Middle School Math: Graphing Virtually
by Rachel Currie Rubin on April 5th 2020
grades 6-8, math, specific learning disability, dyscalculia, slope-intercept, individual instruction
Emily is a seventh grade student with a diagnosis of dyscalculia. She can become anxious and easily frustrated when she does not understand a math concept. She is receiving one-on-one mathematics support.
Rachel Rubin Mathematics Case
Graph from an equation in slope-intercept form
Transition to distance learning
Face to Face
- Use color-coded equations on a whiteboard to identify the slope and the intercept.
- Create a coordinate plane on the floor and move oneself based on the equation.
- Graph an equation on a coordinate plane.
At a Distance
- Together, watch a video showing the process of identifying the x and y intercepts.
- Practice identification using a virtual whiteboard with color-coded equations.
- Student gives instructor graphing instructions that the teacher follows and draws on the whiteboard.
- Student practices problems independently (with support as necessary) through Google Docs.
Face to Face
- Colored markers
- Student’s notebook
- Coordinate plane (life-sized) on the floor made from masking tape
- Equations to graph and a coordinate plane drawn on paper
At a Distance
- Computer with Zoom (with virtual whiteboard)
- Google Docs or OneNote (virtual notebook)
- Prepared equations
- Magnetic whiteboard (for teacher)
- 2-3 magnets (for teacher)
Face to Face
- Use a gradual release model (i.e., show the student first, do the second problem with the student, watch the student do the third problem independently) through identification of slope and y-intercept in an equation, using red for the y-intercept and blue for the slope. Refer to the student’s definitions in her math notebook as needed.
- Model how to use the life-sized coordinate plane before the student uses her own body to show location of the y-intercept as well as “rise over run” as the student moves her body on the graph based on the coordinates (e.g., if the equation is y=2/3x + 5, the student begins at y=5 and moves her body up two spaces on the y-axis and three spots over on the x-axis. The student puts down a circle made of paper to mark the “point” on the graph.)
- Use a gradual release model (see above) to guide the student through the graphing process using written equations and a coordinate plane on paper.
At a Distance
- Identify salient ideas in the video and support the student in taking notes in her Google Docs virtual notebook.
- Use a gradual release model (i.e., show the student first, do the second problem with the student, watch the student do the third problem independently) through identification of slope and y-intercept in an equation, using red for the y-intercept and blue for the slope within the virtual whiteboard feature. Refer to the student’s definitions in her math notebook as needed.
- Model before the student gives guidance to the instructor. Specifically, the teacher holds a magnetic whiteboard with a coordinate plane. The teacher models how to move a magnet to the y-intercept and then move a second magnet based on the slope and plot a second point.
- Use a gradual release model (see above) to guide the student through the graphing process using equations and a coordinate plane in Google Docs.
What worked well
Emily can become easily frustrated, and our first virtual lesson did not go perfectly (see below). However, in this lesson a number of key features seemed to boost Emily’s independence, perhaps even more than in face-to-face settings.
First, using a combination of videos and a virtual notebook allowed Emily to independently think about what she may need to refer to after the lesson when working by herself. She took her own notes and even used the time stamp on the video to document portions of the video she might need to refer back to later.
Second, during the magnetic whiteboard activity, Emily provided me with directions for how to move magnets to the y-intercept and then to a second point on the line. Because Emily was providing directions and I was moving the magnets, I was able to prompt Emily before she made errors, thus reducing frustration. If Emily provided the incorrect direction, I prompted her to look back at the equation and provide the direction again. Checking her work before the error was “written down” seemed to reduce frustration overall.
Finally, the components of the lesson allowed Emily to become fully independent with graphing because she was provided multiple models and had multiple opportunities for practice before she attempted problems independently. Because she was working in Google Docs, Emily felt that she was not alone when solving problems on her own, which appeared to boost her confidence.
I was surprised by
It was challenging at times to switch back and forth from different platforms (Zoom to Google Docs) and within platforms (Zoom whiteboard to video feature), though I think it was more challenging for me than for Emily!
Next time I’ll try
Though it would be possible to do an active lesson as I had originally planned, it would require Emily and her family to prepare prior to the start of the lesson to avoid wasting time during the lesson. I might try to do this next time by providing a little guidance for Emily’s family about how to prepare via email, a shared Google Doc or a short phone conference. I have found that the mode and format of communication needs to be consistent and flexible to families’ needs. Families are juggling a lot right now, and so to deliver high quality support I am finding that I might need to adjust the content of or approach to that support depending on how families are able to engage with me. This means that things sometimes take longer to get organized and implemented than they used to, but that’s ok! The quality of the resulting interaction and learning was still good and impactful.
My big picture takeaways
It is possible to provide the same level of scaffolding and practice as in face-to-face lessons. The online environment allows for multiple ways of practicing and interacting, and the environment is perhaps even better than a face-to-face setting for encouraging students like Emily to become independent. Digital natives like Emily are comfortable using reference documents, and weaving those supports into a lesson allows for a natural gradual release.
- Zoom: There is a virtual whiteboard that the leader of the meeting can use, though the other participant cannot add to the drawings.
- Google Docs: It is possible to write together and refer to the same set of notes. Writing equations is easy, as is drawing pictures.
- Khan Academy: Good reference videos to support learning.
- Free math apps: A set of apps to support concept development.
About the Author
Rachel is the co-owner and education director at Learning Solutions for Learning Success in Northampton, Massachusetts. She has worked in education for 15 years as a reading teacher, learning specialist, and educational assessment specialist. She has worked at the Williston Northampton School, CAST, the Carroll School, and Boston Children’s Hospital. She has taught psychoeducational assessment at Harvard Graduate School of Education, the Carroll School’s graduate training program, and Endicott College. Rachel has published articles on reading development and Universal Design for Learning, and co-edited a book on the school to prison pipeline. She has a B.S. in Speech and Hearing Education from Ithaca College and both an Ed.M. in Language and Literacy and an Ed.D. in Human Development and Education from Harvard Graduate School of Education.