# data[].attributes.headline
Engaging in Mathematical Practice Look-Fors

# data[].attributes.subject
Engaging in Mathematical Practice Look-Fors

# data[].attributes.body
No longer just a numbers game, to succeed in math, ELLs need instruction and assessment practices that help them carry the added linguistic load.

# data[].attributes.attachment_link.readable_text
Laura Varlas

At her district's newcomer center, English as a Second Language teacher Barbara Gottschalk would engage parents in a visual exercise: compare a math textbook from 20 years ago to the one in use today. The former, a familiar reproduction of the kind of math newcomers most likely experienced in their home countries, was defined by rows of computation. In the current textbook, however, words abound.

"You could tell just by looking at the two that even a student with a strong background in math will need some language support in a mainstream math class," says Gottschalk, who teaches at Susick Elementary in Troy, Michigan. A student with interrupted or limited schooling, she adds, will need even more language support.

With the Common Core State Standards and, especially, the skills identified in the Standards for Mathematical Practice, mathematics has increasingly emphasized conceptual understanding and reasoning, in addition to procedural know-how. "Language is the entirety of the mathematics classroom," says Megan Rowe, a math teacher at Borah High School in a linguistically diverse district outside Boise, Idaho. "From the language I use when I'm teaching to the language students use when they're reasoning among their peers-I don't know how you could ever teach mathematics now without focusing on language."

Double-Edged Disadvantage

Yet there's evidence across the education sector that many still assume English language learners (ELLs) don't need language support in math, and that belief can create a double-edged disadvantage for such students. ELLs placed in mainstream math courses with little to no language support are more likely to flounder under increased linguistic demands. However, when ELLs are tracked into remedial classes-and researcher Eduardo Mosqueda reports that this is a common and pernicious trend-it severely reduces the likelihood that they will eventually take advanced math courses.

"Once you start looking at math through the lens of language, you see linguistic demand everywhere," says San Diego State University professor Bill Zahner, a former high school math teacher. Without awareness and planning to support ELLs with that linguistic load, language will continue to be a gatekeeper to the advanced courses that lead to in-demand, well-paying careers in STEM fields. For Zahner and others, it's a question of equity: "How do we meet the needs of linguistically diverse students in math?"

Build a Baseline

When working with ELLs, it can be easy to mistake lags in language for gaps in math learning. "Just because they don't have the words doesn't mean they don't know how to do it," says Gottschalk. That's why middle school ESL teacher Beth Morrow's first rule of supporting ELLs in the math classroom is assess, don't assume. Establishing a baseline of where students are in terms of math knowledge and language proficiency helps teachers tailor the content and English supports ELLs receive.

Gottschalk uses a simple, language-free, calculation-based assessment to screen students' content knowledge. But even with pared-down assessments, cultural differences in math notation can make screening students challenging.

"Although there are some common rules that all mathematicians and scientists use, worldwide, they manifest themselves differently depending on the culture," says Cassie Eatmon, math chair at Herndon Middle School in Virginia. For example, long division is set up differently in the United States than in South American countries, and Arabic notation is written right to left. "Subtracting in Arabic looks wrong to us, but it's actually just flipped," explains Gottschalk.

Incorporate Semantic Supports

For newcomers, Eatmon recommends gradually increasing language demands. "Phrase questions that require them to produce a minimal amount of English at the beginning," she recommends. Choice questions (that require a yes/no, true/false, and ways for them to communicate nonverbally via a word card or hand signals) are a good place to start. As newcomers develop confidence with language skills, stretch expectations for discourse.

"Newcomers need special handling for a while," says Rita MacDonald, researcher at WIDA and the Wisconsin Center for Education Research (WCER). "However, students are newcomers for the short term; they are language learners for a long time."

For the long haul, ELLs will need different levels of support to engage in increasingly language-rich mathematics. Visual representations of concepts, word walls, defining word parts (prefix, root, suffix), sentence frames, and note-taking practice-common tools in language arts learning-can be adapted in order to make math-centered conversations more accessible to ELLs. For example, Eatmon recommends adapting the traditional think-pair-share processing strategy to think- write-pair-share so that students will have a script of their thoughts to refer to. "That reduces the burden on ELLs to think and talk [in a new language] at the same time," she explains.

Language in Use

Researchers at WCER have developed six specific moves teachers can make to strengthen all students' reasoning skills in mathematics, especially ELLs ( see Figure 1), as well as seven tactics students can apply when working with ideas in math ( see Figure 2). These strategies develop language through doing mathematics, what MacDonald calls a "language in use" approach. "It used to be a common belief that you had to learn language before you can do stuff. We don't believe that works," she says. "You really only learn language through shared experience, by doing something."

MacDonald recommends introducing and practicing the student moves one at a time and providing prompts and sentence frames to cue students as they clarify, restate, support, challenge, compare, explain, or build on an idea (see http://stem4els.wceruw.org/resources/Student-and-Teacher-moves.pdf for examples). The goal, says MacDonald, is to "get ELLs in the habit [of understanding] that there are so many things they can do when an idea is presented."

Practice with discourse-centered mathematics helps students build the precision that is the cornerstone of math fluency. "In regular conversation, we don't tend to be precise and specific with our language. In mathematics, you need to be, but you don't just jump to that disposition right away," explains MacDonald. You get there through experiences, like needing to explain precisely the constraints of an argument, of having to use a very specific label for something. Those experiences happen in classes where students are practicing math in all four language domains.

Designed for Discourse

In a language-rich, ELL-supporting math class, students learn math through listening, speaking, reading, and writing-the four domains of language. But many classes, not just math, tend to fixate on the listening domain. "Students get all kinds of practice listening," says Gottschalk. "But they can easily go through a whole day of school without ever having to utter a single word of academic English."

"If you set the goal that every single student has the opportunity to speak, every single day," says Rowe, "you start to realize how few opportunities there are-at least there were for me-for students to talk about math."

Rowe has refocused her teaching from "What's the math for today?" to "What's the language for today?" and says that allows her to structure learning that gets to a deeper level of math thinking. "My students aren't just robots that can regurgitate a process or steps," says Rowe. "To learn math, they have to be able to talk about it."

One of Rowe's favorite strategies for eliciting math discourse is the "partner round-up." This strategy can be used to talk through all sorts of mathematical operations. For example, if students are practicing adding fractions, each student receives a card with a different fraction on it. They then find a partner in the class and work together to successfully find the sum of their fractions. Once they do, they trade cards and find a new partner and repeat the process. "This could have easily been a worksheet-20 problems, practice adding fractions on your own," says Rowe. But when it's done as partner exercise, her students get to talk to 20 different peers and hear the different ways they think through and explain a problem. "You go from something that was content-based to language rich, and that makes a big difference especially for ELLs."

Gottschalk's school uses journaling extensively in math class. Language is modeled and practiced as students discuss, and then write about, a problem of the day, she says. Teachers can get creative with how they set up journal prompts. MacDonald suggests, "Here's my favorite wrong answer from the last class. Let's figure out why that was wrong."

Opportunities to develop language, through identifying relationships or making generalizations within sets of problems, are implicit in some of the materials teachers have, adds Zahner, but those opportunities are often not highlighted. Zahner is currently working with a team of 9th grade math teachers on a project funded by a $1 million grant from the National Science Foundation to design secondary mathematics classrooms focused on meeting the needs of ELLs. There's a real urgency, he argues, to provide teachers with resources and supports to unpack the curriculum so that opportunities for discourse and reasoning, not just right answers, are prioritized.

Weeding Wordy Problems

With language at the center of the modern math classroom, it's important to note that not all words are worthwhile in the service of math learning. In fact, there are a lot of nonessential words and distracting or confusing contexts littering math texts. "If you use an example that talks about a horse, it better be the animal and not the gymnastics equipment," Eatmon warns.

Zahner cites a textbook example of a word problem for calculating the slope of a roof. The problem talks about two- by six-inch sized pieces of wood that will be used as vertical supports for the roof. These pieces of wood are unfortunately written as "2×6's." The dimensions of the board are not actually relevant to the rest of the problem, says Zahner. But for a student from Mexico, this aspect of the problem was derailing. "His answers to every other problem were correct except for this one. He got stuck trying to figure out how to use '12,' which is two times six."

Rowe adds that sometimes her students struggle with names. "If there's a Mr. Brown in the problem, they'll wonder who that is and why his name is relevant to the problem." Rowe changes names to simple identifiers: man, woman, or person.

"When we see language complexity popping up, we have to ask, is this necessary to the mathematical development?," says Zahner. "If it's not, can we take it out or plan around it?"

On assessments, Rowe also provides students with a recording of all test questions-audio files saved to Dropbox or Google Drive and represented as a scannable QR code on students' test sheets. This helps because most ELLs' receptive or oral language proficiency is higher than their reading proficiency. Through school-provided devices or students' own phones, students hear Rowe read each question-sometimes word-for-word or paraphrased, with steps to get started, or breaking down the question in ways that they'll understand.

Context vs. Content

In addition to removing unnecessary language, Zahner advises teachers to think carefully about the number and types of contexts used to develop a mathematical concept. Although it may be helpful to use multiple contexts to show students that math concepts are all around them, don't make students master a multitude of scenarios just so they can access the math content. In one text, Zahner's team found 12 different problem contexts used to explain linear functions.

"If you've never driven on a toll road and a problem is asking you to calculate the per-mile toll, but you're stuck on what is a toll?, that's going to stop you from accessing the content," he says. Instead, Zahner suggests focusing on a few relevant, key contexts. One way to do that is to find out what students are interested in and build math problems with those contexts. For example, teachers he works with recently changed a problem about pumping water out of a pool to one about rates for downloading files to your phone. "When the teacher introduced this context, everyone was engaged because all kids have opinions about who's got the good network or good rates."

"Keep in the forefront of your mind, 'What do I want students to do?', and build your question around that," says Eatmon. Simplifying the language doesn't mean watering down the math. Keep expectations high that these kids can do the math you've taught them, she adds.

Equal Signs

Planning for language supports in math helps ELLs communicate their ideas and invites them into STEM, which can have a profound effect on their career and earning opportunities, says MacDonald. "It's this huge, epistemic equity issue."

"If we equitably involve ELLs in math-position them as idea-generators alongside their peers, instead of just passive listeners-their language is going to develop much more quickly because they'll be creating and negotiating meaning together," MacDonald adds.

Eatmon urges educators not to confuse a lack of language for a lack of intellect. With the right supports, it does not take long for their wheels to catch traction and take off, she says. Eatmon has seen ELLs make five to six years of growth over the course of one year. "It's not that they can't do it; it's that they've never been taught."

Figure 1

© 2017 The Board of Regents of the University of Wisconsin System. Used by permission. Stem4els.wceruw.org.

Figure 2

© 2017 The Board of Regents of the University of Wisconsin System. Used by permission. Stem4els.wceruw.org.

Laura Varlas is the managing editor of ASCD Express and a contributor to Education Update.

# data[].attributes.attachment_link.description
Laura Varlas At her district's newcomer center, English as a Second Language teacher Barbara Gottschalk would engage parents in a visual exercise: compare a math textbook from 20 years ago to the one in use today. The former, a familiar reproduction of the kind of math newcomers most likely experienced in their home countries, was defined by rows of computation.

# data[].attributes.headline
Teacher and Student Talk Moves in Math with Examples

# data[].attributes.subject
Teacher and Student Talk Moves in Math with Examples

# data[].attributes.body
Provides that academic talk moves for clarifying student thinking, listening and thinking with peers, reasoning, and providing time to think, as well as student talk moves to sustain discussion.

# data[].attributes.attachment_link.readable_text
Research-Based Tips to Turn Up Math Talk

Bridget Soumeillan

Hear that? Math class doesn't sound like it used to-at least it shouldn't.

You could hear a pin drop in my childhood math classes. We sat in rows, worked on our own, listened to the teacher at the center of the classroom, and spoke only when spoken to. Today, there is a growing understanding that academic discourse and peer-to-peer collaboration help all students make learning gains in mathematics. Students can exchange ideas in whole groups, small groups, and pairs. The common-sense idea that fostering math discussions would improve math language acquisition and learning is also validated by research. In Visible Learning for Mathematics (2016), John Hattie finds student-to-student and student-to-teacher dialogue positively influences student achievement.

Provide Structures That Promote Discussion

Teachers should plan groups thoughtfully to ensure that discussions elicit evidence of understanding from all students. There should be an emphasis on structuring academically diverse groups, which Hattie's research shows is far more effective than grouping kids by ability. Common to English language arts and social studies classrooms, discussion aids that set a clear structure for conversations (such as Save the Last Word for Me, Whip Around, or Concentric Circles) give teachers strategies for engaging all students in discussions because all students must participate and be active listeners (Harvard Graduate School of Education, 2017). Teachers need to build students' capacity to attentively listen and provide useful feedback through demonstration, or by using tools like Talk Cue Cards, Talking Points, or Ground Rules for Exploratory Talk offered by the University of Cambridge in the Thinking Together project (2018).

For teachers interested in incorporating technology, using a platform like the Desmos Activity Builder and its Polygraphs activities requires every student to be actively involved in developing mathematical language through electronic communication with classmates. Although these tools and strategies work well for specific discussions, implementing an overall classroom structure that fosters ongoing dialogue is also a good idea. The technique Talk Moves, in which teachers use prompts to ensure that all students speak, listen, and respond to one another, helps move conversations in all class settings (Chapin, O'Conner, and Anderson, 2013).

The Talk Moves technique revolutionized my classroom by establishing an expectation for what communication looks like in math class. To begin, I focused on implementing one prompt at a time so that I didn't overwhelm my students. At first, my students were a bit awkward responding to me when I asked, "Caroline, would you repeat or rephrase what Abel just said?" or "Lindsey, would you add on to what Brad just said?" But as we practiced revoicing together, students needed less prompting from me.

Support the Three Different Types of Talk

Research has identified three categories of talk in classrooms: disputational talk, cumulative talk, and exploratory talk (Mercer, 1995). Disputational talk usually centers on a dispute or has a competitive nature in which students go back and forth on decisions. To keep this type of talk productive, I find it helpful to require students to use sentence frames-a sentence or question with words removed. One of my favorite sentence frames for this is, "I disagree with your [answer/process/strategy] because ..."

Cumulative talk is characterized by students simply agreeing with each other. As a deterrent for blindly agreeing with others, I occasionally plant some "wrong answers" within groups by discreetly asking a student to make mistakes on purpose to see if there is any pushback from the other students. I also find it effective to require groups to provide multiple solution strategies or have a group member explain another's work to me.

The most effective type of discussion is exploratory talk (Mercer, 1995). This involves sharing knowledge, providing reasoning, challenging others' reasoning, providing alternate hypotheses, and joint consideration of all ideas. A study of elementary-age students found that the way language is used during exploratory talk within groups positively affects the way students solve problems independently (Dawes, Littleton, Mercer, Wegerif, and Warwick, n.d.).

Measure Participation and Assign Roles

Teachers sometimes believe that it is hard to assess each student's contribution and progress when doing group work. Using clearly defined group roles can ensure that you get active contributions from everyone. One note of caution: Using group roles usually results in a single student being appointed to record the group's cumulative findings. I think it's better to have each student in the group individually record the group's data and formulate written responses. Then, I like to have the group negotiate a collective response to present as their final product to ensure that all students are really learning the material. This individualized thinking can then be recorded in a group chart with each student assigned a specific colored marker. This approach gives all students ownership and evidence of their learning.

Balance Group and Individual Work

Students shouldn't work in groups all the time. Students must also be self-reliant to ensure that they develop individual mental stamina, which the Standards for Mathematical Practice refer to as perseverance, to do complex math. As teachers use more challenging curricular materials, students need time to think deeply before they engage in group discussions. Some teachers find it helpful to pose a few reflective questions or sentence frames for students to consider on their own before calling for small-group discussions.

Worth the Effort

Teachers have to work to build a supportive and highly communicative culture for students. I know this can sound daunting on top of all the other requirements we face every day as math teachers. But fostering true student collaboration by creating an open and safe classroom in which lively math discussions are the norm is worth the investment of time and energy and will reap immense benefits for teachers and students alike.

References

Chapin, S. H., O'Connor, M. C., and Anderson, N. C. (2013). Talk moves: A teacher's guide for using classroom discussions in math, grades K-6. Sausalito, CA: Math Solutions.

Dawes, L., Littleton, K., Mercer, N., Wegerif, R., and Warwick, P. (n.d.). Thinking together in the primary classroom. Milton Keynes, UK: The Centre for Research in Education and Educational Technology. Available at https://www.open.ac.uk/creet/main/sites/www.open.ac.uk.creet.main/files/08%20Thinking%20Together.pdf

Harvard Graduate School of Education (HGSE). (2017). Teaching and learning lab: Discussion protocols. Cambridge, MA: Author.

Hattie, J., Fisher, D., Frey, N., Gojak, L. M., Moore, S. D., and Mellman, W. (2016). Visible learning for mathematics, grades K-12: What works best to optimize student learning. Thousand Oaks, CA: Corwin.

Mercer, N. (1995). The guided construction of knowledge: Talk amongst teachers and learners. Clevedon, UK: Multilingual Matters.

"Resources for Teachers." Thinking Together, University of Cambridge " Resources for Teachers [website]. Accessed December 19, 2017. Available at http://thinkingtogether.educ.cam.ac.uk/resources/

Bridget Soumeillan is a curriculum writer for the nonprofit Great Minds, publisher of Eureka Math. She previously served as a high school math coach and teacher in Lafayette, La. She was also a Teacher Leader Advisor, an educator network that provides peer-to-peer professional development.

ASCD Express, Vol. 13, No. 22. Copyright 2018 by ASCD. All rights reserved. Visit www.ascd.org/ascdexpress.

# data[].attributes.attachment_link.title
Research-Based Tips to Turn Up Math Talk

# data[].attributes.attachment_link.description
Research-Based Tips to Turn Up Math Talk Bridget Soumeillan Hear that? Math class doesn't sound like it used to-at least it shouldn't. You could hear a pin drop in my childhood math classes. We sat in rows, worked on our own, listened to the teacher at the center of the classroom, and spoke only when spoken to.

# data[].attributes.attachment_link.provider_name
Seesaw | Elementary Learning Experience Platform

# data[].attributes.attachment_link.authors[].name
Seesaw | Elementary Learning Experience Platform

# data[].attributes.attachment_link.title
Elementary Learning Experience Platform | Seesaw

# data[].attributes.attachment_link.description
Seesaw is a Learning Experience Platform with 25M+ users, enhancing elementary education, engagement, and school culture while improving academic success.

# data[].attributes.attachment_link.readable_text
PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

Discussion and Supporting Materials

Thought starters

1. What supports does Ms. Colon have available to students to help them write?

2. Why is it important to give students opportunities to speak before writing?

3. How could you use this strategy in your own classroom?

School Details

ENLACE Academy

Lawrence, Massachusetts

Teachers

# data[].attributes.attachment_link.description
Enjoy your first video for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. Enjoy your first video for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. What supports does Ms. Colon have available to students to help them write?

# data[].attributes.body
6 research-based routines for math classes that supports language-focused skill growth.

# data[].attributes.body
Conversation, Math Reasoning and Argument tools

# data[].attributes.headline
ELLs in Math: Challenges and Strategies from Steinhardt

# data[].attributes.subject
ELLs in Math: Challenges and Strategies from Steinhardt

# data[].attributes.attachment_link.readable_text
The 3 Reads instructional routine is designed to develop students' ability to make sense of problems by deconstructing the process of reading mathematical situations. Over time, students will internalize this process, thereby creating a heuristic for reading and making sense of mathematical story problems, math practice 1.

The info-graphic captures the flow of the routine, and resources below will support your implementation of the routine. We've provided a copy of the planner so that you may download and print it, or type right into it. The slides may be customized for a specific task by inserting images and refining the prompts. And, finally, we'll continue to update the tasks section, and hope you'll comment on your own experiences with them, and upload artifacts from your classroom.

You can read more about the 3 Reads in Chapter 6 of Routines for Reasoning, and read about implementing the 3 Reads reasoning routine remotely.

Today I taught the 3 Reads Routine for the first time... to a small group of ELL students whose language proficiencies are between levels 1 and 4. What I noticed is that the format of 3 Reads somehow allows students to be more relaxed about the reading and thinking process. I think the freedom comes partly from being given the time to read the problem 3 times and partly from being asked not to blurt out the answer. The explicit instructions that go with each of the steps of the 3 reads is very helpful to students.

(The 3 Reads) routine has been a way...for meaningful coaching that is not just about implementing a new product/program. I've modeled it now in 3 different classrooms, and teachers have taken the routine and run with it. Students keep commenting to me in the hall telling me they read a problem 3 times following the routine in their head. My favorite was a 3rd grader who has received math support from a special educator since 1st grade. She happily came up to me and said, "I did 3 Reads today! I knew what the problem was about and what I was supposed to do all by myself! ...my teacher was so happy because I figured out what to do without her!" How great is that?!? Her confidence was soaring, ... and she could figure out the problem independently.

I quickly realized how important this routine was to slow students down and have them spend time thinking about the problem as they are so driven to solve and be correct they miss important information.

Watch Grace Kelemanik engage adults in the 3 Reads Instructional Routine at the Heinemann Teacher Tour

Free Resources (Site Registration/Login Required)

# data[].attributes.attachment_link.description
The 3 Reads instructional routine is designed to develop students' ability to make sense of problems by deconstructing the process of reading mathematical situations. Over time, students will internalize this process, thereby creating a heuristic for reading and making sense of mathematical story problems, math practice 1.

# data[].attributes.attachment_link.readable_text
Contemplate then Calculate is an instructional routine designed to shift attention away from mindless calculations and toward necessary structural interpretations of mathematics. This routine fosters structural thinking, math practice 7.

The info-graphic captures the flow of the routine, and resources below will support your implementation of the routine. We've provided a word copy of the planner so that you may download and print it, or type right into it. The powerpoint slides may be customized for a specific task by inserting images and refining the prompts. And, finally, we'll continue to update the tasks section, and hope you'll comment on your own experiences with them, and upload artifacts from your classroom.

Free Resources (Site Registration/Login Required)

Contemplate then Calculate Overview

Classroom PPTX Template

Classroom Planner

Tasks & Discussion

# data[].attributes.attachment_link.description
Contemplate then Calculate is an instructional routine designed to shift attention away from mindless calculations and toward necessary structural interpretations of mathematics. This routine fosters structural thinking, math practice 7. The info-graphic captures the flow of the routine, and resources below will support your implementation of the routine.

# data[].attributes.attachment_link.readable_text
Capturing Quantities is an instructional routine designed to focus students' attention on important quantities and relationships in problem situations. The goal of the routine is to develop students' ability to reason abstractly and quantitatively, math practice 2.

The info-graphic captures the flow of the routine, and resources below will support your implementation of the routine. We've provided a word copy of the planner so that you may download and print it, or type right into it. The powerpoint slides may be customized for a specific task by inserting images and refining the prompts. And, finally, we'll continue to update the tasks section, and hope you'll comment on your own experiences with them, and upload artifacts from your classroom.

Free Resources (Site Registration/Login Required)

Classroom Planner

Classroom PPTX Template

Tasks & Discussion

# data[].attributes.attachment_link.readable_text
Capturing Quantities is an instructional routine designed to focus students' attention on important quantities and relationships in problem situations. The goal of the routine is to develop students' ability to reason abstractly and quantitatively, math practice 2.

The info-graphic captures the flow of the routine, and resources below will support your implementation of the routine. We've provided a word copy of the planner so that you may download and print it, or type right into it. The powerpoint slides may be customized for a specific task by inserting images and refining the prompts. And, finally, we'll continue to update the tasks section, and hope you'll comment on your own experiences with them, and upload artifacts from your classroom.

Free Resources (Site Registration/Login Required)

Classroom Planner

Classroom PPTX Template

Tasks & Discussion

# data[].attributes.attachment_link.readable_text
Recognizing Repetition is an instructional routine that supports the difficult road to generalizing problem situations. Students enlist multiple modalities while they attend to the repetition in their counting, calculating, and constructing processes. In doing so, they leverage their repeated reasoning to make abstract generalizations, math practice 8.

The info-graphic captures the flow of the routine, and resources below will support your implementation of the routine. We've provided a word copy of the planner so that you may download and print it, or type right into it. The powerpoint slides may be customized for a specific task by inserting images and refining the prompts. And, finally, we'll continue to update the tasks section, and hope you'll comment on your own experiences with them, and upload artifacts from your classroom.

Free Resources (Site Registration/Login Required)

Classroom Planner

Classroom PPTX Template

Tasks & Discussion

# data[].attributes.attachment_link.description
Recognizing Repetition is an instructional routine that supports the difficult road to generalizing problem situations. Students enlist multiple modalities while they attend to the repetition in their counting, calculating, and constructing processes. In doing so, they leverage their repeated reasoning to make abstract generalizations, math practice 8.

# data[].attributes.attachment_link.readable_text
Decide and Defend is an instructional routine in which students make sense of another's line of mathematical reasoning, decide if they agree with that reasoning, then draft an argument defending their decision. The routine fosters math practice 3, construct viable arguments and critique the reasoning of others.

The info-graphic captures the flow of the routine, and resources below will support your implementation of the routine. The powerpoint slides may be customized for a specific task by inserting images and refining the prompts. Check back in regularly as we continue to expand and update the tasks section. We hope you will comment on your own experiences with the tasks and share others you've used.

Free Resources (Site Registration/Login Required)

Classroom Planner

Classroom PPTX Template

Tasks & Discussion

# data[].attributes.attachment_link.description
Decide and Defend is an instructional routine in which students make sense of another's line of mathematical reasoning, decide if they agree with that reasoning, then draft an argument defending their decision. The routine fosters math practice 3, construct viable arguments and critique the reasoning of others.

# data[].attributes.headline
Math Practices- An Inclusive Climb- Supporting Special Populations

# data[].attributes.subject
Math Practices- An Inclusive Climb- Supporting Special Populations

# data[].attributes.attachment_link.readable_text
The ways in which students think and reason mathematically are now described as explicitly as ever in the Standards for Mathematical Practice. Our greatest fear is that, if these standards are not developed in all students, we will be widening the achievement gap. In addition, the practice standards describe research-based supports for special populations - students with learning difficulties (SWLDs) and English Language Learners (ELLs).

See the graphic organizer for the overlap between strategies to support SWLDs and ELLs. Then, watch a 5 minute video in which Amy Lucenta lays out the symbiotic relationship between the math practices and supports for special populations.

# data[].attributes.attachment_link.description
The ways in which students think and reason mathematically are now described as explicitly as ever in the Standards for Mathematical Practice. Our greatest fear is that, if these standards are not developed in all students, we will be widening the achievement gap.

# data[].attributes.body
The instructional activities, tools, and resources offered by this project are designed to support teachers to learn about and take up practices of ambitious teaching and engage children in rich mathematics.

# data[].attributes.headline
Instructional Routines for Supporting English Language Learners- TEDD.org

# data[].attributes.subject
Instructional Routines for Supporting English Language Learners- TEDD.org

# data[].attributes.body
Ambitious instruction for students learning English as an additional language recognizes that these culturally and linguistically diverse students bring with them cultural and linguistic resources upon which the teachers must learn and draw as well as pay explicit attention to the teaching and learning of both language and content in their instruction. Our goal is to provide students access to grade-level academic content, explicitly support students in their English language development, and provide opportunities for students to participate meaningfully in their own learning.

# data[].attributes.headline
Mathematical Practice Standards Supported in Math Routines

# data[].attributes.subject
Mathematical Practice Standards Supported in Math Routines

# data[].attributes.attachment_link.readable_text
Three of the math practices described in the Common Core State Standards for Mathematics- reason abstractly and quantitatively (MP2), look for and make use of structure (MP7), and look for and express regularity in repeated reasoning (MP8) - describe three different avenues of mathematical thinking that provide entry into and through all kinds of math problems (see graphic). Click on the table for an overview of what a math doer pays attention to, the questions they ask themselves, and the subsequent actions they take when using a particular avenue of thinking. Click on the video for an engaging five-minute presentation describing the three avenues of thinking.

Use our routines for reasoning to develop these avenues of thinking in your students and they will become powerful math problem solvers!

Grace Kelemanik ignites the 2015 NCTM audience with a framework for the Standards for Mathematical Practice,
When does 2+7+8=1?

Watch a five minute overview of a framework for the Standards for Mathematical Practice. Pause when you'd like to spend more time considering the mathematics and the student work.

# data[].attributes.attachment_link.description
Three of the math practices described in the Common Core State Standards for Mathematics- reason abstractly and quantitatively (MP2), look for and make use of structure (MP7), and look for and express regularity in repeated reasoning (MP8) - describe three different avenues of mathematical thinking that provide entry into and through all kinds of math problems (see graphic).

# data[].attributes.attachment_link.title
Reading Math_ Starting with Visuals – Choice Literacy

# data[].attributes.attachment_link.readable_text
PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

Discussion and Supporting Materials

Thought starters

1. Why is it important for students to talk it out before writing?

2. What supports are in place to help students write out their ideas?

3. Why is this an especially effective strategy for English Language Learners?

School Details

Banting Elementary School
2019 Butler Drive
Waukesha WI 53186

Data Provided By:

Teachers

# data[].attributes.attachment_link.title
My Thinking Logs: A Literacy Practice for Math

# data[].attributes.attachment_link.description
Enjoy your first video for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. Enjoy your first video for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. Why is it important for students to talk it out before writing?

# data[].attributes.headline
Owning the Common Core Mathematical Practice Standards in Grades 6-8

# data[].attributes.subject
Owning the Common Core Mathematical Practice Standards in Grades 6-8

# data[].attributes.attachment_link.readable_text
PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

Discussion and Supporting Materials

Thought starters

1. How does Ms. McPhillips help her students "own" the math practices?

2. Why is it important to use the language of the Common Core with students?

3. How does Ms. McPhillips make discussion about the math practices a part of her daily routine?

School Details

John F. Deering Middle School
2 Webster Knight Drive
West Warwick RI 02893

Data Provided By:

Teachers

# data[].attributes.attachment_link.description
Middle school math coach Audra McPhillips helps her students understand the Common Core math practices through discussion and daily reflection. Audra explains how she shares Common Core language with her students and has them think about how they've used the practices each day.

# data[].attributes.headline
Divergent Questioning in 8th Grade Math- Teaching Channel

# data[].attributes.subject
Divergent Questioning in 8th Grade Math- Teaching Channel

# data[].attributes.attachment_link.readable_text
PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

Discussion and Supporting Materials

Thought starters

1. In this classroom shift, what challenges will Mr. B face?

2. What challenges will his students face?

3. Why?

4. What could Mr. Brettle do at the beginning of his lessons to get students invested?

5. What could Mr. B do to help his students work in groups more effectively?

School Details

Washington Grover Jr School
201 East Olney Avenue
Philadelphia PA 19120

Data Provided By:

Teachers

# data[].attributes.attachment_link.description
Mr. Brettle's class is observed by teacher evaluator Barbara VanDenberg. Barbara suggests he work on divergent questioning, try having students work in groups, and put more of the cognitive load on his students. Over four weeks, Mr. B implements her suggestions. Watch the challenges of making these big shifts in your classroom.

# data[].attributes.headline
My Favorite No- Warm up for Middle School Math, Teaching Channel

# data[].attributes.subject
My Favorite No- Warm up for Middle School Math, Teaching Channel

# data[].attributes.attachment_link.readable_text
PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.
Have questions about subscribing?
Click Here to learn more about individual subscriptions.
Click Here to learn more about School and Institution access.

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.
Have questions about subscribing?
Click Here to learn more about individual subscriptions.
Click Here to learn more about School and Institution access.

Discussion and Supporting Materials

Thought starters

1. How does this strategy allow for immediate re-teaching?

2. What criteria does Ms. Alcala use to pick her favorite no?

3. How does Ms. Alcala use assessment data to inform her teaching?

School Details

Martin Luther King Middle School
1781 Rose Street
Berkeley CA 94703

Data Provided By:

Teachers

# data[].attributes.attachment_link.description
Leah Alcala gives her students a warm-up problem at the beginning of every class, which they solve on index cards. She quickly sorts through them, and from the wrong answers chooses her "favorite no." She and her kids then analyze what's right about the solution before delving in to what the writer doesn't understand that led them to answer incorrectly.

# data[].attributes.attachment_link.description
Fostering the Mathematical Practices in All Students

# data[].attributes.headline
Visible Learning in the Mathematics Classroom

# data[].attributes.subject
Visible Learning in the Mathematics Classroom

# data[].attributes.attachment_link.title
Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning | SAGE Companion

# data[].attributes.attachment_link.description
Welcome to the Companion Website"Visible Learning for Mathematics situates highly effective teaching practices in three phases of learning-surface, deep, and transfer learning. This framework offers a precise way to consider when particular teaching practices most benefit students' learning, considering where students are in the learning process."-Diane J.

# data[].attributes.attachment_link.readable_text
Available Formats

ISBN: 9781483353654

Electronic Version

Suggested Retail Price: $28.95

Bookstore Price: $23.16

ISBN: 9781483331782

Paperback

Suggested Retail Price: $31.95

Bookstore Price: $25.56

Should you need additional information or have questions regarding the HEOA information provided for this title, including what is new to this edition, please email sageheoa@sagepub.com. Please include your name, contact information, and the name of the title for which you would like more information. For information on the HEOA, please go to http://ed.gov/policy/highered/leg/hea08/index.html.

Foreword by Miriam A. Leiva

1. Developing Conversational Language: Help English Learners

2. Developing Academic Language: Develop Mathematics Concepts and Vocabulary for English Learners

3. Scaffolding: Give Support for Both Mathematics and Language Learning

4. The Role of Concrete Materials: Utilize Objects to Develop Mathematical Understanding for English Learners

5. Visual Learning: Provide Mathematical and Organizational Representations As a Regular Component of Instruction

6. Questioning Strategies: Ask Questions to Foster Students' Learning of Mathematics and English

7. Comprehensible Input: Combine Many Strategies to Develop Mathematics Concepts Through Clear and Effective Instruction

Each chapter's lesson scenario and chapter questions are newly written or adapted to address Common Core State Standards and a specific Standard for Mathematical Practice. Lesson scenarios illustrate a variety of ways of supporting ELLs' comprehension and English language development.

The instructional aspects of the lesson scenarios that span from primary to middle school classroom settings are intended to be generalizable across many grades and to be sources of discussion among educators. The scenarios demonstrate a variety of ways in which classroom teachers might provide mathematics instruction that addresses CCSSs and Standards of Mathematical Practice

Each chapter's commentary on the mathematics teaching example, along with targeted chapter questions, provides opportunities for educators to contemplate, discuss, and envision helping all students, but particularly ELLS, work towards proficiency with the Standards for Mathematical Practice and the CCSS

Each chapter's discussion of research and teaching tips serve as a "tool" for educators to understand, discuss, and visualize their own highly effective standards-aligned mathematics teaching of all students, including ELLs

# data[].attributes.attachment_link.title
English Learners in the Mathematics Classroom

# data[].attributes.attachment_link.description
Available Formats ISBN: 9781483353654 Electronic Version Suggested Retail Price: $28.95 Bookstore Price: $23.16 ISBN: 9781483331782 Paperback Suggested Retail Price: $31.95 Bookstore Price: $25.56 Should you need additional information or have questions regarding the HEOA information provided for this title, including what is new to this edition, please email sageheoa@sagepub.com.

# data[].attributes.attachment_link.readable_text
We express ourselves in different ways. On Flip, you can use our simple and fun built-in camera to record your thoughts, add effects and share within your Flip group as video, audio only or text in your web browser or mobile app.

# data[].attributes.attachment_link.title
Flip is a video discussion and sharing app, free from Microsoft.

# data[].attributes.attachment_link.description
Flip (formerly Flipgrid) is a video discussion and video sharing app, free from Microsoft, built for classrooms and beyond. Learn more.

# data[].attributes.attachment_link.readable_text
Join the Peartember celebration for giveaways, exclusive templates, and more! Learn more >

EFFORTLESSLY BUILD ENGAGING INSTRUCTIONAL CONTENT, RIGHT FROM GOOGLE SLIDES

The fastest way to transform presentations into classroom conversations

Imagine if you could engage every student in your class, every day. What if you could instantly see who's confused and who's ready for more? That's the power of Pear Deck. And now, with the Pear Deck for Google Slides Add-on, you can add the magic of formative assessments and interactive questions to your presentations right from Google Slides.

Design brilliant slides & engage your class

Open up Google Slides & the Pear Deck sidebar

Design a new presentation or open an existing one in Slides. Just getting started with Google Slides? Upload your PowerPoint or Keynote lessons to Google Slides and get going!

DROP IN FORMATIVE ASSESSMENTS

Our team of educators created a library of templates to support learning objectives typically found at the beginning, middle, and end of a class. Think: bell ringers, checks for understanding, exit tickets, and more. Simply drop in one of these templates for instant engagement and watch your class transform.

Create custom questions

You can always create your own custom activity or question from scratch. Use Text, Number Response, Multiple Choice, and Web Slide questions to engage students. Or upgrade to Pear Deck Premium to add Drawing and Draggable™ response types.

ADD AUDIO TO ANY SLIDE TYPE

With the Pear Deck Add-on, you can leave audio instructions, descriptions, or examples for your students to hear while they read the prompts and respond to Interactive Questions in your Pear Deck Slides presentations. Make a new recording instantly or upload one from your computer. The recordings you insert will play in the Student View of your live presentation Sessions, so it's perfect for any remote learning lesson!

Present with Pear Deck

Start your presentation and students will join your Session from any device with a web browser. As you advance your slides, students will be prompted to answer your questions! Students' answers can be displayed anonymously on the classroom projector, so instead of worrying about getting the right answer and feeling silly in front of peers, your students are putting ideas out there in a safe, anonymous way, discussing, and learning from each other.

GO DEEPER WITH THE tEACHER dASHBOARD

As an instructor, you can quickly see what each individual thinks on the Teacher Dashboard. Noticing a lot of wrong answers? Adapt! Take a pause, back up, re-explain. But don't forget to help the learners help each other: Why did some people choose this while others chose that? How can we find out the right answer? What else do we need to know?

INVITE TEACHERS TO YOUR SHARED tEACHER DASHBOARD

This feature enables teachers using Pear Deck Premium to share Session controls and valuable student insight with other designated educators, including student teachers, special educators, co-teachers, or even substitutes. With a real-time view of individual student work and the ability to guide and provide direct feedback, educators teaching together can better support the diverse needs of learners everywhere!

Using Videos, Animations and GIFs in your Pear Deck? Get ready to Power-up!

Want to show a video about the Mars Rover in your Pear Deck presentation? Need to carefully layer in information on a slide to reduce information overload? Found a perfect GIF of a plant emerging from its seed? If you want your videos, animations, and GIFs to play at full resolution when you present with Pear Deck, install the Power-Up Google Chrome extension.

The Power-Up is a free Google Chrome extension. Installing it ensures that videos, animation, and GIFs embedded in your Pear Deck slides play at full-resolution on the projector and student devices - exactly the way they should!

Install the Power-Up from the Chrome Web Store on the device you use in class. Now when you present with Pear Deck, the Power-Up magically enables the display of your videos, animations, and GIFs.

Get the Power-Up

Learn Pear Deck for Google Slides

Watch a video for self-guided Google training:

Or, dive into a self-paced Pear Deck for Google Slides practice deck:

# data[].attributes.attachment_link.description
Pear Deck for Google Slides is the #1 Slides Add-on, making it effortless for educators to add interactive questions and formative assessments to their presentations.

# data[].attributes.attachment_link.readable_text
Our screen capture tools help you easily create, edit and communicate with videos and images. Simple and intuitive tools to share your ideas.

Windows, Mac / iOS, Android, and Chromebook | No account required

Easy video communication for everyone

190 countries

Million of users in ourglobal community

Trusted

by Fortune 100 companies, school districts,
and 98 of the top 100 universities in the US

100,000,000+

Videos captured (and counting) since 2006

How can ScreenPal help you?

I need to capture videos and images.

Highly rated by our community

Overall rating: 4.6 out of 5 based on 4,516 reviews.

What our community is saying

With ScreenPal I've been able to extend my expertise and automate some of my more routine tasks by creating high-quality video content and feedback, which then frees up my time for more personalized mentorship.

Cal Poly University Professor and founder and CEO of Mentorship Academy

ScreenPal's user-friendly interface and seamless integration into our existing teaching methods made it an obvious choice. From day one, it was clear that ScreenPal was not just another tech tool; it was a catalyst for active learning and collaboration.

Technology Integration and Innovation Coordinator, Arlington ISD

We use ScreenPal internally to create and manage all of the videos we share with educators. ScreenPal makes it easy to create videos with a consistent, branded look and feel, and then to share all of those videos from a central repository.

Chief Program Officer, The Modern Classrooms Project

Join millions of people communicating through video.

# data[].attributes.attachment_link.description
At ScreenPal, we don't believe that video recording and editing should be difficult, or cost a fortune. Our simple and intuitive tools help you get the job done easily.

# data[].attributes.attachment_link.description
These glossaries are to provide permitted testing accommodations of ELL/MLL students. They should also be used for instruction during the school year.

# data[].attributes.attachment_link.title
Topic Briefs: Linguistically Diverse Learners and the NYS Next Generation P-12 Learning Standards

# data[].attributes.attachment_link.description
The New York State Education Department (NYSED) is pleased to present to you a series of eight topic briefs produced for NYSED by Nonie K. Lesaux, Ph.D. from Harvard University & Emily Phillips Galloway, Ed.D. from Vanderbilt University.

# data[].attributes.body
Common Core Math Vocabuary Word cards- contains word, picture and definition.

# data[].attributes.attachment_link.readable_text
This page contains math vocabulary cards for Kindergarten through 8th Grade and Secondary 1 Mathematics. These cards can also be found in Spanish, Chinese, and French under the Dual Immersion menu. Portuguese, German, and Russian vocabulary cards are located at the following website: USOE Dual Immersion Vocabulary Cards

# data[].attributes.attachment_link.description
This page contains math vocabulary cards for Kindergarten through 8th Grade and Secondary 1 Mathematics. These cards can also be found in Spanish, Chinese, and French under the Dual Immersion menu...