Math Without a Pencil
Anyone who has ever taken a math class has heard or read the words, ‘Show your work,’ or ‘show your thinking.’ Many math teachers won’t award full credit to any solution for any math problem unless the student has shown their thinking, or shown their work.
And then the Pandemic happened. It forced math teachers and students to not be in the same room for math class. All over the world math classes are now being held via video conferencing platforms like Zoom, or Big Blue Button, or Google Meet, or many others. Students aren’t able to so easily share their thinking with their teacher or their classmates. Some of the video conferencing platforms have whiteboard simulations, but in the video conferencing environment it’s difficult for a teacher to view and comment on student work.
Video conferencing makes a teacher’s ability to direct students to work together on solving a problem impractical. A teacher can’t say “slide your chairs together” or “work at your table” to try out some possible solutions to this problem. Breakout rooms don’t make sharing their work with the other students easy to do. Students must typically write on paper and hold it up to the camera or upload photos of handwritten work. Neither method provides a way for teachers or other students to comment on the work. And, collecting and keeping track of that student work is cumbersome, at best. These are big problems for teachers who show students how to construct meaning collaboratively, a teaching strategy preferred by many teachers.
SABIER has provided a global solution to this problem using GeoGebra’s app version of Illustrative Mathematics middle school math curriculum. SABIER has created Moodle courses that include links to all of the GeoGebra Illustrative Mathematics apps.( High school courses will be available by fall of ‘21.)These free openly licensed Moodle courses increase communication between teachers and students, and build community by enabling students to communicate with their teacher and each other using video, chat, audio, or photos. Multiple standards aligned assessment options synced to student information system are available. Families appreciate the links to the Illustrative Mathematics material provided. The LMS course gives teachers quick access to extensive narratives that describe the mathematical work that will unfold in each lesson in every unit, as well as, scope and sequence charts, standards alignment, and course maps.
All of the GeoGebra Illustrative Mathematics OER courses work in all of the major LMSs — Canvas, Schoology, and D2L. Anyone, anywhere in the world with an internet connection can get a copy of the LMS course files.
The first lesson in the first unit of the 7th Grade course asks students to create a scaled drawing of the letter ‘F’ using the math construction tools built into the GeoGebra app. Before this task is assigned, students are introduced to scale with several hands on tasks. You can see them here.
Teachers are able to see what each student is doing in real time by using GeoGebra’s Classroom. GeoGebra Classroom enables teachers to, without requiring students to share their screens, view live updated progress of students working on a specific task, ask the entire class questions, see all student answers instantly, and share students’ work anonymously with the whole class. GeoGebra Classroom is explained in the video on this page.
Then, students put the drawing they make in the GeoGebra app into a discussion in the LMS course and explain their thinking about the process they used to create the scaled drawing. Students share their drawings with their classmates in groups and comment on or ask questions about the drawings of their classmates. One useful discussion prompt is to have students share what they learn from their classmates’ work in a reply in the discussion.
These LMS courses are a mashup of multiple openly licensed works. The original Illustrative Mathematics curriculum was designed primarily for in-person F2F teaching using paper and pencil. The Illustrative Mathematics curriculum is rated very high by EdReports, an independent nonprofit that reviews K–12 instructional materials. The I-M curriculum is licensed CC BY and has been used by several major U.S. publishers in proprietary versions. GeoGebra, founded in 2001, has won a long list of awards, is translated into 52 languages, used in 190 countries, and has over 6 million registered users; the GeoGebra apps are licensed CC BY NC. Moodle is open source and is the most widely used learning management system globally. The LMS course content is authored by SABIER and is licensed CC BY NC.
The courses provide significant benefit to schools, teachers and students. Since they’re OER, there’s no cost to schools or governments for acquiring the material. One large school district in the U.S., for instance, estimated a savings of $4.5 million per year compared to paying fees for the commercial proprietary digital versions of Illustrative Mathematics. But, an even more significant benefit is the ability of teachers and administrators to modify the content to meet the language, accessibility, equity, and inclusion requirements of their community. Those affordances will still be critical for schools in a Face to Face instruction model when teachers can again comment in person on work that students are doing with pencil and paper.
- Dan McGuire is a former elementary and middle school teacher in Minneapolis, Minnesota. He is the Executive Director of SABIER, a nonprofit that enables philanthropy and foundation funding to go directly to supporting teachers and students to be able to use free openly licensed content that can be adapted to meet the needs of students. Dan is a member of The Creative Commons Open Education Platform and promotes the use of OER with learning management systems.
