relatively easy counting problem is that of determining the number of squares of aU sizes on a checkerboard. In this article, we pose and solve several related extensions involving enumerating squares and rectangles. Preservice and in-service secondary teachers participating in a problem-solving course at the University of Northern Colorado produced most of the investigations and conclusions illustrated here. In addition, a recent statewide mathematics contest, attended by about a thousand students in grades 7–12, included versions of the explorations. We were pleased that a significant number of students successfully rose to the challenge. Given appropriate guidance, these problems can be a source for wonderful classroom explorations and discovery for both the student and teacher.

Preservice and Inservice Secondary Teachers' Orientations Toward Content Area Reading

Abstract This study examined preservice and inservice secondary teachers' orientations toward content area reading and instruction. Instruments included two sets of belief statements and three sets of lesson plans; for comparison, each instrument incorporated three explanations of the reading process. Based on their selection of statements and plans, preservice teachers favored an interactive model of reading but a reader-based instructional approach, whereas in-service teachers held reader-based beliefs in both areas. In addition, both groups selected primarily reader-based vocabulary and comprehension lessons but varied in their choices of decoding lessons. Further, only teachers holding reader-based beliefs consistently chose corresponding vocabulary and comprehension plans.