# Checks for Understanding in Math

## 8 Quick Checks for Understanding

One of the most efficient and successful ways to improve and increase student learning is to utilise formative assessments, which are designed to check for understanding as well as offer students with feedback and help. However, because teachers are required to cover a large amount of material and develop a large number of skills, they may not take the time to check whether or not students understand a concept or are able to effectively apply a skill, and if they are not, they may not figure out ways to improve their students’ learning.

Teachers are fortunate in that there are a variety of tried-and-true methods of formative assessment at their disposal that can serve as a “pulse check” to judge their students’ level of comprehension. The following eight strategies are adaptable for use in a variety of learning contexts, including those that are fully online, partially online, or a hybrid of the two.

Since the goal of formative assessment techniques is to gather feedback that may be used to improve teaching and learning, rather than to evaluate learning, the outcomes of these checks shouldn’t be graded. This is because the objective of formative assessment techniques is to obtain feedback. It is essential for students to have a clear understanding of the goals behind the use of these strategies, that making mistakes is acceptable (and even to be expected), and that they will not be graded on their responses.

### 1. SIGNAL IT

Ask the students to demonstrate a predetermined hand gesture to show the level of confidence they have in their comprehension of a certain idea, principle, or procedure. Take, for instance:

Two thumbs up: I have full comprehension of ___ and can articulate it using my own words.
I’m sorry to say that I don’t have all the answers to _____, and I’m not even sure I could describe it.
The answer to the question in the negative is that I do not yet understand ____ and I cannot describe it.
It is possible for self-assessment and self-reporting to be unreliable; thus, you should utilise a technique called random calling to occasionally choose students who have their thumbs up (for example, take names out of a bowl), and then ask those students to explain themselves.

Students are able to communicate their levels of comprehension in virtual learning environments by either gesturing on camera or posting specially designated emoticons.

The George Lucas Foundation for Educational Excellence

### 2. CHOOSE IT

Have students select an answer (such as True or False, Agree or Disagree) and share it via a whiteboard, cell phone app, or hand signal after being presented with a few binary-choice statements or questions that contain an understanding or a common misperception (e.g., thumbs up or down). Before commencing new education, using this method that is both efficient and effective is a great way to check whether or not pupils have any preexisting knowledge or potential misunderstandings.

The following is a selection of “choosing” forms, along with some examples:

If both objects are dropped from the same height, a bowling ball will descend on the ground first, regardless of their size.
To what extent do you agree or disagree that this is an example of alliteration?
Students have the ability to record their responses to polls and choice questions in virtual learning environments through the usage of the chat box function.

### 3. PICTURE IT

Visual representations are used extensively to improve learning, and they can also serve as a kind of formative assessment. Examples of such representations include graphic organisers and idea maps. Students should be prepared to explain their graphics once they have been instructed to produce a visual or symbolic representation of information and abstract concepts (for example, a graphic organiser, web, or concept map). The use of approaches that involve picturing things is very helpful for determining whether or not students comprehend how various aspects of a process are related to one another.

Examples:

Create a graphic diagram illustrating the factors that influence the growth of plants.
Create a concept map that depicts the process of how a bill is transformed into a law.
Construct a story map or a sequence diagram to highlight the most important moments in the narrative.
Students are able to publish their visual work in a virtual learning environment by uploading it to a Google slide or a Pinterest board, or by using Nearpod or Jamboard.

On behalf of the George Lucas Educational Foundation, Catherine Madden

### 4. TROUBLESHOOT IT

The process of troubleshooting is one of the quickest checks for understanding, but it is also one of the most efficient and effective. Introduce pupils to a widespread misunderstanding or an error in procedure that is frequently made. Examine to see whether they can:

Locate the problem or mistake, and then (even better) make the necessary adjustments.
Their comments will provide a fast indication of how much depth they have gained in their comprehension.

Examples:

Introduce students to a first draught of a piece of writing and invite them to act as editors by identifying grammatical and compositional problems in the piece.
Have the students analyse their work on a multistep word problem to search for computational flaws and reasoning errors, and then have them remedy the mistakes they find.
Show students in a photography class examples of common compositional faults, as well as problems with exposure or lighting, and ask them to suggest how the problems could be fixed using digital picture editing software.

### 5. SUMMARIZE IT

Not only is it a great way to assist students improve their comprehension and retention of new content, but it may also give teachers with insight into whether or not students are truly absorbing crucial ideas when they are asked to periodically summarise what they are learning.

The following are some illustrations of this strategy:

Tweet an answer to the following question using no more than 280 characters: What’s the most important thing you’ve picked up about (insert topic here)?
Create a podcast or vodcast that is one minute long to summarise the important topics from one or more of the lessons you have taken using an application on your smartphone or tablet.
You should compose a letter to your instructor (or your parents) every week, in which you briefly explain something new that you’ve learned over the course of the previous week and what it means to you.
There are instructive films on Khan Academy that summarise both nonfiction and fictional works of literature.

### 6. APPLY IT

Students’ ability to apply what they’ve learned to novel scenarios is a clear indicator of their level of comprehension. As a consequence of this, one of the most effective methods for determining whether or not pupils have understood the subject is to determine whether or not they can apply it in an unusual setting. In this method, students are tasked with coming up with fresh and original illustrations of recently acquired knowledge either independently or in collaboration with their peers.

Here are several examples:

To determine whether or not other students understand how to calculate surface area, you can ask them to solve a “real life” word problem.
Find a post or article in the news or on a blog that illustrates a situation in which individual rights and the general good are in conflict with one another.
Find several examples of symmetry around the school, either on the playground or in the hallways.

### 7. TEACH IT

This method of formative evaluation is more involved, but it is also quite beneficial. Have the students teach a new idea or ability to another person, such as a younger child, a student who has recently returned from an absence, or a student who has just joined the class. As you review or witness their lesson, you will be able to evaluate the level of comprehension that they have achieved. Here are two illustrations of this:

To educate a younger kid how supply and demand can affect the price of products, you should develop a lesson that takes no more than five minutes to present. Give one or more concrete instances of things that we haven’t talked about yet.
Your friend has been away for the past two classes, during which you learnt about members of the community who provide assistance. To better grasp the concept of a community helper, have them draw a picture that includes at least five people who provide assistance in our community.
Students have the ability to record a class on a laptop, tablet, or even their cell phone camera when they are participating in online learning environments.

### 8. ANALOGIZE IT

Students are encouraged to generate an analogy or metaphor in order to convey a newly learnt subject or ability as part of a more advanced instructional strategy. You can glean some insight into the person’s level of comprehension by analysing how well they explain using analogies or metaphors. Be wary, though, when attempting to interpret the responses of students to this method. A student might have a solid grasp of a certain idea, but fail to be capable of developing an acceptable parallel for it. You will gain a deeper sense of the kids’ comprehension if you ask them to explain the parallels they have created.

The following is a thought starter for the students: Because of this, a ____ is comparable to a .

Examples:

A wheel is a component of a bicycle, just like a fraction is a component of the total.
Formative evaluation is analogous to tasting a dish as it is being prepared since it offers feedback that can be used by the preparer to make improvements that will result in a better meal.
Visual analogies are another option for the students (combining techniques 3 and 8). Students have the ability to share their analogies and metaphors in virtual learning settings by posting them in a chat box, on a Google slide, or on a Pinterest board.

Note: Several of these techniques, particularly 1, 2, 5, and 8, can naturally be used in conjunction with another common formative assessment technique called an exit card, which is given to students at the end of a class period or at the end of the school day. This is especially true for technique number 1.

Even if these methods have the potential to offer insightful data regarding the efficiency of pedagogical practises and the level of comprehension attained by students, they are not ends in and of themselves. Instead, one ought to consider them the initial stage in something called a “feedback cycle.” The subsequent step is to take action based on that feedback, which may consist of re-teaching something that a large number of students failed to grasp, correcting misconceptions that may have been exposed, or providing scaffolded support to students who have demonstrated a requirement for such assistance. In addition, when students are provided with feedback, they should also be provided with opportunities to use it, such as opportunities to revise their work, opportunities to practise the skill, or opportunities to remedy errors. (Obtaining feedback without the opportunity to put it to good use is analogous to eating without the opportunity to digest!) After then, the cycle of formative assessment is restarted since adjustments may be reassessed, progress can be recorded, and new learning goals can be established.