Mathematics

A classroom study was conducted to understand how to engage in responsive teaching with 18 seventh grade students at three stages of units coordination during a unit on proportional reasoning co-taught by the first author and classroom teacher. This paper focuses on the practice of inquiring responsively in small groups.

Learning trajectories in early mathematics instruction have received increasing attention from policymakers, educators, curriculum developers, and researchers. They are generally deemed useful for guiding curriculum standards, instructional planning, and assessment. However, the specific contributions of learning trajectories to education and children’s learning are unclear. We review research over the last five years to describe what is known and what still needs to be learned about methods of development, refinement, and validation of the goals, developmental progressions, and instruction of learning trajectories in early mathematics and possible advantages and disadvantages in the educational application of learning trajectories.

Learning trajectories in early mathematics instruction have received increasing attention from policymakers, educators, curriculum developers, and researchers. They are generally deemed useful for guiding curriculum standards, instructional planning, and assessment. However, the specific contributions of learning trajectories to education and children’s learning are unclear. We review research over the last five years to describe what is known and what still needs to be learned about methods of development, refinement, and validation of the goals, developmental progressions, and instruction of learning trajectories in early mathematics and possible advantages and disadvantages in the educational application of learning trajectories.

We discuss transforming STEM education using three aspects: learning progressions (LPs), constructed response performance assessments, and artificial intelligence (AI). Using LPs to inform instruction, curriculum, and assessment design helps foster students’ ability to apply content and practices to explain phenomena, which reflects deeper science understanding. To measure the progress along these LPs, performance assessments combining elements of disciplinary ideas, crosscutting concepts and practices are needed. However, these tasks are time-consuming and expensive to score and provide feedback for. Artificial intelligence (AI) allows to validate the LPs and evaluate performance assessments for many students quickly and efficiently.

Mathematics is a core component of cognition. Unfortunately, most young children and teachers cannot access research-based early childhood mathematics resources. Building on a quarter-century of research, we are developing and evaluating an innovative, integrated, intelligent, and interactive system of technologies based on empirically validated learning trajectories that provide the best personal and digital tools for assessing and supporting children’s mathematics learning.

Critical elements of the expertise of mathematics teacher educators (MTE) can be identified in the artifacts they design for working with prospective teachers (PT), specifically for engaging PT in the double role of practitioners and students of practice. While MTE are increasingly utilizing designed multimodal representations of practice (such as storyboards), theoretical frameworks and methods for analyzing these pedagogical artifacts and the meanings they support are still in early development. We utilize a semiotic framework, expanding systemic functional linguistics to encompass non-linguistic elements, to identify aspects of what we call navigational expertise—which supports PTs in engaging both as practitioners and students of the practice.

Integrated STEM education (iSTEM) is recognized for its potential to improve students’ scientific and mathematical knowledge, as well as to nurture positive attitudes toward STEM, which are essential for motivating students to consider STEM-related careers. While prior studies have examined the relationship between specific iSTEM activities or curricula and changes in student attitudes, research is lacking on how the aspects of iSTEM are operationalized and their influence on shifts in student attitudes towards STEM, especially when considering the role of demographic factors. Addressing this gap, our study applied multilevel modeling to analyze how different iSTEM aspects and demographic variables predict changes in student attitudes.

Integrated STEM education (iSTEM) is recognized for its potential to improve students’ scientific and mathematical knowledge, as well as to nurture positive attitudes toward STEM, which are essential for motivating students to consider STEM-related careers. While prior studies have examined the relationship between specific iSTEM activities or curricula and changes in student attitudes, research is lacking on how the aspects of iSTEM are operationalized and their influence on shifts in student attitudes towards STEM, especially when considering the role of demographic factors. Addressing this gap, our study applied multilevel modeling to analyze how different iSTEM aspects and demographic variables predict changes in student attitudes.

Integrated STEM education (iSTEM) is recognized for its potential to improve students’ scientific and mathematical knowledge, as well as to nurture positive attitudes toward STEM, which are essential for motivating students to consider STEM-related careers. While prior studies have examined the relationship between specific iSTEM activities or curricula and changes in student attitudes, research is lacking on how the aspects of iSTEM are operationalized and their influence on shifts in student attitudes towards STEM, especially when considering the role of demographic factors. Addressing this gap, our study applied multilevel modeling to analyze how different iSTEM aspects and demographic variables predict changes in student attitudes.

With the rise of the popularity of Bayesian methods and accessible computer software, teaching and learning about Bayesian methods are expanding. However, most educational opportunities are geared toward statistics and data science students and are less available in the broader STEM fields. In addition, there are fewer opportunities at the K-12 level. With the indirect aim of introducing Bayesian methods at the K-12 level, we have developed a Bayesian data analysis activity and implemented it with 35 mathematics and science pre-service teachers. In this article, we describe the activity, the web app supporting the activity, and pre-service teachers’ perceptions of the activity.