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Constructing and Role-Playing Student Avatars in a Simulation of Teaching Algebra for Diverse Learners
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This study examines the design and implementation of a simulated teaching environment in Second Life for prospective teachers.
From the perspectives of Graduate Research Assistants (GRAs), this study…
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Dear Colleagues,
To close out November, we are excited to share a new product, developed in collaboration with DRK-12 awardees, which offers practical design guidelines for online and blended professional…
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Dear Colleagues,
This month we are featuring DRK-12 projects with a focus on STEM pathways. Though there may not be consensus of what constitutes a STEM job, we might all agree that educational…
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Greetings from CADRE
Dear Colleagues,
There is a lot to share since we last saw you at the November DR K-12 PI Meeting. We have been pulling together resources that we expect will be interesting and hopefully valuable to…
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Dear Colleagues,
CADRE introduces our new report, Classroom-Based STEM Assessment: Contemporary Issues and Perspectives. This report highlights the latest insights from DRK-12 program-funded research and underscores the…
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Dear Colleagues,
This month's Spotlight on Games in STEM Education showcases innovative research into the role of gaming as a powerful tool to boost engagement and learning in STEM classrooms. Two blog posts featured in…
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Linear Algebra and Geometry is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. The materials are organized…
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In this article, we describe an example of differentiating instruction (DI) involving middle school students from a five-year project funded by the National Science Foundation.
Differentiating…
Backward Transfer Influences from Quadratic Functions Instruction on Students’ Prior Ways of Covariational Reasoning about Linear Functions
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The study reported in this article examined the ways in which new mathematics learning influences students’ prior ways of reasoning. Authors conceptualize this kind of influence as a form of transfer of learning called…
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The researchers conducted a qualitative analysis of the perceptions of school personnel and pre-service teachers about an Algebra I tutoring program for students with learning disabilities. The researchers surveyed and…
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The Transition to Algebra (TTA) curriculum seeks to quickly give students the mathematical knowledge, skills, and confidence to succeed in a standard first-year algebra class and to show them that they can explore…
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A symmetric polynomial is a polynomial in one or more variables in which swapping any pair of variables leaves the polynomial unchanged. For example, f(x, y, z) = xy +xz + yz is a symmetric polynomial. If we interchange…
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Dear Colleagues,
This newsletter highlights the work of DRK-12 projects, particularly those developing products for the practice of scientific modeling and several mathematics projects featured in an AERA…
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Dear Colleagues,
The 2019 DRK-12 grants have been awarded, and new projects are beginning. Welcome to all the new members of the CADRE community! We send a special congratulations to former CADRE Fellows Camillia Matuk and…
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Dear Colleagues,
This month, we are preparing to launch a new iteration of CADRE. Meet our team and learn more about our new initiatives. We are also revising some of our existing programs, such as our CADRE Fellows and…
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Dear Colleagues,
Thank you to those who have completed the survey we recently sent to gather information about DRK-12 projects. The majority of results are aggregated, but we have also collected information about DRK-12…
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Dear Colleagues,
This month’s Spotlight on Algebra Education in DRK-12 features projects focused on the connections between teaching practices, student reasoning, and the effectiveness of interventions. The projects…
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Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.
Shifting people’s judgments toward the…
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Presentation slides from the 42nd Conference of the International Group for the Psychology of Mathematics Education.
Presentation slides from the 42nd Conference of the International Group for the…
Cognitive Instructional Principles in Elementary Mathematics Classrooms: A Case of Teaching Inverse Relations
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This study examines how three cognitive instructional principles including worked examples, representations, and deep questions are used in eight experienced elementary teachers’ early algebra lessons in the U.S…
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This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying…
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Seeds of Algebraic Thinking are sub-conceptual resources coming from life experience that students call upon when responding to mathematical prompts. This site includes resources students could activate when thinking about…
Developing Algebra-ready students for Middle School: Exploring the Impact of Early Algebra (Blanton, Knuth)
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This is a 3-year project designed to build the preliminary components for investigating the impacts of early algebra education on students’ algebra readiness in middle grades.
Algebra…
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CADRE has compiled sortable Excel lists of DR K-12 projects that work in a particular topic area (e.g., algebra, earth science) or with a particular target audience. These lists can be useful tools in writing proposals for…
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Dear Colleagues:
While it isn't completely clear how the new presidency will impact education policy, schools, and students, those of us in the DR K-12 community will continue to research how to help children learn. And…
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Dear Colleagues,
This month's Spotlight focuses on improving science and mathematics education in rural America. Though rural areas differ, they often share similar assets (e.g., community orientation) that can…
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Dear Colleagues,
The National Academies report, Call to Action for Science Education: Building Opportunity for the Future, calls on communities across our nation to provide time, materials, and resources to support…
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Dear Colleagues,
Happy New Year! As we look at our plans for 2023—including the CADRE Learning Series, CADRE Fellows program, 2023 DRK-12 PI Meeting, new outreach, topical groups, and more—we are excited to continue…
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Dear Colleagues,
A new National Science Board brief on the science and engineering landscape asks, “How can we ensure U.S. leadership in critical and emerging technologies and a robust STEM workforce?” (NSB, 2004).…
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A first-year algebra student’s curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics…
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Presentation slides from the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.
Presentation slides from the 41st annual meeting of…
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This study examines how sampled Chinese and U.S. third and fourth grade students (NChina=167,NUS=97) understand the commutative, associative, and distributive properties.
This study examines how sampled…
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Several recent studies have focused on helping students understand the limitations of empirical arguments (e.g., Stylianides, G. J. & Stylianides, A. J., 2009, Brown, 2014). One view is that students use empirical…
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This site provides three online activities focused on covariational reasoning as a foundation for middle school students to build more abstract algebraic knowledge. These tasks provide students with opportunities to…
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The Concord Consortium has developed 19 activities for teaching and learning algebra that are available online or as an app for iPad or Android tablet computers. These activities—which cover a variety of algebra topics,…
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Dear Colleagues:
All our appreciation goes to June's DR K-12 PI Meeting participants. In this issue, we highlight some of the information, ideas, and resources that came out of your good work and conversation at the…
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Dear Colleagues,
Many of you may be thinking about your next NSF DRK-12 proposal submission now that the deadline (November 13, 2019) is less than five months away. This newsletter contains several articles that may…
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Dear Colleagues,
With over 500 registrants, the 2021 DRK-12 PI Meeting was our largest meeting ever! Aspiring, new, and experienced DRK-12 awardees, NSF staff, and guests came together to share research, discuss critical…
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Dear Colleagues,
NSF receives many Design and Development proposals but fewer DRK-12 proposals for Exploratory projects. This month we're featuring a Spotlight on Exploratory Research, where in addition to highlighting…
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Dear Colleagues,
We have several opportunities to add to your summer calendar. First, we invite you to bring your questions about submitting a proposal in response to the DRK-12 solicitation to the upcoming office hours…
Challenges to Using the Regression Discontinuity Design in Educational Evaluations: Lessons from the Transition to Algebra Study
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This article describes the use of RD design to evaluate the impact of a supplemental algebra-readiness curriculum, Transition to Algebra, on students’ mathematics outcomes.
Interest in the regression…
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The LEAP program is the first early algebra curriculum for students in grades 3-5. The program includes 18-20 one-hour lessons at each grade level and teacher support and assessment. Professional development …
Teaching Early Algebra through Example-based Problem Solving: Insights from Chinese and U.S. Elementary Classrooms
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Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-…
Eliminating Counterexamples: A Case Study Intervention for Improving Adolescents’ Ability to Critique Direct Arguments
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Students’ difficulties with argumentation, proving, and the role of counterexamples in proving are well documented. Students in this study experienced an intervention for improving their argumentation and proving…
The Centrality of Student-Generated Representation in Investigating Generalizations about the Operations
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This article addresses the nature of student-generated representations that support students’ early algebraic reasoning in the realm of generalized arithmetic.
This article addresses the nature of…
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On February 10th, 2012, five Fellows presented on the work of their projects. Many thanks to the presenters and to the audience of Fellows who followed up each presentation with great questions and discussion.
Due to…
Knowledge for Algebra Teaching for Equity (KATE) Project: An Examination of Virtual Classroom Simulation Approaches
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In this paper, we present an overview of the National Science Foundation (NSF) funded Knowledge for Algebra Teaching for Equity (KATE) Project and experiences from preservice teachers who are preparing for teaching middle…
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Dear Colleagues:
If you haven't heard, we lost a very well respected NSF colleague, Dr. Janice Earle, who was program director for many of us over several decades. We and others had wonderful professional relationships…
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Dear Colleagues,
We are saddened to share the news that Julio Lopez-Ferrao passed away on March 25. Julio had been a DRK-12 program officer since the inception of the program, and was CADRE's first program officer. He…
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Dear Colleagues,
This month we’re featuring DRK-12 CAREER awardees. The next deadline for CAREER proposal submissions is July 26. We encourage you to explore resources in our NSF Proposal Toolkit if you are considering…
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Dear Colleagues,
As we welcome the spring season, we also welcome a new group of DRK-12 awardees. Congratulations to the recent CAREER and RAPID award winners!
Our newsletter is full of information and resources for you,…
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Dear Colleagues,
This month’s Spotlight on Social Studies and STEM Integration showcases how educators and researchers are melding history, geography, economics, and civics with STEM to support real-world applications,…
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Dear Colleagues:
With spring almost here and preparation for conferences underway, we are all thinking more about dissemination strategies. Let us help you! Send us a quick update on your project with an accompanying link…
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This study is a case of using second-order models of students’ mathematical thinking to differentiate instruction, and it reveals that inquiring into research-based knowledge and inquiring responsively into students’…
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Designed to be integrated with any curriculum, each grade level includes 18-20 one-hour lessons to be conducted throughout the school year. Each LEAP lesson lasts about an hour is designed to fit within a typical daily…
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Students’ difficulties with contrapositive reasoning are well documented. Lack of intuition about contrapositive reasoning and lack of a meta-argument for the logical equivalence between a conditional claim and its…
Impact of the Design of an Asynchronous Video-Based Learning Environment on Teacher Noticing and Mathematical Knowledge
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In this paper, we share the design and impact of a set of two-hour online mathematics professional development modules adapted from face-to-face video-based materials.
In this paper, we share the design…
A Geometric Path to the Concept of Function: Transformations using dynamic software can provide a unique perspective on a common topic.
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The concept of function spans elementary school through high school. When introducing the topic to elementary school and middle school students, we ask them to work with a variety of examples and representations of…
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Dear Colleagues:
We've begun summer with a lot of enthusiasm about the coming year. Please save the date of June 1-3, 2016 for the DR K-12 PI Meeting to take place in Washington, D.C. On the basis of your evaluations of…
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Dear Colleagues,
October was National Disabilities Awareness Month, and December 3 is International Day of Disabled Persons. So this month, CADRE is featuring DRK-12 projects studying STEM education for children and…
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Dear Colleagues,
The CADRE Fellows nominations are open! Please spread the word about this professional growth opportunity for early career researchers. Applications are due October 8, 2020.
Schools are back in session.…
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Dear Colleagues,
This month, we’re taking a pause from our standard articles to reflect on 2021, highlight resources and information that the DRK-12 community found most compelling, and invite you to revisit those that you…
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Dear Colleagues,
As we end 2023, we want to thank all of you who shared your research and what you’re learning about preK-12 STEM education (e.g., through project Spotlights, the DRK-12 PI Meeting, and the assessment…
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Dear Colleagues:
The CADRE team wishes you a productive professional year in 2015!
In the fall, we welcomed the newest cohort of Fellows to the CADRE community. They are an exceptional group of early career researchers and…
Eliminating Counterexamples: A Case Study Intervention for Improving Adolescents’ Ability to Critique Direct Arguments
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This case study investigates U.S. eighth-grade (age 13) mathematics students’ conceptions about the validity of a direct argument after the students received instruction on the eliminating counterexamples (ECE) framework…
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This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign.
This research focuses on ways in which balance scales mediate students’ relational…
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This presntation addreses 4 research cquestions
•What extant criteria do Grade 8 students use to choose the better line
of fit between two lines “fit” to a set of data, when both lines express
the trend of the data…
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We investigate the algebraic discourse of secondary mathematics teachers with respect to the topic of equation solving by analyzing five teachers’ responses to open-ended items on a questionnaire that asks respondents to…
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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…
Pre-Service Teachers' Knowledge for Teaching Algebra for Equity in the Middle Grades: A Preliminary Report
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This article presents our plans and initial work to explore how mathematics teacher education programs can prepare teachers for diverse middle grades classrooms. It describes the start-up of a five-year National Science…
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Dear Colleagues,
We've heard! CADRE has been awarded a grant to continue serving the DRK-12 program and its awardees for another two years. Here's what we know. We will continue to share news and resources with you…
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Dear Colleagues,
In 2018, NSF and IES released a companion to the Common Guidelines which identifies principles to help education stakeholders design and report reproducibility and replication studies in the…
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Greetings from CADRE
Dear Colleagues,
With the December PI meeting behind us, we are now planning some follow-up support for grantees who participated in special interest groups and job-alike groups. We are organizing…
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Dear Colleagues,
This month’s Spotlight on Research and Practice Partnerships highlights current DRK-12 project work and the pivotal role of partnerships in advancing our understanding of effective teaching and learning…
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Dear Colleagues,
Last week, NSF announced significant changes to preK–12 funding with the launch of the NSF STEM K–12 program and solicitation. DRK–12 will no longer accept proposals. (Read our full article below.)
New…
Growth in Children’s Understanding of Generalizing and Representing Mathematical Structure and Relationships
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Authors share results from a quasi-experimental study that examines growth in students’ algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an…
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A cluster randomized trial design was used to examine the effectiveness of a Grades 3 to 5 early algebra intervention with a diverse student population.
A cluster randomized trial design was used to…
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The Advancing Reasoning Covariationally (ARC) curriculum is a curriculum for working pre-service and in-service teachers. ARC targets and develops quantitative and covariational reasoning as connecting threads to major…
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There is strong empirical evidence in support of learning from comparisons in mathematics education research. The Animated Contrasting Cases in Geometry project seeks to extend this research and transform the learning of…
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Professional development (PD) for mathematics teachers often emphasizes transformative instructional change. However, a more modest, incremental approach may offer a higher likelihood of success in ways that complement…
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Algebra
Presentation
High
Mary Ann Huntley
Maria Terrell
2010…
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Dear Colleagues,
It has been a busy spring for CADRE and the DRK-12 community who have been working hard on dissemination and outreach efforts. Representatives from DRK-12 projects have been spreading the word about…
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Dear Colleagues,
The current pandemic is making it impossible to ignore the health, economic, and educational disparities in our country. At the same time, current education research has been greatly impacted—through…
Newsletter
Greetings from CADRE
Dear Colleagues,
Summer is coming to an end, and CADRE is planning the 2010 DR K-12 PI meeting. Scheduled for Dec. 1-3 in D.C., we are trying hard to incorporate evaluation findings, advisors’…
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Dear Colleagues,
A recent budget memo outlines US priorities for research and development (R&D) in fiscal year 2025, emphasizing a range of sectors including artificial intelligence, economic competitiveness, social…
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Dear Colleagues,
Happy summertime!
Some of you may be engaged in professional development with teachers, others may be analyzing data, and still others might be taking a well-deserved break or vacation. This month’s…
Scaling up innovative learning in mathematics: exploring the effect of different professional development approaches on teacher knowledge, beliefs, and instructional practice
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The purpose of the current study was to explore different ways for teachers to engage in Professional learning experiences (PLEs) and how these approaches might enable the field to scale up these efforts in a sustainable…
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Three 18-session design experiments were conducted, each with 6–9 7th and 8th grade students, to investigate relationships between students’ rational number knowledge and algebraic reasoning. Implications for teaching are…
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The Math Pathways & Pitfalls K-8 curriculum was designed with built-in support for teachers, alignment to the Common Core State Standards and Mathematical Practices. The curriculum can be flexibly used as an…
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The ReLaTe-SA project investigates the research question: what language do teachers use to describe and explain routines in algebra classes? The goal of this article is to inform readers about some ways we have learned to…
Transforming Learning Opportunities in Linguistically Diverse Secondary Classrooms Through Promoting Discussions: Results of an Intervention
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This article presents results from a design experiment intended to develop students’ understanding of linear functions and rates of change in a linguistically diverse ninth grade classroom. The intervention focused on…
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This session considers teachers’ transitions from teacher-centered mathematics to student-centered mathematics, including issues of meaning, coherence, and learnability, as well as the importance of working with colleagues…