Seven vital student classroom actions identified as critical by the Common Core State Standards, Standards for Mathematical Practice (CCSS-M SMPs).
Use this measure:
The SERP 5×8 Card can be accessed on the SERP Institute website
Measurement instrument overview
This is a math observation tool that focuses observers’ attention on what students are saying and doing during math activities that involve some student discussion, whether whole-class, group, or in pairs.
The tool was originally designed with principals in mind to help them gain awareness of what goes on in classrooms and attend to students’ thinking as they guide standards-based instructional changes at their schools. The card’s name stems from the developers’ commitment to providing principals with useful guidance that would fit on a 5×8 Card.
Connection to student learning
This tool was developed as the Common Core State Standards were first being adopted across the United States. School district leaders, working in collaboration with Strategic Education Research Partnership (SERP) Institute partners, recognized that the shifts demanded by the CCSS-M SMPs would require considerable learning from teachers and students. They also recognized that mathematics classroom changes would need to be led by site principals ultimately responsible for what goes on in classrooms. They wanted an observation tool that would be accessible to, and easily used by, principals.
The 5×8 Card identifies seven important principles for high-quality and equitable math instruction aligned to the CCSS-M SMPs. The 5×8 Card also provides a brief rationale for why each principle is included, a short descriptive heading for the principle, hints about what evidence a principal might look for during a classroom observation (referred to as student “vital actions”), and information about which SMPs are associated with each vital action.
For example, one of the principles focuses on the idea that “logic connects sentences.” The rationale for this principle focuses on the importance of students using mathematical reasoning to construct and defend an argument (“this is what I did and why it makes sense”). The rationale goes on to clarify that “brief single-sentence student utterances are generally insufficient for a viable argument” (SERP Institute, 2021). The evidence hint for this principle suggests that observers attend to the vital action of whether students say a second sentence to extend and explain their thinking. The 5×8 Card also provides the additional information about which SMPs are connected to the vital action (in this case SMPs 1, 2, 3, and 6).
What we know about how well this measure works for its intended use
The 5×8 Card was not designed as a teacher evaluation tool, but as a “tool that focuses observers’ attention on what students are saying and doing so that their work (their thinking) can be at the center of educators’ discussions” (SERP Institute, 2021). The tool is intended to be educative, helping observers “learn a great deal about good instructional practice simply through focused observation” (SERP Institute, 2021). Strategically, the 5×8 Card focuses observers’ attention on students’ actions — rather than the actions of the teacher — to reinforce the use of the tool for learning rather than for teacher-evaluation purposes.
SERP partners have used the 5×8 Card to organize professional development for teachers, assistant principals, and principals. In those settings, the 5×8 Card provided a framework for gathering evidence of student thinking during classroom observations carried out between meetings. The observations were then discussed and action plans to stimulate the practices were put into place.
Measurement routine details
An observation using the SERP 5×8 Card should be scheduled for a lesson in which discussion plays an important role.
Regular use of the observation tool by principals or other classroom observers could: (a) improve users’ ability to observe math classroom instruction and understand what evidence might point to high-quality math teaching and learning, and (b) generate information about students’ vital actions to inform subsequent teaching moves and student growth.
Data analysis details
Both users we spoke with indicated that the measure did not facilitate aggregate data collection well. However, it did support conversations about practice.
That said, we could imagine at least two analysis scenarios. One scenario might be to compare observation results gathered from multiple lessons. An observer could document which vital actions were observed during classroom observations. Results for individual classrooms could be compared across multiple periods, supporting a discussion about what was happening during the observation periods that might have produced the evidence gathered. Similarly, using the observation tool in multiple classes implementing the same lesson might also spark a discussion about the features of the lesson that provided more or fewer opportunities for the student vital actions to occur.
A second scenario might focus on comparing the evidence gathered by multiple different observers watching the same lesson. Analysis might focus on the nature of the evidence gathered by the different observers for each vital action, providing an opportunity for observers to learn from what their colleagues noticed.
Conditions that support use
- Familiarity with the SMPs
- It may be useful to bring together observers who are more and less experienced with and knowledgeable about mathematics classroom instruction and the CCSS-M to conduct shared observations. This may support their professional development and their “professional noticing.” Time built in for discussion after a collaborative observation may enable the less experienced observers to learn from the observations of those with more experience, and vice versa.
- SERP’s online 5×8 Card documentation emphasizes the importance of creating math classroom cultures that are conducive to the vital actions. If a supportive classroom culture is not in place, there may be limited opportunity to observe evidence of the vital actions.
Other tools and resources to support use
SERP online resources include a page describing the Seven Vital Actions. Each action shows the associated principles and rationale, with additional citations to related research.
A related resource, the Deck Behind the 5×8 Card, suggests teaching moves that could be used by educators to increase the prevalence of the observed student vital actions.
A series of professional learning videos with Phil Daro (one of the CCSS-M authors) describes the principles associated with the 5×8 Card and the Common Core State Standards more generally.
The SERP Institute was founded as an independent nonprofit organization in 2003 to bridge the worlds of education research, practice, and design. One of the underlying reasons for starting SERP was its founders’ recognition that the U.S. education system is “missing a coherent approach for turning evidence-based ideas into effective programs and practices that fit within the routines of the classroom, and can therefore readily spread” (SERP Institute, 2021). SERP’s approach is to bring together education researchers, designers, and practitioners to create and test “equitable, scalable solutions, a majority of which are freely accessible to everyone.”
At the time the CCSS-M were adopted in California, SERP was working in close partnership with two California Bay Area school districts — San Francisco and Oakland Unified School Districts — on district-identified problems of practice. The 5×8 Card observation tool emerged from a request by school principals participating in SERP to have a simple and easy-to-use tool that would support their observations of math classrooms. They were enthusiastic about the idea of fitting the tool on a 5×8 index card. Designers worked within the constraint of the 5×8 Card, which compelled them to pick a few of the more critical mathematical ideas to guide principals in what to look for. They decided to focus on a few key ideas in the new standards and make these “look fors” as vivid and concrete as they could. To get away from principals using this as a formal evaluation tool, designers strategically omitted a rating scale.
SERP introduced the measure to a group of middle school principals during 30 minutes of a regular principal staff meeting. Principals were encouraged to try out the measure at their own sites and come back to the meeting ready to talk about this experience with each other. The feedback on the tool was overwhelmingly positive, with many principals commenting on how the tool articulated what they sensed to be good teaching practice in concrete terms. Through this learning process, some school principals began using the measure more regularly, and some shared the 5×8 Card with teachers as well. SERP had hoped that eventually the measure could be used with teachers visiting each other’s classrooms, but this idea did not come to fruition in the districts because of other structural barriers.
To give further purpose to the observation routine and give principals the opportunity to observe some of the actions on the Card, principals were encouraged to check in with the teacher before the observation. This check-in might help the principal and teacher develop a shared understanding of the lesson focus and identify one or two higher priority items on the Card for the principal to pay attention to. For example, a principal might specifically state that they were coming in hopes of seeing high-quality mathematical discourse among students, encouraging the teacher to plan some opportunities for discourse into the lesson for that day.
Lizzy Hull-Barnes, the current director of mathematics and computer science in San Francisco Unified School District, used the measure to support teachers at her site with their math instruction (at the time, she was an Instructional Reform Facilitator at a district elementary school). She observed and scribed during an observation, filled out the 5×8 Card, and then had a conversation with the teacher, using her evidence. At the time, her school was also using the idea of choosing a few focal students to help focus classroom observations. Hull-Barnes could listen to and watch these focal students particularly closely and reflect information about her observations back to the teacher.
In Oakland principal trainings, district math leaders helped principals see that most of the items were focused on student (not teacher) actions. They also encouraged principals to gather specific data (e.g., by videotaping class segments on their phones or scripting second sentences said by students). Daro reported that this guidance helped Oakland principals understand that counting the student vital actions was useful, but it was even more useful to gather more specific information about the quality of the student action.
The learning from using the 5×8 Card was powerful for principals, especially the idea of focusing on student vital actions rather than teacher actions. Daro reported that principals realized that beginning a conversation with a teacher after the observation with “this is what I saw your students doing” led to a better conversation than when starting with “this is what I saw you doing.”
The learning was also powerful for the designer group. Daro mentioned that some of the items on the measure were more useful than others. They found, for instance, that principals generally felt that the “students say a second sentence” item mapped onto who they knew to be the best math teachers — those who worked hard to establish opportunities for mathematical discourse (principals rarely saw evidence of this item in the classrooms of less proficient math teachers). Other items, such as “students talk about each other’s thinking” or “students revise their thinking” were important theoretically but were observed less often in practice because most math classrooms did not provide such opportunities for students.
Many of the following factors contributed to the development and use of the 5×8 Card in San Francisco and Oakland:
- The collaboration between SERP, the Stanford Design School, and district practitioners to focus on practical solutions to identified district challenges
- The introduction to principals during regularly held principals’ meetings and the natural spread from there to school sites for principals who found it useful
- The clear purpose for the measure to support learning and relationship building rather than teacher evaluation
Phil Daro, former Director, Strategic Education Research Partnership
Lizzy Hull-Barnes, Director of Mathematics and Computer Science, San Francisco Unified School District
SERP Institute, www.serpinstitute.org