Six Strategies That Can Lead to More Equitable Online Mathematics Instruction
By Joe Dostilio and Laurie Speranzo
Institute for Learning
Every student has the right to be engaged in meaningful learning that draws on their unique abilities and backgrounds for making sense of mathematical ideas and relationships. Educators who believe this have looked for ways to engage all students in equitable mathematics instruction that advances each student’s conceptual understanding as they navigate this new world of virtual instruction.
These are three teaching practices that work in combination and can be used in virtual spaces for keeping every student engaged, talking, and supported in online learning.
- Keeping Learning Focused and Advancing
- Engage Students in Talk/Hear Student Voice
- Engage In Formative Assessment
For each of these practices, there are strategies that support equitable mathematics instruction when teaching virtually.
NCTM (2014) research shows that “Student learning is greatest in classrooms where the tasks consistently encourage high-level student thinking and reasoning and least in classrooms where the tasks are routinely procedural in nature” (Boaler and Staples 2008; Hiebert and Wearne 1993; Stein and Lane 1996) and “Not all tasks provide the same opportunities for student thinking and learning” (Hiebert et al. 1997; Stein et al. 2009).Even when instructional time moves online, students need time to consistently engage in high-level tasks on their own and with their classmates in order to keep learning focused on sense-making.
Strategy #1: Use Tasks that Require High-Level Mathematical Thinking and Reasoning
High-level tasks
- have multiple entry points;
- include or can be solved using a wide range of representations and tools; and
- require problem-solving.
Focus tasks, a subset of high-level tasks, are a type of cognitively demanding task that requires thinking and reasoning that leads to sense-making, but they do not require the same level of investigation or problem-solving. Focus tasks explicitly press student thinking about a key mathematical concept or relationships by leveraging one of the following methods. Try using a focus task that
- provides a model for students to interpret and make sense of the mathematics.
- shows an accurate and an inaccurate solution, then asks students to analyze and name which is accurate and which is not, and explain why.
- shares a way of solving that is not a traditional algorithm. Ask students to discuss the way of solving and apply it to a new situation or set of numbers.
Use focus tasks to help provide a steady diet of high-level tasks that leads to greater and deeper learning, especially in a time of potentially decreased instructional time due to the pandemic.
Investigating and discussing high-level tasks to make sense of mathematics supports students in seeing themselves as doers of mathematics.
Strategy #2: Provide “On Your Own” Time for Students to Begin Thinking and Reasoning about the Mathematics in the Task
- honors each student’s thinking and develops their identify as a doer of mathematics;
- provides formative assessment opportunities for teachers; and
- makes it possible for students’ ideas and solutions to be discussed and compared in small breakout groups and in whole-class discussions.
When time is a concern, consider sending the task to student in advance with a pre-recorded set-up that supports students in understanding the context of the task (without unpacking or giving away the math concept for them). Ask students to engage in “On Your Own” time and come to the live class meeting time prepared to share and discuss their solutions.
It is critical to provide time so that students can process the task, formulate their own mathematical thoughts and solution path, and put their thinking on paper before engaging in discussions. Providing this time makes it more likely that every student—regardless of native language, identification, background, or grade point average—will share their ideas with others, instead of just hearing from those students who work faster and/or louder.
Carpenter, Franke, and Levi (2003) talk about the importance of student voice. “Students who learn to articulate and justify their own mathematical ideas, reason through their own and others’ mathematical explanations, and provide a rationale for their answers develop a deep understanding that is critical to their future success in mathematics and related fields.”
When engaging students in virtual classrooms, look for ways to keep students generating, talking about, and making connections between their ideas and solution paths. Making time for and providing ways for students to use their voice and agency will build positive math identities.
Strategy #3: Incorporate Manipulatives into Lessons
Representations help to clarify the reasoning of specific students, while also leaving a visible trace of the strategy, which allows other students to enter into and follow the mathematical thinking of their classmates.
NCTM (2017) Taking Action
Manipulatives allow students to show their thinking and provide a reference when explaining their reasoning. Consider these options for having students use and discussion manipulatives in virtual classrooms.
- Use Virtual Manipulative Apps: They are available from several sources, such as the Polypad from Mathigon, National Library of Virtual Manipulatives and NCTM Illuminations.
- Make Virtual Manipulatives: PowerPoint or free software like Google Slides or Google Draw can be used to make virtual manipulatives. Here are links to an IFL high-level tasks and an example of Google Slides being used to make virtual manipulatives for the task.
- Clare’s Packs of Crackers Task and Lesson Guide
- Clare’s Packs of Crackers Student Facing Google Slides with Virtual Manipulative
- Repurpose Home Materials that Serve as Manipulatives: These may include crayons or cereal as counters, coloring one side of dried beans one color to create two-sided counters, or using something like toothpicks to construct geometric shapes.
Using student manipulative representations allows students to discuss their own understanding and to comment on and explain the thinking of others. When using virtual manipulatives, sending out the link in advance is a good idea, as students (and adults alike) need to “play” with the manipulatives before using them for a task.
Strategy #4: Create Space for Students to Share Their Thinking
Victoria Bill, longtime Senior Math Fellow at the IFL, always says, “The person who talks the most, learns the most!” Use ways to provide time and provide space to ensure each and every student has opportunities to talk and for their voice to be heard.
Check out 4 Go-To Learner-Centered Routines to Bolster Math Discussions, In-Person and Online to read about some routines that prepare students to engage in discussions about deep mathematics. Consistently using these and other routines that get students to share their mathematical thinking, provides similar benefits as those listed above for “On Your Own” work time, honors student thinking, develops their identify as doers of mathematics, provides formative assessment opportunities, and makes it possible for students to generate solutions to share and compare with other students.
Wiliam noted that “the important point is that we must acknowledge that what students learn is not necessarily what the teacher intended, and it is essential that teachers explore students’ thinking before assuming that students have ‘understood’ something. In this sense, assessment is the bridge between teaching and learning” (2005).
As mathematical ideas and solutions are shared, translate some formative assessment best practices to the virtual world. When students say or write about what they think, these strategies honor that thinking and students develop a sense of worth of their ideas—that their ideas are worth sharing and will be discussed in the process of learning mathematics.
Strategy #5: Ask for Agreement/Disagreement . . . Then, Ask Why?
Asking every student to weigh in on whether they agree or disagree is a simple means of formative assessment that teachers may use throughout a lesson. In virtual classrooms, identify ways to continue to use agree/disagree to keep students engaged and provide on-going formative assessment throughout the lesson.
- Ask students to use a Reaction or an Emoji.
- Poll students using a simple “Agree” or “Disagree”.
- Have each student send a message through the chat box; ask that the message be sent only to you when you want to make sure students are not swayed by others’ responses.
Then, prompt students to say more about why they agree or disagree! Without the justification of their agree/disagree stance, there is a missed opportunity for students to share their mathematical reasoning. If teachers are not in the habit of asking for students to back up their thinking, students may agree or disagree out of habit and not out of math content knowledge.
Asking every student to weigh in on whether they agree or disagree is a simple means of formative assessment that teachers may use throughout a lesson. In virtual classrooms, identify ways to continue to use agree/disagree to keep students engaged and provide on-going formative assessment throughout the lesson.
- Ask students to use a Reaction or an Emoji.
- Poll students using a simple “Agree” or “Disagree”.
- Have each student send a message through the chat box; ask that the message be sent only to you when you want to make sure students are not swayed by others’ responses.
Then, prompt students to say more about why they agree or disagree! Without the justification of their agree/disagree stance, there is a missed opportunity for students to share their mathematical reasoning. If teachers are not in the habit of asking for students to back up their thinking, students may agree or disagree out of habit and not out of math content knowledge.
Strategy #6: Provide Effective Feedback
Learners engage better when feedback is focused on their work, identifies what they have shown in their work in regards to the mathematical learning goal, and provides an actionable way for moving forward from their work. Feedback that assigns a grade or score that can often send a message that the learning is complete and has been assessed (Butler 1988, Black & Wiliam 1998, Hattie & Timperley 2007).
When providing written or verbal feedback, call attention to what work the student(s) have done and pose actionable next steps that press the student(s) toward deeper meaning-making.
Characteristics of Feedback and Guidance
| Feedback | Guidance |
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Check out these two examples of feedback and guidance given to two different groups by a teacher who utilized Google Slides during small group work a focus task.
Provide time for the student to take action/respond and then respond/resubmit. As time with our students is often reduced in hybrid and remote learning, this process of providing effective feedback and having students take action and respond/resubmit can create a better virtual experience for students and strengthen student-teacher relationships.
Regardless of where students are in their mathematical thinking—not yet fully expressing their reasoning, exhibiting faulty or overgeneralized thinking, or even having the correct answer with sound justification— they all deserve feedback and guidance. Every student should be pressed to move forward from where they are to deeper mathematical understanding. This makes the instruction both equitable and differentiated!
Tell Us About the Strategies You Use When Implementing High-Leverage Teaching Practices in Virtual Classrooms
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References
Black, P. & Wiliam, D. (1998) Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7-74.
Boaler, J. & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of railside school. Teachers College Record, 110(3), 608-645.
Butler, R. (1988). Enhancing and undermining intrinsic motivation: The effects of task-involving and ego-involving evaluation on interest and performance. British Journal of Educational Psychology, 58(1), 1-14.
Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary schools. Portsmouth, NH: Heinemann.
Hattie, J. & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), p81-112.
Hiebert, J. Thomas, P., Carpenter, E., Fennema, K. C., Fuson, D., Wearne, P., Human, H. M., & Alwyn, O. (1997). Making-sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425. Retrieved from https://doi.org/10.2307/1163241
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A & Wearne, D. (1997). Making mathematics problematic: A rejoinder to Prawat and Smith. Educational Researcher, 26(2), 24-26.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
Smith, M. S., Boston, M., Dillon, F., & Miller, S. (2017). Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 9-12. Reston, VA: National Council of Teachers of Mathematics.
Smith, M. S., Huinker, D. & Bill, V. (2017). Taking Action: Implementing Effective Mathematics Teaching Practices in K – Grade 5. Reston, VA: National Council of Teachers of Mathematics.
Smith, M. S., Steele, M. D., & Raith, M. L. (2017). Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 6-8. Reston, VA: National Council of Teachers of Mathematics.
Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2 (1), 50–80.
Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.
Wiliam, D. (2005). Keeping learning on track: Formative assessment and the regulation of learning. In M. Coupland, J. Anderson, & T. Spencer (Eds.), Making mathematics vital: Proceedings of the twentieth biennial conference of the Australian Association of Mathematics Teachers (pp. 26–40). Adelaide, Australia: Australian Association of Mathematics Teachers.
Accountable Talk and Learning Walk are registered trademarks of the University of Pittsburgh.
Using 4 Learner-Centered Routines to Build Positive Math Identity in Equitable Classrooms
By Laurie Speranzo and Kristin Klingensmith
Institute for Learning
Equitable mathematics instruction that honors the lived experiences, ways of knowing, and linguistic and cultural assets of students should always be at the forefront of our minds. Each and every student has the right to ongoing, high quality, rigorous instruction that recognizes them as learners and that is designed for students to advance their conceptual understanding. Both inside and outside of the classroom, students are thinking, reasoning, and problem-solving daily. It is imperative that we honor the fact that students are doers of mathematics and that the lives students lead provide greater context for mathematical knowledge than what our lessons alone provide. Black and Brown students are doers of mathematics. Emergent multilingual students are mathematicians. Students identified as needing specialized educational support are “math people.” So how can teachers use learner-centered routines to support students in seeing themselves as doers of mathematics?
This article is the second of a two-part series focused on four learner-centered routines:
- Turn and Talks
- Stop and Jots
- Step Backs
- Quick Writes
It explores how these four routines can be used to foster a positive math identity in students by creating space for voice, agency, and actually doing mathematics. For more information about these routines, check out the first article 4 Go-To Learner-Centered Routines to Bolster Math Discussions, In-Person and Online.
Using Routines to Invite Student Voices and Promote Agency in a Math Classroom
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Voice: Students have choice, control, challenge, and opportunities to collaborate. [Toshalis, E. & Nakkula, M. J., (2012). Motivation, Engagement, and Student Voice] |
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Agency: The capacity and propensity to take purposeful initiative… [Ferguson, R. F., Phillips, S. F., Rowley, F. S., & Friedlander, J. W., (October 2015). The Influence of Teaching Beyond Standardized Test Scores: Engagement, Mindsets, and Agency] |
Having students build their identity as doers of mathematics starts with providing opportunities to access voice and employ agency in math classrooms. Student voice in class does not just mean hearing from a student. It means they have the opportunity to share their thinking and to challenge the thinking of others; it means they have the opportunity to work together while engaging in the math so they are constructing meaning, not just taking in information. It also means that they see their words and their mathematical activity as having an impact on the outcome of the classroom discussion. When teachers make the deliberate move of talking less, it leaves more space for students to share their thinking, understanding, and lived math experiences. By attending to student voice in the classroom and providing opportunities that foster agency, students can build agency.
Turn and Talks & Stop and Jots
Imagine this happening in a classroom:
Two students have just shared their solution paths – Josiah used repeated addition to solve the task and Martina used multiplication. The teacher asks, “Can both solution paths be correct? Be ready to say why.”
Four hands shoot up, the same four that are always up.
Though it is exciting to see students ready to share, in an equitable classroom all students are given a chance to process their thinking and be ready to engage in the discussion of the task.
The Turn and Talk and Stop and Jot routines can be used to create time and space for all students to think about and construct a response to the question. Providing opportunities for students to get their own thinking out verbally or on paper honors what every student brings to the table, such as use of a language other than that of instruction, algorithms more dominant in other countries, representations that are not traditional in American classrooms, and student connections to a context related to their own experiences. Consider these examples.
| Learner-Centered Routine | Example for Use in the Scenario | Recognizes Students as Doers of Mathematics |
|---|---|---|
| Turn and Talk | Ask students to turn to a partner and discuss their thinking. After a minute or so, make sure that the second person in each partnership has had a chance to share so all of the talking is not done by one person. |
Every student has the opportunity to verbally share their reasoning to a rigorous mathematics question with a peer. Additionally, every student has the chance to
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| Stop and Jot | Pause and say, “Take a moment. Stop and jot. Can both solution paths be correct? Why or why not.” to allow students time to process their thinking. |
Every student has the opportunity for and responsibility to privately respond to a rigorous question about mathematics and construct a response that may be shared with the whole class. Additionally, every student has the chance to
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Turn and Talks and Stop and Jots provide opportunities for students to process independently or collaboratively the question posed by the teacher.
Take a look at these two routines being used in math classes.
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In this grade three classroom, they are working on unpacking patterns in multiplication (when doubling one factor, the product doubles). The teacher uses a Turn and Talk to ensure every student has a chance to work through their thinking before hearing from a few students publicly. |
In this seventh grade classroom, watch as the teacher uses a Stop and Jot that turns into a Turn and Talk to give students the chance to process their ideas while she uses the time to formatively assess where students are in their understanding. |
Step Backs & Quick Writes
Return to the scenario from earlier involving the two solutions paths (multiplication and repeated addition scenario) and think about how the conversation may have progressed. Step Backs and Quick Writes can be used later in such a discussion to build in additional opportunities for student voice and agency, but these would likely be done with a slightly modified question.
| Learner-Centered Routine | Example for Use in the Scenario | Recognizes Students as Doers of Mathematics |
|---|---|---|
| Step Back | Use one of the other routines and then after students have heard from multiple classmates, ask the step back question “Why is multiplication with [whole] numbers the same as repeated addition?” |
Students benefit from repeated public marking of the key structures of the mathematics being studied, by teachers and classmates. Asking students to respond to step back questions, shifts the responsibility of pulling the ideas together to students. Students are expected to
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| Quick Write | Because this is an opportunity for a major “a-ha” moment for students, it offers the chance for students to dissect a more narrow piece of the thinking to be able to apply it to the question of if both paths are correct. Start with an independent Quick Write of “How are repeated addition and multiplication similar? Different?” |
Using the more narrow Quick Write allows students to be ready to add their voice to the discussion by
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Using Routines to Build Positive Student Identity in Math Classrooms
We have all heard people say, “I’m not a math person.” The reality is that math is all around us and impacts how we interpret the world. Therefore, we all need to feel that doing math and thinking mathematically are a part of who we are.
“How students are positioned to participate in mathematics affects not only what they learn but also how they come to see themselves as learners,” according to NCTM (2018), Catalyzing Change, p. 28. Ensuring that student voice is at the forefront of the classroom experience builds students’ confidence, honors the lived experiences they bring to the table, and sustains a belief that they can do the math and that their thoughts matter. As students’ positive identity grows, their voice will be leveraged even more. Students’ math identities are a reflection of the opportunities that have been provided in the classrooms to build voice, agency, and the belief in being a doer of math!
Letting only the four students, who first raised their hands, be the only ones who contribute to the discussion, reinforces the false narrative that math is about speed and that the few whose hands went up first were those “good in math.” By utilizing the learner-centered routines, more students are going to feel that their thinking is worthy of sharing, both in writing and in discussion, and, therefore, build a cadre of learners who believe they can do math! It is incumbent upon us as educators to not only hear student voices in the classroom but listen to what the students are telling us about how what they know and can do as mathematicians.
To read more about instructional approaches that foster student agency, check out the article Focusing on the Instructional Approach Nurtures Agency.
Tell Us About How the Routines You Use Led to Greater Voice
Tell us here. |
Every Student Needs High Cognitive Demand Instruction
By Rosita Apodaca
IFL Executive Director
Peter Compitello
Project Manager
Disrupting inequitable practices, examining biases, creating inclusive and sustainable school environments for students, and finding and cultivating the assets and interest that every student brings to school are part of what is needed for all students to develop to their full potential in and out of school. Lauren Resnick, cognitive psychologist and founder of the Institute for Learning (IFL), believes we can teach all students to reach or exceed world-class standards.
Resnick knows that, in practice, it is proving hard to meet the twin goals of equity and higher achievement. This is because schools are trapped in a set of beliefs about the nature of ability and aptitude that makes it hard to evoke rigorous academic effort from students and educators.
Students who have not been taught a demanding, challenging, thinking curriculum do poorly on tests of reasoning or problem solving, confirming many people’s original suspicions that they lack the talent for high-level thinking.
Students cannot learn what they are not taught, and depriving them of high-cognitive-demand curriculum and instruction is not an equitable education.
For decades, Resnick and others have advocated for thinking and problem solving to be the “new basics” of the 21st century. Still, the common idea that we can teach thinking without a solid foundation of knowledge had to be abandoned, as does the idea that we can teach knowledge without engaging students in thinking. Knowledge and thinking must be intimately joined. This implies a curriculum organized around major concepts in each discipline that students are expected to know deeply. In short, in every subject, at every grade level, the curriculum has to include a commitment to a knowledge core, high-thinking demand, and active use of knowledge.
Despite widespread support for disciplinary literacy, not all students have been given opportunities to achieve this high standard. Ramón Antonio Martínez (2019) believes that building on the assets students bring to school can support them in accessing and participating in a high-cognitive-demand curriculum. Changing how we view learners is also critical to improving the educational experience of students of color and those who are labeled upon their entry in school. When we view students as struggling or “at risk,” we make assumptions that they are students in need of remediation. When we begin to see students’ multilingualism as an asset and their use of multiple languages as tools to help them access high-cognitive-demand work, we can turn the dime on its head and make small modifications in learning plans that will enable emergent multilingual students to access complex text and engage in high-cognitive-demand activities.
Practitioners have made arguments that mediating instruction does not need to be labor-intensive; it is about making decisions while teaching a well-designed lesson. Teachers focus on the goal of the lesson and find ways for every student to meet that goal. Knowing and building on the students’ assets should serve as a guide to making the small modifications to support students. Simple supports, such as offering a student the text in a language the student understands or allowing a student to write the argument about something familiar, are ways to make modifications that allow for access. We can begin by abandoning deficit thinking and keeping our minds open to see our students’ situations as opportunities to try ways that will support them where they are and enable movement toward the goal.
Martínez (2018) argues that for emergent multilinguals, we may have to “learn to see students anew—to imagine them as competent readers and writers and to treat them accordingly.” The labels students are given in school, more often than not, are not helpful. Martínez thinks that for us to “recognize the richness of bi/multilingual students’ linguistic repertoires requires that we think beyond the convenient labels that serve to mask their brilliance, their competence, and their tremendous potential.” Martínez’s recommendation may serve us well once we decide that high-cognitive-demand work will be made available to every student.
In a similar vein to Gutiérrrez and Martínez, Dr. David E. Kirkland reminds us “rigor in education cannot be about broken students but about supporting students who are vulnerable to broken systems.” Before we can address the systems that support inequitable practices, we have to acknowledge systemic root causes: “Rigor often codes a set of hierarchal social and cultural values that reinforces a narrow concept of learning and achievement. Too often, rigor is about who is recognized and who is not. By flattening rigor in the image of the seen, a narrow version of us gets baked into educational success—a version that is incomplete, favoring an intersection of cis, heteronormative, White, abled, English-speaking, monied, and Judeo-Christian—or put simply, privileged—identities. I’ve learned the farther away students are from this identity, the less likely they are seen to be ‘rigorous;’ the less likely the classroom works for them.”
While being keenly aware of systemic disparities in equity and rigor, Kirkland aims for a hopeful solution: “…teaching and learning must be about preservation—the incredible acts that help people preserve our languages and cultures, to tell history on our terms, to preserve it too, to preserve ourselves by preserving the congregation of ideas that will make the world better, that will free our bodies and heal our souls. Thus, academic rigor comes close to equity when it connects teaching and learning to acts that are meant to sustain us.”
Engaging Emergent Bilingual Students in Daily Academic Talk
Rosita Apodaca
IFL Executive director
Sara DeMartino
IFL English language arts fellow
Tabetha Bernstein-Danis
Assistant professor, Kutztown University of Pennsylvania
English learners (ELs)—or emergent bilinguals (EBs) as educators now refer to these students to remove the deficit stigma from their identity (Garcia et al., 2008)—must engage in academic conversations every day to gain access to the world of knowledge. Their educational mission is the simultaneous acquisition of knowledge and English. As educators committed to equity know, EBs cannot wait until they are fluent English speakers to participate in academic conversations. Academic language is an essential component of an equitable educational program for EBs, and equitable teaching practices that embed academic language development for these students must support deep thinking, conceptual understanding, argument, and discussion. All of these practices are grounded in two Principles of Learning—Accountable Talk® Practices and Academic Rigor in a Thinking Curriculum (Resnick, L. et al., 2005). These practices are central to being ready for college, career, and life. There is a body of work that demonstrates that well-structured talk produces robust learning and helps “build the mind.” These benefits show up in standardized tests, transfer to other content domains, and persist over the years (Resnick, 2015).
Using Accountable Talk practices (or generically, “academically productive talk”) as a tool to support EBs to engage in academic conversations requires a change in mindset about how we educate students learning a new language. Rather than limiting instruction to teaching students a language, we propose using both the native language support and emerging English skills to learn concepts and ideas. Challenging academic work results in productive struggle for students and requires that a lesson’s cognitive demand is not diminished. Rather than removing the struggle and potentially encouraging learned helplessness in students, teachers need to maximize EBs’ access to challenging content without depriving them of the opportunity to grapple with difficult new concepts.
Accountable Talk Discussions
At the IFL, we believe academic discussion is purposeful and productive, occurring via sustained conversations about meaningful content that is anchored in grade-level culturally relevant texts and tasks. Students work together to co-construct knowledge, and both students and teachers negotiate meaning through “talk moves,” such as asking for clarification, paraphrasing, and building on or disagreeing with previous ideas.
The following examples show ways in which teachers can mediate rigorous discourse in a fourth grade classroom. Teachers play an important role in augmenting ways for students to be successful when they use complex academic language. The development of this complex language positively impacts students’ vocabulary and reading outcomes, allowing them to more quickly keep pace with their native English-speaking peers.
To reach these goals, EBs need opportunities to listen to academic language in authentic contexts. They also need opportunities to use purposeful language, such as to explain, disagree, agree, or build on others’ ideas. Teachers who call on various students to explain their thinking about the same idea provide students with opportunities to hear new concepts explained multiple times in multiple ways, maximizing their ability to make meaning from these new ideas. EBs also need to be taught vocabulary indirectly during discussions to get to the gist of the subject being discussed and directly after they have had the opportunity to hear it used in context.
Developing knowledge and academic language requires having something meaningful to discuss, and that usually means using culturally relevant texts. Fillmore (2010) says that the only way for students to acquire the language of literacy is to encounter these structures and patterns in the materials they read. The texts they discuss need to be sufficiently complex so that students can discover how academic language works.
The teacher whose work is illustrated here had one or more of the following goals of Accountable Talk practices in their lessons (Michaels, S. and O’Connor, C., 2012):
- Help individual students to share their reasoning so that it can be heard and understood.
- Help students to orient to others and listen to what others say.
- Help students to work on deepening their reasoning.
- Help students to work with the reasoning of other students.
Example 1: Building on Ideas
In the first example, EBs are engaged in an instructional unit on child labor. The teacher is working to help students understand a complex informational text through utilizing Questioning the Author (QtA) for comprehension. In the excerpt, the teacher has asked students to explain why the author used different examples of child labor from around the world.
Student 1: That there is not only one place that has child labor. That they have it like around the whole world.
[Turn and talk]
Teacher: Carlos, go ahead Carlos.
Student 2: I want to add something also. Because, he is telling us about all these places because if somebody wants to stop child labor, they just can’t say one country. Because other countries does it. So, you can’t say, “Oh El Salvador does child labor” because they, they will tell on the other people. “Egypt does it too, so you can’t just blame us too.”
Student 3: …if they are going to do something for that for the whole world should care. Because there’s… child labor in the whole world. Even in the United States.
Rather than explaining to students why an author might use various examples to support his or her point, the teacher presented students with an open-ended question, gave students an opportunity to talk about the question (represented by crosstalk in the transcript), and then gave students an opportunity to share their thinking with the whole group. The teacher’s use of a probing question and then providing students an opportunity to clarify their thinking first with a classmate allowed EBs to have confidence sharing their thinking in front of the group and building on the ideas of others.
Example 2: Academic Vocabulary
In this second example, the class is still engaged in the QtA lesson on an informational text about child labor. In this excerpt, the teacher has just asked a question about the agricultural work referenced in the article.
Student 4: Okay, I think the author is trying to tell us that, it isn’t like…all they’re getting right to have children do um like carry a lot of things and they are not like learning, and they are just like… They are doing things like adults are supposed to do.
Teacher: How did you know that children were not learning? Where in the text did you…
Student 5: Right here, Their work is harsh and violates their rights to health and education. Education is the same as learning so..
Student 4: Okay
Student 6: Okay, I want to, I want to add something else. I wanna like they say here that they are….like dangerous. Maybe like if they have an accident, they can hurt themselves, like really hard.
Student 7: I think they are like really exploding the kids.
Teacher: What do you mean by exploding the kids?
Student 7: They’re, they’re using them, like that’s not right. They shouldn’t be doing that.
Student 5 in this example utilizes the author’s language (harsh and violates, both Tier Two vocabulary words) to help Student 4 explain why he thinks the authors say that children are not learning. Tier Two vocabulary words are more difficult for both native English speakers and EBs to learn because they are words not often heard in everyday speech. The teacher provided exposure to less frequently used Tier Two words through her choice of text. Students also continue to build on peers’ thinking, an expectation that was set for students at the beginning of the year and had become commonplace for students.
The teacher is also willing to accept the student’s use of imprecise language. Student 7 confuses the word exploiting for exploding possibly because explotar means both exploit and explode in Spanish, but rather than correct the student or ignore the student’s use of the improper term in English, the teacher asked the student to explain his thinking. This explanation helps the teacher and the student’s peers to better understand what the student meant when he said “exploding,” and it also allows the teacher some additional insight into the student’s thinking about the ideas in the text. Even though the student used the wrong word, he was still comprehending an essential concept from the text.
Both of these examples provide just the tip of the iceberg when it comes to considering the arsenal of tools teachers need to build EBs’ academic English and content knowledge. Overall, we recommend the following for teachers of EBs to push their students to meet goals more on par with their native English-speaking peers:
- Start with a good set of norms that are established with the help of the students for using talk respectfully, and for ensuring equitable participation
- Utilize culturally relevant texts that provide opportunities for students to see themselves, develop knowledge around a topic or idea, and learn ELA content.
- Design high-level tasks that engage students with open-ended questions by utilizing classroom routines that ask students to generate, share, revise, and reflect on thinking.
- Have a set of talk moves that serve as tools for accomplishing the established goal(s).
- Have a set of mediation tools to support the varied levels of language acquisition represented in the room.
- Be willing to accept imperfect language from students as they learn to master English and academic language.
Engaging EBs in complex tasks around challenging texts in English is no simple feat, but with the right tools at teachers’ disposal, we know that it is one they can accomplish. Careful planning and consideration about appropriate texts, student characteristics, and the tasks that best scaffold instruction help facilitate EBs to engage in the kinds of discussions that will not only build English, but also create critical thinkers and speakers.
References
Garcia, O. , Kleifgen, J. A., and Falchi, L. (2008). From English language learners to emergent bilinguals. (Equity Matters: Research Review No.1)
Resnick, L. B., & Hall, M. W., with the Fellows of the Institute for Learning (2005). Principles of learning for effort-based education. Pittsburgh, PA: Institute for Learning.
Resnick, L., Asterhan, C., & Clarke, S. (Eds.). (2015). Socializing intelligence through academic talk and dialogue. Washington, DC: American Educational Research Association.
Fillmore, L. W. (2010). Charting the course of success for English language learners conference: Common Core State Standards implementation. Council of Chief State School Officers (CCSSO).
Apodaca, R. (2007). Mediating learning for English learners. Unpublished research presented at The General Administrators Meeting in Austin, TX and at The California Association for Bilingual Education, San Francisco, CA.
Filmore, C. J. & Filmore, L. W. (2012). What does text complexity mean for English learners and language minority students? Understanding Language: Stanford University School of Education.