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opportunities for explorations in which students experience the need for the core concept

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opportunities for explorations in which students experience the need for the core concept

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making sense of partitioning-measuring relationships in proportional reasoning

making sense of part-whole relationships in proportional reasoning

making sense of discretized-continuous relationships in proportional reasoning

making sense of parent-child relationships in geometry ("drag tests")

making sense of input-output relationships in algebra

making sense of dependencies and models (SMP #4) in dynamic mathematical spaces in general

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opportunities for explorations from which students develop their own resources for forming the core concepts

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opportunities for explorations from which students develop their own resources for forming the core concepts

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identifying quantities and geometric objects

estimating

comparing and contrasting

guessing and checking

changing perspectives

changing parameters

testing edge cases

exploring degress of freedom

investigating hierarchies

composing and decomposing

changing perspectives (moving, zooming, scaling)

looking for and making use of patterns and other structures (SMP #7)

codifying and formalizing (variable assignment, definitions in students' own words)

organizing (sorting, categorizing, grouping, labeling, color-coding)

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from 4Hs of Belonging-Centered Instruction

from prior sessions

from their teachers

from survey feedback

from classroom visits, videos

from student interviews

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students establish norms in Unit Zero

"key to success for today" prompt (a teacher innovation) to initially focus students on their group collaborative norms

subsequent check-in screen for students to revisit, reflect on group collaboration

teachers facilitate before (framing), during (monitoring), and after (debriefing) sessions

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students click "try it" buttons, creating new math to

notice

wonder about

interpret

discuss

make sense of

refer back to

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students create their own safe spaces in VMT chat

... rather than students fill-in-blanks that do not inform subsequent activity, with answers to questions that they did not/do not have

students share suggestions, feedback on prototype

R&D team honors and responds directly to students

R&D team incorporates into next iterations of content

R&D team incorporates into next iterations of software

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groupworthy and collaborative

much to Notice & Wonder about

"less is more"

limit number of individual screens

imbue each with depth or impact

keep direction lines brief

avoid exposition in favor of opportunities for student sense-making in the chat

offer reusable mathematical tools when feasible

low floor/high ceiling

opportunities for multiple approaches

opportunities for multiple “correct” and “incorrect” answers

opportunities for multiple representations created by students

interpretive feedback (rather than evaluative) with varied pacing:

initially engage students with immediate cause-and-effect

then judiciously delay feedback to elicit students' predictions or explanations

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when to take control, and when to release it

when to explore one's own ideas, and when to explore the ideas of others

planning what to do once in control

using appropriate tools strategically (SMP #5)

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when to talk in chat, when to create space there for others, and when to explicitly call others out

considering the ideas of others

checking the understanding of others

referencing and other ways of making connections in chat

when to make use of prior knowledge or work

when and how to manage the group's time

when to "step back" to discuss group norms