The purposes of this study are to report current Preservice Teachers' (PTs) decimal abilities regarding the types of error patterns that they commit and to analyze characteristics of the errors in the problems posed for multiplication and division in decimals. We have determined common concept- and procedure-based errors made by the PTs. 37 PTs in…

This article reports on the findings of manipulative analyses performed by preservice and in-service teachers in an early childhood teacher education program mathematics methods course. The activities are intended to model and promote mathematical analyses for better discrimination between mathematics manipulatives by early childhood teachers.…

The implementation of the Common Core's Standards for Mathematical Practice can pose a challenge to all teachers of mathematics but especially to preservice teachers. These standards require teaching in a way that often differs from what preservice teachers have experienced as learners. Standard 1--"Make sense of problems and persevere in…

The goal of this study is to develop the professional noticing abilities of prospective elementary school teachers in the context of the Stages of Early Arithmetic Learning. In their mathematics methods course, ninety-four prospective elementary school teachers from three institutions participated in a researcher-developed five-session module that…

Prospective elementary teachers must understand fraction division deeply in order to meaningfully teach this topic to their future students. This paper explores the nature of the subject content knowledge of fraction division possessed by a group of Taiwanese prospective elementary teachers at the beginning of their mathematics methods course. The…

The goal of this study is to develop the professional noticing abilities of preservice elementary teachers in the context of the Stages of Early Arithmetic Learning. In their mathematics methods course, the preservice elementary teachers participated in a researcher-developed multi-session module that progressively nests the three interrelated…

Most future teachers are familiar with number patterns that represent an arithmetic sequence, and most are able to determine the general representation of the "n"th number in the pattern. However, when they are given a visual representation instead of the numbers in the pattern, it is not always easy for them to make the connection between the…

The role of a teacher is different from that in traditional mathematics instruction when the implementation of a lesson is based on students' ideas. The author's experience teaching the same lesson (of the latter format) to two different classes of pre-service teachers in an elementary mathematics methods course is described. Since whole-class…

Using the structure of a metacognitive journal, this article describes the author's discovery of an unusual method for adding fractions after carefully considering a student's response. (Contains 3 figures.)

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…