Thanks for taking a look at our project and for your questions. 

In the design of the simulations, we focus on using multiple representations and creating a strong interaction-feedback tie where the dynamic visualizations and representations change immediately in response to student interaction, enabling them to identify relationships and patterns. And in a number of the simulations, we have done internal scaffolding from more concrete contexts - such as coins - to the more abstract - such as combining terms in expressions - to help bridge students as they explore mathematical relationships. 

Regarding the teachers use, one of Ian's studies under this grant examined the various ways teachers position a simulation within the lesson, showing five different sim and student roles that emerged across teacher lessons. Paper is "Orchestrating Mathematics Lessons with Interactive Simulations: Exploring Roles in the Classroom". Another study looked at one teacher and found two different sets of norms - with the sim enabling the teacher to create a more student-centered environment, compared to BAU. In interviews, its clear that the teacher values and desires a student-centered environment, but finds it more challenging to create without the sim. The sims are specifically designed to be flexible tools, that can meet teachers where they are at in the pedagogy and then through PD help them shift to more student-centered pedagogy.

We have used a couple of different ways of coding the classroom videos (MQI and IQA protocols) - I'll ask Ian and David to elaborate. 

Hi, Bill!

As Kathy mentioned, we have used MQI and IQA to compare the quality of sim vs. non-sim lessons. If you're especially interested in that, I'd be glad discuss it with you. MQI is more comprehensive but also much more difficult and time consuming. IQA is narrower and not as clearly aligned with the SMPs, but the coding is much friendlier.

In the study that I mentioned, we coded for indicators of social and sociomathematical norms. I mentioned "math practices" in the interview as a shorthand way of describing the kind of mathematical activity that took place in the sim lessons. In that study, focusing on one teacher's classroom, we coded specifically for the teacher's role (evaluator vs. facilitator), student agency (disciplinary vs. conceptual), and for specifically mathematical obligations (i.e., indicators of sociomathematical norms). Cobb, Gresalfi, and Hodge (2009) provided the inspiration for this approach. 

So glad to hear you've been able to use them as a resource in your doctoral class! 

In science, we have researched the use of PhET simulations with college students. However, we haven't yet conducted research with college students or other adult populations within mathematics. Because of the overlap in the content, I have been encouraging the use of these simulations within developmental math courses with the idea that these tools can provide students who have previously struggled with math with a new way to engage with and learn mathematics. 

Anecdotally, we have heard positive reports of the use of PhET simulations with adult prisoners (importantly the simulations can be run offline on devices without internet connection) and with non-traditional students in community colleges. We would love to understand more about how the simulations support these adult learners. 

Jeffrey, thanks for your question! I have been curious for a long time about how PhET sims might support the development of mathematical content knowledge for teachers. I'm planning some professional development sessions for inservice teachers for next school year, and I'm going to incorporate PhET sims as a way to start piloting some of that work. I have used PhET sims in my master's classes for math and science teachers, and from what I have observed informally, the teachers tend to respond in similar ways as students -- they are highly engaged with the mathematics and ask a lot of questions, then use the sim to help them answer those questions. I'm hopeful that with this tool, we'll not only be impacting teacher practice but their knowledge as well. 

Great to hear, and thanks for sharing the simulations will all the teachers in your district! We would love to hear about how your teachers are using these simulations in the classroom, and what supplementary resources would best help you support your teachers use of PhET - more posted sim-based lessons? videos of classroom use? specific coaching resources? other ideas?

It's great to hear you are finding these resources useful with ESL students! We would love to hear more about how you are implementing the simulations with this population and how the students are responding. 

That is great to hear! I'm curious how you structure your use of the sims -- with students or teachers, and as supplemental tools or as core components of a lesson (or maybe both)? 

Thank you for your kind words, Abby. I agree that it can be difficult to allow this kind of "open play" that is very student-directed, and we often remind teachers that the entire lesson isn't like that, it is just the first 5 minutes to explore the tool. After that initial exploration, the teacher facilitates the lesson by providing a guiding activity sheet, walking around the room to listen to conversations, pause the class for discussions, and lead a summary discussion. We have some teaching resources on our website for teachers to peruse, but we also run workshops with teachers where they get to experience this lesson format and write their own activities following the research-based guidelines. They then post them to the website for anyone else to download, which further helps to spread the word. We are hoping to revamp some of our resources to be math-specific, as well as succinct enough that someone doesn't need to dedicate a lot of time to reading everything. Please let me know if you have any suggestions for what could work well! 

We also see variation in how teachers structure and facilitate the "play" phase of the sim lessons where they are balancing competing priorities of fostering student ideas versus keeping pace for the lesson - written up here: 
https://www.tandfonline.com/doi/abs/10.1080/0020739X.2018.1532536?journalCode=tmes20

We've used this work to inform our teacher PD approaches.  

Hi Quinn, Great questions. We do have an alignment document between the NGSS and PhET's science simulations - but the way I think about it is that we build PhET simulations to be "NGSS-ready". We add capabilities that enable and support learning disciplinary core ideas through engagement in the practices, etc., but it all depends on how the lesson is designed (the sim PLUS the tasks PLUS the facilitation and setting).

Back in 2015, we ran one collaborative summer working group with teachers on building NGSS-aligned PhET lessons, and created these materials and guidance. 
https://phet.colorado.edu/en/contributions/view/3990

The basic alignment between NGSS and PHET sims is here:
https://phet.colorado.edu/en/contributions/view/4127 

I do know that PhET simulations are leveraged in the physics by the Modeling curriculum/community.

One last thing ...  I love is seeing researchers pick up PhET simulations and use them to extend research and our understanding of student learning in new directions, so I encourage you to explore. You should connect with Jodi Asbell-Clarke at TERC on this specific idea of combining with computational thinking/modeling. She may have some materials that her teachers have created that could be shared with your teachers, using PhET with these sorts of goals.

Happy to connect if you would like to collaborate.

Yes, time is always a factor for teachers! The content we cover is aligned to content being taught in classrooms, so using a sim would simply enhance the teacher's standard lesson. Alternatively, a teacher could replace a textbook lesson with a sim-based lesson to achieve the same learning goals but with more student exploration. 

We do find that the simulations offer a natural game-like environment where students are drawn to certain implicit challenges, such as balancing a scale or creating the largest expression. 

Hello Amir, 

I hope you don't mind me including an English translation of your comment (via Google)

"Thanks to your professional collection

Your work is excellent and I try to introduce the site and collection in all classes so teachers and instructors can have a dynamic and attractive classroom.

Thank you for your support in Persian

Good luck."

Hi Catherine, 

Thank you for your question! Some aspects of the current work will transfer nicely into mathematics (like keyboard navigation of structures that are common across sims), but new research will be needed to really dig into leveraging the affordances of interactive simulations in the context of making math accessible to students with disabilities. Working with students in the disciplinary context is critical to extracting strategies for supporting students to learn that discipline (their interpretation of the auditory descriptions, sound feedback, etc). Simulations also contain new types of elements that require new research advances. This area is led by Dr. Emily Moore, and we see some very powerful opportunities to engage in new research around combining technologies to build on work that has been done previously in this area. It's an exciting possibility that we hope to pursue in the coming years! 

Thank you for your comments, Idris! It's great to hear about your use of PhET simulations and the positive response of your students! 

Hi Jared, Glad you like the simulations. We have simulations in other subjects (physics and chemistry mostly), and we enjoy building collaborations with disciplinary education researchers to explore how this approach and extend learning and advance research in other disciplines or aspects of education. 

Hello Peter,

Regarding learner discourse with and without technology, from what we have observed in math teachers' classrooms (comparing tech use to non tech) sims that are designed to provide a sandbox for students to explore, wonder and conjecture can shift the discourse to students' insights and ideas. If teachers' understand student exploration as important math activity, and lesson plans include such time, sims that have the capacity for sustained student exploration can be used to increase the showcasing and use of student initiated ideas.