Dianne Goldsby

Middle-Grade Preservice Teachers’ Mathematical Problem Solving and Problem Posing

Empirical data were gathered from 51 middle-grade preservice teachers who were randomly assigned into one of two groups. The first group solved a task and then posed new problems based on the given figures, and the second group completed these activities in reverse order. Rubrics were developed to assess the written responses, and then thoughts and concerns related to problem-posing experiences were collected to understand their practices. Results revealed that the preservice teachers were proficient in solving simpler arithmetic tasks but had difficulty generalizing and interpreting numerals in an algebraic form. They were able to pose some basic and reasonable problems and to consider important aspects of mathematical problem solving when generating new tasks. Thus, teacher educators should provide substantial educational experiences by incorporating both problem-solving and problem-posing activities into engaging instruction for preservice teachers.

A Mile of Pennies

There are 84,480 pennies in a mile. Yes, that is correct – 84,480 pennies! An interesting fact to know: 16 pennies laid side by side constitute 12 inches in length, or one foot, and since 5,280 feet equals one mile, that gives us 84,480 pennies in a mile.

Area of a Circle

The formula for the area of a circle is one which can be derived by middle grades students with a hands-on activity.

The Two-Minute Lesson

Most instruction in the schools is highly formalized, complete with curricular specifications, implying lesson plans, talking points, and testing measures. Teachers are constrained by the formalism; teachers are almost powerless to teach beyond the specs.

Mentoring Viewed through an Open Classroom Experience

This chapter explores the specific experience of a mentor and mentee as they participated in the Open Classroom program, a program designed to encourage observations of department classrooms by faculty and graduate students. The mentoring relationship is described and viewed from the perspectives of both the mentor and mentee.

Preservice Teachers’ Problem-Solving Lesson Engagement and Knowledge and Beliefs about Teaching for Equity

Preparation for teaching for equity requires both mathematics knowledge for teaching (Ball, Hill, & Bass, 2005; Kulm, 2008) and knowledge of how to address the complexities of teaching all students with wide-ranging needs (Achinstein & Athanases, 2005).