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ideas and the thinking task selected needs to be compatible with the capabilities of both the tech nology and students ’ abilities to use the technolo gy. One such tool is Google Jamboard, a collabora tive online whiteboard that allows users to type and draw synchronously in real time from many devic es on one shared workspace that is accessible via hyperlink. It acts similarly as a Google Doc but al lows for more varied forms of input. Although it offers advanced tools, students tend to use only the most basic of its functionality. For instance, one student may only want to use the typing option since it may be easier to use with a desktop com puter, while another may be more comfortable with the drawing feature that is more natural to use with a mobile device or touch screen computer. Taken together, the technological tools available to stu dents that they will willingly use to communicate their mathematical thinking should be taken into account when selecting and devising appropriate thinking tasks. This is because the technology can be a hindrance or a catalyst for thinking about the task depending on the student ’ s technological com petencies. As such, it is best to hold the assumption that students will have a range of technological competencies and that as long as the task does not require overly complex notation or diagramming to communicate its basic principles, students should be able to adequately communicate their thinking. To illustrate what such tasks could look like, we offer a few examples of thinking tasks that have been introduced in a Zoom environment along with samples of the kind of written work students pro duced when working on these tasks in breakout groups with a Jamboard. The first of these tasks is a number puzzle that could be introduced as fol lows: Below is a list of five answers. These are the answers to five arithmetic expressions each consisting of two numbers and an operation.

__ __ = 3

__ __ = 2

Using each of the numbers from 1 to 10 exact ly once, and each of the operations (+ - ×÷) at least once, find what the five expressions are such that the answers are 17, 2, 21, 3, 2. When students solve this problem for the first set of answers, they are then given a more difficult one, etc. Below in Figure 1 is a sample student work on this task on a Jamboard.

Figure 1: Example of student work on a Jamboard in a breakout room

It may be observed in the above student work that the group of students used a combination of drawn inputs and typed inputs to communicate their think ing. This was based on what each student was most comfortable using to make their contributions. No tably, the complexity of notation required in this task was not overly obstructive of the communica tion among group members. It is interesting to contrast this work with what stu dent work looked like for this same thinking task in a face - to - face thinking classroom as seen in Figure 2. As may be observed, the main difference in the face - to - face student work is that there were more small workings on the side (see the far - right of Fig ure 2) that are not present in the online setting. This may be because students in an online setting may have been using their own paper to help them work through a problem and only wrote what they identi fied as correct on the digital workspace. Alterna tively, they may also have been discussing their ideas verbally rather than by writing them down in

__ __ = 17

__ __ = 2

__ __ = 21

Virginia Mathematics Teacher vol. 47, no. 1

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