I really enjoyed the video. How does the teacher facilitate public discussion around the shared artifacts?

Hi Jeffrey, Thanks for your comment. The CMP curriculum is designed to elicit from students as many ways of solving a problem as possible. With this in mind, we designed our environment to allow students to work individually, but also see what other students in their group of four are doing and borrow from them if they choose. Once individual students are ready, they can publish their work to the class. Then, throughout an activity and on a larger scale, throughout a unit, teachers work to refine students ideas through presentation of their work and discussion. The environment supports this refinement with individual "Learning Logs" where students bring together their more refined ideas. There are multiple ways students and teachers can share student work. Depending on the available classroom technology, individual students may project their work directly. Alternatively, teachers may project student work or their Learning Logs. Most often in the classroom, I've seen teachers pull work for presentation that illustrates different, but equally valid ways of solving problems.

Hi William,

Presently, the environment allows rules to be written in tables such that a given value for (say) x will generate a value of y. Tables and graphs may be "connected" so as to present the data in the table. In addition, linear equations with their line may be created directly in a graph. (In the seventh grade curriculum that we have been working with only linear functions appear.) Any object in a graph (point, shape, line, etc.) may be annotated with a movable "call out" style comment.  

Dear Kathy,

Thanks for your encouraging comments.I am a graduate student at Michigan State University and have been involved with this project since its inception.

The issue of measuring student participation and its impact on learning is, as you indicate, a tricky one. We are trying to focus on Engle and Conant's (2002) framework on Productive Disciplinary Engagement (PDE) as a theoretical lens to measure the effectiveness of the digital environment. While we are not pursuing quantifiable causal effects on learning, we are attempting to measure and document changes in productive disciplinary engagement of the students. Our initial observational, interview and survey data (from students and teachers) are very promising.

I am really glad to know that your kids will be CMP classrooms next year and am confident that they will have a great learning experience. Regarding accessing the tools, unfortunately, we don't have them up for general access, as yet. 

Great video. I love that students who might normally be discouraged from getting started on a problem have a way to enter through digital collaboration. We are also using CMP and would love to have access to the tools! 

Thanks, Ellen,

In line with the CMP philosophy of testing curriculum /pedagogical interventions with extensive feedback from users ( teacher and students), we are studying the affordances (and limitations) of this platform. I hope we can bring this to the CMP classrooms soon.

Hi Brian,
Thanks for your comment. I am a graduate student at Michigan State University. I am fortunate to be involved with this project since its inception.
The conceptualization, design, development of the digital environment, is driven and informed by CMP's curriculum and pedagogical philosophy. Ensuring the natural fit to CMP was one of the main consideration. We wanted to leverage the years of the learning experience we have in the paper-pencil context while exploring the affordance of the digital environment. The iterative development process of the collaborative environment (and other tools) was informed by concurrent testing in selected CMP classrooms and embedding the feedback into the design.

Regarding your second question, about some math topics to be a better fit than others, we are mindfully examining this. Since the issue of collaboration gets conflated with the affordances of digital inscriptions, among other issues, we don't have a definite answer for it, as yet. I am glad to note that you pointed to an aspect that is very much in our radar.

Hi Jennifer,

Thanks for your comment. I'm a graduate student working on the project, and I agree completely that the opportunity to collaborate digitally can bring out perseverance and new problem-solving strategies. These are hugely important for developing a growth mindset in students and in teachers (as in your work). With the digital work that we are currently doing on facilitating students' deep mathematical learning, there is huge potential for archiving student strategies and teachers' pedagogical moves to create professional development resources for teachers to collaborate. This could be amazingly valuable to teachers who don't have another math teacher down the hall, or anyone else teaching their grade-level nearby.

I can certainly see the value of the professional development resources that could be created through your work.  We are always open to new partnerships, so please reach out to me to discuss further when/if you have interest.

Jennifer

Hi Kenia,

Thanks for your comment. I'm a graduate student working on this project, and from my time watching students use this platform it really does seem that how easy it is to look at others' work really helps shy students in the classroom. There's not currently a chat tool in the platform, but there are other features that can help students to try out new ideas more privately. For example, students can turn the visibility on or off on their own work, so that they choose when they are ready for group members to see their work. If they need a little private think time to try out a new idea, then they might click they icon to temporarily "hide" their work, and then "show" it again when they're ready to talk about it. There's also the option for students to publish pieces of their work so that the whole class has access to it.

Although it is not a 2-way chat feature, teachers do have the option to send prompts to students within the digital platform to help guide their thinking. The cool thing is that teachers can write and send prompts to the whole class, specific groups, or even individual students. Some of our test teachers have really enjoyed having the opportunity to look at what students did during class, and then set up group-specific prompts for the next day's work. 

Hi Julie,

This video reports on the work of the third year of a four-year project. As such, the platform has only been available to our hearty field-test teachers. It was designed for one-to-one classrooms with students working in groups of four. It runs in a browser, and works well on computers or Chromebooks. (The Chromebooks bring down the classroom cost significantly.) For the fourth year, we are exploring the possibility of making the software work on tablets which would require some alteration of the user interface and methods of manipulation. One big benefit of running on tablets would to facilitate the teacher's interaction with the teacher dashboard as he/she circulates around the class. The topic of when and how to release the software for wider use is currently under discussion.

This is great! Thanks for the details! I am glad there is conversation around when and how to release the software for wider use. Thanks!

Hi Denise. Thanks for your question. It is a good one, and one that we've been thinking about for quite some time. We've been using student engagement in mathematics as a lens for designing and developing the digital resources. This includes student authority and accountability - two ideas that have helped framed your question. And so students can control whether or not their work is "live" for others. And use it as a resource during the negotiating process with each other about how they work in groups. It provides students with a resource to help show others that they are authors of mathematics as well as a mechanism for students to hold themselves and each other accountable to the ideas. Interestingly, teachers report that using the digital platform is easier to support the dynamics of four-to-a-group when many teachers often use pairs and then have two pairs discuss. As you can heard in the video, students often feel good to hear that others are looking at their work and want to incorporate it into their ideas, which we are finding interesting and encouraging.

I did hear that in the video and I too find it encouraging.  We want students to see themselves as authors of mathematics and to feel good about sharing their thinking with others when they are ready to, which is exactly what your digital platform allows them to do.  And you make a good point about holding themselves and others accountable as they learn to work as a group.  Developing teamwork skills is essential in today's world.  This is really exciting work.  Thank you again for sharing.

Dear Amy,

Thanks for your questions.

This project is a design based research and the platform is still under development (improvement) based on the continual feedback that we are collecting. While CMP does support the teachers with professional development on the use of technology, we will surely have to look into the professional development of teachers for this specific technology platform, as we scale up this project. Presently, there are only a few teachers involved in the design, testing and feedback process. The teachers involved in the testing are experienced with CMP and they have undergone several briefings / online sessions about the features and affordances of the platform tools. We did introduce the project to a few of the CMP teachers during professional development workshops and invited suggestions/ reactions which were largely positive and encouraging. 

The tool currently does not work with iPads but we are exploring that possibility.

Hi Dave. Thanks for your questions. The teachers are not integrating with a specific learning management system to prompt on-going dialog among students as the digital platform is a stand-alone resource.

One of the premise of the ideas of the project has been to think about how technology can support student discourse. Often times when technology is used in a one-to-one setting, teachers report that the technology can be more distracting from the goals of collaboration. With the tools we are developing, teachers are reporting more conversations in small group settings because the computers are linked in the platform and that students have more access to other people's thinking. 

The drawing tools have been an ongoing development. Because we've incorporated the feedback from students and teachers through multiple interrelations and years of development, the tools have evolved to be important and useful for students to solve mathematics problems and communicate their thinking with others. With the variety of tools available in the workspace, it is interesting to see how students prefer to use the drawing tools, and have remarkable skills with touchpad technology.

Hi Susan,

Thanks for your questions. The project is directed toward the development of the platform to encourage seamless and effective student work and collaboration. Since CMP teachers have significant expertise in facilitating inquiry-based collaborative classrooms, we are not specifically examining the teacher actions, at least at this stage. We want to ensure that the design and interface of the platform are responsive to the CMP philosophy and organic to the classroom culture.

Based on the feedback from teachers and students, the digital tools seem to offer affordances for more effective, efficient and advanced mathematical thinking. Also, access to others work and real-time collaboration seems to be contributing to strengthening the mathematical community. Most teachers have reported increased ownership shown by the students. Due to these affordances, the need for teacher intervention seems to have gone down especially during the 'explore' phase and the 'summary' phase is allowing the teachers to reference the work of multiple students more easily.

Having said this, there are a few things that have stood out in terms of teaching strategies. Teachers' own knowledge and comfort with the technology, is being reflected in the use of the platform. Also, some students have reported the need for individual work-time before directly working in a collaborative space. Some teachers have been experimenting with the assignment of roles in the student groups while others allow for more open roles. In line with the CMP philosophy of trusting the teachers' autonomy and decisions, we are concentrating on equipping the platform to be responsive to the varied instructional decisions made by teachers.

Thanks.

Thanks, Amit.  This all seems very promising, especially the increased ownership by students.

Thanks for the thorough response. I am excited to see the final results of  your study. 

Treasure trove!

Thanks

Johnny

Hi Jessica,

Thanks for your question. At the moment, we primarily have baseline data about how students participate when first introduced to the technology, and we are hoping to collect more data about how this shifts over time as students become experienced with learning mathematics in a collaborative, digital environment. Based on this early data, the platform seems promising for increasing student participation for a wide variety of students. We've been able to do quite a few student surveys/interviews and teacher interviews, and they've dominantly expressed that there is more participation in class and that it is easier for students to find ways to participate. One thing we've noticed is that students are able to connect verbally with their peers' strategies as well as by remotely viewing what they did. For example, one student might produce some mathematical work silently and later in class a peer notices it and brings up that strategy for further discussion. This has really helped students who are less willing to talk in a more traditional paper-and-pencil classroom. Since there are more ways to participate and see others' mathematical ideas, there are more opportunities for discussion among students.

Hi Zen,

Thanks for your questions.

Adding onto Nathan, I would say, since the platform is designed for in-class use, the teachers continue to see the value of physically circulating in the class. A feature that we have been experimenting with is the ability for teachers to digitally pass on thinking prompts to an individual / a group of students/whole class. Through this, the teachers can pass on pre-populated and/or customized prompts directed at specific students. We are still working on improving this tool and will be able to report on the enactment in the near future.

I will also add that currently, the platform works only on laptops/computers and not on iPads (or mobile devices). We are exploring the possibility of customizing the platform for iPads. It will be interesting to see the changes with respect to teachers' movement in the class if teachers start using iPads / tablets. In addition to the relative ease of mobility, the use of stylus will be another big affordance of tablets / iPads.