Reflection should be part of any well-designed lesson. Student work from the lesson should inform part of the reflection, but teachers should seek out other data to see if and how planned elements of the lesson had the desired effect. A reflection can be even stronger if it is observed by another professional who uses an observation tool that looks for a teacher's use of particular math teaching practices. These and other tools are part of the District Sample Curriculum Project's (DSCP) Phase IV focus on instructional strategies.
SERP 5x8 Card
Source: The Strategic Education Research Partnership (SERP)
School principals and others without strong mathematical content knowledge are the intended users of the 5x8 Card. As the name implies, this simple observation tool fits on a 5x8 index card. The 5x8 Card helps an observer recognize when students are engaged in the Common Core Standards for Mathematical Practice.
Achieve the Core Coaching Tool
Source: Student Achievement Partners
Achieve the Core's online Coaching Tool is designed around the key Common Core Shifts of focus, coherence, and rigor. The Coaching Tool is also available in paper versions. The Coaching Tool is more detailed than the 5x8 Card but borrows some of its ideas. The Coaching Tool is organized around three "Core Actions":
- Ensure the work of the lesson reflects the Shifts required by the CCSS for Mathematics.
- Employ instructional practices that allow all students to learn the content of the lesson.
- Provide all students with opportunities to exhibit mathematical practices while engaging with the content of the lesson.
Source: Carnegie Foundation for the Advancement of Teaching
"Practical Measurement" is not a ready-made tool, but instead a set of ideas about measuring things not usually captured by typical student achievement measures. Practical measures might address math anxiety, mindsets about potential, attitudes about the value of coursework, or feelings about social belonging. Some item ideas:
- If you are interested if your lesson is engaging students, you could use a question like, "Today in math class, I felt (check all that apply): excited/confused/confident/like a mathematician/bored/none of the above."
- If discourse is your focus, you could use an item that says "Today I shared my thinking out loud: with people in my small group/in a whole class discussion/with a small group and the whole class/with no one."
- If you want to gauge if your lesson is perceived by students to be student-centered or teacher-centered, you could try a Likert scale (1-5) item with the question, "How did you learn today?" and "The teacher told us everything we needed to know" on one end of the scale and "We figured everything out as a class, with the teacher helping but not telling us what to do" on the other end of the scale.