Should you check in on students every year to make sure they’re progressing? Or every few minutes to make sure they’re challenged and engaged? The answer is both.
Although all subjects contend with questions of assessment, math presents a special challenge. Students who fall behind are faced with increasingly large gaps to fill, and peers and mentors sometimes perpetuate the myth of being or not being a “math person.” To ensure progress in math, it’s important to take time each year to see if students are progressing in overarching concepts like operations, equations, and measurement. It is also important to check in frequently so instruction can be fine-tuned to students’ specific needs.
How to Assess Students in Math
There are a variety of ways to assess students in math—everything from performance tasks to classroom conversations. Assessment is widely viewed as a spectrum with summative and formative being on opposite ends. Large-scale assessment, like final exams or state-level tests, corresponds to summative assessment, where information is gathered about student achievement at the end of a unit of study. Formative assessment is typically smaller in scale and done more frequently. In other words, summative assessment is assessment of learning, whereas formative assessment is assessment for learning.
What Is Formative Assessment?
The Council of Chief State School Officers (CCSSO) provides a definition that many educational bodies have since adopted:
Formative assessment is a planned, ongoing process used by all students and teachers during learning and teaching to elicit and use evidence of student learning to improve student understanding of intended disciplinary learning outcomes and support students to become self-directed learners.
Observe how formative assessment is a process, not any particular kind of assessment. Formative assessment does not comprise a list of assessment types like “quiz” and “warm-up”; rather, there are a number of formative assessment strategies that can be implemented during classroom instruction that range from informal observations to purposefully planned techniques designed to elicit evidence of student learning.
Formative Assessment Examples in Math
This article discusses different examples and strategies of formative assessment in mathematics. Since effective formative assessment informs both your teaching and your students’ learning, the examples below will look different across students and classrooms. These examples of formative assessment can all be integrated into your class in whatever way best suits you and your students’ needs.
Math Exit Tickets
Exit tickets are brief questions or problems that teachers give to students at the end of a lesson. They’re frequently used as a student’s “ticket” to exit the class. They can be incredibly effective because with just one or a few questions, teachers get so much control over what’s in the ticket and what to do with the information.
In particular, exit tickets offer fast insight into gaps in knowledge. For instance, a straightforward question asking students to solve an equation can be more than a ticket out of class; it can showcase a range of errors like incorrect order of operations or arithmetic mistakes and be used to determine the focus during next class. Seeing student responses can also help determine student groups, since the tickets should help clarify who understood the day’s lesson and who may need some more attention tomorrow. Take a look at some exit tickets below from our Into Math program. Feel free to use them directly or adapt them to your class!
Download Math Exit Ticket (Grades 1–2, addition)
Download Math Exit Ticket (Grades 3–4, finding quotients)
Download Math Exit Ticket (Grades 3–4, distributive property)
Download Math Exit Ticket (Grades 5–6, evaluate an expression)
Ideally, formative assessment checks in on student progress quickly and adaptively. One technique to try is to have students use a thumbs-up/down technique. It commonly looks like this. The teacher presents a problem or makes a statement, and then students react using their thumbs. Thumbs up means “I’ve got this.” Thumbs down means “I’m confused.” This can be a fast method to divide students into groups or to determine whether you are free to continue with the lesson or need to stop and slow down. It is also a way to add physical movement to the classroom, a potential aid to learning. In Judy Willis’ 2007 book Brain-Friendly Strategies for the Inclusion Classroom, she clarifies that the simple act of having students physically gesture with their hands “has the added benefit of linking the material to be learned with sensory input, thereby increasing access to the brain’s memory banks.”
There are many ways to extend this idea. The thumbs expressions can have different meanings, for example one problem’s thumbs-down reaction could mean “the solution is incorrect.” Many teachers include a thumb to the middle (that is, pointing to the side) for students who feel between thumbs-up and thumbs-down. Students could also use other hand gestures, for example holding up three fingers to mean, “I have something to say.” Ultimately you get to decide what the hand gestures mean and when you want to use them.
Discussions in and of themselves are not necessarily assessments. But they can be! Discussions can reveal misconceptions and help guide teachers in what to teach next. Facilitating classroom discourse with and among students can be a form of formative assessment. Teachers must constantly make moment-by-moment classroom decisions like “should I ask a follow-up question?” or “what’s another way of showing this concept?” In-class discussions are a way for teachers to come up with quick answers, check in on student knowledge, and figure out how to proceed.
Just because in-class discussions aren’t formal, that doesn’t mean they can’t be prepared for. Teachers can build formative assessment opportunities into classroom conversations by being strategic about what questions to use. Being cognizant of your students’ most common errors and referencing program teacher guides can be invaluable.
The structure and frequency of homework will no doubt vary depending on the student, teacher, and school. However, when a class environment permits it, homework does not need to be graded for performance and can instead be leveraged as a tool for students to think through problems on their own pace and for you to check in on their strengths and challenges. Homework becomes in effect a guide for your teaching. Education professor Cathy Vatterott offers her perspective in Rethinking Homework: Best Practices That Support Diverse Needs: ”The current consensus is that homework should be formative assessment that helps prepare students for summative assessment. Therefore, in a truly standards-based system, homework is not graded [but] is reviewed and feedback is given.”
In this vein, homework is not usually rote practice of what was learned that class. Instead it becomes a way for students to independently explore new ideas. In fact, homework doesn’t always need to be directly related to the skill or concept being taught! Homework can be an opportunity for students to learn deeply about topics they’re already interested in that already have rich mathematical connections, for example sports, homebuilding, fashion design, or entrepreneurship.
Trying to figure out what your students should do next? Ask them! Polls can be administered during or after any classroom activity. They also work well whether the teaching is in person or online. They can range from a variation of an exit ticket (“What do you think the solution is?”) to metacognitive reflections (“How do you feel about this math topic?”).
Polls are an especially flexible tool. Teachers can exploit polls to cater to many specific instructional purposes in mind. As examples, polls can do the following:
- Give the teacher a status check by polling student confidence
- Stimulate discussion with questions having multiple reasonable answers
- Quickly assess prior knowledge
- Elicit a misconception
These are powerful tools that grab students’ attention and, depending on how the polls are used, can foster the activation of other formative assessment strategies.
A KWL chart is a tool that students can use to organize their knowledge. It can broadly be used across any subject, as it helps students to synthesize what they know (K), what they want to know (W), and what they have learned (L) about a topic. In math class, a KWL chart can be a valuable opportunity for students to take a step back and reflect on their learning avoid thinking that mathematics is just a “series of steps” but rather a world of connected ideas.
The KWL chart is useful as formative assessment in the classroom. It allows the teacher to find out students’ prior knowledge on a particular topic and then gear upcoming lessons based upon this information. The KWL chart can be completed when starting a new topic and be added to throughout the unit. Further, when planning across a year, the teacher is able to find out what the students have learned by the end of their lessons.
Digital Games and Apps
Student digital experiences, whether educational video games (like those found in Math Expressions or Math 180), math practice apps (which would include our own Waggle), or anything in between can be a dynamic way to assess students. Sometimes it’s the software itself doing the assessment, where based on the results of one level or activity, the app determines what the student should do next. Digital and online experiences have the added benefit where most students will find it a safe and positive learning environment, and some who struggle with a traditional classroom environment challenging will thrive.
Plus, many digital games and apps provide data for teachers about anything from curriculum-based performance to student mindset. That data can turn the digital experiences into formative assessment too, helping teachers determine what to do next. Consider the challenges of forming effective small groups and what to do with them. Are students ready for new concepts? Or is reteaching in order? Automatically-generated data help teachers differentiate instruction according to their students’ learning.
Trying Out the Strategies
These strategies do not work in isolation. They are designed to help you determine where students are in their mathematical progress and how you should proceed to prepare them for success. Try them with your students, and if one strategy doesn’t work, try another!
For formative assessment in math along with ways to adapt instruction, explore HMH Into Math, where K–8 math students become fearless problem solvers.
Senior Director Community Engagement, HMH; Host of HMH Learning Moments: Teachers in America Podcast