Thanks, Becky. One of the things we often hear is how easy it is for students to create multiple representations of their mathematical thinking using the digital tools. And when students discuss their thinking, they often publish or share their their work and students can incorporate "copies" of that thinking into their work and make any changes.

Hi Becky.

Thanks for your comment. I am a graduate student and have been on a research assistantship with the Connected Mathematics Project since the start of this project. To add on to what AJ has mentioned, I would say that the ease of sharing lends itself to increased accountability on the part of the students. 

I am aware of some of the very interesting projects going on through the HUB. I hope that as this crisis gets over we will get the opportunity to connect in person and discuss some ideas about potential new projects for CMP. 

Thanks, Bonnie, for your comment. Most of our data analysis focuses on computer screen recordings but we're also exploring how the analytics information from the digital platform (that records data log files) can inform our research efforts as well. 

Thanks, Alden, This is great work for students and teachers.  
Can you talk about the data that you get from the recordings? Constructs? Measures? Assessments? Performances? Validity and Reliability? Connection to traditional metrics (e.g., grades, improvement scores, state assessments)?

Thanks for your interest, Michael! Our research primarily focused on the collection of video and screencast data from focus groups from all of our project classrooms to look closely at evidence of productive disciplinary engagement as students interact with the platform. We are also just at the beginning of analyzing learning analytics that the platform produces for additional evidence of productive disciplinary engagement. We also have teacher interview data that suggest the digital environment has potentially measurable impact on learning, especially for students who are not as engaged with the traditional paper-and-pencil version of the curriculum. We hope to connect this with achievement data in future work.

Those of you who are interested in some of the ways we are able to trap and gather usage data may want to read this article about how the files are constructed: https://concord.org/newsletter/2020-spring/sharing-real-time-collaborative-documents/ 

The format is important both because it is what allows the realtime view for peers and teachers, and because it allows us to build a "play by play" of how students construct their responses to questions. That, in concert with the clickstream data we retain on what actions students take as they move through the material builds a unique view into the entire ebb and flow of inscriptional activity in the classroom. We are analyzing this now, and as Alden mentions elsewhere will be publishing results soon. 

I agree, Kathy. We have been having similar kinds of discussions in project meetings. We went into the project hoping to enhance collaboration in face-to-face classrooms. And with the COVID-19, I think there is some potential worth exploring for remote learning. The digital platform would allow students to see and share their work with other students (and the teacher). What I'm wondering about is what kind of support is also needed to support small group and whole group discussion.

Thank you for your questions. We are currently writing a manuscript that reports on the framework and offers examples on the use of the framework. But we are a few weeks out before submitting.

You may be interested in our current dissemination efforts, which I'll add a link below. In particular, I would recommend the PMENA paper on the nature of uncertainty in mathematics classrooms (Going, Kursav, Slanger-Grant, Bieda, & Edson, 2018).

Project dissemination link: https://connectedmath.msu.edu/research/ongoing-...

Thank you! :)

Our work is focused on a couple units at the seventh grade level. Luckily, our field testing this year mostly finished right before the stay-at-home protocols. But we are thinking about ways to expand field testing next year, including exploring ways to support remote learning.

Good questions, Renae.

Question 1 - Next year we are hoping to expand our testing with a few more CMP teachers. As a design research project, we have developed the digital platform using an agile development process involving rapid cycles of development, testing, and feedback. So next year we would like to see how the digital platform is used with teachers that have not been part of the design process to gain additional feedback on its usability and feasibility. 

Question 2 – As a first reaction, maybe at the upper grade levels. I say this because we are working very hard to make the tools very intuitive for students. But I’m wondering about the nature of mathematics classrooms between elementary and middle schools, particularly around mathematics problems. In that sense, there may need to be adaptations or modifications. That being said, I know other projects are working hard to create digital solutions at the elementary grade levels. I would check out the INK-12 project if you are not familiar.

Renae,

One of the outcomes of the project that is intriguing to me is that each of the participating teachers has reported that some students are engaged with the mathematics that weren’t in the paper and paper pencil environment. While it is only a small set of classrooms, I am curious to see if we get  similar comments next year. I have many conjectures as to why this might happen and many more questions, but we need more data.

Thank you both for your thoughtful responses! Alden, I'll check it out for sure. Elizabeth, I look forward to seeing what you all present next year!

We are not collecting and analyzing any longitudinal data. Our design research project makes use of the agile development process, which means that we are iteratively designing, developing, testing, collecting data, and gathering feedback. Multiple times per year. Each year we gradually add more and more features for students and teachers to support their enactment of the CMP curriculum. We also have been working closely with the same teachers and their students (new students each year). So we have been following the design research project throughout the years, but not necessarily studying longitudinal data in the traditional sense where we would be looking at characteristics of the population of students and teachers.

Thank you Michael!

Thank you, Michael. The balance that we tried to strike in our technology design efforts at Concord Consortium were informed by the strong pedagogical philosophy developed over many years by the MSU team prior to this project. This foundation served as a reference for our work. CMP teaching emphasizes collaboration, seeking a multiplicity of approaches to problems, and a continual refinement of ideas. Each of these elements had direct consequences for software design. For instance, in small group collaboration, each student has his or her own workspace, but group members can easily see and share each other's work. Students can choose to publish their work to the class to present a wide variety of approaches. Teachers can see all students' work and select and share back a variety of approaches to problem solutions for discussion. Students can keep a persistent log of their reflection of major ideas or exemplary problems that show evidence of the growth of their ideas. The final and crucial input to the design process was provided by the unstinting feedback provided by the field test teachers and students who made sure we were on track. 

Hi Heather, Thanks for giving our video a careful view and for sharing it. I think your observations are right on! At Concord Consortium we have been impressed that the collaborative approach of the CMP curriculum re-orients math study from getting the right answer to understanding a whole mathematical context for each topic area, say, proportion or linear relationships. It also makes mathematics discursive. Students need to be able to talk to each other to explain how they got their answers and understand on how different approaches relate to each other. Teachers' responses have generally been enthusiastic. So far, with have worked with a small pool of teachers who have seen us through from the beginning of the project and their 7th grade students. The teachers are very experienced with the CMP curriculum and so can give us a comparative description of how things have worked in the paper-and-pencil world as opposed to the digital world. Right away, some things work better in the digital world, like the seamless sharing of student work. When teachers report a preference for the paper-and-pencil approach for certain aspects of learning or teaching we direct our design effort to see how we can be better. There are certain things that may always be better on paper, the physical action of drawing or scaling, for instance. For these things, students can take a picture and incorporate it into their digital space to keep all of their learning together. Also, for teachers (and for us) there is a learning curve on how best to use this platform. With six or more groups working independently in a classroom there is a lot going on! We do plan this year to expand our classroom use to a larger number to get even greater real-world feedback.

Heather,

Since our project is a design research project, we used a small set of CMP 7^th grade field site teachers. Their input and enthusiasm from the beginning were very influential creating the collaborative digital platform. In addition, each teacher reported that more students were engaged in the problem-solving process than they were in a paper and paper environment. Next year we will expand the field testing to CMP 7^th teachers who will be new to the digital environment, which will provide more information on teachers use of the environment.

Cindy, thanks for your kind remarks.

Next year, during our no-cost extensions, we will test the viability of the platform with new sites across the country, with the possibility.  Feel free to recommend any CMP seventh-grade teachers and have them indicate their interest in testing the digital platform on our website. We are also considering  adapting the digital environment so that it is available for a year-long CMP mathematics course on a very small sample. Yes and the next challenge is remote access.

Dr. Smeltzer,

CMP is a problem based- curriculum which opens the mathematics classroom to exploring, conjecturing, reasoning, and communicating. Both the teacher and student take on more responsibility for the learning process. The CMP instructional model looks at instruction in three phases: launching, exploring, and summarizing that supports this kind of “inquiry-based” teaching. Teachers move from demonstrating how to do the mathematics to one who guides, prompts, questions, and facilitates students to do and make sense of the mathematics. In CMP classrooms teachers are encouraged to recognize and use student thinking more effectively in developing a deeper understanding, reasoning, and skills. Students collaborate, challenge each other, think in new ways, gain mathematical confidence, and communicate their understanding and reasoning as they solve problems. With support teachers become more comfortable in creating these collaborative environments. For more information about the collaborative nature of CMP classrooms, you might want to look at: connectedmath.msu.edu/.

Thanks, Dave, for your question. Next year we are hoping to expand our testing with a few more CMP teachers. The current CMP teachers using the digital platform have been involved for several years. Now that we have a robust digital platform, we are interested in seeing how other CMP teachers use it. And of course we are also thinking about the nature and kinds of professional development needed as well.

Interested in this question, too. I purposefully pair my students when using Desmos or PhET sims to foster communication/sense-making/collaboration. Since those kinds of skills are targeted in this project, I'm wondering if 1-to-1 is preferable.

Collaborative strategies tend to be a hallmark of my classroom, so making a sudden transition to 100% online learning with few opportunities to be "together" as a class was challenging for me. I love the possibilities here for continued collaboration from a distance--both synchronous and asynchronous.

I have been interested in CMP for many years, and I like seeing this digitized platform experience.  On the question of 1:1 or 2:1, we ran projects on tablet-based computing with screen-sharing, and discovered, by chance, that having students work in pairs provided a more durable and engaging experience than when the students were working on their own devices.  

I want to reply to both William and Sarah about the collaboration model. Despite what you saw in the video all of our classrooms were 1-to-1. Ultimately, each students does his or her own work. However, students do get up and look at each other's screens and you see them pointing. Students can see each other's work on their own computer, but (as of yet) we don't have a way for students to indicate shared attention between two members of a group on different machines. That could be an interesting feature. The important thing is that the students are discussing over a shared inscription.  Pointing is a powerful method of sharing attention. This work was intended for face-to-face classrooms, so getting up and looking at each other's screens is a natural way to share. We are certainly giving consideration to enabling a collaborative distance learning situation where methods of discussion and shared attention would be required. These are some of the technical hurdles of moving to a distance learning model, but there are many others that we are trying to understand.

As for the pros-and-cons of shared machine vs. 1-to-1 when working with math apps or computer models, I think either can work. The shared machine approach can learn a lot from techniques developed for pair-programming that is effective in both industry and education. One member of a pair is designated at "Driver" and the other as "Navigator". Each has roles and responsibilities, and, generally, switching roles at regular intervals in important. (See this link for more information.) One-to-one allows each student to produce a product, which for many schools is essential. Certainly, that has been the case for us. Hope this helps.