Tag Archives: modeling

Interview with MSNBC.com

A few weeks ago I was interviewed for MSNBC.com’s “Future of Technology” series for a story on Khan Academy and online lectures. I appear in these two videos:

Vodpod videos no longer available.

View it on MSNBC.com: Khan Academy sparks education reform debate

Vodpod videos no longer available.

View it on MSNBC.com: Teaching with technology: What works in class

I am grateful to the show’s producers, Matt Rivera and Wilson Rothman, for giving me the opportunity to share my work in the classroom and for staying true to my main criticisms. And extra kudos to Matt for what I fear is now commonplace in journalism: he was a one-man show — he brought and set up all the equipment (camera, lights, and sound) AND conducted the interview. Thanks!

Khan vs. Karplus: Elevator Edition

Exhibit A: Sal Khan on elevators

Exhibit B: My students on elevators
Framed around the Karplus learning cycle (Exploration, Invention, and Application) my students construct the conceptual and mathematical models themselves.

1. Exploration Phase:

2. Invention Phase:

• Draw a motion diagram for the object attached to the scale when the scale is stationary, then being pulled up and then stops.
• Draw a force diagram for the object attached to the scale when the scale is stationary, then being pulled up and then stops. Decide whether the force diagram is consistent with the motion diagram. How is the force diagram related ot the reading of the scale?
• Use the force diagram and the idea under test to make a prediction of the relative readings of the scale.
• Observe the experiment and reconcile the outcome with your prediction.

(Video and questions for this phase taken from Eugenia Etkina’s awesome site Physics Teaching Technology Resource which has many more video experiments.)

3. Application Phase:

Instead of showing our students a better lecture, let’s get them doing something better than lecture.

UPDATE: Welcome New York Times readers! Other recommended posts:

Angry Birds in the Physics Classroom

I recently blogged that you can now play Angry Birds in your web browser. This opens up all sorts of video analysis possibilities for physics lessons and assessment. Students can easily make their own videos or you can pre-record your own. Videos can be recorded using Jing, Screencast-O-Matic, or Camtasia Studio. Analysis can be done in Logger Pro or Tracker.

Here are some possible investigations to carry out (shared by Michael Magnuson on the WNYPTA email list):

1. Make a reasonable estimate for the size of an angry bird, and determine the value of g in Angry Bird World. Why would the game designer want to have g be different than 9.8 m/s²?   Download Angry Birds video.

2. Does the blue angry bird conserve momentum during its split into three?  Download Red and Blue Birds video.

3. Does the white bird conserve momentum when it drops its bomb? Why would the game designer want the white bird to drop its bomb the way that it does?  Download White Bird video.

4. Describe in detail how the yellow bird changes velocity.  You will need to analyze more than one flight path to answer this question.  Download Yellow Birds video.

5. Shoot an angry bird so that it bounces off one of the blocks. Determine the coefficient of restitution and the mass of the angry bird.  Download Red Birds and Falling Block video.

Other posts with ideas about how to use Angry Birds in physics class:

How have you used (or will use) Angry Birds in the classroom?

UPDATE 12-28-2011: Our class has been featured on CUNY-TV’s “Science and U!” Jump to 10:25 in the video below:

Many people aren’t getting the nuances of my recent Khan Academy arguments. I’ll make my final remarks and then put this thread to rest.

Khan Academy videos are nothing new. MIT OpenCourseWare has been around for TEN YEARS now. Walter Lewin’s awesome physics lectures have been available for most of those 10 years — despite the fact they are pseudoteaching, and his students emerged with no greater understanding of physics than those of professors before him.

And I didn’t have a problem with Khan Academy (as a collection of videos) until very recently.

For me, the problem is the way Khan Academy is being promoted. The way the media sees it as “revolutionizing education.” The way people with power and money view education as simply “sit-and-get.”

(c) tcoffey (via Flickr)

If your philosophy of education is sit-and-get, i.e., teaching is telling and learning is listening, then Khan Academy is way more efficient than classroom lecturing. Khan Academy does it better.

But TRUE progressive educators, TRUE education visionaries and revolutionaries don’t want to do these things better. We want to DO BETTER THINGS.

Ironically, everything that is wrong with Khan Academy has been addressed in two previous TED talks:

According to Dan, today’s math curriculum is teaching students to expect — and excel at — paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. How does Khan Academy foster problem posing and creativity?

Rather than instructing students with Khan’s videos, we should be inspiring them to figure things out on their own and learn how to create their own knowledge by working together. For example, instead of relying on lectures and textbooks, the Modeling Instruction paradigm emphasizes active student construction of conceptual and mathematical models in an interactive learning community. Students are engaged with simple scenarios to learn to model the physical world. In comparison to traditional instruction, Modeling is extremely effective — under expert modeling instruction high school students average more than two standard deviations higher on a standard instrument for assessing conceptual understanding of physics.

Watch one Modeling class in action:

In the clip, the teacher says, “I don’t lecture at all. Instead, I create experiences for the students either in the lab or puzzles and problems for them to solve and it’s up to them to try to figure that out.” I’ve often wondered why this type of teaching hasn’t gotten more attention in the media. Maybe because the teacher is using simple things like whiteboards and bowling balls rather than shiny iPads and SmartBoards?

While Khan argues that his videos now eliminate “one-size-fits-all” education, his videos are exactly that. I tried finding Khan Academy videos for my students to use as references for studying, or to use as a tutorial when there’s a substitute teacher, but I haven’t found a good one. They either tackle problems that are too hard (college level) or they don’t use a lot of the multiple representations that are so fundamental to my teaching (kinematic graphs, interaction diagrams, energy pie graphs, momentum bar charts, color-coded circuit diagrams showing pressure and flow, etc.) Khan Academy videos do not align with proper Physics Education Research pedagogy.

I find it troublesome that the Khan Academy team is not spending time and energy on the pedagogy of teaching math and science, but rather on refining the gaming mechanics of Khan Academy in response to “good” and “bad” behavior of students working through the software exercises. The “gamification” of learning in Khan Academy has had disastrous consequences at the Los Altos school pilot.

There are some truly innovative learning technologies that have been
around for years. If Khan Academy wants to grow out of their infancy as electronic worksheet drills, I hope their team takes a look at these more transformative educational technologies, all of which have been researched and tested:

Khan Academy also promotes the “usefulness” of its dashboard for its exercise software. I find most of that information useless, like knowing how many times a student rewound the movie, how many times she paused it, or how long he spent on a module. Those times could be affected by distractions from family, self-imposed distractions like facebook and texting, etc.

Feedback I would find WAY MORE useful:

• knowing how many times a student attempted the same problem
• knowing the student’s answer history to each problem; i.e, what the student’s wrong answers were
• knowing the type of mistake a student made when choosing a wrong answer; e.g., did he forget to square the distance, did she apply kinetic energy conservation instead of momentum conservation, did he disregard the fact that the forces where in opposite directions, did she confuse force of friction with coefficient of friction, did he assume constant velocity when in fact it was accelerating, etc.
• software that anticipates and recognizes those common mistakes (like all great teachers do) and gives the students immediate, tailored feedback during the exercise

Finally, everyone is talking about using Khan Academy as a way to do more inquiry and more project-based learning. However, Bill Gates and Sal Khan are not showing any examples about what students and teachers are doing beyond Khan Academy. The news stories are not showing the open-ended problems the kids should be engaging with after mastering the basics — instead they show kids sitting in front of laptops working drills and watching videos. The focus is on the wrong things.

Khan Academy is just one tool in a teacher’s arsenal. (If it’s the only tool, that is a HUGE problem.) Khan Academy can be useful for some kids as vehicle (build skills) to help them get to better places (solving complex problems).

Now let’s please shift the focus (yours and mine) toward the destination.

More Blog Posts Critical of Khan Academy, from me and others

Increasing Engagement in Science

As part of a session on innovative practices in science at TeachMeet New Jersey 2011, I gave a presentation entitled “Tips, Tools, and Techniques for Increasing Engagement in Science”

I have posted that presentation, complete with speaker’s notes and plenty of links to further information, here: http://bit.ly/EngageSci

Any feedback you have would be greatly appreciated! (e.g., is there a bigger theme I am missing, etc.) Thanks! J3BC3J3HSY8J

Vote for Student Engagement

The voting for the 2010 Edublog Awards has begun! I am stunned that my blog post The \$2 Interactive Whiteboard has been shortlisted for Most Influential Blog Post. In the comments, you’ll see many teachers across disciplines and grade levels have gone out and started whiteboarding with their students.

Micheal Doyle wrote in his post Technology Even a Luddite Can Love:

I cut up two 4 x 8′ white shower boards (\$25.87 including tax) into twelve 24 x 32″ white boards.

Best money I’ve spent on a classroom, and I’ve spent a lot.

Mistakes are no longer permanent red marks. A quick swoosh with an eraser or back of a hand, and the board is clear.

Mistakes do not simmer for a day or two; I walk around and we work together to fix misconceptions on the spot.

I know immediately where the students stand, a bit humbling when you realize maybe your brilliantly scripted lectures posed as directed discussions are no more effective than the textbook you sneered at with your fellow twits on late summer eves.

And (drum roll please….) the kids dare to think. I mean think as in “Look at me I’m coming up with solutions and I want to share them!” think.

Physics and chemistry teacher Brian Post recently tweeted:

John Burk started an entire Posterous blog called Physics Whiteboards for teachers and students to share their whiteboards with the world!

My post was even written about in Sweden: Interaktivitet? Dialog! (translate into English)

Enough about me. Please look at my other nominations below. All these teachers are working hard to engage kids everyday and make their time in school as meaningful as possible.

Best individual blogScience Teacher
Michael Doyle wants his students to experience science, not regurgitate it. Take, for example, his recent post Un-teaching Science.

Best individual tweeterjerridkruse
Jerrid Kruse is a former middle school science teacher who now teaches pre-service elementary teachers about inquiry in the classroom.

Best new blogQuantum Progress
John Burk, physics teacher and modeler, is trying to change his students mindset about learning, grades, and getting into college. He wants his students to change the world and he is helping them get there.

Best teacher blogThink Thank Thunk
Shawn Cornally’s students are doing amazing inquiry in physics and calculus. Plus his standards-based grading posts are bar-none.

Best educational use of video / visualdy/dan
From basketball parabolas to filling up a water tank, Dan Meyer series strives to make math more meaningful to students through carefully constructed videos and pictures in his “What Can You Do With This?” series.

Dan’s was the first blog I read regularly. His “How Math Must Assess” manifesto is what put me and many others on the road to better grading practices. Follow that up with an appearance on Good Morning America for his WCYDWT-Groceries and  a TEDxNYED talk about a makeover for math curriculum, and you’ve got a math guy whose influence is being felt in all subject areas.

These are not votes for us, but rather votes for improving science teaching and for engaging and helping students. ANYONE can vote, not just fellow bloggers. (Only 1 vote per IP address to prevent cheating, so you may have to vote at home rather than at school.)

Some Resources for New Physics Teachers

In a comment from an earlier post, Matt Wasilawski writes:

Thank you very much for these posts, I am looking forward to using them in physics. I have been teaching Earth Science and AP Environmental Science for the past 10 years. I was assigned to teach Physics this year. I was hoping that you could direct me to more specific modeling suggestions for topics in Physics. I do not have a strong background in Physics but have been working hard to develop my knowledge base.

Here are some of my resource recommendations to help new physics teachers with planning and instruction:

Get yourself a copy of Randy Knight’s Five Easy Lessons: Strategies for Successful Physics Teaching. He discusses the best in physics education research, describes several methods for interactive engagement, and goes through a typical physics course unit-by-unit with lesson plan ideas and places where students have misconceptions and stumbling blocks. Every physics teacher should have this book because we all should be incorporating more teaching strategies based on physics education research.

Walking in front of motion detectors to kinesthetically match graphs of motion -- highly recommended by physics education research

The K-12 Physics standards by Heller and Stewart have lesson plan ideas and activities which are founded on physics education research.

The ASU Modeling Website has their Mechanics curriculum available for download, including teacher notes.

Mark Shober is a modeler who put all his materials on his class website. It’s tied to his class calendar, which makes it great for pacing.

And lastly, there is the Physics Classroom website. While it doesn’t mesh perfectly with modeling, it is much better than the most widely used physics textbook. The website has online readings and animations for you and your students, worksheets with links to the corresponding online readings, problem sets with audio solutions, labs, rubrics, and objectives. There are also Minds-On Physics modules, which are good for formative assessment.

I know there are many more, but these are the ones that stick out in my mind as being most helpful.

The \$2 Interactive Whiteboard

Yes, you read that correctly. The TWO DOLLAR interactive whiteboard.

But first…

The \$2,000 interactive whiteboard

While watching the video, count how many times the kids are interacting with each other while using the board. Mouse over here for the answer. But I guess that’s OK, because, according to one teacher, “It really does cut down on behavior problems ’cause they’re really motivated and interested to sit and look at the board and pay attention.” Is that what good teaching is?

Before you jump to the conclusion that I am some technology-hating Luddite, I want you to know that I love technology. I train other teachers how to use technology effectively. In my physics lessons, I use technology with my students, but only when the pedagogy demands the technology.

I have a SMART Board in my classroom. I’m a SMART Exemplary Educator. My waves lesson on the SMART Exchange website has over 400 500 600 700 downloads — the most of any high school physics lesson. There was an article written about me when I first got my SMART Board. Some students say I’m the best SMART Board user in my school. But no one said the SMART Board helped them understand physics.

According to this Washington Post article, some educators question if electronic interactive whiteboards raise achievement:

As he lectured, Gee hyperlinked to an NBC news clip, clicked to an animated Russian flag, a list of Russian leaders and a short film on the Mongol invasions. Here and there, he starred items on the board using his finger. “Let’s say this is Russia,” he said at one point, drawing a little red circle. “Okay — who invaded Russia?”

One student was fiddling with an iPhone. Another slept. A few answered the question, but the relationship between their alertness and the bright screen before them was hardly clear. And as the lesson carried on, this irony became evident: Although the device allowed Gee to show films and images with relative ease, the whiteboard was also reinforcing an age-old teaching method — teacher speaks, students listen. Or, as 18-year-old Benjamin Marple put it: “I feel they are as useful as a chalkboard.”

The word “interactive” for the the \$2,000 electronic interactive white board (eIWB) means interaction with a piece of hardware to manipulate virtual objects on a screen. And most eIWBs only interact with one person at a time.

The \$2 interactive whiteboard

The word “interactive” for the \$2 IWB means interaction among students. Students are working together to collectively construct knowledge, explain their reasoning processes, and get feedback from the teacher and each other. Students are interacting with each other in small groups when preparing the whiteboards. Then they interact with the whole class when they present and field questions from the class and the teacher. At all times, the teacher can see and hear student thinking and challenge them with questions. This process is called “whiteboarding.”

So, what are some of the benefits of whiteboarding with \$2 whiteboards?

1. Encourages students to think, question, solve problems, and discuss their ideas, strategies, and solutions.
2. Allows students to articulate their preconceptions so the teacher can confront and resolve them.
3. Allows for regular classroom and evaluation and interpretation of evidence. Students come to know not only what they know, but how they know it.
4. Provides opportunities for students to learn from and correct their own mistakes, and to learn from the successes and mistakes of others as they check and critique each others work.
5. Helps create a culture of questioning. (<– go read this!)
6. Allows for the discussion of student-generated ideas rather than the teacher merely presenting information.
7. Engages students in a collaborative learning community.
8. Promotes strongly coherent conceptual understanding while decreasing traditional lecture.
9. Provides opportunities for students to teach one another, practicing using the language of the science to one another in order to develop personal meaning.

(List compiled from Whiteboarding in the Classroom and Whiteboarding.)

In my year-end survey, my students frequently comment about how the whiteboarding process was an effective teaching method for them. For example:

The whiteboard discussions are different from the traditional “put your answers on the board” in that we can really see what went wrong and explain our understanding. I feel as though we learn through the explanations we have to give and the little question prompts you give us.

Districts spend tens of thousands to hundreds of thousands of dollars on electronic interactive whiteboards, plus thousands more for professional development to show teachers to use them in order to write, move, reveal, and resize virtual objects. How about taking all that money and spending it on professional development for learning how to engage students in Socratic dialogue, effective questioning, reformed science teaching methods like modeling instruction, and other inquiry learning methods? How about using the money for substitutes so an entire department can go and watch other teachers using these instructional methods in other schools?

Teachers should be spending their precious lesson planning time designing lessons to engage kids mentally and push them to higher levels, not creating flashy Powerpoints.

What skills do we want our students to have when they leave our classrooms? How to use a piece of technology? Or how to work collaboratively, ask great questions, think critically, and problem solve?

Please, instead of thinking about how to get your students to interact with a \$2,000 electronic whiteboard, think about how you can get your students to interact with each other using a \$2 whiteboard.

Where should we place our time and money?

Here?

Or here?

credit: whiteboardsusa.com

Resources for whiteboarding

• Home Depot and Lowes sell large 4’x8′ sheets of white shower board or tile board for about \$12 each. You can have it cut at the store into 6 pieces that are 24″x32″ in size. Hence, the \$2 whiteboard. If you say you’re a teacher, they may do the cutting at no extra charge.
• Whiteboards USA sells the 24″x32″ boards for \$9 each with rounded edges and a handhold cut. (I am not affiliated in any way this company.)

How to use them (including academic references):

Endnotes

If anyone knows of a lesson where the pedagogy demands an electronic interactive whiteboard, let me know. I’m talking about the \$2000 physical IWB itself. If you can do it with just the computer, software, and projector, it doesn’t count. I do think those are a necessity for many classrooms.

I like my SMART Board because it is convenient for ME. The ability to save digital ink is useful to ME. Yes, eIWB are just tools. And, yes, what you do with the tool matters. But the things that are most effective for student learning do not require an electronic whiteboard.

I realize that you can have both types of whiteboards in class at the same time (my classroom does). I also realize that most teachers don’t use their eIWB everyday or all period and shift to student-centered instruction. But let’s not kid ourselves into thinking it improves student learning.

Update: Whiteboards vs. Chart Paper

Please check out this great follow-up post by Thomas Ro. In it, he talks about how student collaboration dynamics are different when using whiteboards instead of chart paper, including “the power of the eraser.” Students are more likely to take risks with their work when using whiteboards and more students get involved.

Lesson Progression: Projectile Motion

(Feed reader users may need to click through to view embedded content.)

Stage 0

“So, as you can see by this free body diagram, gravity is the only force on the ball. Therefore, the ball will move with constant velocity forward while accelerating downward at 9.8 m/s2. Any questions? Great!”

Stage 4

Lesson: Kobe Bryant jumping over a pool of snakes. Real or Fake?

I’m no genius when it comes to this teaching thing. It took me 12 years to get from Stage 0 to Stage 4 for this lesson. And I still have plenty of lessons stuck in Stage 0 and Stage 1!

Real or fake?

This video (taken from the Win/Fail Physics collection) is the beginning and the end of a mini learning cycle during my projectile motion unit. At the beginning of the unit, it’s the hook. At the end of the unit, it’s the assessment.

Creating a need to know

By the end of their first viewing, all of my students are yelling “That’s fake! No way!”

And students come up with all kinds of weak excuses like “It just LOOKS fake!” or “No one could do that!”

“No,” I say. “Convince me with physics. Justify your claim with scientific evidence.”

(*crickets chirping*)

The kids now have a need to know. They want to know if the video is real or not, but they lack the tools and knowledge to support or refute their original claim. They are now willing to go down the rabbit hole with you.

Whenever possible, I frame my lessons around the Karplus learning cycle: Exploration, Invention, and Application. (It’s nothing special. In fact, most other learning cycles like 5E, 7E, and Modeling are strikingly similar.) Instead of relying on lectures and textbooks, I use the learning cycle so students can construct the conceptual and mathematical models themselves, all within an interactive learning community.  By this point in the year, my students have been through several cycles, including constant velocity motion, accelerated motion (including vertical free-fall motion), and balanced/unbalanced forces.

Exploration Phase

Our goal as a class is to develop a model for Kobe’s motion through the air. After some Socratic discussion, we conclude that Kobe’s motion, if real, could be similar to tossed ball. After all, both Kobe and the tossed ball only experience the downward pull of the Earth while in the air. Both Kobe and the ball move vertically and horizontally at the same time. However, as my Force Concept Inventory (FCI) results indicate, many of my students do not grasp the independence of horizontal and vertical motion. So I ask them to forget about Kobe for a minute, and we do two exploration activites:

• Pirate Treasure Hunt: Each group gets 10 directions (e.g., “Walk 44 tiles north”). What they don’t know is that all the groups have the same 10 directions arranged in different orders. However, if they follow the steps in order, they will be walking through walls and out windows. Eventually, students realize they can combine all the north-south directions and all the east-west directions and simply walk X paces west and Y paces north. The follow-up class discussion about “Why did you do that?” really gets at the independence of horizontal and vertical motion.
• Dropping/Shooting a Bullet: Student use ice cream cone shooter toys to answer the question: “When released at the same time, which hits the ground first: a horizontally shot bullet or a bullet dropped from the same height?” Predictions and justifications must be made. Some students see the connection right away. Others don’t, but the results make for great discussion afterwards.

Which hits the ground first?

Invention Phase

Now we know that horizontal and vertical motion are independent. But we need to create (invent) a more detailed model to describe the motion of a tossed ball. But how will we get the horizontal and vertical motion data in order to create the model? Through Socratic discussion, student decide that trying to mark the position of the ball in the air as it moves won’t work. Nor will using motion detectors.  Students decide to use our Flipcams to video themselves tossing the balls and then do a video analysis of the motion in Logger Pro. (Students had done video analysis earlier in the year.) But there are still more questions:

• “Wouldn’t the motion depend on how fast the ball is tossed?”
• “Wouldn’t the motion of a tall/skinny arc be different than a low/wide arc?”
• “Wouldn’t the mass of the ball affect the motion?”

So, as a class, we decide to split up the data collection. One group will vary ball mass, another toss speed, and another arc shape. We’ll share the position vs. time and velocity vs. time graphs created and look for patterns in their shapes and in their equations. This is whole class inquiry — groups are doing different experiments and everyone’s data is needed. Everyone makes a contribution to our classroom scientific community.

Video analysis in Logger Pro (image credit: vernier.com)

After the data collection and analysis, students “whiteboard” their graphs and we have a “board meeting” where each group presents their results and then as a class we try to make connections among the groups and come to a consensus. At the end of the board meeting, the class has created a model for projectile motion:
In the horizontal direction…

• All position vs. time graphs are straight lines. The slope of the line represents the horizontal speed, which remains constant during flight.  This is like our previous model of constant velocity motion.
• All velocity vs. time graphs are flat lines. This means the horizontal acceleration is zero which matches up the horizontal position vs. time graph. Again, this is like our previous model of constant velocity motion.

In the vertical direction…

• All position vs. time graphs are in the shape of upside-down parabolas, with the time-squared coefficient being about 5 m/s/s. This is like our previous model of accelerated motion in free-fall.
• All velocity vs. time graphs have a slope of about -9.8 m/s/s. Again, this is like our previous model of accelerated motion in free-fall.

Also…

• The mass of the ball doesn’t matter. Again, this is like our previous model of accelerated motion in free-fall.
• Projectile motion is simply the combination of the constant velocity model (horizontal) and the acceleration motion model (vertical).

Presenting lab results

Application

We are now ready to return to the Kobe Bryant video to apply the student’s newly created model for projectile motion. They decide to immediately feed the video into Logger Pro for analysis. Students are able to make a claim regarding the realness of the video, and justify that claim with evidence and reasoning. I ask them to accumulate as much evidence as possible in order to make a stronger case for their claim.

Groups that finish early are pushed further with more questions: Is Kobe’s horizontal speed reasonable? Is the vertical and horizonatal distances he leaps reasonable? How will you figure those out and make a claim to their possibility?

At the end, groups whiteboard their work again, groups present their results to the class, and we reach a class concensus. The debate here sometimes gets very heated.

And when they are all done, they still ask me, “Is it real?”

“You just figured it out yourselves!” I say. (*sigh*)

Notes

1. Robert Karplus workshop materials on reasoning and the learning cycle.:

2. If you don’t have Flipcams, a regular digital camera that shoots movies will do fine. And if you don’t have a digital camera, there are plenty of pre-fab projectile videos to use — have a look at Dolores Gende’s collection of physics videos for analysis.

3. Levels of Inquiry. This cycle has elements of both guided (Level 2) and open (Level 3) inquiry. I stay away from confirmation/verification (Level 0) at all costs. The coupled-inquiry cycle is an easy way to do more open inquiry in class.

4. For additional information about modeling, see the Modeling Workshop Project web site at Arizona State University. Here’s a great introductory article: Modeling Instruction: An Effective Model for Science Education

5. Rhett Allain’s wonderful analysis of the Kobe Bryant video was the inspiration for this learning cycle. Thanks, Rhett!