Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, and James Hiebert

In this editorial, the editors return once again to the collaboration between fourth-grade teacher Mr. Lovemath and mathematics education researcher Ms. Research, who are mentioned in previous editorials.

Marsha Ing and Artineh Samkian

There are great opportunities and challenges to sharing large-scale mathematics classroom observation data. This Research Commentary describes the methodological opportunities and challenges and provides a specific example from a mathematics education research project to illustrate how the research questions and framework drove observational choices, and how these choices might constrain or limit sharing of data for other research purposes.

Justin K. Dimmel and Patricio G. Herbst

The authors investigated how secondary mathematics teachers check student geometry proofs. From video records of geometry teachers checking proofs, they conjectured that teachers have different expectations for details that follow from written statements than for details that are conveyed by diagrams. They found that participants rated lower instruction that deviated from what they hypothesized to be their expectations, confirming their hypotheses.

Philip Sadler and Gerhard Sonnert

This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus—(a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? Mastery of the mathematics considered preparatory for calculus was found to have more than double the impact of taking a high school calculus course on students’ later performance in college calculus, on average. However, students with weaker mathematics preparation gained the most from taking high school calculus.

Kathy Liu Sun

The belief that mathematics ability is a fixed trait is particularly common and may be a key reason for many students’ disinterest and underperformance in mathematics. This study investigates how mathematics teaching practices might contribute to students’ beliefs about mathematics ability being a fixed or malleable trait (mindset).

Leslie Nabors Oláh and André A. Rupp

Review of *Psychometric Methods in Mathematics Education: Opportunities, Challenges, and Interdisciplinary Collaborations*, edited by Andrew Izsák, Janine Remillard, and Jonathan Templin.