Stop Stopping to Test: How to Seamlessly Embed Assessment into Daily Math

For generations, the rhythm of the math classroom has been predictable: teach for two weeks, stop everything, hand out a high-stakes paper quiz, and hope for the best. But treating assessment like a final destination creates a massive lag time. By the time a teacher grades those quizzes, the learning gaps are already two weeks deep, and the class has moved on to a completely new unit.

What if we stopped treating assessment like an event and started treating it like a pulse?

Embedded assessment (also known as formative assessment) is the practice of weaving quick, actionable checks for understanding directly into the fabric of your daily lesson. It transforms assessment from something you do to students into something you do with them, providing real-time data to steer your instruction in the moment.

Here is how you can seamlessly embed assessment into your daily math routine without losing a single minute of instructional time.

If you are still calling on individual students who raise their hands, you are only assessing your most confident learners. To get a snapshot of the entire room, pass out dry-erase boards. Instead of asking, "Does anyone know the slope of this line?" have everyone calculate it on their slate. On your cue, have the entire class hold their boards up simultaneously. In three seconds, you get a visual dashboard of the room. If 80% of the slates show the correct slope, you can safely move on. If half the room made the exact same sign error, you can immediately pivot to clear up the confusion before it hardens into a habit.

Use a hinge question with the class. A hinge question is a carefully crafted diagnostic question placed at a critical juncture in the lesson—the "hinge" where the lesson will either move forward or loop back based on student data.

To make this work, the question must be multiple-choice, take less than two minutes to answer, and feature clever distractors.

Example Hinge Question (Fraction Addition):
What is 1/3 + 1/4?
A) 2/7 (Distractor: Student added numerators and denominators)
B) 7/12 (Correct Answer)
C) 2/12 (Distractor: Student found common denominator but added numerators as 1+1)

By scanning student finger signals (holding up 1, 2, or 3 fingers) or digital clicker responses, you instantly know whichmisconception a student has based entirely on the wrong answer they chose.

You don't need a 10-question quiz to know if a student mastered the day’s objective. A single, well-targeted problem on an index card at the end of class—an Exit Ticket—is more than enough.

Keep the grading barrier incredibly low for yourself. Sort the collected cards into three piles on your desk before you leave:

1. Got it (Ready for enrichment)

2. Almost (Minor calculation errors; ready for a quick warm-up fix)

3. Not yet (Conceptual misunderstanding; needs a small-group intervention tomorrow)

When you embed assessment into every single day, something beautiful happens to your classroom culture: the fear of testing evaporates. Students begin to view mistakes not as a permanent scar on a report card, but as useful data points that guide their next steps.

By making assessment invisible and continuous, you create a responsive, agile math classroom where no student falls through the cracks.

One Way To Encourage Note Taking Via Assessment.

 

In math, we are always trying to encourage students to take notes and them use them.  Many teachers even have students copy down notes so they have them but then need a way to have them look at the notes later.  One teacher found a way to do this. Although she teaches government classes, the technique works as well in Math.

The way this works is that students take the test twice.  First they take the test without using their notes and then they take the test a second time with access to their notes.  The two scores are averaged to provide their final score.

When notes are taken by hand, it improves retention of material and improves understanding. I realize students can have a difficult time staying organized if they take notes on sheets of paper, I usually have students take notes in either a composition or spiral bound notebook.  They write in the notebooks and their notes are there.  The other advantage to this is it allows the instructor to spend time teaching students how to take notes since few learn how to do it.  It is an important skill for college or training.

If you use a system like Schoology or Power School, you can modify it so it allows students the chance to take the test twice and average the scores. When they take the test first without using the notes, they must rely on what they have learned through classwork, notes, and studying.  In order to get a higher grade, they need to do well on the first test due to averaging the test scores. When they retake the test, they retake the exact same test using their notes.  

One thing to remember is that students need to be taught how to take notes.  We need to show them a method to use so they have a way of organizing their thoughts.  I've use Cornel notes in the past because it allows for additional comments and learning. One way to teach students note taking is to give a lecture with examples of good note taking technique. Take time to grade student notes while providing feedback on their notes.  In addition, give open note quizzes so students get practice looking at and using their notes.

As the teacher, you decide when and how often to do this type of assessment.  This could be used on the major tests rather than every assignment, quiz, or assessment.  It is acceptable to tell students they will be able to use notes on tests but not on which tests.  You would never use the double testing method for any pretests.  It works best on material that is much more complex such as algebraic fractions.

You can include short answer questions which ask what the next step is, or why would you do this at this point, or something similar. If students answer these correctly on the first test, let them skip them on the retest because they know them but they do need to retake any calculations problems. No matter what type of questions you use, you need to look at the length of time you have in class.  When you have them take the test twice in a row, that takes time so you may end up with two days being taken up.  In addition, the length of the test needs to be set so students have time to really work the problems.  I had a professor in college who felt that if he could do it in 10 minutes, we could do it in the regular class period.

You need to always grade both tests because some assessment software does not always read the way the answer is inputed.  Once students have taken both tests and you've graded them, you can let them know what their final score is.  On Friday, I'll explore the question of how to get your students more independent so you are not doing all the thinking for them.  Let me know what you think, I'd love to hear. 

Dan Meyer's 3 Act Math Tasks and Assessments

I have been wanting to implement Dan Meyer's 3 Act Math Tasks because I've been very impressed with the ones I looked at but I've never figured out how to implement them.  I need to continue moving due to the amount of material I need to teach while trying to help students develop perseverance. 

Since I've switched from word problems to performance tasks, I do have a place I can slip these math tasks into the same slot I do performance tasks because they are another item to help build persistence.  I could easily spread this activity over two or three days.

I realized today that there is nothing in the rules that states I must give a test with all four parts in one class period. I should explain that I write the every test with four parts.  The first three sections have tests current materials while the final section covers previous material.  A student does not need to retake any part they pass.  This means if they pass parts 1, 2, and 4, they receive a 75 percent.

In addition, I have them select say four out of six problems.  I usually have one easy problem, one hard and the rest are medium level problems.  I find that some students do the bare minimum while others attempt all the problems so if they miss one, they have another chance to pass the section.

I’m playing with the idea of giving the test over four days, one part each day but only assign it after I do the warm-up and the day’s lesson with perhaps one or two guided practice problems.  I know many of my students suffer from big time test anxiety. 

Or I could set up the test in 4 sections on a web based test site or google docs so the students can take it on a digital device.  The test could be set up for answers only while they show the work on a scratch paper.  I think I'm going to administer my next test this way to see if my students do a better job and are less anxious during the test.