Six Shifts for Math Teachers Moving Online: appendix

Earlier this summer I wrote a post for Global Online Academy sharing Six Shifts for Math Teachers Moving Online. The final version of that article provided an example for each of the shifts, but earlier drafts shared multiple examples for each shift. This appendix shares the additional examples that were cut for space in the original piece.

Here is a reference of the six shifts:

1. Content

   OK so there were not additional examples for content, but I promise the next idea is OK and I think the extra examples for Assessment (Shift #6) is pretty good.

   Fundamentally for content, the idea is to be intentional. The goal- in my mind- is to limit the breadth to increase the depth.

2. Content Delivery

   Example 1:

   Example from Garnet Valley GOA Partnership:

   Course day rotation: “Day 0 homework: Students watch teacher made intro video on the topic. She used EdPuzzle to make sure students watched. Day 1 via Zoom Video: teacher gives direct instruction extending ideas from the intro video; for second part of class students work in small groups (Zoom breakout rooms) to do problems. The problems consist fo 3 levels. For sake of time, easy, medium, hard. Students continue that work on their own for "homework".  Day 2: students select into 3 "breakout" rooms based on their progress and comfort on the problem set. Teacher starts with Group 1, remedial work. 10 minutes direct instruction, Meanwhile group 2 and 3 work among themselves to help each other. then 10 or so mins in teachers "goes" to group 2.  Gives them direct instruction to extend them into the next unit. Group 1 works on previous work and group 3 watches curated videos on next unit and works on hard problems together; maybe even helps students from groups 1 or 2. Teacher returns to group 1 for more individual instruction. Now some sort of formative assessment: maybe an online quiz with immediate feedback or a video of a student walking through a new problem.  You can work through 3 or 4 topics over a few days and have a problem set. (OR students take ownership of a problem, and present via video/zoom to the rest of the class). 

   Example 2:

   The following is an example from GOA’s designing for Online Learning Bootcamp by participant Emina Alibegović using Geogebra

   “ I think that delivery via video is one of the way to present ideas that students can't necessarily discover on their own. If you choose to "deliver" the material through video, the issue is that you don't know what the students gained from it, what questions they still have, and what they actually understand. Edpuzzle is a really good tool that allows you to: 

   • ask questions of students during the video presentations

   • provide notes you may want the students to have, or maybe remark on something that is important in the video that you want to emphasize

   • allow them to ask a question of you and for you to respond. “

   Another tool for mathematics classroom is Geogebra website. You can make experiences in which you embed activities such as the one pictured below, but then you can follow it up with questions such as the one I list below. You can have a conversation with your students through an activity such as this one.

   ACTIVITY CODE Link: 

   https://www.geogebra.org/m/zyakccyy

3.Homework (i.e. Learning)

Example 1

One example for student learning and practice uses a model for student work that has 3 sections:

1. Learn It -Students watch video, read, or explore new content

2. Look In - Students apply content to their experience or previous material/content

3. Look Out - Students apply concepts to new circumstances by find their own examples.

Example 2

Students need practice. We need to incentivize authentic practice, so students take that work seriously. So, let’s take a page from our writing colleagues and treat homework as a first draft and “assess” the revision process. Then, there is no need to give students points just for completing their homework.

Many discussion boards allow students to only see replies once they have submitted a response (for example, here’s how to do it in Canvas LMS). If the first “response” they see is a completed solution set, then they can check their own work and that can be the assignment that is graded. Assess students not on their first draft of homework or their final product, but on their revisions and reflections. Let them see the final solutions, then focus, assess, and incentivize the revision process.

4. Feedback

Example 1

I like the use of videos by students to demonstrate their understanding. I would scaffold work so students are able to video themselves completing one problem.  Say graphing a trig function. They would articulate that they know the y-intercept, the period, the amplitude, etc. But they would be talking through their graph. Then you can assess where they go wrong (these videos become useful to show other students). I have also used a model of testing that includes 1-on-1 video chats for 5-10 minutes where students do a problem "in front of me" and I ask them questions about their process if they get stuck or to gauge their understanding.

5. Interaction

Idea 1: Teachers need to intentionally design for interaction in online formats. Students cannot ask the student next to them an innocent question during a Zoom lecture. We need to create structures that empower student voices in online and hybrid classrooms- math in particular.

Use protocols and structures that mandate students interact. Give prompts and stems to help students generate a vocabulary of feedback. Here is the first result from google: https://www.teachthought.com/critical-thinking/sentence-stems-higher-level-conversation-classroom/ (and it is good)

Idea 2: Group work can be done in many different formats online and this provides opportunities for creativity. Breakout rooms work, but only with a structure (see above). But Google Docs or Slides provide opportunities for collaboration that honor students’ individual time needs and responsibilities.

6. Assessment

Example 1

Automate some assessment. Thoughtful multiple choice problems like the following assess student conceptual understanding. Create 20 and have an assessment that randomly chooses 10 for students to complete in 15 minutes. Here is an example of a problem I created for rational functions:

I love this problem. A student needs to understand asymptotes and intercepts, and needs to be comfortable with coefficients.

Example 2

Ask open ended questions such as “What would need to be the relationship between a and b in a quadratic function in order for the axis-of symmetry to be negative?” or “Write a quadratic function whose vertex is ( 1 , 4 ) [maybe add and the leading coefficient is not 1 or is negative].”

These remove the ease of academic dishonestly, are not easily “google-able,” and ask students to think about mathematics rather than recite formulas or reproduce wrote processes.

Conclusion

These are just a few extra examples that were “cut for time” in the original post. These are certainly not exhaustive. Please share ideas in the comments below! All teachers would love to hear more ideas!