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

Students need time to generate their own thinking and solutions to a task. Consistently giving students independent work time
  • 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.

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.

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
  • Highlights mathematical ideas or strategies and lets the student know the benefit or usefulness of the idea or strategy.
  • Acknowledges student’s actual work.
  • Is focused on student’s work, not the student.
  • Conveys to students that they have an audience for their work, “I noticed…” “When looking at your work…”
  • Highlights components of the program that are valued (e.g., connections between representations, communication of mathematical reasoning).
  • Extends the student’s work from where the student is in his or her work to the next stage of the work.
  • Encourages the student to do the work, serves as a call to action, “Give it a try…”
  • Presents students with a challenge or a counter to their method.
  • Prompts the learner to consider the use of alternative representations, strategies, or processes.

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

  • Which of these strategies that support equitable mathematics instruction do you already use in virtual classrooms? How is it going?
  • What other strategies that support equitable mathematics instruction do you recommend for virtual classrooms? Why?

Share your story here.

    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.

    Tagged with: Academic Rigor, Agency and Voice, Equitable Instruction, Formative Assessment, High-Level Tasks / Curriculum, High-Leverage Teaching Practices, Math, Multi-Lingual Learner Instruction, Online Instruction, Principles of Learning

    Organizing Instructional Tasks with Landing Pages

    By Sara DeMartino

    Institute for Learning

    Organizing Instructional Tasks with Landing Pages

    What is a Student-Centered Routine in ELA?

    A student-centered routine in ELA is a sequence of actions that students are asked to take to develop a response to open-ended, text-based task.
    This document shows the various elements of student-centered routines used during ELA instruction. We always recommend that students get an opportunity to capture their thinking in writing before being asked to share in pairs or with the larger groups. This practice offers students a chance to surface what they initially think, gives them a document to speak from as they share, and allows them to add to or revise their thinking.

    Although we are not physically present in your districts, we’ve been working with and talking to many of you virtually throughout the fall. In reflecting on our conversations with you, it’s clear to us that teachers are leading the way in understanding how various online tools work to facilitate student-to-student and student-to-teacher interaction. You’ve found that how teachers provide students opportunities to interact with a text, share their thinking with a peer (either synchronously or asynchronously), share their thinking whole group, and then reflect on what they’ve learned should remain consistent whether students are in class or at home. Keeping the routine consistent and using online tools to facilitate interactions among students allows them to know what to expect, whether they are present in the classroom or at home. It also provides opportunities for students who are in the classroom to interact with students who may be learning at home.

    Teachers have found great success using landing pages to organize learning for students across one text or across multiple texts in a unit. A landing page is a page on a website where students “land” to do their work or engage in a task. We’d like to share with you an example of a landing page designed for a sequence of work with the text, “The Censors” by Luisa Valenzuela. You can access the sample landing page here.

    Why Landing Pages?

    Landing pages, much like task sheets, provide students with both the why and the what of an instructional task. They support more equitable access to instructional activities by making expectations clear and providing step-by-step guidance for students as they engage in learning.

    Landing pages provide the why by explaining to students the purpose of the work they will be engaging in during one task and across multiple tasks. Purpose statements help students see where they are going and help them to see that the task isn’t just busy work.


    Purpose statements for an arc of work across one text and for a task.

    Landing pages also provide students with the what–the steps they need to take to be successful with a task and the tools they need to help them along the way. If you’re familiar with our student-centered task sheets, then landing pages should feel pretty similar. Landing pages help to alleviate some of the “Miss, I don’t know what to do!” comments we often hear from students, and students report that they appreciate the consistency that working from a landing page provides (whether students are working at school or at home).

    Setting Up a Landing Page

    We used Google Sites for creating instructional landing pages because it’s easy to use (no coding required!) and plays nicely with other tools in Google Suite (i.e., Google Classroom). You can link directly to landing pages in Google Classroom and provide students with a calendar of when the work will be completed.


    Once students navigate to the landing page, they will see that it includes links to sub-pages for each instructional task. For example, the first linked subpage for “The Censors” is the comprehension task.

    Subpages are built to mirror paper task sheets. We strongly recommend that when planning an instructional task through a landing page, that you begin planning as if you were creating a paper task sheet and then take a step back to decide how you’ will facilitate the student-centered routines (Do you need to structure the routines for a class with students who are both in school and online? Are your students entirely asynchronous?) and how students will demonstrate their learning (Will students work in a collaborative slide deck? Will you add links to an assignment in Google Classroom?). This guide provides a few suggestions for translating student-centered routines to online spaces. You will notice that we’ve annotated the following images of the comprehension landing page to provide some insight into how we structured the comprehension task for the text, “The Censors.” This task was structured for a class that utilizes some synchronous time with students.

    The comprehension subpage provides students with the purpose statement and information that students may need to help them engage with the task and text.
    Each step of the task is provided for students as well as links to the applications or tools needed to complete the step.
    In STEP 1, students are expected to add to a Jamboard to allow the teacher an opportunity to assess what students understand about censorship.

    STEP 2 engages students with the text. This work is linked through Google classroom. It allows students to individually work through reading and annotating the text, while giving the teacher an opportunity to see how students interact with the reading.
    In STEP 3, after reading the text, students are asked to complete a quick write in response to a comprehension question. Working asynchronously, students are asked to post the quick write to a Pear Deck presentation with the expectation that when the class meets for their synchronous time, students will share and discuss what they wrote.

    STEP 4 is the final step in the work for the comprehension task. It lets students know that they will be expected to have steps 1-3 finished when they meet with the rest of the class online to collaborate around a slide deck that will be used during a virtual gallery walk and whole class discussion of the text.

    We love hearing from our teachers!

    • How are you organizing online learning experiences for your students?
    • Have you tried landing pages? How are they working for your students?
    • What are some other digital tools that have proven useful for you and your students as you work together online?

    Tell us your story here.

      Tagged with: ELA, Elementary, High School, High-Level Tasks / Curriculum, High-Leverage Teaching Practices, Middle School, Online Instruction, Reading / Comprehension, Writing

      Remote Coaching for Rigorous and Engaging Online Classroom Discussions: Layering New Forums with Fresh Insights

      By Lindsay Clare Matsumura and Dena Zook-Howell

      Institute for Learning and LRDC

      In many districts, teachers have worked hard to incorporate Accountable Talk® practices that enable rich classroom discussions. In the COVID-19 pandemic, inequities in resources available to students have been further exacerbated. Often student learning is interrupted by inequitable access to computers and to the internet. Burdens on teachers and other educators also are extreme. Teachers are contending with their own hardships in addition to teaching online for the first time with little training. It can feel like rigorous and interactive conversations are no longer an option. It is possible, however, to engage students in the kinds of rigorous and interactive discussions online that are foundational to student learning. Coaches, even while practicing social distancing, have an important role to play in assisting teachers to continue, rather than abandon, this important pedagogy. Here we describe some things that we are learning from our ongoing research at the University of Pittsburgh’s Learning Research and Development Center on how coaches can support teachers remotely to engage students in rigorous and interactive online discussions.

      What is different about coaching in a pandemic?

      Coaching teachers remotely during a pandemic is similar to face-to-face coaching in its focus on student thinking, rigorous content, and cultivation of an inquiry stance toward instruction. Overlaid on top of these, however, is a new role for coaches to support teachers to use features of online platforms to achieve particular learning goals and establish positive online communities. Compounding these knowledge demands is the very real uncertainty that teachers themselves are experiencing in this pandemic. Uncertainty and anxiety provide a weak springboard for learning and responding to teachers emotionally in this new environment is a larger part of the coaching context than it was previously. In the following sections, we discuss specific ways coaches can support teachers to move their discussions online.

      ⁘ Helping teachers reestablish their classroom learning community.

      Even though teachers may have established a strong learning community in their face-to-face instruction, it is likely they will need to reestablish their learning community in the new online environment. Teachers may find, for example, that students who jump in right away during in-person discussions are reluctant to participate in online conversations (and vice versa). Encouraging teachers to take the time to promote the same climate and norms online is essential. This is not a step backwards but instead a path forward to creating the necessary conditions for optimizing online instruction.

      Coaches can assist teachers to think imaginatively about options that develop a new sense of community.

      Coaches can assist teachers to think imaginatively about options that develop a new sense of community. These should begin with non-academic, low-risk interactions that build toward the academic, robust interactions that support student learning. A sample sequence might begin with each student showing a pet or a favorite toy/hobby to the group. The next interaction could require students to share or upload a picture or description of their favorite place in their home to read or relax, and then, in turn, explain to the group why they chose that place. The idea is to reintroduce students to each other, strengthen a home and school connection, and allow students to get used to the platform before launching into rigorous academic content.

      Certain features of online discussion platforms also can be useful to support a low-risk way for students to gain entry into online discussions. This can be especially important for students who are developing their English language skills or for other reasons may feel shy to participate. For example, the polling feature on many platforms can be a useful way to start a discussion or keep students engaged throughout a discussions in the same way that turn and talk can be useful for students to try out their ideas with a peer before speaking with a whole group. We describe this further in the next section.

      Establishing powerful and clear online learning routines.

      Clear and consistently applied routines that scaffold students’ engagement with complex content are critical to effective classroom discussions, and this is especially the case for online class discussions. An important job of coaches is to help teachers think through what their learning routines will be to achieve particular purposes and goals in discussions, and then connect these routines to features and functions of learning technologies and platforms. Online learners can very easily get lost and confused. Teachers must be far more explicit when giving directions to students online than when teaching face to face (which is all the more reason to develop routines and stick with them). Coaches can assist teachers by helping them develop and trouble shoot directions for participating in different activities. This can help ensure that students’ energy is spent learning and not figuring out what they are supposed to be doing. Fortunately, technologies have advanced to the level that powerful routines for in-person instruction can be translated to an online environment.

      ⁘ Learning new technologies to support student learning. 

      The ability to put online student-centered learning routines into play is dependent on teachers’ familiarity with technology (e.g., discussion platforms such as Microsoft teams). For many teachers, however, the demands entailed in learning new technologies and discussion platforms are overwhelming. The need for differentiated assistance from coaches includes understanding and responding to the range of comfort levels and knowledge of technologies/platforms that provide current instructional options. Coaches can differentiate tech support in a number of ways, such as the following:

      • Modeling a classroom online discussion. One way coaches can support teachers is to engage a group of teachers in a discussion (e.g., a model lesson), showing them ways that features can be used to meet particular learning goals (e.g., small group breakout rooms in place of “turn and talks” or a polling feature or chat box to gather individual student thinking for all to see.).
      • Creating a safe place to experiment. Coaches also can act as students in practice meetings so that teachers can “try on” various teacher moves through the features of the platform, or convene a group of teachers to take turns conducting a mock discussion and using the features.
      • Co-teaching. If teachers feel unsure about conducting online discussions, coaches can co-teach with teachers, acting as a co-host to assist with technology, if that is necessary (e.g., moving students in and out of breakout sessions, switching to a whiteboard or document reader, etc.).
      • Cultivate peer mentoring. Coaches need not have all the tech wisdom. Coaches can also assist teachers to share their knowledge and support mentor/learner partnerships between teachers via conference calls or video meetings. This is a time to cultivate peer mentoring and “think partners,” and coaches are uniquely positioned to know the strengths and needs of the individual teachers and grade levels, and harness the potential for new kinds of professional learning communities.

      ⁘ Planning lessons for teachers.

      Ordinarily, coaches support teachers to plan for class discussions. In a pandemic, however, coaches can ease the stress teachers may be feeling by creating model lessons for class discussions to support individual teachers or groups of teachers. In planning for an online lesson, it is important to consider how particular features of an online platform might be used to further particular learning goals. For example, what kinds of questions might be more productively taken up in whole group discussion or small group breakout sessions? Students can sometimes get antsy sitting in online discussions—what kinds of activities (e.g., polls, responding to teacher questions in the chat feature, doing a stop and jot on sticky notes to share onscreen) might be useful for helping students stay engaged in the discussion?

      ⁘ Choosing texts.

      Something to consider in lesson planning is that students may miss multiple days of school. It might be a good idea to plan around short texts that contain sufficient grist to support a rich online discussion but would not pose a barrier to students reengaging in discussions after several absences. Another consideration is that students are likely to feel more disconnected from school when attending online than when they are attending in person, in addition to grappling with challenges and hardships. We always want students to read engaging texts. But now more than ever is a time to think about texts that will pique student interest and get them thinking, but not require extensive scaffolding to wade through the language. Notably, if groups of teachers want to use the lessons, as described earlier, coaches could engage the teachers in a run through of the lesson with the teachers providing instruction around the platform use throughout.

      ⁘ Reestablishing a positive professional collaboration. 

      In the same way that teachers need to reestablish their classroom learning community when they move to an online format, it is important that coaches work to reestablish their professional learning communities with teachers when coaching remotely. Now more than ever, the balance of content for initial coaching conversations, if not all coaching conversations, will require much more time upfront supporting the social emotional aspect of professional collaboration. Teachers, like many other Americans, are stressed, anxious, lonely, fearful for loved ones, and/or may be experiencing financial distress. Many of their students are also facing significant hardships. Listening to teachers speak to their own experience and concerns is important for both supporting teachers emotionally and helping coaches gauge the kinds of options to pursue together, based on each teacher’s interest and readiness to try new things—one new thing or many new things. Some teachers might feel ready to learn all of the ins and outs of a platform; other teachers might want to move a little slower if they are feeling overwhelmed.

      ⁘ Reestablishing a positive professional collaboration. 

      Although the sense of co-accountability and collaborative problem solving may already be a foundation for your coach-teacher relationships, it is incumbent upon coaches to reframe an inquiry stance in light of this moment. Reminding teachers that we, as a national and global educational community, are all learning together right now, positions discussions to lean into tests of small change. Cultivating an inquiry stance about technology options and which factors seem to be supporting or impeding student learning is critical. Additionally, focusing on student engagement, which is easier to assess and address in-person, requires a critical stance.

      Adopting an inquiry stance also can help draw teachers’ (and coaches’) attention to some of the potential affordances of online instruction—for now and for later. Many teachers are reporting that some students participate more in this online environment and some participate less. By studying student engagement, coaches can support teachers to notice aspects of online instruction that support the majority of students as well as specific students. Again, approaching this as an inquiry allows actual study to occur. It may well be that some students will be most supported with a part of their day online, even when instruction becomes in-person again.

       

      ® Accountable Talk is a registered trademark of the University of Pittsburgh.
      Tagged with: Academic Rigor, Accountable Talk® Discussions, ELA, Equitable Instruction, High-Level Tasks / Curriculum, High-Leverage Teaching Practices, Instructional Coaching, Online Instruction, Principles of Learning, Reading / Comprehension

      Teaneck’s Advantage: Educational Excellence Through Rigorous Teaching and Learning

      By Jennifer Lin Russell, Jennifer Zoltners Sherer, and Jennifer Iriti

      Partners for Network Improvement, Learning Research Development Center, University of Pittsburgh

      At Teaneck Public Schools (Teaneck, New Jersey) we are focused on establishing common instructional practice across all classrooms that is designed to increase our students’ opportunities to engage in demanding curriculum content in both mathematics and English language arts lessons. We have determined to meet this objective by supporting all our teachers with content-specific professional development grounded in the Principles of Learning, developed by the University of Pittsburgh’s Institute for Learning (IFL).

      We are currently in the first phase of this endeavor. With support from the IFL, we are working to ensure that our students in Grades K–5 have access to high-level tasks and text and high-quality learning opportunities to build the critical thinking and deep reasoning skills that are essential for academic success. We have identified characteristics of high-level mathematics and English language arts tasks. After working to gain a common vision of rigorous tasks—by studying examples and discussing their characteristics—we have incorporated them into our classrooms. We have made sure to align our definition of high-level tasks with research’s named criteria, emphasizing the importance of tasks that require thinking and reasoning.

      With this understanding of high-level tasks, our educators are equipped to ensure that all students are expected to think and reason at a high level and to provide the support and resources needed to maximize their learning potential. We found that we had to work consistently to make sure students could think and reason cognitively. Research on factors that contribute to a task being carried out as intended tells us that students actually get such opportunities only 37% of the time. Participating in learning labs has provided opportunities and guidance for teachers to adapt their individual instructional practices and increase those opportunities. Hosting teachers collaboratively plan lessons with IFL fellows using high-level tasks and texts, and then implement the planned lessons in front of their colleagues. Following the lesson, the hosting teacher and their colleagues debrief and make connections to their own work to increase intentionality of planning and implementing specific pedagogical practices. As such, the learning labs serve as a means to learn and refine pedagogical practice through apprenticeship. Teachers and administrators have had the opportunity to see, plan for, and model high-level tasks that make it possible for students to share and discuss their mathematical reasoning and also develop student agency.

      Our overall goal as a district is to give all students access to academically rigorous mathematics learning opportunities. This means that we have a commitment to teach mathematical reasoning as well as the knowledge core. We will ensure students are academically engaged in making connections, looking for relationships and patterns, and forming generalizations related to mathematical ideas. In our journey, we will keep our eye on the target, by collecting and analyzing student work in order to determine if students are thinking in rigorous ways about mathematics.

      Based on set indicators associated with academic rigor, we set out to collect and analyze student work samples. The data below has been coded for aspects that lead to the development of conceptual understanding, but are not limited to

      • use of representations;
      • connection between representations;
      • explanation for how a problem was solved; and
      • explanations of mathematical reasoning.

      In looking at our work, we are proud to notice the following: 

      • At every grade level, more than half of the students are using representations in their work, and some students are making connections between representations.
      • We have several examples of mathematical reasoning to guide our instructional practices.

      We look forward to our next analysis of student work in March. We are using this opportunity to monitor and ensure that we are advancing student learning. At the same time, our teachers are developing a shared vision of teaching and learning.

      Tagged with: Data and Assessment, High-Level Tasks / Curriculum, Leadership, Online Instruction, Partner Spotlight, Principles of Learning

      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.”

      Tagged with: Academic Rigor, Equitable Instruction, High-Level Tasks / Curriculum, Multi-Lingual Learner Instruction