### Daniel Chazan, Patricio Herbst, Sandra Crespo, Percival G. Matthews, and Erin K. Lichtenstein

### Hemavibushani Khodai

Ear to the Ground features voices from several corners of the mathematics education world.

### Nicole M. Joseph, Toya Jones Frank, and Taqiyyah Y. Elliott

The purpose of this commentary is to acknowledge, illuminate, and counter the noticeable silences in the investigations of mathematics education researchers who conduct equity research with Black communities and other marginalized groups. For far too long, these communities have experienced a lengthy and complicated history of structural barriers; epistemological, symbolic, and intellectual violence; dehumanization; and antiblackness in mathematics education research. We advance the Critical–Historical (CritHistory) framework, which is rooted in critical race theory (CRT) and further explicates CRT’s tenet of challenging ahistoricism. We discuss methodologies and implications, including example questions that could be posed, types and locations of archives that could be examined, and populations with whom oral histories could be conducted.

### Atara Shriki and Dorit Patkin

Success in STEM fields depends largely on robust spatial skills, in particular on the ability to perform a mental rotation. Given that this ability can be nurtured, this article includes examples of diverse relevant tasks appropriate for grades 6–8 students.

### Jonathan A. Supovitz, Caroline B. Ebby, Janine T. Remillard, and Robert Nathenson

In this article, we use a two-dimensional assessment to examine the experimental impacts of a mathematics learning trajectory–oriented formative assessment program on student strategies for problems involving multiplication and division. Working from the theory that the development of students’ multiplicative reasoning involves improvements in both problem-solving accuracy and sophistication of strategies used to solve problems, we designed an assessment instrument to measure both dimensions of student learning. The instrument was used to measure the impact of the Ongoing Assessment Project (OGAP), which develops teachers’ capacity to regularly assess student thinking in relation to a learning progression to develop instructional responses that are based on evidence of student thinking. The results showed significant impacts of OGAP on both students’ problem-solving accuracy and the sophistication of their strategy. The findings suggest that capturing both dimensions of students’ multiplicative reasoning offers important information for researchers and program designers who seek to understand different dimensions of student mathematics performance.

### Cheng-Yao Lin and Aviva Hamavid

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

### Jonathan D. Bostic, Brooks Vostal, and Timothy Folger

All students have strengths that can be leveraged through universally designed instruction.

### Danny Bernard Martin and Introduction by: Robert Q. Berry III

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.