Preservice teacher education programs worldwide are increasingly becoming field based with student teaching as the capstone experience for preservice teacher learning in the program. Consequently, mentor teachers at field-placement program schools are bestowed with new and unique functions to support preservice teachers’ learning to teach, which calls for new conceptualizations of teacher mentoring approaches. This article critically examines the theoretical underpinnings of four existing approaches to teacher mentoring during student teaching, analyzes the focuses and practices associated with each approach, and identifies the major challenges that each approach faces in guiding preservice teachers to learn to teach as expected by the field based teacher education reforms. Finally, it proposes an integrated approach to teacher mentoring for field-based teacher education that transcends the four existing teacher mentoring approaches.

This paper reports our efforts to develop a measure of pre-service elementary teachers' geometry knowledge for teaching 2-dimensional (2D) shapes and to evaluate the psychometric properties of this measure. Specifically, the GKT-2D scale was designed to assess pre-service elementary teachers' geometry content knowledge, knowledge of geometry and students, knowledge of geometry and teaching in relation to 2D shapes, based on the van Hiele theory and mathematical knowledge for teaching framework. Using 307 pre-service elementary teachers' responses on the instrument, we examined item-and scale-level reliability and hypothesized factor structure of the instrument. The results suggested that the GKT-2D scale is a reliable and valid measure of the three facets of pre-service elementary teachers' geometry knowledge for teaching 2D shapes, with some limitations further addressed. This paper offers directions for future research in evaluating content-specific knowledge for teaching mathematics to unpack the complex relationship between teacher knowledge, teaching quality, and student learning.

Horizon mathematics knowledge, i.e., teachers’ understanding of how various mathematical topics are interrelated, can help mathematics teachers organize the discrete parts of mathematical content to develop coherent teaching lessons. For example, when teaching whole number addition and subtraction, connections to concepts such as base-10 concepts and the inverse relationship between addition and subtraction could help students solve the addition and subtraction problem better. Thus, teacher training programs have been increasingly promoting this knowledge among pre-service teachers (PSTs) to help them enhance their teaching skills and better prepare them for future teaching. However, little is known about what kind of horizontal knowledge PSTs have developed and how well they utilize it in their teachings. By analyzing video presentations of 43 elementary PSTs, this study examined their horizon mathematics knowledge related to backward and forward conceptual connections of whole number addition and subtraction concepts. The findings revealed that PSTs tend to make connections with previously learned mathematics concepts (i.e., backward conceptual connections) but pay relatively less attention to connecting with other relevant mathematics concepts students will learn in future grades (i.e., forward conceptual connections). In addition, the findings showed that PSTs displayed various types of inaccuracies when connecting base-10 place value and regrouping. These findings offer important insights for teacher training programs to adapt their mathematic method courses to help PSTs improve their horizontal knowledge and proactively address inaccuracies observed in the present study.

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