If you're a secondary math teacher, you have likely been a part of multiple conversations about formative assessments.

### What are formative assessments?

Formative assessments are short assessments (less than 15 minutes) that are given often and on which the teacher checks for accuracy and gives feedback to the students.

Formative assessments are an excellent way for the students to see where any misunderstandings lie and give the teacher important feedback about where re-instruction or reinforcement needs to occur.

One key aspect of formative assessments is that they are graded expeditiously and returned to the students either the same day or the next day. Feedback is most effective when it is given quickly.

### What types of questions to ask

I usually ask knowledge or comprehension questions that cover the most recent lessons to check how well the students understand the topics I taught. Here are some examples:

ðŸ–‰Identify 3 methods that can be used to solve a system of equations.

ðŸ–‰Identify the scenarios for which the Law of Sines should be used.

ðŸ–‰Circle the problems for which using the Quotient Rule is required to find the derivative.

ðŸ–‰Determine if the graph shown represents a function.

ðŸ–‰Factor the following expressions.

ðŸ–‰Sketch the graph of the function with the given equation.

ðŸ–‰Find the derivative.

ðŸ–‰Approximate the area under the curve by using 4 trapezoids.

### How to deliver the formative assessments

#### ✔On paper

The easiest way to

*deliver*any assignment to students is to do it on paper.**are a popular way to do paper formative assessments (you can do digital exit tickets, too - more on that below). Put 4 or 5 questions on a half sheet of paper and give each student a copy during the last 5 to 10 minutes of class. Students turn them in before they exit class.**

__Exit Tickets__(Some people use exit tickets to get general feedback from students, such as, "On a scale of 1 to 5, how well did you understand today's lesson?" or "What questions do you have about today's lesson that you did not get the chance to ask?" I love exit tickets for that purpose, but I would not categorize that as a formative assessment.)

What I do most often in my class is

**or ONAQs (I pronounce it "OH-nacks"). As suggested by the name, they are open-note. I put 4 or 5 questions on one side of a sheet of paper. I allow no more than 15 minutes. The students must work alone and can use their notes, but no computers or smartphones.**__Open Note Accountability Quizzes__If a student is virtual, they must complete the ONAQ with the same time limit as the in-person students.

Sometimes I do an ONAQ at the end of the period, sometimes I will do it at the beginning of a workday period (e.g., review day before a summative assessment), and then I grade them quickly and return them to the students before the end of class - in those cases, I sometimes do different forms for different class periods to prevent cheating.

**whether you're going to put it in the gradebook or not (more on that below). Not only does this force you to look at a sample of work from each student, but also it might be one of the few times the students get detailed feedback from you and understand what your expectations are before a major assessment.**

__It is imperative to check the students' work for accuracy__For example, when I do the ONAQs in my calculus classes, it's often the first time the students realize how serious I am about using the correct notation. (It drives me nuts when students will write f(x) = x^2 and then in the next line write =2x instead of f '(x)=2x.) Students would rather be penalized on an assignment that counts for nothing or counts very little than be penalized on a summative assessment (e.g. unit test).

#### ✔Online

Since distance learning became normalized during the pandemic, teachers have been forced to find digital platforms to use for giving both formative and summative assessments.

Some of the most common platforms are:

•Edia.com (pronounced "ee dee uh")

•Formative (aka. GoFormative)

*To read more about these platforms, check out my blog post about websites for giving a math test during distance learning.*

Personally, I am partial to DeltaMath (the paid version) because of the database of questions. Edia is a newer website that I have been exploring and I like it so far! (check out my blog post about DeltaMath vs. Edia here). I also like Google Forms because it's free, it has been around for a long time, and I am comfortable on the platform.

If you have to give a formative assessment digitally because you have virtual students, I suggest that you don't record a grade in the gradebook. Instead, tell the students that you want to see how much they understand and give them feedback. It is nearly impossible to prevent virtual students from cheating, and we all know that sometimes students make bad decisions when grades are on the line.

*Read my post about Digital Exit Tickets.*

### To grade or not to grade?

Many teachers say that formative assessments shouldn't count against the student (read this edweek.org article for more); I usually attach a grade to mine and put it in the gradebook.

It may seem like a waste of time to give your students an assessment but then not put the grade in the gradebook. I understand. To that, I would respond:

•the best way for your students to learn and grow as a mathematician is to get feedback from you.

•the formative assessment is not only for the students' benefit, but it's also for yours; you will see where the students are struggling, and that can help to direct your teaching and/or also be used in conversations with parents or administrators about specific students who are struggling.

•if you only ask 4 or 5 questions, then it won't take very long to grade.

•you are a teacher; grading papers is part of your job.

I almost always put my students' ONAQ grades in the gradebook. Usually, I have them count a small portion (such as 1/5 or 1/8) of a unit quiz or as twice a homework grade.

Once or twice I gave an ONAQ, and all the students did horribly. When that happened, I either did not put any grade in the gradebook or put it in the gradebook to have a record of it but made it weigh 0%. On the students' papers, instead of a percentage, I might write something like "below standard," "approaching standard," "meets standard," or "exceeds standard." I don't use any kind of scale; I just use my best judgment. Then I make a point of reteaching the material during the next class.

### How to grade

Because the ONAQs have so few questions on them, there are very few total points available.

For example, if there are 4 questions and each question is worth 4 points, that's a total of 16 points. I normally grade with percentages, but if a student misses two points out of 16, then that's 88%, which seems harsh. So instead, I will do a

**square root curve**which is super easy - just take the square root of the raw percentage, so √(14/16) becomes 94%.**What kind of formative assessments do you use in your class?**

Let's continue the conversation in my Facebook group for Algebra 2, Precalculus, and Calculus teachers.

Hi Rebecca,

ReplyDeleteLove what you do with this blog...I started using DeltaMath this year and I'm just as enamored with it as you are. That aside, I have a separate question.

On the order of learning something new every day, I've been teaching 31 years and had never heard of a square root curve. I see the positive that such a class curve helps the lowest scores more than the higher scores who don't need it as much or at all. However, there seems to be the dilemma that it could be giving a false sense of achievement when, say, 12.5/25 (50%) becomes 71% on this curve. Do you consider that a dilemma or, how do you resolve that dilemma yourself?

Thanks for considering my question. And please keep up what you're doing! I don't yet use much of the things you have available, but I feel like your things are "in my back pocket" for when I might need them.

Jim Greenwood

Mt. Everest Academy

San Diego, CA

jgreenwood@sandi.net