Now that schools have started the year, this is the time of year where getting students to more deeply engage with the content becomes the higher priority. As we continue to navigate this global pandemic, many classrooms are still online fully or in a hybrid way - which extends the conversation of "how do I do this online?"

**The context of our problem is compounded with what we know is good content area teaching, like in math with the **__Math Language Routines__**, or MLRs, by Stanford. **

Based in the best practices created from good online teaching before COVID, one of my favorites is using the The SAMR Model for Tech Integration *(forgive me for not knowing where SAMR originated; I've encountered it in so many different iterations over the years and the linked blog post is a clear definition of how it can be used now). *What I've created below is a **SAMR Model for Tech Integration for the Math Language Routines**, used across the nation in schools and math curriculums. Check out the image below to see how this has a similar feel while being laser focused on the following questions related to student-centered math pedagogy.

How can virtual learning help students access their own and other's math thinking more often and more deeply?

How can teachers uncover student math thinking in order to adjust instruction?

How can virtual learning expand what I can see about individual students' math thinking?

In the context of different iterations and combinations of the aspects of distance learning, we provided examples of how the MLR can be accomplished using SAMR separated first into synchronous and asynchronous ideas then the levels of SAMR. Here's what we define has synchronous and asynchronous.

Educators currently use a lot of digital tools, and some are indicated by name in the examples below. Here's a list of examples of tools that could be helpful if not explicitly named or ones you have access to that could be used instead.

Shared virtual documents:

__Google Docs__,__Google Slides__,__Google Jamboard__Shared organization tool:

__Padlet__Live annotation tool: Zoom/Google/Teams annotation

Live chat tool: Zoom/Google/Teams chat

Interactive real time activity platform:

__Desmos__,__GoFormative__,__Nearpod__

Here's a helpful __spreadsheet__ of the below for your reference as well.

**Let's get to it!**

**MLR1: Stronger and Clearer Each Time**

Purpose: To give students a piece of mathematical writing that is not their own to analyze, reflect on, and develop.

**Synchronous**

**Substitution:**Model with a selected student (warm call) how one could question another during the protocol. Then send students to breakout rooms in pairs to share their responses. Use breakout rooms for student pairings.**Augmentation:**In the whole group, give students time to independently craft a first draft of their response, then send them into breakout rooms to share and edit their second drafts. Remain in the main room until all students have been paired, then start a five minute timer. Have the students return to the main room when the time is up, and start the process again.**Modification:**When in synchronous breakout rooms, have students type their answers in a class-wide shared document to use the comment feature about why they updated their response.**Redefinition:**Direct students to make connections between other students' 2nd drafts by creating a summary sentence about what is the same between everyone's responses after viewing all of the 2nd drafts in a class-wide virtual document.

**Asynchronous**

**Substitution:**Have students submit an example of their thoughts, then respond to questions you provide (as a set) to make their responses stronger. Students get credit for a first draft, then an updated second draft based on responses to the question(s) you provide.**Augmentation:**Use a discussion board to have students submit their 2nd draft as well as ask a question in response to another post. Then when a student receives a post, the assignment is completed when the student responds to the question posted under their original post with and edited version of their original post.**Modification:**Tell students to students compare and contrast the concepts in their first draft statements in a class-wide shared document with other students' thoughts or an exemplar response.**Redefinition:**With an example video, prompt students to create a video outlining the difference between their first response and their second response, focusing on why or how their understanding changed.

**MLR2: Collect & Display**

Purpose: To capture studentsâ€™ oral words and phrases into a stable, collective reference.

**Synchronous**

**Substitution:**Post example work in a discussion board, Google Doc, or slideshow for students to view on a shared screen while the teacher explains the connections between the representations and the concepts.**Augmentation:**Have students annotate on the screen what is the same or different between their representations and the example representation screen-shared by the teacher.**Modification:**Ask students to volunteer to show and explain their own work using screen-share.**Redefinition:**Use a tool like Padlet across a section or unit to display all of the student representations, using the comment feature to help draw connections across the unit.

**Asynchronous**

**Substitution:**Have students submit worked out problems to the teacher and share a virtual document that shows the connections between the representations.**Augmentation:**Using an example worked out problem, students use a comment feature to explain how their own representation or understanding is connected to the example representation.**Modification:**Students write, draw, or make a video explaining how their work relates to the concept available in a shared document and discuss how their work relates to other students' work.**Redefinition:**With example worked out problems, instruct students to draw connections between the different representations or between a representation and the math concept using drawing tools.

**MLR3: Clarify, Critique, & Correct**

Purpose: To provide a structured and interactive opportunity for students to revise and refine both their ideas and their verbal and written output.

**Synchronous**

**Substitution:**Use a student response to ask all students to clarify, critique, and correct the same student's response in a shared document.**Augmentation:**Choose one student's response (warm call) and ask students to clarify, critique, and correct using the chat or unmute.**Modification:**Using Jamboard, require students to underline or highlight what needs to be adjusted in another student's response, then have the student rewrite the response.**Redefinition:**Ask students to video themselves saying a response, then have them watch the video and write a better version of their response.

**Asynchronous**

**Substitution:**Provide a sample response to a question for students to clarify, critique, and correct as part of an asynchronous assignment.**Augmentation:**Provide a number of statement pairs and have students identify what what clarified, critiqued, or corrected in the 2nd of the pair as it relates to the math concept.**Modification:**In a shared virtual document, students can review other student's work to ask questions and make more connections with others besides just the students in their group. Assign a certain number of students to each response to maximize this opportunity.**Redefinition:**Have students explain their representation to family members or volunteers so that the adult can ask clarifying questions to prompt further questions and thinking from the student.

**MLR4: Information Gap**

Purpose: To create a need for students to communicate.

**Synchronous**

**Substitution:**As a whole group, students share possible questions with the teacher, who holds the data card. As groups of students agrees they have enough information to move forward, those groups work on solving the problem in a breakout room.**Augmentation:**Present the question then send students into breakout rooms. While students are in breakout rooms, use the Zoom broadcast feature to feed them additional information every couple of minutes.**Modification:**Have students use a shared document to track the justifications and new information gathered to solve the problem.**Redefinition:**After students have enough time to solve the problem, have students explain why they asked the questions they did in the order they did.

**Asynchronous**

**Substitution:**Match students in pairs, where one of has the problem card and the other the data card. They can use a Jamboard or Google Doc to communicate. Assign each student in a group pieces of the information card.**Augmentation:**In a discussion board, post the problem card and students ask questions and those with the information they need, share that information in the board as other students ask the matching question. Students who think they have answers as information becomes available to all then put those answers in the discussion board and the teacher lets them know if they have the correct answer or not.**Modification:**Use a self-paced pathway, like in Google Docs, where students click on a question in one slide to show the information that answers that question on another slide. Students can then choose another question to be answered or complete the problem and submit.**Redefinition:**Each student has the problem card and a piece of information from the information card. Instruct students to video themselves explaining why each piece of information is important to solve the problem on the information card.

**MLR5: Co-Craft Questions and Problems**

Purpose: To allow students to get inside of a context before feeling pressure to produce answers, and to create space for students to produce the language of mathematical questions themselves.

**Synchronous**

**Substitution:**After presenting students with a hook, ask students to submit questions that could be created from the situation in the chat.**Augmentation:**Using breakout rooms, have students compare questions and problems to revise them in relation to the goals of the lesson or a math concept.**Modification:**Steer the group conversation to create a shared mind map, stemming the questions asked to the context of the problem situation/hook.**Redefinition:**Guide students to create a mind map that links their question/problem to an actual question or problem, comparing and contrasting the structure, wording, and math concepts used.

**Asynchronous**

**Substitution:**From questions/problems submitted by students, have students evaluate whether or not the question is appropriate given the criteria of being mathematically relevant or assumptions about what is important in the math context.**Augmentation:**Using a shared work document, have students create problems for another student's questions.**Modification:**Have students create and share a representation that could solve another student's problem. Assign these in student pairs so the discussion can continue easily.**Redefinition:**After students answer their own questions/problems, assign students in pairs to review how their representation or strategy is the same or different from another student's.

**MLR6: Three Reads**

Purpose: To ensure that students know what they are being asked to do, and to create an opportunity for students to reflect on the ways mathematical questions are presented.

**Synchronous**

**Substitution:**Walk students through the three reads, posing the questions in the chat for students to respond to after each read.**Augmentation:**Monitor students as they annotate on the screen the part of the problem that has the information they used to answer each of the three read questions.**Modification:**Have students submit their answers to each three reads in a class-wide shared document and ask them to compare and connect their responses to other student responses.**Redefinition:**After students work in breakout rooms to solve their problems, ask them to identify which of the strategies/answers from the three read questions they used to help them.

**Asynchronous**

**Substitution:**Provide students with the three questions to answer on their own.**Augmentation:**Record a think-aloud of each of the three reads, modeling how you use the information in the problem to answer the questions.**Modification:**Advise students video their answers to the three reads so they can rewatch those thoughts as they solve the problem.**Redefinition:**Have each student compare their answers to the three reads questions of others and draw connections between their problem answers and other's three reads answers.

**MLR7: Compare and Connect**

Purpose: To foster studentsâ€™ meta-awareness as they identify, compare, and contrast different mathematical approaches, representations, and language.

**Synchronous**

**Substitution:**Model with a selected student the difference between comparing and connecting representations on a shared screen in front of the entire class.**Augmentation:**Have students annotate the screen showing two representations as the teacher prompts for similarities in mathematical relationships, operations, quantities, or values available.**Modification:**Have students vote in a Padlet which student-created representation is the most accurate for the problem and why it is the most accurate using the comment feature.**Redefinition:**In a Padlet, have students explore each other's representations to vote which one is most efficient.

**Asynchronous**

**Substitution:**Provide an example of two representations for the same problem with questions about where they see the quantities or relationships in the different representations**Augmentation:**Share samples representations in a discussion board post for students to identify the important mathematical connections in a certain number of representations, using provided sentence stems.**Modification:**Have students submit their own representations in a discussion board and ask other students to identify the connection between the representation and the mathematical concepts they know.**Redefinition:**Ask students to be the teller of their representation in a video responding to other student's questions about their representations.

**MLR8: Discussion Supports**

Purpose: To support rich discussions about mathematical ideas, representations, contexts, and strategies.

**Synchronous**

**Substitution:**After introducing the problem context, ask students what strategies might be helpful to solve the problem.**Augmentation:**After providing the problem, instruct students to draft the steps for solving the problem in a virtual document that they will share with the class when they return to the whole group.**Modification:**Have students create and share their own representations, videos, diagrams, etc to represent the mathematical contexts before solving the problem.**Redefinition:**Tell students attempt to use the strategies of others to solve the problem in breakout rooms.

**Asynchronous**

**Substitution:**Model for students a metacognitive think aloud about understanding the problem context and include this in their assignment.**Augmentation:**In discussion boards, provide a list of sentence starters and questions to answer when responding to other students.**Modification:**Have students submit in a discussion board what strategy the used to solve the problem. Make this interactive by having students vote on which strategy is the best or the limitations of other strategies.**Redefinition:**Give feedback to every student, focusing on developing student responses by asking them whether their strategy works if a certain part of the problem context is changed.

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