iPads for Masterful Math: Randomizing Formative Math Assessment

Dr. Sean Nank’s research shows that the single biggest method for improving learning with iPads is to use online formative assessments. However, his formative assessments have a twist — students are all answering DIFFERENT math questions. This intriguing research is a must listen for any school with access to technology. You do not need iPads to implement and learn from this research.

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Masterful Math: Randomizing Formative Math Assessment

Link to show: www.coolcatteacher.com/e228

Date: January 10, 2018

Vicki: Today we’re talking to Dr. Sean Nank, @Sean_Nank.

He is a Presidential Award winner for Math and Science Teaching.

But he’s really quite unique, in that he teaches for two universities, and he also teaches high school math.

Now, Sean, you’re currently working with iPads and some online formative assessments for STEM classrooms.

What kind of research are you doing right now?

Sean: About seven years ago, three colleagues and myself wrote a grant proposal for a quarter of a million dollars to implement iPads into math and science classrooms.

Honestly, when we started it, we didn’t know what to expect. We didn’t know what was going to work, what wasn’t going to work. So we started doing research.

In the past seven years, I’ve found that the single biggest factor for student success with the iPads is being able to use online formative assessments. More so than any apps or anything else.

Vicki: So, what kind of formative assessments are you doing on the iPads?

Formative assessment on the iPad that Works

Sean: We decided to code certain assessments ourselves.

Quite honestly, the first time I coded the first test, it took a little bit of time, and I thought to myself, “I’m never spending this time making an assessment again.”

But then, seeing the students’ results after the first test, I thought, “There’s no way I can’t do this.”

So what we do is use randomization. We use Moodle as a Learning Management System. We created Assessment Items.

So what happens is that the students can take tests as many times as it takes for them to achieve and show mastery.

And I was quite surprised at the results. I had a ton of students coming in every single day after taking a test, if they weren’t successful, getting help from me, getting tutoring, and trying to take the test again and again.

Vicki: So… formative, typically, you don’t give a grade. It’s while while you are forming knowledge, right?

Formative Assessment and Grading

Sean: Right. Some people think that formative assessments cannot happen if you give any type of grade at all.

I think that formative assessments can happen with grades, as long as you give students the protocol and the opportunity to learn from that assessment, and to continue on and maybe get a better grade as a result.

So for me, it’s less a matter of giving them a grade, and more a matter of giving them feedback, giving them help, giving them opportunities to improve.

The Frequency of Formative Testing

Vicki: So they’re actually taking these daily…

Sean: Right.

We coded for warm-up activities, for exit activities — which was wonderful because we just go to our computer, refresh your menu, and you can see real time exactly how students are performing.

So those, they take every day. When we take any type of quiz or test, then all they need to do is…

The trick was that we didn’t have any type of protocol to start out with. We just let students retake assessments. That didn’t work, because they would keep re-taking it, and keep getting the same grade.

So, we started doing things like telling them that they needed to have all of their work completed, they needed to come in for…

Different teachers make different decisions, but usually it’s at least one or two sessions of tutoring so that they can learn from their mistakes, so that they can re-take it again.

Student and Teacher Feedback from Formative Assessment

Vicki: So, are they getting instant feedback on each question as they answer it, or are you the one giving the feedback after you look at their results?

Sean: You can do both!

And that was one of the amazingly wonderful, unforeseen circumstances.

So you’re giving a warm-up in class. And instead of just going through the three or four questions for the warm-up, and asking students if they have trouble, I can look at the data. I can say, “Number 1 and 3 you did great on. Number 2? Ahhh, 72% of you didn’t do well. So we’re going to go over this before we can continue with the lesson.”

But also, you can code in responses. So if somebody’s solving something like 2x + 4 = 8.

Then you know what the three major misconceptions are probably going to be, if they’re having trouble with this. So when they input that answer, you can not only code “Partial Credit” but you can also code “Hints”… so it will blast out hints to them.

So maybe they added 4 instead of subtracting 4.

So you could have the hints like, “Did you subtract the 4?” or something more vague, like “Watch the signs.”

So you can code in the major misconceptions so that they can get instant feedback, and they can know the right answer. Or you could block that. Like you could give them hints as well.

Vicki: Sean, it sounds like your view of excellent math teaching has evolved with using formative assessment.

How Sean’s Views of Excellent Math Teaching Has Changed

Sean: It has, quite a bit.

There’s actually a few things that have made it evolve.

One is that over the years, I’ve passed probably 40 more students per year than I should have, if I was the average math classroom.

And it’s not me. It’s not that I’m a wonderfully excellent teacher that’s reaching all the students.

It’s that I’m giving them a chance. And if you give them a chance, then it’s not that they take the first chapter assessment, they get an F, and they have to ride through with tha F for the rest of the semester. Students start giving up.

They never have to give up, up until the semester ends. They can always try again.

Another thing that’s changed my perception a lot is teaching at American College of Education and Cal State San Marcos.

I see a lot of credential students and Masters students and Doctorate students. With the papers they write, quite honestly, we borrow a lot in education.

A lot of the things that I’m doing in my classroom come straight from them, from their Master’s theses, from papers they’ve done in my class, because people have a lot of wonderful ideas out there.

Vicki: So if you could condense this down. Math teachers across the world are listening to this show.

It sounds like you’re saying that having formative assessment with instant feedback to you as the teacher, right at the beginning and ending of class… and then the opportunity to retake questions, the opportunity to have hints…

Does that summarize it, or are there other things that you want them to take away from what you’ve learned?

How Formative Assessment Changes the Conversation

Sean: Most of it is how it changes the conversation, because when you give them feedback and they have a chance to do it again…

Let’s say two students are sitting right next to each other. They’re doing a warm-up activity. Instead of one student being able to turn to the other and say, “What did you get for #2? The answer is 17,” and then people just move on. They have to turn to their partner and say, “How did you get that answer?” They could have a similar problem, but the numbers will change from the bank and from the randomization of the testing items.

So it absolutely changes the conceptual and procedural conversation that happens between you and students, and between students as well.

Testing for Concepts but Using Different Numbers and Problems for Each Student

Vicki: Oh, wow! So I think I missed that.

So what’s actually happening is, they're having a warm-up activity, but each student is being asked a similar conceptual question but the numbers are different.

Sean: Right. So like for the problem 2x + 4 = 8, you can set up the parameters to where the student next to them has 3x – 9 = 16.

Vicki: Ahhhh.

Sean: So it’s not much of a difference, but it’s enough to where they can’t just copy off of each other. Some of it’s procedural, but you can also design conceptual questions, so they can talk about the question behind it. They can talk about the misconception.

So that’s one of the biggest things. Whenever I design any of these, I always have the three most major and common misconceptions in mind. Conception and procedural misconceptions. Then that helps to catch them before you send them home for the day.

Vicki: Wow. So where can people access what you’ve done? This sounds like a whole lot of work. I totally understand why having them do similar problems, but not exactly the same problem. That actually blows my mind. It makes sense that that would work. But how can the everyday math teacher apply this and use this in their classroom?

Sean: I would try as much as possible to find resources that are already out there. As teachers, we have a ton of work. There’s not enough hours in the day.

So I’ll go to different sources. One of the sources I use a lot is learnzillion.com — or any other type of resource that already has test banks. That will give you a good idea for which lessons and what types of assessments can go well with them.

There are some outlets that are starting to give you access to already-randomized assessment items. But honestly, my biggest concern — and the biggest consideration — is that it’s all contingent on what your district's doing.

So you can have these types of assessment items on a Moodle platform. You could have it on Canvas. You could have it on Haiku. That’s what you would need to find out first, is what system is your district using?

Otherwise, you would have to spend your own money, which I don’t want any teacher to do. And you would have to get a website, and you would have to house it on your own website.

Vicki: (sighs)

So I think the important thing concept here is that we’ve got a lot to re-listen to, and to learn from Sean. This whole idea of randomized formative math assessment, and assessing on concepts,and encouraging students to have that conversation.

I know, Sean, that for me the lightbulb has really gone on. I’m even wondering how I would apply this into the subjects that I teach, because it really makes a whole lot of sense to test for the concept — and to make it so that it becomes more about the process of solving the problem, and less about the right number to answer. Right?

Sean: Right.

And I think, overarchingly, I’m glad you said that… because I hope people don’t think that this has to be just for math, or just for science. You can use this in any subject matter. I think one of the biggest things is realizing that we talk a lot about growth mindset now. But all of that tends to stop — and I was just as guilty as anybody else — when we give assessments.

“Let’s grow as students. Let’s have the conversation. Here’s your test. This is it. You either pass or you fail, and we’re finished with it . And you have to live with that consequence for the rest of the semester.”

So I think what it really boils down to is giving students multiple opportunities, and doing something I call Grading for Learning which is letting them retake assessments until they achieve mastery.

Something I talk about in my first book is something that concerns me — especially with standardized assessments — is that we try to boil schools, students, teachers down to one test result. Just one score, and that determines how good or bad they are.

There’s nothing wrong with standardized assessments. It’s just the meaning that we’re making, and the way we’re using them — concerns me.

If I had it my way, one of the major thing I would change is to always look at the student as a whole, and always look at multiple measures of how the student is doing.

So assessments are important, but they’re no means the only thing.

Vicki: So we’ve been listening to Dr. Sean Nank.

We’re also going to be doing a giveaway, of Teaching Over Testing.

He has a lot of other resources, so check the Shownotes.

This is a fascinating conversation about excellent math teaching.

This whole idea of randomized formative assessment is definitely one that I’ll be investigating more.

I think it’s one that all math teachers should be discussing, as well as teachers of other subjects.

So thank you, Sean!

Sean: Thank you!


Transcribed by Kymberli Mulford


Bio as submitted

Dr. Sean Nank earned a Ph.D. at the University of California Riverside. He received the Presidential Awards for Excellence in Mathematics and Science Teaching (PAEMST) in 2009 for mathematics from California. He has published two books titled Testing over Teaching: Mathematics Education in the 21st Century and The Making of a Presidential Mathematics and Science Educator, has published numerous articles, was a lead in writing the world’s first cloud based open source CCSS-M aligned K-8 texts (www.learnzillion.com), and is currently working on his third book.

He has worked in leadership positions with the United States Department of Education, White House Office of Science and Technology Policy, National Science Foundation, California Department of Education, California Commission on Teacher Credentialing, and Smarter Balanced Assessment Consortium. He was appointed to represent the USA at the International Congress on Mathematical Education in Korea as the mathematics assessment expert, which culminated in a congressional address as to the current state of mathematics education in the USA. Sean Nank is the President and Program Chair of the Greater San Diego Mathematics Council.

He has been a coach, Domain Specialist, and is currently a Facilitator and Ambassador for LearnZillion. He also continues to consult for various districts across the country at the elementary, middle, and secondary level training teachers and administrators. Topics include transitioning to CCSS-M while aligning classroom and district curriculum, pedagogy and assessments in a coherent manner using technological resources.

His current research agenda includes how teachers negotiate the balance between the procedural, conceptual, and application via technological resources. Sean has been on numerous conference planning committees. He is currently the chair for a national educational summit in Washington, DC which will include Presidential awardees and members of various state and national educational agencies.

He has authored several articles:

Nank, S. D. (2017). Seven steps for adapting technology to the classroom. Southeast Education Network (SEEN) (19, 1).
Retrieved from: http://www.seenmagazine.us/Articles/Article-Detail/ArticleId/6500/Seven-Steps-for-Adapting-Technology-to-the-Classroom

Nank, S. D. (2011). Editor of The making of a presidential mathematics and science educator. Volume 1. Chicago, IL:
Discovery Association Publishing House.

Nank, S. D. (2011). The present moment. In S. Nank (Ed.), The making of a presidential mathematics and science
educator. Volume 1 (pp. 77-84). Chicago, IL: Discovery Association Publishing House.

Nank, S. D. (2011). Testing over teaching: Mathematics education in the 21st century. Chicago, IL: Discovery Association
Publishing House.

Blog: www.SeanNank.com

Twitter: @Sean_Nank

Disclosure of Material Connection: This is a “sponsored podcast episode.” The company who sponsored it compensated me via cash payment, gift, or something else of value to include a reference to their product. Regardless, I only recommend products or services I believe will be good for my readers and are from companies I can recommend. I am disclosing this in accordance with the Federal Trade Commission’s 16 CFR, Part 255: “Guides Concerning the Use of Endorsements and Testimonials in Advertising.” This company has no impact on the editorial content of the show.

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Vicki Davis

Vicki Davis is a full-time classroom teacher and IT Director in Georgia, USA. She is Mom of three, wife of one, and loves talking about the wise, transformational use of technology for teaching and doing good in the world. She hosts the 10 Minute Teacher Podcast which interviews teachers around the world about remarkable classroom practices to inspire and help teachers. Vicki focuses on what unites us -- a quest for truly remarkable life-changing teaching and learning. The goal of her work is to provide actionable, encouraging, relevant ideas for teachers that are grounded in the truth and shared with love. Vicki has been teaching since 2002 and blogging since 2005. Vicki has spoken around the world to inspire and help teachers reach their students. She is passionate about helping every child find purpose, passion, and meaning in life with a lifelong commitment to the joy and responsibility of learning. If you talk to Vicki for very long, she will encourage you to "Relate to Educate" or "innovate like a turtle" or to be "a remarkable teacher." She loves to talk to teachers who love their students and are trying to do their best. Twitter is her favorite place to share and she loves to make homemade sourdough bread and cinnamon rolls and enjoys running half marathons with her sisters. You can usually find her laughing with her students or digging into a book.

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