Two classic hands-on tasks address conceptual understanding of functions. The tasks center student discourse and rough draft mathematics as students grapple with the relationship between input and output.

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### Krystal Jones Carter

A well-crafted classroom engineering challenge can effectively answer compelling questions about social and global responsibility.

### Kristin Doherty

Support students in conjecturing in ways that can promote their agency in the learning process.

### Jodie A. Bailey

This author used Number Talks as an asset-based approach to build on students’ prior knowledge and make connections across strategies in a Grade 7 mathematics class to address unfinished learning that occurred as a result of the COVID-19 pandemic.

### George J. Roy, Matthew Cunningham, and Kenneth Rafanan

Teachers have the opportunity to make mathematics relevant. We leveraged the popularity of *Star Wars* to engage students in exploring and connecting two dimensions and three dimensions to careers in toy design.

### Christine Andrews-Larson, Jonee Wilson, Matthew Mauntel, Jessica Smith, and Thomeca Hawthorne-Glover

Support students in developing contextual reasoning about integer subtraction.

### Sean Nank, Jaclyn M. Murawska, and Steven J. Edgar

Mathematical action technology can foster equitable student discourse. Students engage in cycles of proof to create, test, and revise conjectures through dynamic exploration of the Pythagorean theorem.

### Richard Carlos L. Velasco and Kate Degner

Leverage Desmos to help students develop their mathematical identity and foster their sense of agency.

### Karen Zwanch and Bridget Broome

This game teaches algebraic generalizations through differentiated play in pairs, small groups, or as a whole class and uses manipulatives to bridge numerical and algebraic thinking.

### Rachael H. Kenney, Michael Lolkus, and Yukiko Maeda

Mathematics teacher educators play a key role in supporting secondary mathematics teachers’ development of effective, research-based formative assessment (FA) practices. We used qualitative research synthesis as a tool to identify actionable recommendations for mathematics teacher educators as they work with teachers on FA practices in secondary classrooms. These recommendations can strengthen the research-based practices of mathematics teacher educators as they support teachers’ collections and uses of FA data to move student thinking forward in secondary mathematics. We share and discuss recommendations for mathematics teacher educators to connect pedagogical content knowledge of students, teaching, and curriculum to FA practices. We also highlight the usefulness of the qualitative synthesis method, meta-aggregation, for generating research-based connections between theory and practice in mathematics education.