Hello everyone! In this video we present an overview of the Graspable Math and From Here to There Projects that have been supported through IES research and development awards over the last several years! 

The goal of our projects are to develop new ways for students and teachers to engage with math notation both in and outside of the math classroom! 

Please post your questions or comments below! We look forward to an exciting exchange this week!

I wish I had this when I was learning algebra! Have you noticed if students who engage with this compared to more traditional forms of algebra teaching show a shift in their attitude toward? I can imagine many students find this more engaging, interesting, and helpful with the feedback, and this might make them like math more than they previously had.

Congrats Erin & team!

Dear Erin and Graspable Math Team,

Congratulations on such an awesome tool! 

Based on the video, I am most struck by your last statement, that this project is focused on figuring out "how algebra notation bridges to other representations." I see from some of the video snippets that the tool includes the ability to dynamically move around pieces of an expression, and also to sometimes have a graphical representation. Are these the kinds of "other" representations you are speaking of? (Or are you mostly focused on multiple algebraic-only representations, such as ratio expressions, exponential numbers, functions versus expressions, etc.).

I am particularly curious about this because of my own work in Modeling Instruction in physics, where we do a lot of coordination of representations among algebraic expressions, graphs, vector diagrams, verbal descriptions, physical models, pie charts, histograms, etc., and, most recently, computer programs (https://aapt.org/K12/Computational-Modeling-in-Physics-First.cfm).

Another point I note is the implication that the software makes it easier for students to approach problems from different ways. If I am accurate in my assumption, what is it about the software that facilitates this kind of "try it again" attitude? And, do you think that this pedagogy is replicable without the software?

Thank you so much!

Sincerely,

Rebecca

Would this tool be publically available?

This is a wonderful teaching, learning and research tool with an excellent student interface that makes explicit how mathematical notations are related to various representations.  It supports a more flexible form of problem solving that would likely lead to a deeper understanding of mathematics.  Its sophisticated yet appears deceptively simple to the user.  This is very promising work and an excellent platform for examining the strategies that were used.

If I understand the tool, it could help teachers know what student understand and maybe even what misconceptions they are carrying forward.  Your system can track the steps the student uses and somehow characterize his or her work, information critical in any teaching/learning system.  I am curious about the how that is done...do you use technology to do some sort of analysis.  How is it reported?

Thank you Michael! We are currently deep in the process of identifying ways to analyze student strategies as they solve problems. The GM system logs all user actions, clicks, errors, mouse trajectories, and behaviors. We then aggregate that information by problem, student, content, and overall.  Using the raw data and timing information, we can create detailed visualizations about their strategies using data analytics (we are currently using sankey diagrams and tree diagrams). We can also conduct cluster analyses and machine learning techniques on the data to understand patterns in students problem solving strategy. The data files are extremely large and we are just beginning to dig into new ways to extract patterns of student mathematical thinking and behaviors. Its an area that has endless possibilities to apply computer science, data science, and machine learning approaches to educational intervention data. 

I love how students can use touch screens to quickly manipulate algebraic expressions. I'm curious about the learning curve - do students struggle to understand what their manipulations mean? Or, by manipulating expressions, do they develop better understanding of those expressions? I'd love to hear more about what you know about student thinking as they manipulate expressions on screen.

 Susan- we find that students pick up the gesture-actions fairly quickly. We have found that gif videos that show one action at a time, mapping it onto a property, and the following it up with a few practice problems is enough for most students. 

We do find that students with higher initial prior knowledge pick up the system much faster and progress through activities much faster than lower knowledge students. However, lower knowledge students are more likely to reset and reattempt problems multiple times, even after completing them. We are currently writing a manuscript that examines the relations of these clusters of profiles to learning gains for conceptual understanding and flexibility. We find that both of these clusters of students demonstrate improved gains in their understanding and there are no interactions by prior knowledge. 

We also have found positive impact findings in both elementary and middle school students of the From Here to There game, compared to both business as usual controls, as well as comparisons to other technology programs that have demonstrated efficacy. 

One study that we were planning on running in the fall was conducting structured interviews to ask students.to explain their thinking as they solved problems and then map their explanations onto their strategies and data that is logged in the GM system. These in person will likely have to be delayed due to COVID but it is definitely a direction that we will go as we explore the variation in problem solving strategies in more detail.

Really interesting!  I look forward to reading about some of the outcomes of this work. 

This is such a great project and has developed into a mature technology that can really transform how students engage in algebra and arithmetic symbol manipulation. The emphasis on developing multiple ways of understanding is so important for an area like algebra. I am curious if you see students' gestures carry over from one solution method to another when they explain their thinking or during peer collaboration, suggesting that the gestures they develop from the interface serve to ground their understanding of symbol manipulation. I would especially expect to see this as a way to reveal how they think about equality of expressions, and when they perform inverse operations, either with addition/subtraction or multiplication/division. Thank you for sharing this and for making such a well crafted video!

What level of students is this appropriate for? I teach at a community college. Has your research looked at how higher ed students do with this program? I am especially interested in community college student gains.

Enjoyed the presentation!

Great research from Drs. Ottmar and Chan and team

Enjoyed the presentation!

Great research from Drs. Ottmar and Chan and team

Dear GM team, I can't wait to share this resource with my son, who is just starting to learn algebra! I was wondering what sort of role you envision for teachers scaffolding or facilitation of this tool. Furthermore, do you have a vision for how this resource will be integrated into the classroom?

Thanks in advance.

What an interesting project! I'm fascinated with the dynamic modeling of algebraic equations and transformations and the ability for kids to try things out and see what happens. My current project (Data Clubs) engages students in creating graphs to explore data and having good technology makes all the difference! But getting back to algebra-- Often I've found that some of the biggest stumbling blocks for students in algebra is a disconnect with the action of the operation. Students move from work with numbers in the elementary grades to work with variables in the upper grades--what is left for them to focus their reasoning on is the operation, yet many have fragile understanding of the behavior of the operations. I am wondering if you have had a chance to begin developing supports for students based on what you see them doing when they use the graspable math technology.  My earlier work involved the transition from elementary to middle school and I'm really curious about how the difficulties we saw with that transition play out as students continue with algebra. I'm also nearby and would love to connect at some point learn more about this project!

I had a chance to see your project at CL19 and loved it! Your video is great, but I would really encourage the viewers to try out From Here to There for themselves so they can understand why it's such a powerful tool. As a math educator with 10+ years of experience, I can say it's one of the best I've seen for conveying the usefulness of algebraic properties. Thank you for sharing your work!