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This video provides a deep-dive into the components of the Imagine IM print resources and highlights the digital platform.

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by LaToya Byrd and Jenna Laib
School looks different this year. It's easy to focus on the changes that will need to be made-the new practices, the new routines, the new technologies-but we must first focus on our central beliefs about teaching and learning, and use those beliefs to determine what's important. It is essential to build a strong classroom community.

What does it look like?

This community should strive to be one where learners know, use, and enjoy mathematics. How do you envision this math class? And how does that relate to your own mathematical experiences?

Think back to your time as an elementary school student. How would you have defined "mathematics"? How did you feel about math class? There's no monolithic experience for teachers. When we ask this at professional development, we have heard teachers say things like:
Math was always about getting the right answer. No collaboration or sharing out our thoughts. Now that I am a classroom teacher, I ensure students get think time and encourage group work. We all have something to learn from each other. I also don't want my students to think I hold all of the answers. We are a team. I thought I was a good math student and smart, because that's what I was told. I knew my math facts and I completed assignments fast. That stopped when I was sitting in an Algebra I class with no reasoning skills. I didn't know what to do or how to ask for help. Math was fun! It was a different game every game. We had to work together to solve math mysteries. My teacher kept everyone engaged so we learned without knowing we were learning.
The kind of community we want to create rarely happens by accident. As educators, we can make deliberate choices that support and sustain our math communities. To support this, the authors of IM K-5 Math (currently in beta pilot across the US) embedded plans to build community into the first two weeks of lessons in the curriculum. This work then continues and is regularly reinforced throughout the school year.

At the Heart of Building a Math Community

Students need to feel ownership and agency within the math community. IM K-5 Math builds in opportunities for students to explore what it means to learn math by doing math, identify the associated actions, and relate the actions of doing math to norms that support that work.

There are two important considerations when planning the student experiences used to establish norms:

1. The experiences should be reflective of how learning math will look, sound, and feel all year.

2. The experiences should be connected to convey the message that learning math is a coherent journey.

Understanding What It Means to Learn Math by Doing Math

The work on community in IM K-5 Math is not a detour; it fits seamlessly into the curriculum. Lessons provide students opportunities to build on their prior understandings and experiences, to share their thinking, and to interact with the thinking of others. They begin with an invitational warm up, like the one below.

From IM K-5 Math, Grade 2, Unit 1

After engaging in authentic and meaningful mathematical ways, students are asked to reflect on what it felt like, looked like, and sounded like. The teacher records this in a T-chart titled "Mathematical Community," like the one below. For the first 3 days, the focus is on the left side of the chart: Doing Math.

Students mathematize. This might be in a classroom, or at home, or anywhere in between, but first things first: students must do some math!

Afterwards, students contribute to this chart in person or virtually. In the virtual environment, students might share out during a synchronous session while the teacher records responses on a slide, doc, or even paper or chart paper that the teacher is able to show on the camera. Students could also contribute ideas asynchronously that the teacher then consolidates into one chart.

Here is an example from a IM K-5 Math alpha pilot classroom after the first day.

Photo c/o Viri Hawkins, Grade 5

Identifying Actions Associated with Doing Math

The work continues the next day. After the second lesson of the unit, which again follows the same design structure as all IM K-12 Math curricula, students are asked to review the chart, and to revise or add to it based on their experience during the second lesson. The process continues on day 3, as students are prompted to think about the actions associated with doing math. What specifically did students and teachers do?

For classes that are meeting in person, the T-chart can be hung up in the room for students to review. The teacher should direct students to it before the lesson. After the lesson synthesis, the teacher may again direct students to review the chart, but this time to consider any revisions or additions.
The teacher may make similar moves in a virtual setting. The teacher can show the slide with the chart at the start of the lesson, and lead a brief reflection. The teacher cues the class to revisit the chart to close the lesson, as well.

Affirming and Reaffirming Norms

After the class has spent a few days fleshing out the Doing Math side of the T-chart, it is time to discuss explicit norms that make these actions possible. For example, "it may help us share our ideas as a whole class if we have the norm 'listen as others share their ideas.'" It helps to spotlight different norms, and to pause the class while working to call attention to them.

Photo c/o Valerie Effland, Kindergarten

For classes that are held in person, it is helpful to continue to reference the physical recording of the T-Chart. For virtual classes, the teacher can make the decision to show the entire record of the T-chart, or just the one norm in focus that day.

By week two, the teacher can start the class with a quick refresher of the agreed upon norms, and then end the class by asking students to share what norms they experienced during that class session. Or the teacher may ask students, "which one of the norms did you feel was most important in your work today, and why?" This could be done as a journaling exercise, or, e.g. in a synchronous setting, a class or small group discussion.

This work is not completed in September. Classes should revisit the T-chart throughout the year, to reflect on the state of collaboration and discourse, and recommit to class norms.

Impact on Classroom Community

Co-crafting explicit norms alongside students does more than create shared ownership and a productive atmosphere. This process is designed to promote equitable teaching practices, and impact teacher beliefs.

Co-crafting norms honors student voices. It centers student ideas, and positions teachers as learners, too. In a recent professional learning session with IM K-5 Math beta pilot teachers, one educator stated that they "[couldn't] think of a math training that talked about giving a voice to marginalized students the way [IM] did." Other teachers noted that crafting norms builds community, and that this work echoes how lessons emphasize community, from the invitational warm up to the lesson synthesis.

Co-crafting norms with students also asks a teacher to examine their own beliefs about math learning and teaching. "IM's curriculum is different," a teacher shared. "Different in a good way. Being forced to think about my beliefs and positioning can only make me a better teacher. I think we call that humanizing math."

Resources

There have been two IM featured blog posts about co-crafting norms with students: (1) Building a Mathematical Classroom Community; and (2) Co-Creating Classroom Norms with Students. The first post offers a downloadable resource that is similar to what is written into IM K-5 Math. Educators participating in the beta pilot benefit from having this built into their lesson plans, but it would be easy enough to incorporate into any lesson!

Next Steps

If you use this process, we would love to see your students' ideas and hear about your experience. You can share your pictures, blog post links, and reflections in the comments section below, or on Twitter using our #LearnWithIM hashtag and tagging @IllustrateMath!

Get more support with IM's collection of distance learning resources. This includes curriculum adaption packs for the 2020-21 school year that incorporate this work.

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Helping Elementary Students Cultivate a Strong Math Community - IM CERTIFIED® BLOG

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by LaToya Byrd and Jenna Laib School looks different this year. It's easy to focus on the changes that will need to be made-the new practices, the new routines, the new technologies-but we must first focus on our central beliefs about teaching and learning, and use those beliefs to determine what's important.

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FAQ IM Pilot K-5 - Imagine Learning Classroom

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Assessments
Illustrative Mathematics offers opportunities for both formative and summative assessment that empower teachers to measure student understanding and progress against learning goals.

Data Reporting
Real-time reporting gives teachers access to actionable data. The data dashboard and display lets them track student progress.

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Use the login below to explore the IL Classroom Platform with Imagine Learning.

URL: https://imdemo.ilclassroom.com/

Username: imdemoteacher@example.com

Password (4/1-4/14): #Showers7!

Password (4/15-4/30): #Blossom8!

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Please use this to place any questions or issues during the pilot that we can support you with. https://docs.google.com/document/d/1l9vNK-u6qVDgEA6Oow8cS0V9omVGjmz-2_DM9-3FVuM/edit?usp=sharing

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This guide will assist you in reviewing Imagine Learning's comprehensive print and digital solution.

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Kori McAbee

kori.mcabee@imaginelearning.com
714.300.8373

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Math teachers can talk all day about math! We get super excited when we encounter someone else who enjoys these conversations as well.

But too many of our students don't get to experience that joyful discourse, which limits their understanding of and positive experiences with math.

How would our students' math learning and perception about math improve if they also had regular opportunities to talk about math? How might these opportunities help us create a world where learners know, use, and enjoy mathematics?

Let's explore the Math Language Routines, which are embedded in IM K-12 Math.

What are math language routines?

Stanford Graduate School of Education's Understanding Language and the Stanford Center for Assessment, Learning, and Equity (SCALE) designed eight Math Language Routines (MLRs) to help teachers "amplify, assess, and develop students' language" in math class. These routines are structured, but adaptable to the content and classroom context. The routines "emphasize the use of language that is meaningful and purposeful, not inauthentic or simply answer-based . . . [and] can and should be used to support all students learning mathematics." (from Understanding Language/SCALE's Principles for the Design of Mathematics Curricula: Promoting Language and Content Development ) There are four specific design principles used to entice students to discuss the concepts and ensure that the discussions provide opportunities for students to learn something new. The Math Language Routines also provide opportunities for students to engage in the Common Core's Standards for Mathematical Practice .

As students engage in math language routines, MLRs help students to advance their thinking in the following ways:

OPTIMIZING OUTPUT as students describe their own math thinking to others orally and visually or writing as physical, graphical, pictorial, or symbolic representations.

SUPPORT SENSE-MAKING as students scaffold their thinking and amplify language so students can make their own meaning between concepts and representations.

CULTIVATE CONVERSATION by providing opportunities to simultaneously make meaning, communicate that meaning, and refine the way content understandings are communicated.

MAXIMIZE META-AWARENESS as students organize their own experiences, ideas, and learning for themselves through reflection of the experience of discussing their math ideas, reasoning, and language.

This doesn't just mean that teachers tell students to talk about math and they do. We know that if we simply open the space and tell students to talk, much of the discussion will veer off-topic. Math Language Routines help teachers create a structure in which students can bring those four design principles to life.

Let's see what opportunities each MLR provides for students to practice exploring their math thinking and the MLRs' connections to the Standards for Mathematical Practice .

MLR 1: Stronger and Clearer Each Time - Students write a response to a math problem, then verbally share their response with a partner to get feedback from the listener to improve the response, and revise their original written response based on the feedback they received.

Students learn to both listen to their own thoughts and the thoughts of another with the purpose of strengthening their "first draft" thinking. This MLR strengthens student communication of their thinking. They make their explanations clearer through repeated "reviews" and revisions, which allow them to practice giving, receiving, and applying constructive feedback, and develop listening skills. This MLR helps students communicate their mathematical reasoning with greater clarity and focus.
(This connects to Standards for Mathematical Practice 1: Make sense of problems and persevere in solving them, 3: Construct viable arguments and critique the reasoning of others, and 6: Attend to precision. As students verbalize and review in writing the strategies they used and justification of those strategies, students have the opportunity to get feedback which can be used to critique the precision of their solution strategy and answer.)
MLR 2: Collect and Display - Students access their own and others mathematical ideas as the teacher scribes the language, strategies, and concepts students use during partner, small group, or whole-class discussions using written words, diagrams, and pictures.

By creating stable representations of student thoughts, the teacher extends the involvement of students in the math classroom. Student contributions are displayed for everyone to see. During that discussion as well as future conversations, students refer to these written ideas to improve the clarity and focus of their own communication. They can use the vocabulary, reference previous relationships between concepts, and identify new connections. This MLR helps make student thinking visible and promotes student ownership over mathematical ideas.
(Standards for Mathematical Practice 3: Construct viable arguments and critique the reasoning of others, and 6: Attend to precision. As students view the thinking of their classmates from the representation, they can address any differences they see between their representation and their classmates' representation in type and kind, further pushing students to find the most efficient or precise representation to solve the problem.)
MLR 3: Critique, Correct, and Clarify - Students rewrite a math response from an example that is incorrect, incomplete, or otherwise ambiguous.

In addition to providing students with a space to further engage in math, students employ a "growth mindset" and consider revisions to their work in order to strengthen their communication. This MLR helps students "try on" others' math thinking in order to improve it.
(Standards for Mathematical Practice 3: Construct viable arguments and critique the reasoning of others. Similar to doing error analysis, students have the opportunity to engage with a strategy for solving that might be different from theirs in order to find ways to improve the situation representation, address and clarify misconceptions about the math, and "borrow" parts of the strategy that were relevant to add to their toolbox.)
MLR 4: Information Gap - In a group, each student has different parts of the math context and they work together to piece together that information orally and/or visually to bridge the gap between the parameters of a math situation and a question to solve a math problem.

As students work to make sense of individual pieces of information about a math context, they also identify what information they need in order to answer the math question. This creates an environment where students work together as they consider which strategies are the most efficient and what information they need to know to solve the problem. This MLR helps students explore math contexts with a purpose.
(Standards for Mathematical Practice 2: Reason abstractly and quantitatively, and 4: Model with mathematics. As students imagine the kinds of information they need to know and explain why they need to know that information, they are building an understanding of the problem and possible solutions related to the parameters of the problem and the kinds of data they need to solve for an answer.)
MLR 5: Co-Craft Questions and Problems - Students take a provided math "answer" to create a problem that could result in that answer or use a given context to create a problem that can be answered using that context.

With this MLR, students use their creativity to explore a math context as they iterate their understanding in order to identify questions that can be asked and answered by the context. As students share their understandings with others, they also uncover the importance of slowing down to explore and think before they try to answer a question, which results in students understanding the math more deeply. This MLR helps students define math contexts.
(Standards for Mathematical Practice 4: Model with mathematics. By creating their own questions and problems, students learn to visualize the parameters of the problem as they consider what kind of answers are possible with the information the problem provides.)
MLR 6: Three Reads - Students are guided to read the problem three separate times with three separate purposes with quick discussions between each read.

When students slow down to consider how they can use the information in a problem, they notice things about their understanding of the problem context and their own math understanding that they wouldn't have noticed before. Giving students a purpose to read helps to focus students to identify (1) the context of the mathematical situation, (2) relationships that exist within that context, and (3) strategies that can be used to answer the question using the problem context. This MLR helps students think metacognitively about their math problem solving.
(Standards for Mathematical Practice 1: Make sense of problems and persevere in solving them. As students set a purpose for reading each of the three times, students practice and see the importance of understanding the problem context and using the information they know from the problem in order to identify a strategy for solving that relates directly to the problem context and available information.)
MLR 7: Compare and Connect - Students identify, compare, and contrast their own understandings with other students' mathematical approaches, representations, concepts, examples, and language.

As students encounter other's math thinking, this MLR opens the floor for students to consider how they see and talk about math. This MLR specifically helps students interact with each other's thinking.
(Standards for Mathematical Practice 4: Model with mathematics, 6: Attend to precision, and 7: Look for and make use of structure. As students compare (find differences) and connect (find similarities) between their strategy for solving and another classmate's strategy for solving, students mine their understanding of the math concept in relation to the structure and steps of another student's understanding of the math. This allows both students to attend to precision because to be understood by another, they have to be precise with their explanation.)
MLR 8: Discussion Supports - Students access strategies in multi-modal ways, like visuals, aural, animation/movement, and symbols as modes, to help students better make sense of complex language, ideas, and classroom communication.

Enhancing access to the mathematical context through these multi-modal supports helps students develop understanding while also continuing to work on their mathematical communication. This MLR helps students deepen their mathematical understandings, and find ways to communicate their understandings in different ways.
(Standards for Mathematical Practice 1: Make sense of problems and persevere in solving them, 3: Construct viable arguments and critique the reasoning of others, 5: Use appropriate tools strategically, and 6: Attend to precision. Using discussion supports helps students to see the reasoning of others as well as identify which tools to solve are most appropriate. In using these supports, students can be successful with in-depth or multistep problems with support from teachers and classmates.)
Next Steps

Consider what your students need to encounter math more deeply and in collaboration with others. More heads are better than one!

Looking for more support for distance learning ? Check out IM's collection of resources.

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Math Language Routines: Discourse with a Purpose - IM CERTIFIED® BLOG

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Asynchronous Learning for Imagine Learning Classroom

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Asynchronous Learning for Imagine Learning Classroom

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Allison Russell

allison.russell@imaginelearning.com
949.630.5856

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Watch to learn more about how students learn math in a problem based learning curriculum.

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Alyssa Scharf

alyssa.scharf@imaginelearning.com

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Making IM Centers Work: Joyful Practice, Meaningful Fluency, and Authentic Assessment - IM CERTIFIED® BLOG

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By Maureen D. O’Connell “How is it going with your implementation of IM K–5 Math Centers?” That’s my favorite question to ask during professional learning for IM K–5 Math. The response is a pedagogical temperature check about where teachers and grade levels are in their IM journey. Schools that repo…

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Office Hours Recording: IM Lesson Structure & Overview

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Office Hours Recording: Centers Overview

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Office Hours Recording: Pacing with Imagine IM

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Log into Imagine Learning Classroom (ilc) via Clever

--> K-5 Grade Band

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Log into Imagine Learning Classroom (ilc) via Clever

--> K-5 Grade Band

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