. Formative Assessment of Professional Noticing of Students’ Mathematical Thinking Effective teaching requires that teachers be responsive to students’ thinking and use it as the basis for instruction ( National Council of Teachers of Mathematics [NCTM

### Stephanie Casey and Joel Amidon

### Teruni Lamberg, Linda Gillette-Koyen and Diana Moss

, 2017 ; Pyle & DeLuca, 2013 ). Formative assessment involves administering assessments, analyzing the data, and making instructional decisions to support student learning ( Black & Wiliam, 2009 ). According to Black and Wiliam (2009) , this process

### Katie A. Hendrickson

This article examines the use of formative assessment practices in Finland classrooms, including intervention, teacher feedback, and student self-evaluation, and explores connections between standardized testing and formative assessment.

### Caroline B. Ebby and Marjorie Petit

Numerous research studies have shown that formative assessment is a classroom practice that when carried out effectively can improve student learning (Black and Wiliam 1998). Formative assessment is not just giving tests and quizzes more frequently. When assessment is truly formative, the evidence that is generated is interpreted by the teacher and the student and then used to make adjustments in the teaching and learning process. In other words, the formative assessment generates feedback, and that feedback is used to enhance student learning. Formative assessment is therefore fundamentally an interpretive process: It is less about the structure, format, or timing of the assessment and more about the function and use by both the teacher and student (Wiliam 2011). For teachers of mathematics, the heart of this process is making sense of and understanding student thinking in relation to content goals.

### Francis (SKIP) Fennell, Barbara Ann Swartz, Beth McCord Kobett and Jonathan A. Wray

*Principles to Actions: Ensuring Mathematical Success for All* (NCTM 2014) recognizes the need to find a way to leverage assessment opportunities to improve teaching and learning at the classroom and school level. And although we know a lot about the importance and potential impact of formative assessment done right and well (NMAP 2008; Black and Wiliam 2010), a disconnect continues to exist among planning, teaching, and assessment—and thus, between teaching and learning—in too many classrooms. Assessment must be linked to the planning and instruction of a lesson—every day—ensuring that lesson activities inform teaching and learning for all students. *Principles to Actions*'s eighth Mathematics Teaching Practice directs teachers to “*elicit* and use evidence of student thinking” (NCTM 2014, p. 53, emphasis added), but what are some ways to elicit this evidence?

### Nicole Panorkou and Jennifer L. Kobrin

This research study was designed to evaluate the extent to which professional development (PD) designed around a learning trajectory (LT) on geometric measurement of area was successful in helping teachers use the LT to conduct formative assessment. Six 3rd-grade teachers from the Midwest participated in 20 hours of PD centered on the LT. Data to evaluate the PD were obtained from a set of questionnaire prompts administered before and after teachers' participation in the PD. The results suggest that teachers increased their ability to elicit and interpret student thinking and use assessment results to make instructional decisions. We consider the design and evaluation of this PD to be valuable for future efforts aiming to use LTs to support teachers in their formative assessment practices.

### Kyle T. Schultz and Kateri Thunder

This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

### Brent Duckor, Carrie Holmberg and Rossi Becker Joanne

A seventh-grade teacher finds that the notion of attention—to student and teacher thinking about student thinking—is key to orchestrating standards-based mathematical learning.

### Yong S. Colen

Algebra students create their own funny faces onscreen after studying several parent functions and their transformations.

### Lorraine M. Baron

Assessment tools–a rubric, exit slips–inform instruction, clarify expectations, and support learning.