September 06, 2020

How to Give a Math Test During Distance Learning

updated on Sep 23, 2020

If you are teaching math in 2020, then your school hashttps://www.hoffmath.com/2021/06/precalculus.html probably adopted an all-virtual or a hybrid model (some virtual students, some face-to-face). You have naturally wondered, "How am I supposed to give a test when the students are at home?"

You are not alone.

I am going to share my experience and also discuss what I have heard from other math teachers.

If you want a FREE Google Sheets version of my Compare and Contrast chart, scroll down to the bottom of this page.

Ways the students could cheat.

Preventing students from cheating seems to be math teachers' number one priority when giving an assessment to students at home. If we first consider how students could cheat, we can think of ways to prevent it. Here's what I have come up with so far.

Students could use Photomath to scan the problem from their phones.
Students could share the questions with their friends taking the same assessment later in the day or the next day.
Students could type the question into an online calculator (such as symbolab.com).
Students could have a friend, family member (!), or tutor either take the assessment for them or have the friend coach the student through the assessment.

Avoid cheating by asking different types of questions.

When considering how to give an assessment to students at home, I always come back to the challenge of "assessing differently." Maybe this is an opportunity to completely change how we assess our students. Maybe we abolish pencil and paper assessments; let's just do projects instead. But completely changing how we assess comes with another set of challenges for which I am not prepared.

So much about teaching right now is difficult. Many teachers are teaching virtually from home while their own children are trying to learn from home. I'm teaching on a hybrid schedule, which is like teaching 2 classes at once. It is exhausting. Using two devices, learning new websites and technology, dealing with additional duties and cleaning procedures, handling the emotional toll of the pandemic for myself and my family... I need as much to be the same as possible. I cannot handle more change at this time. Therefore, I choose to make my assessments as similar to traditional assessments as I can handle.

But I *can* try to ask questions differently to to prevent students from using Photomath or other online calculators.

Here are a few different types of questions that you could ask:

Open-ended questions

Instead of asking, "Do these sets of ordered pairs represent a function?" you could ask, "Given the sets A={4, 5, 6} and B={-3, -2, -1}, create a set of ordered pairs that represent a function from A to B."

Instead of asking, "Is f even, odd, or neither?" you could say, "Describe 2 methods that you could use to determine whether the function f is even, odd or neither."

Use more word problems.

Photomath can't interpret a word problem so consider giving less "remembering" questions (from Bloom's taxonomy) and more "applying" level questions. Or you could even write out the problem such as, "if the square a number plus twice the number is less than or equal to 25, find all possible values of that number."

You could make each question different for each student.

For example, "Consider the function f(x)=mx^2 - dx where m represents the month you were born, and d represents the day you were born. Evaluate (f(x+h) - f(x))/h."

Doing this means you then have potentially 100 individualized questions to grade!

Let's continue the conversation. Join me in my Facebook group.

Sandwich-style questions.

A "sandwich style" question is one in which you give the students both the question and the answer and ask the students to "fill in the fixin's" (a.k.a. show the work to get from the question to the answer). You could have the answer next to the question or have an answer bank.

In my calculus class, I sometimes ask "show that" questions; see the example below. (In normal testing circumstances, I find these useful for questions that have multiple parts. So part a could be "show that this is the derivative," and part b could be, "find the x-values of the relative extrema." Students can still get full credit on part b, even if they mess up part a.)

I have suggested to my students in the past that I would make an entire test "sandwich style" but tell them one of the answers is wrong. I never implemented that because the anxious students I have (and I always have a handful of highly anxious students) said they would re-work each question multiple times, trying to figure out which answer was wrong.

Error analysis.

Give a question completely worked out, but there's an error. Students have to describe the error and correct the problem.

Write the next step.

Give the first few steps of a problem; students must write the following steps and finish the problem.

Put the steps in order.

The question and all the steps are given; students have to put the steps in the correct order.

Give the students a choice.

Give students a tiered question and ask them to choose one of the tiers. The points they could earn depend on the tier they choose. For example,

Tier 1 "For a maximum of 3 out of 4 points factor x^2 + 2x - 35."

Tier 2 "For a maximum of 4 out of 4 points, factor 2x^2 + 7x - 15."

Tier 3 "For a maximum of 5 out of 4 points, factor "15x^2 + 16x - 7."

I have done this in the past - it was only one question on the assessment. I told the students that if they did more than one tier, I would grade them both and give them credit for the worse one. It was interesting to see which students challenged themselves with the tier 3 question and which students went with the easiest tier.

Ask the students to explain their steps.

In addition to working on the problem, ask the students to explain the steps.

How to deliver the test

Once you decide on the questions or style of questions you want, you need to determine what "vehicle" you will use to deliver the questions to the students. I do not recommend simply sending your students the Word doc or pdf version of the assessment via email. You are just inviting your students to send it to their friends who will take it later.

5 Websites For Giving a Math Test During Distance Learning

Here are 5 websites that I have used to deliver an assessment.

DeltaMath Plus (the paid version)
Edia.app
Edulastic
Formative (a.k.a. GoFormative)
Google Forms
Exam.net

For each of these websites, I ask my students to show most (if not all) of their work on their own paper. The students at home must scan their work and upload it to our LMS (we do not use Google Classroom (GC) at our school, but GC allows you to do this). For Exam.net, students can upload their work directly to the website. The students in the classroom turn in their papers in a basket in my room, and then I don't touch the papers for a couple of days.

Having students do their work on paper is especially necessary with graphing questions or questions that require a lot of steps. In both Edulastic and Formative, you could eliminate some of that with the type of question you choose. For example, Formative has a "show your work" type of question. Students would write directly on their screen to show their work; this is ideal if they have devices they can write on (such as an iPad or tablet).

DeltaMath Plus

I have been a fan of DeltaMath since 2017. When @MrDeltaMath released the DeltaMath Plus version in Spring 2020, I did not hesitate to get it. I then convinced most of my department to get it, too.

The Create Test feature is only available to DeltaMath Plus subscribers.

Read more about the history of DeltaMath.

What I like about DeltaMath

Since I assign a lot of homework/practice from DeltaMath, the students are already familiar with the platform and have a username and password.

My favorite feature is that if you assign a module and don't care which question from the module gets assigned, then each student gets a different question.

This might seem like it would be tedious to grade since they all get a different question, but actually, I only look at the students who missed a question. Often I can determine how much partial credit I want to award based on their answer compared to the correct answer. For more challenging problems, I do have to look at their work.

You can assign a specific question to all students from a module (if you have the Plus subscription).

When assigning a test in DeltaMath, you can set a 'time limit' and then assign it to your entire class at once. Each individual student's countdown timer will begin when they click on Begin Assignment Now.

What the students see when they log into DeltaMath for an assignment with a time limit.

From your end, you will see that students have opened the test and whether or not they have looked at any of the questions.

Not only can you limit the amount of time the students have for the assessment, but you can also manually add extra time for students with accommodations.

Ending the test

If you have set a time limit on a test and a student finishes before their time runs out, then they can click on Back to go back to their list of Upcoming Assignments, and they will have the option to end the test early.

What I don't like about DeltaMath

While I am a massive fan of DeltaMath, even for regular homework or practice assignments, I don't always use it because sometimes I need questions that are more challenging or have more rigor - particularly for my Honors Precalculus class.

There is now a Teacher Created Question feature. There is a learning curve to figuring out the right way to create your own question and have it grade automatically. There is a helpful video you can watch in the Help section.

When you create your own question, all students will get that question (instead of a random question from a module), which makes students cheating more of a risk.

Read more about how I use DeltaMath in my classes here.

Edia.app

(This section was added in July 2022)

What I like about Edia.app

Like DeltaMath, each student gets a different question when you assign a skill.

My favorite feature is some anti-cheating features, such as the Anti-PhotoMath background, and that students cannot paste answers into the answer box. If they use an online calculator to solve the problem, they will, at the minimum, have to type their answer in the answer box.

Edia does contain some higher-order thinking questions that DeltaMath does not have.

In the free version, I cannot see how much time a student spent on a quiz. I can see the time the student started and stopped.

You can add custom questions to a quiz only with the Teacher+ subscription ($119/year). You also need the paid version of DeltaMath to add custom questions. In fact, you need the paid version of DeltaMath to make an assessment. With Edia, you can create a quiz with the free version.

I have not yet assigned an assessment to actual students, so I cannot speak to the usefulness of any grade reports. (I created a student account with a separate email address so I could some of the features.)

You have the option to give every student identical questions or different questions.

You can allow 0, 1, 2, 3, 4, 5, or unlimited attempts (retries) on the questions.

When they log into Edia, they can see how many questions are on the quiz and how much time they have to finish. While taking the quiz, students can see a countdown at the top of the page.

In the paid version, you can change questions from free response to multiple choice and vice versa.

In the paid version, you get an email when a quiz deadline has passed with a summary of the scores.

What I don't like about Edia

A couple of times while creating an assignment, I forgot to click on add question, chose a new skill, then lost the previous question I had wanted to keep. I anticipate that I will make that mistake less with more experience on the site.

You cannot change the point values of a quiz in the free version, but you can in the paid version.

Edia does not have any calculus questions (besides the Intro to Limits unit in Precalculus), but I understand they’re in the process of adding calculus (as of July 2022).

After submitting a quiz, a student can immediately see the answers and explanations. I don’t love this for fear of students taking screenshots of those explanations and sharing them with a friend who has not yet taken the quiz. There is no option to turn that feature off or prevent students from seeing their answers and explanations until after a specific date/time.

For quizzes, there’s no option to extend the time for a sub-group of students or to add more time for individual students.

There does not seem to be a way to assign a specific question to all students from a skill in either a quiz or a regular assignment.

Edulastic

So far, I really like Edulastic and plan to give future assessments using it. I like the different types of questions that I can give in the free version. I like that the students have options for typing correct math symbols - such as the U symbol for union.

Click here to read more about the paid and free versions of Edulastic.

There is a learning curve with Edulastic. While you're learning it, seek out help. Find another teacher who has used it. Be patient with yourself. Look for instructional videos on youtube. Join the Edulastic Community Facebook group.

The first time I tried Edulastic, it was a disaster because 80% of the students were denied access to the assessment. Eventually, I learned from tech support that students needed to clear their cache and cookies in their web browser, then log out and log back in. I haven't had any problems since then.

Avoid these mistakes in Edulastic.

While you are writing your Edulastic assessment, be sure that you are putting in the correct answer and the correct point value of the question - it can be tedious to make those changes after students have already taken the assessment.

Also, be sure that if you're choosing a multiple-choice question, you pay attention to the difference between multiple-choice with one answer and multiple-choice with multiple answers.

What I like about Edulastic

It appears that the person who created Edulastic was a math teacher or designed it for math teachers. I like that there's a tolerance for students typing their answers differently.

For example, if the answer is 3000, students can type "3000" or "3,000," and either way gets marked correct.

You can also set a tolerance for error, such as accepting 3.49 when the answer is 3.50. There is an extensive database of questions that other teachers have written, but it can be overwhelming to search through it.

What I don't like about Edulastic

Unless I make different versions, all students will get the same questions. Whereas in DeltaMath, each student gets a different question.

Go Formative

I haven't done as much in Formative, but I have been pleased with it so far. In some ways, it's a toss-up between Edulastic and Formative. I find that there are some features in the free version of Edulastic that I like better - in particular, the ability to see the amount of time a student spends on an assessment.

One of the best features of the Premium version of Formative is the anti-cheating tool, which detects if a student has copied and pasted answers.

Click here to learn more about the Go Formative premium features.

What I like about Formative:

Many types of questions can be given - even in the free version.

There is a database of questions to choose from.

You can type mathematical equations, and it’s a bit more user-friendly than Edulastic.

What I don’t like about Formative:

There's not much not to like about it. I love the idea of doing a Show Your Work question, but my students don't have devices they can write on. If they did, then Formative would be my go-to for online assessments.

Formative has the same issue as Edulastic: unless I make different versions, all students will get the same questions.

Google Forms

I used Google Forms for assessment years ago before they had the Quiz feature (back when you had to use the Flubaroo add-in). More recently, I have been using it for digital homework assignments.

One of my colleagues has been giving her assessments in Google Forms. One thing she has been looking into is setting a time limit on the form and being able to give extra time to students with accommodations.

She has explored an add-on called FormLimiter and another add-on called Quilgo. At the time of writing, she is more interested in Quilgo.

What I like about Google Forms

The best part about Google Forms is that they're free.

What I don't like about Google Forms

Doing an assessment in Google Forms feels a bit like a hack; it is designed to suit a vast variety of Form needs, and giving a math assessment is just one way to use them. DeltaMath, Edulastic, and Formative were designed for teachers; as a result, they all have many more features and are more powerful.

Because you don't "log in" to a Google Form, when you are looking at the results, you can only see the students who *did* complete the assignment; you cannot see the students who did not - so you have to compare the results to your roster.

Exam.net

I gave exam.net a try on September 23 (seventeen days after I initially wrote this post). I got some tips and advice from @di_afrikan_techa on Instagram and decided to try it.

Creating a new test

On the website, I created a new exam. I chose to use a PDF file.
In the Student Workspace settings, I gave the students a writing area so that I could turn on the option to "scan handwritten work with a mobile phone."
For security, I chose the Allow any browser option. I would like to try the high-security option in the future, but it would require software to be installed on the student's laptops.
For "settings for the lower security mode," I chose "require explanation and manual unlock (by the teacher).
The other settings you can change to suit your needs.
After you create the exam, it will be assigned an exam key.

What the students did:

I sent the students to exam.net and gave them the exam key. Students do NOT have to create an account. They simply entered the exam key and other identifying information (name, teacher name, student ID, etc.).
When students began the test, the website locked them into the browser. They can get out of the browser, but then they will be locked out of the test - I can get them back in quickly.
While the students were taking the test, I was on the Surveillance/Results screen to see any chat messages or issues that popped up - like students getting locked out.
Students did all of the work on their own paper.
When they were finished, they clicked on Scan work, got a QR code that they scanned with their smartphones, and followed the instructions for how to scan. Students have to upload one page at a time. It's pretty easy.
Once all students submit the test, I can download their tests in one large pdf file or as one pdf file per student.

What I like about Exam.net

I like that it locks the students' browser and then locks them out of the test if they get out of the browser. This prevents the students from saving screenshots or attempting to type the question into another website, such as symbolab.

I like that students don't have to create an account. I simply sent them an email with the exam key. I could send them the exam key hours before the test starts and just keep the test closed until I'm ready for them to take it.

It's easy to give students more time, and it's easy to force submit the test for all or a select group of students.

It was straightforward to create a new test by simply uploading a pdf.

One more tip: since I used the pdf option, there was no place for me to add special instructions (e.g., do all their work on their own paper) so I created a title page for the test and put all special instructions there; it was the first page of the pdf.

What I don't like about Exam.net

I wish the countdown timer could be created ahead of time and then lock them out automatically when time runs out. As it is, you must wait until the students begin the best before you start a countdown timer. They are not automatically kicked out when the time is up, but you can force all students or a select group of students to submit - when you do that, the test closes immediately for those students.

Since the students are locked into the browser, they will not be allowed to click over to Google Meet or Zoom to ask you a question. However, there is a chat feature on exam.net. Another solution is to have the students join Google Meet or Zoom on their phones while taking the test on their computers. I always ask my students to keep their microphones off and their speakers on. So, I watched my students on Google Meet while they were taking it, but they couldn't see me. A couple of times, I had to unmute myself to make an announcement to the group. I asked for a thumbs up if they understood.

In summary, I liked exam.net as it was the most straightforward website out of all that I have tried. I will definitely use it again.

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Compare and Contrast

I put together a table to compare and contrast the websites I have used.