# What's New on CADREK12.org

**Resource | “Approximate” Multiplicative Relationships between Quantitative Unknowns**

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. Students were to represent in drawings and equations two multiplicatively related unknown heights (e.g., one was 5 times another). Twelve of the 22 participating students operated with the second...

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*Friday, May 22*

**Resource | Tiering Instruction for Middle School Students**

Differentiating instruction (DI) is a pedagogical approach to managing classroom diversity in which teachers proactively adapt curricula, teaching methods, and products of learning to address individual students' needs in an effort to maximize learning for all (Tomlinson, 2005). DI is rooted in formative assessment, positions teachers and students together as learners, and involves providing...

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*Friday, May 22*

**Resource | Exploring Prospective Teachers’ Ability to Generate and Analyze Evidence-based Explanatory Arguments**

In this paper, using written responses of 37 PSTs preparing to teach grades 1-8 mathematics, we examined explanations they constructed to support their problem solutions and explanations they provided in support of their critiques of student-generated explanations. We also examined features of explanations on which PSTs drew in their critiques of mathematical explanations of students. Our results...

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*Friday, May 22*

**Resource | Restoring Mathematics Identities of Black Learners: A Curricular Approach**

Black learners are subject to systemic physical, symbolic, and epistemological violence in mathematics classrooms. Such violence has negative ramifications for Black children’s mathematics learning and identity development. The authors argue that space should be made within the mathematics classroom to repair the harm caused by this violence. This article describes an identity-based curriculum,...

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*Friday, May 22*

**Resource | Getting a Grip: A Framework for Designing and Adapting Elementary School Science Investigations**

This column provides ideas and techniques to enhance your science teaching. This issue describes a framework for designing and adapting elementary school science investigations. Manz, E. (2019). Getting a Grip: A Framework for Designing and Adapting Elementary School Science Investigations. Science & Children.

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*Friday, May 22*

**Resource | Backward Transfer Effects when Learning about Quadratic Functions**

Presentation slides from the 42nd Conference of the International Group for the Psychology of Mathematics Education. Hohensee, C., Willoughby, L., & Gartland, S. (2018, July). Backward transfer effects when learning about quadratic functions. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd Conference of the International Group for the Psychology of...

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*Friday, May 22*

**Resource | Backward Transfer Effects on Action and Process Views of Functions**

Presentation slides from the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Hohensee, C., Gartland, S., & Willoughby, L. (2019, November). Backward transfer effects on action and process views of functions. In S. Otten, A. G. Candela, Z. de Araujo, C. Haines, & C. Munter (Eds.), Proceedings of the 41st annual...

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*Friday, May 22*

**Resource | Building Mathematical Knowledge for Teaching Proof in Geometry**

Presentation slides and handout from the 2019 NCTM Regional Conference in Nashville, TN.

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*Thursday, May 21*

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*Thursday, May 21*

**Project | Synchronous Online Video-Based Development for Rural Mathematics Coaches (Collaborative Research: Amador)**

This project will create a fully online video-based model for mathematics teacher professional development focused on supporting mathematics coaches in rural contexts, building on the investigators' previous work focused on online professional learning opportunities for mathematics teachers in rural contexts. Results from the previous project focused on rural teachers and their coaches show that...

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*Thursday, May 21*

**Project | Synchronous Online Video-Based Development for Rural Mathematics Coaches (Collaborative Research: Choppin)**

This project will create a fully online video-based model for mathematics teacher professional development focused on supporting mathematics coaches in rural contexts, building on the investigators' previous work focused on online professional learning opportunities for mathematics teachers in rural contexts. Results from the previous project focused on rural teachers and their coaches show that...

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*Thursday, May 21*

**Project | Pandemic Learning Loss in U.S. High Schools: A National Examination of Student Experiences**

As a result of the COVID-19 pandemic, schools across much of the U.S. have been closed since mid-March of 2020 and many students have been attempting to continue their education away from schools. Student experiences across the country are likely to be highly variable depending on a variety of factors at the individual, home, school, district, and state levels. This project will use two,...

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*Thursday, May 21*

**Organization | National Opinion Research Center**

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*Thursday, May 21*

**Project | Place-Based Learning for Elementary Science at Scale (PeBLES2)**

To support equitable access to place-based science learning opportunities, Maine Mathematics and Science Alliance in collaboration with BSCS Science Learning, will develop and test a model to support 3rd-5th grade teachers in incorporating locally or culturally relevant place-based phenomena into rigorously tested curricular units that meet the expectations of the NGSS. The project team will...

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*Thursday, May 21*

**Project | Fostering Equitable Groupwork to Promote Conceptual Mathematics Learning**

This exploratory study involves a long-term partnership between the principal investigator (PI) and a middle school teacher and her students. Two major goals of the study are to describe how students learn to collaborate with one another over time to make sense of mathematics, and how students and their teacher negotiate what constitutes equitable collaboration, with African American students'...

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*Thursday, May 21*

**CAREER Spotlight | Designing Learning Environments to Foster Productive and Powerful Discussions among Linguistically Diverse Students in Secondary Mathematics (NSF #1553708)**

We are studying how to create high school math classrooms where bilingual students who are classified as English learners (ELs) can participate in robust classroom discussions. Our redesign focuses on creating accessible and powerful curriculum materials, developing equitable instructional routines, and supporting student engagement in mathematical discourse practices.

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*Thursday, May 21*

**Project | Developing a Suite of Standards-based Instructionally Supportive Tools for Middle School Computer Science**

This project will develop a set of educative resources, assessment tools and teacher professional development (PD) activities to support teachers in developing knowledge of CS standards and improving their instructional pedagogy. Teachers will learn to use formative assessments related to these standards to determine student understanding. Improved CS instruction that is responsive to the needs...

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*Thursday, May 21*

**CAREER Spotlight | Proof in Secondary Classrooms: Decomposing a Central Mathematical Practice (PISC Project) (NSF #1453493)**

Through lesson study, the PISC Project explores the effect of an intervention to support the teaching and learning of proof in secondary geometry. PISC takes as its premise that if we scaffold proof, by first teaching particular sub-goals of proof, then students will be more successful with proof later on.

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*Thursday, May 21*

**CAREER Spotlight | Spreading Computational Literacy Equitably via Integration of Computing in Preservice Teacher Preparation (NSF #1941642)**

This project studies the effect of integrating computing into preservice teacher programs across grade bands and disciplines. The project explores how to connect computing concepts and integration activities to teachers' subject area knowledge and teaching practice, and which computing concepts are most valuable for general computational literacy.

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*Thursday, May 21*

**CAREER Spotlight | Noticing and Using Students’ Prior Knowledge in Problem-based Instruction (NSF #1253081)**

For this project, we created an adaptation to lesson study. Teachers discussed animations made by the research team to get ideas for planning a problem-based lesson. We recorded the teachers’ implementation of the lessons and led video clubs in the reflection step for teachers to pay attention to student thinking.

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*Thursday, May 21*

**CAREER Spotlight | Promoting Equitable and Inclusive STEM Contexts in High School (NSF #1941992)**

This project centers on creating STEM classrooms where students from all backgrounds feel included and empowered to intervene if they observe stereotyping, bias, and prejudice. Using surveys and interviews of adolescents as well as testing a new intervention, the findings will document factors related to resilience in STEM fields.

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*Thursday, May 21*

**CAREER Spotlight | Cultivating Teachers’ Epistemic Empathy to Promote Responsive Teaching (NSF #1844453)**

This project aims to study and cultivate science and mathematics teachers’ “epistemic empathy”—their capacity for tuning into and valuing someone’s cognitive and emotional experiences in the process of constructing, communicating, and critiquing knowledge. The research will examine how such empathy influences teachers’ responsiveness and how it shapes students’ engagement.

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*Thursday, May 21*

**CAREER Spotlight | Supporting Model Based Inference as an Integrated Effort Between Mathematics and Science (NSF #1942770)**

This project is exploring how to productively coordinate instruction around data, statistics, modeling, and inference in middle grades mathematics and science classes. We will conduct design-based research to develop and study innovative tools that support students to generate knowledge about ecological systems by using models of variability to make inferences.

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*Thursday, May 21*

**CAREER Spotlight | Investigating Differentiated Instruction and Relationships between Rational Number Knowledge and Algebraic Reasoning in Middle School (IDR2eAM) (NSF #1252575)**

This project is investigating how to differentiate instruction to meet middle school students’ mathematical learning needs. We are also investigating how students’ ideas about rational numbers and algebra are related. We have studied the PI’s teaching of students in after school classes and then in classrooms, co-teaching with teachers.

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*Thursday, May 21*

**CAREER Spotlight | Implement Mathematical Modeling for Emergent Bilinguals (IM2EB) (NSF #1941668)**

Responding to the rapid increase of emergent bilinguals (EBs) and their need to learn quality mathematics, this project implements modeling through co-developing and co-teaching with math teachers. This study investigates how mathematics teachers change their positioning and practices for EBs through a teacher-researcher collaboration of effective mathematical modeling instructions.

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*Thursday, May 21*

**CAREER Spotlight | L-MAP: Pre-service Middle School Teachers’ Knowledge of Mathematical Argumentation and Proving (NSF #1350802)**

This project supports grades 1-8 prospective teachers in developing knowledge and dispositions for teaching and learning K-8 mathematics with a focus on mathematical argumentation. The project explores the development of prospective teachers’ knowledge of argumentation in mathematics and mathematics-focused pedagogy and field experience courses and follows them into their student-teaching...

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*Thursday, May 21*

**CAREER Spotlight | Investigating Changes in Students’ Prior Mathematical Reasoning: An Exploration of Backward Transfer Effects in School Algebra (NSF #1651571)**

This project is examining how learning about a new STEM concept changes students’ reasoning about concepts that are not new to them and focuses mainly on mathematics concepts. We also examine how to teach new concepts in ways that enhance students’ reasoning about not-new concepts.

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*Thursday, May 21*

**CAREER Spotlight | Algebraic Knowledge for Teaching (AKT) (NSF #1350068)**

This project explores how elementary teachers can teach arithmetic that prompts students’ algebraic thinking. Guided by cognitive research, we analyzed videos of Chinese and U.S. expert teachers’ lessons on inverse relations and properties of operations. Insights suggest an “example-based problem solving” approach, documented in an upcoming book for the field.

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*Thursday, May 21*

**CAREER Spotlight | Expanding Latinxs' Opportunities to Develop Complex Thinking in Secondary Science Classrooms through a Research-Practice Partnership (NSF #1846227)**

This project aims to reduce youths’ opportunity gaps in secondary science classrooms by building a sustainable research–practice partnership. We explore how deliberately coordinated activities that facilitate the collaboration between researchers and practitioners can reduce opportunity gaps at schools, promote complex thinking in youth, and build on student ideas to promote responsible...

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*Thursday, May 21*

**CAREER Spotlight | Job Embedded Education on Computational Thinking for Rural STEM Discipline Teachers (NSF #1942500)**

This project cultivates a professional development model that allows rural teachers to build their professional skills at integrating STEM. Focusing on Pacific Islanders, a group with a unique cultural identity largely underrepresented in STEM fields, the project seeks to help teachers better teach STEM and Hawaii's computer science education standards.

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*Wednesday, May 20*