Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.
This article shows how to empower students in their own learning by their own creation of instructional videos and assessment.
Jeff Gregg, Diana Underwood Gregg, and Introduction by: Melissa Boston
From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.
Corey Webel and Sheunghyun Yeo
In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a “Math Buddy") on mathematics for 30 minutes per day. We focus on the development of PSTs’ skills for exploring children’s thinking and the structures and tools that we used to support this development. Data sources include screencast recordings of interactions with Math Buddies and written reflections completed by PSTs. Although the responsiveness of interactions varied across individuals and interactions, in general, PSTs showed improvements in exploring children’s thinking. We share implications of these findings for similar field experience models and for practice-based approaches to teacher education generally.
Susie Katt and Megan Korponic
This document contains the actual problems for April 2020.
Susan Baker Empson, Victoria R. Jacobs, Naomi A. Jessup, Ms. Amy Hewitt, D'Anna Pynes, and Gladys Krause
The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing this understanding are provided.
George J. Roy, Jessica S. Allen, and Kelly Thacker
In this paper we illustrate how a task has the potential to provide students rich explorations in algebraic reasoning by thoughtfully connecting number concepts to corresponding conceptual underpinnings.
Daniel Edelen, Heather Simpson, and Sarah B. Bush
The incorporation of the “M” in STEAM must extend beyond simply a tool to address science and engineering standards (Authors, 2016; NCSM/NCTM, 2018). We present a mathematics- rich STEAM inquiry in which elementary students engaged in solving the issue of homelessness for one family in need.
Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty
Try these meaningful alternative approaches to helping students make sense of word problems.
Stefanie D. Livers, Kristin E. Harbour, and Lindsey Fowler
In our attempts to make a concept easier, we may hinder student learning.