This article provides teachers with a toolkit for assessing students in the context of data-based individualization (DBI) in mathematics. Assessing students is a critical component of DBI because it provides teachers with information about what they may need to modify in their instructional programs. In this article, we provide teachers with…

As ideas from data science become more prevalent in secondary curricula, it is important to understand secondary teachers' content knowledge and reasoning about complex data structures and modern visualizations. The purpose of this case study is to explore how secondary teachers make sense of mappings between data and visualizations, especially…

Adaptive teachers use student data to guide instruction. Learn about using an anecdotal record form to support adaptive teaching. In this article, the authors describe how teachers can use learning trajectories to make adaptive decisions to meet the needs of their students. They provide an example using the U .S. Math Recovery Council's learning…

This article aims to present a first approximation of the conceptual field of measures of central tendency (MCT), grounded in the theory of conceptual fields. We propose six situations according to type of variable, data presentation (raw or grouped) and amount of data. We revisit specific situations for the mean and exemplify several…

Since data collection technologies has become a part of daily life, measurement and data requirements now permeate many state mathematics standards, beginning as early as kindergarten and extending through high school. For example, the Standards for Mathematical Content, recommend that kindergarteners "describe and compare measurable…

This is the fourth in a series of statistical articles for mathematics teachers. In this article, the authors discuss topics in General Mathematics in Unit 2 Topic 1 (Univariate data analysis and the statistical investigation process) and topics in Essential Mathematics, Unit 2 Topic 1 (Representing and comparing data).

Being able to understand, interpret, and critically evaluate data is necessary for all individuals in our society. Using the PreK-12 Guidelines for Assessment and Instruction in Statistics Education-II (GAISE-II; Bargagliotti et al., 2020) curriculum framework, the current paper outlines five evidence-based recommendations that teachers can use to…

As data are 'numbers with context' (Cobb & Moore, 1997), contextual knowledge plays a prominent role in dealing with statistics. While insights about a specific context can further the depth of interpreting and evaluating outcomes of data analysis, research shows how it can also hinder relying on data especially if results differ from…

This article illustrates one of several learning sequences from the Interdisciplinary Mathematics and Science (IMS) Learning project, connecting science and mathematics learning in the primary school. Investigating Body Height involved a series of investigations conducted in Years 5 and 6 across six classes in one school. The project teachers…

More than ever in the past, researchers have access to broad, educationally relevant text data from sources such as literature databases (e.g., ERIC), an open-ended response from online courses/surveys, online discussion forums, digital essays, and social media. These advances in data availability can dramatically increase the possibilities for…

The purpose of this quantitative systematic literature review was to identify and describe published mathematics studies from 1980 to 2021 that incorporated a self-monitoring component (k = 22 studies; N = 1,787 students). We examined specific self-monitoring procedures, instructional contexts, implementation variables, and methodological quality.…

Every application of integration by parts can be done with a tabular method. The trick is to identify and consider each new integral in the table before deciding how to proceed. This paper supplements a classic introduction to integration by parts with a particular tabular method called Row Integration by Parts (RIP). Approaches to tabular methods…

The gold-standard for evaluating the effect of an educational intervention on student outcomes is running a randomized controlled trial (RCT). However, RCTs may often be small due to logistical considerations, and resulting treatment effect estimates may lack precision. Recent methods improve experimental precision by incorporating information…

This study investigated the process of instructional change required to translate data on student progress along learning trajectories (LTs) into relevant instructional modifications. Researchers conducted a professional development session on ratio LTs, which included analyzing 3 years of district-level data from Math-Mapper 6-8, a digital…

At the school level statistics begins with exploratory data analysis, or EDA. Statistical learning goes on to include statistical inference, which will be discussed in the second part of this article. In this article, the author will talk about EDA and CODAP. EDA can be thought of as looking for patterns in data using graphs and simple statistics…