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

    Translating Accountable Talk® Practices Between In-Person and Virtual Teaching

    By Jazmin Rotger de Parra and Kristin Nuñez

    Teaneck Public Schools

    Like many of you, we are still navigating the world of remote instruction and virtual classrooms while wanting to stay focused on providing academically rigorous instruction and having high expectations for all students.

    At the center of most of our decisions is the idea of instructional equity. Equity does not mean that every student should receive identical instruction. Instead, it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students (NCTM 2000)[i]. Up until now, the decisions that led to a greater degree of instructional equity largely occurred in schools and classrooms. But now we are having to apply all that we know about teaching and learning to maximize equitable opportunities for every one of our students in a world outside the school walls.

    …we are having to apply all that we know about teaching and learning to maximize equitable opportunities for every one of our students in a world outside the school walls.

    During the 2019-2020 school year, the use of Accountable Talk practices was a pedagogical foci for our Grades 3–5 mathematics classrooms. Through our work, we incorporated and refined our use of discourse and supported students as they engaged in verbal, visual, and written communication. We increased opportunities for students to learn from one another through the collaborative clarifying of ideas, unpacking misconceptions, and making connections across different ways of doing mathematics. Because of our focus on the use of Accountable Talk practices in the classroom, we know how important talk is to developing mathematical understanding. And even in the time of COVID we are continually trying and tweaking different ideas and approaches during online instruction to foster a learning community that engages in meaningful math discussions that advances student understanding.

    Mrs. Nuñez is one of our third grade teachers, and she continues to reimagine instruction while holding students and the role of instructional conversation at the center of her efforts. Read on as she describes her first-hand experience with establishing Accountable Talk discussions in her classroom and then transitioning to accountable communication between and among her students and herself in an online world.

    Why focus on talk, and specifically, the use of Accountable Talk practices?

    From the moment a new group of learners come together, establishing community is vital for their academic success, and the foundation of the community is talk. Skillful teachers recognize the power in leveraging talk to guide understanding and collaboratively construct knowledge.

    Building the community this year has been a bit different because we started the school year working online. For the first couple weeks of virtual learning, we engaged in many whole group conversations about respect, uniqueness, and culture. We centered our conversations around read alouds that focused on different social emotional skills. Over the course of a week, we developed class promises to hold each other accountable for our learning and make the most of our time together.

    How have you been able to capitalize on the unique opportunity to build community from a distance while students are at home?

    Even though I miss teaching in-person, one of the advantages of our current situation is that we have been able to truly expand the walls of the classroom to better encompass students’ lives at home. We unpacked and shared elements of our cultures to learn more about one another. From morning meetings and brain breaks to icebreakers and structured assignments, our classroom community is building a foundation of patience, perseverance, and celebration, which is integral to establishing community both virtually and in-person.

    How did you start using Accountable Talk practices during instruction?

    There is an assumption that students know how to talk about their thinking; however, this specific type of discourse needs to be explicitly modeled and practiced. Students need opportunities to engage in academic talk that leads to learning. Accountable Talk stems on charts or flip-rings can be used as scaffolded support and referred to during discussions. Similar approaches can be used when working online. Talk stems work because they provide students with diverse backgrounds a common language with a specific, intended conversational purpose to use during our discussions. As students take ownership of what it means to be accountable to their learning community, to accurate knowledge, and to rigorous thinking and truly internalize the expectations, academic conversations flourished, providing rich opportunities for students to build knowledge together and think deeply about content.

    What conversation dynamics do you plan for during your instructional minutes?

    At the beginning, we do a lot of partner and whole group discussion, and within that I balance student voices and keep mine to a minimum.

    After routinely hearing and engaging in Accountable Talk discussions as a whole group, the students adopt the language practices and lead their own conversations—acknowledging and building on each other’s ideas, questioning one another, and supporting claims with evidence. The conversations can seem almost natural in small group discussions, partner conversations, and conferences with me.

    I plan for a combination of teacher to student(s) and student(s)-student(s) discussions.

    What challenge(s) have you faced integrating Accountable Talk practices into instruction, in person and online? How have you met the challenge(s)?

    Though the path to having a language-rich classroom sounds easy, it is not. Not all students are comfortable exposing their thinking, especially when they are aware of the expectation that thinking can (and should) be questioned and challenged. As an adult, it is hard to feel comfortable with the idea that after sharing my best thinking, I am going to have to explore it more deeply—and publicly.

    It takes time and intention to create an instructional space where students feel safe enough to willingly take these risks. Since some students may feel more comfortable than others with this exploratory thinking and talking, I have to think critically about the ways in which equity and engagement intersect.

    One of the ways I’ve met this challenge, both in person and online, is by establishing expectations for participation. Within the structure and routine of a lesson, I find a variety of ways for students to participate. Everyone gets time to work on and is responsible for working on the problem independently. When working in-person, I have them talk with a partner who works at a similar skill level and pace. Then I have two partner groups talk with each other before we have our grand conversation as a whole class.

    When working online, the students share their thinking in a variety of ways. One low-risk way I got them started was by using polls. The polls let me do quick whole class snapshots, and, using follow up “why” questions, let me hear from individual students about their thinking. I also have them use a collaboration board to share their thinking with others after working independently. They use a shared white boards or Google slide in breakout groups. I’ve had students take pictures and send them to me to share with the group. These intentional decisions are the scaffolds for supporting students as they grow their own Accountable Talk practices. Through these efforts my students are more comfortable taking academic risks and have learned the value in hearing and seeing diverse ideas from all members of our classroom learning community.

    Say more about how and why you used the collaboration board with students.

    When we first started digital learning, I was losing students left and right. Students and families struggled with using the attachments in “order” or had difficulty toggling between multiple sources. I needed to regain control of the wheel, so I researched and experimented with different apps and resources to better guide students in their virtual learning spaces. I searched for digital ways to increase and improve collaborative interactions among the members of our learning community.

    I embedded virtual drawing and collaboration boards to engage students in our learning community. Virtual drawing boards allowed students to share their processes and thinking. These boards gave me an opportunity to digitally “walk” through my classroom—to listen in on student conversations, provide feedback through assessing and advancing questions, and make adjustments to my instructional practice. Collaboration boards provided students the ability to respond to the content and each other.

    What else did you consider when making decisions about platforms?

    These instructional decisions empowered students and created space for them to use their voices. It was important that I strategically chose platforms where they could share their diverse ideas in this virtual space not just with me, the teacher, but also with each other.

    Jazmin Rotger de Parra is the Supervisor of Instructional Programs – Mathematics and Kristin Nuñez is a Third Grade Teacher at Teaneck Public Schools.

    IFL Step Back

    Mrs. Nuñez’s story illustrates the art and science of teaching. She tried several small tests of change as she translated her Accountable Talk practices from in-person to online instruction.

    • Honor students for who they are and all that they bring to the classroom.
    • Make time for and expect talk from students.
    • Provide scaffolds for students to support them as they engage in learning discussions.
    • Allow for a range of communication dynamics.Plan and experiment with different ways of getting students to collaborate and communicate with each other using pictures, images, and written words in addition to spoken words.

    Click here to tell us how you are translating Accountable Talk practices during your online, in-person, or hybrid teaching. We want to celebrate your successes and support you in facing the challenges.

    [i] p. 12. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
    Accountable Talk is a registered trademark of the University of Pittsburgh.

    Tagged with: Accountable Talk® Discussions, Agency and Voice, Equitable Instruction, High-Leverage Teaching Practices, Math, Online Instruction, Partner Spotlight, Principles of Learning

    Principals Leading with a Coaching Lens

    By Ariane Watson and Veronica Strueve

    Principal and Assistant Principal, Propel Schools- Pitcairn
    Before becoming building principals, we were instructional coaches, each of us having coached either mathematics or ELA. Instruction was always the focus of our coaching work. After several years as principals, we realized that though supporting teaching and learning was a component of our work, it was no longer the focus. Once we came to that realization, we knew that we needed to make some changes.

    At the end of the 2018–2019 school year, in anticipation of the next year, we took stock of what was going well with instruction in the classrooms. We reviewed the state data across the years and looked more closely at the district and building data. We also inquired about new instructional materials being purchased by the district and learned that the new materials were comprised mainly of tasks and texts of high-level cognitive demand.

    The insights we gained from this preliminary work suggested that students needed more rigorous learning opportunities and that teachers needed opportunities to learn about and refine their practices related to instructional conversations. It was at that moment that we committed to making support for instruction the priority, and in doing so, revived our coaching lens.

    We engaged the Institute for Learning as a partner in education and began crafting a plan for the 2019-2020 school year. We started by conducting an Asset Walk was which allowed us to name aspects of classroom practice that could serve as the foundation on which to build. With the adoption of high-quality instructional materials, we decided that the best way to increase academic rigor and enhance the quality of scholar discourse was to focus on Accountable Talk® practices.

    We knew that as instructional leaders, the changes we sought would only happen if we maintained a laser-like focus on facilitating Accountable Talk discussions and supported teachers in both learning and refining their instructional practices. Although we were in the role of principals, we knew that putting on our “coaching hat” was key to supporting the teachers. With this in mind, we built a yearlong PD plan dedicated to the study of Accountable Talk practices. It included a series of cross-content professional development sessions. The sessions provided educators opportunities to gain insights about high-leverage instructional practices of which facilitating Accountable Talk discussion is one, the dimensions of equity as related to equitable instruction, ways to support the development of student agency, and the role of socializing intelligence. The plan allowed for frequent content-based PLCs so that Accountable Talk practices could be explored deeply within a content area. As part of the PLC work, educators coded classroom transcripts for Accountable Talk features to better understand what it takes to implement these practices and to track the implementation of these practices over-time.

    Since we know that refining practice doesn’t just happen overnight, so in addition to the work outlined in the PD calendar and plan, we also linked our walk-throughs and formal evaluations to the learning and insights gained by educators during PD sessions and PLCs. We also committed to providing time for classroom educators to reflect on practice through classroom case stories so that they can share their implementation journeys. The work also includes learning labs so that classroom educators can see each other engage in planning for, facilitating, and reflecting on Accountable Talk discussions of high-level tasks.

    As a community of educators, everyone is encouraged to continuously look for and name what is working related to the implementation of Accountable Talk practices, so there is regular feedback on our collective efforts. As part of the feedback (and central to improvement work), we wonder about and identify a specific aspect of practice for further inquiry. We know that sustainable change takes time, and we have committed to a three-year process to support classroom educators as they refine their professional skills and competencies related to content pedagogy.

    Having the intentional focus of increasing academic rigor and the use of the high-leverage practice facilitating Accountable Talk discussions has allowed us to reclaim our coaching lens. And, in doing so, we have been able to more effectively support classroom educators as they refine their instructional practices to create more equitable learning environments.

    Tagged with: Accountable Talk® Discussions, High-Leverage Teaching Practices, Instructional Coaching, Leadership, Math, Partner Spotlight, Principles of Learning

    Amplifying the Academic Rigor in Math Classrooms: Butler Area School District’s Journey

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

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

    Getting students to think deeper about the content takes intentional choices and instructional moves on the part of teachers and administrators. One of our partners, Butler Area School District in western Pennsylvania, has worked this year to increase the academic rigor in their mathematics classrooms.

    The district has worked in several arenas in order to focus the work. Teachers and administrators have worked on curriculum mapping in all areas so that content and standards are linked. Through a partnership, the Institute for Learning (IFL) has provided professional development. The PD focused on the use of high-level tasks in math classes, teacher questioning to press on deeper student thinking, and how to engage students in Accountable Talk® practices. As a result of the PD, the district is working to include tasks of high cognitive demand in the curriculum map for every grade level. Data is being collected as an indicator of the effectiveness of the curriculum maps.

    Victoria Bill, math fellow with the IFL, has been working with Butler Area School District. She reflects on the impact of the PD in the district: “Teachers recognized that their students were not getting enough opportunities to think and reason deeply about mathematics. Teachers worked together to identify the high-level tasks or to modify tasks to increase the demand of tasks. All the teachers in the districts used the high-level tasks identified, thus giving students opportunities to problem solve and to reason about mathematics.”  

    Hopp and Robb also share that there are still areas of need. “One of our biggest struggles is having a large number of teachers across six buildings. This means that there are six different administrators who are supporting this work. Logistics, communication, and coordination are a big challenge. Our strategy for consistency has been to select high-level tasks that are integrated into the curriculum map. Every teacher at the grade level will complete the high-level tasks. Our hope is that this provides accountability for implementation.”

    That said, the district is already seeing the impact of their work both in the classroom and on high-stakes assessments. Hopp and Robb stated that the pedagogy studied in the IFL PD sessions “provides a basis for making our classrooms more student-centered. The use of Accountable Talk practices has increased the communication between students and enhanced their ability to discuss mathematical concepts.” In addition, they share that there have been increases in assessment scores: “We have seen significant increases in our PVAAS (Pennsylvania Value-Added Assessment System) growth scores. We have also seen increases in most of our buildings in the number of students scoring advanced on the PSSAs (Pennsylvania System of School Assessment). We feel there is a direct connection between our work with IFL and these increases.”

    Tagged with: Academic Rigor, Accountable Talk® Discussions, High-Leverage Teaching Practices, Leadership, Math

    The Principles of Learning in Action

    By Dr. Annine Crystal

    Assistant Superintendent for Curriculum and Instruction, Guilford Public Schools

    Contributor: Emily Jermine

    Math coach, Melissa Jones Elementary School

    Dr. Annine Crystal
    Guilford Public Schools

    The Guilford Public Schools’ vision is that of a professional learning community where instruction invites effort and supports academic rigor for all students and educators. To that end, our daily work in classrooms is rooted in and supported by the Principles of Learning (POLs). These nine principles have been foundational to our work over the past 10+ years.

    The importance of the POLs in Guilford is evidenced by just how prominently they factor into ongoing district work. Prior to the start of the school year, Guilford administrators participated in a retreat focused on equity.

    A portion of the retreat was a retrospective on the Principles of Learning during which each POL was defined and mapped to both the high-leverage practices and the TRU Framework.

    Administrators watched several classroom scenarios and considered the application of the Principles of Learning as a way to frame instructional conversations with their faculties. Principals and administrators brought this work back to their buildings to support a deeper understanding of each principle as well as to clearly represent each principle’s impact on classroom instruction. 

    A deep and growing understanding of the Principles of Learning has been established through our long-standing partnership with the Institute for Learning and is reflected daily in our schools’ cultures and in the way our students engage with content and process.

    In our classrooms, we see evidence of the Principles of Learning in action every day. For example, our content-focused coaches have supported teachers as they continue to grow their conferring practice.

    Effective conferring helps teachers and students develop clear expectations for growth and encourages self-management and self-assessment of learning.

    Clear Expectations:
    Student-generated criteria chart clarifies expectations about quality mathematical explanations

    Self-Management of Learning:
    This student identified “Use precise math vocabulary” as a goal and is keeping notes on a sticky note to support her progress.

    Effective conferring helps teachers and students develop clear expectations for growth and encourages self-management and self-assessment of learning. Teachers keep notes of conference teaching points and use these notes to track the trajectory of learning, to plan, and to individualize instruction to meet the needs of each student. Conferring also facilitates the identification of strengths on which to build and the creation of goals for improvement by the students themselves.

    Let’s step into a classroom to see the impact of several of the Principles of Learning, specifically Clear Expectations and Self-Management of Learning. Students in Ms. Pierce’s 4thgrade classroom at Melissa Jones Elementary School have been working on clearly communicating their mathematical thinking.

    This work has included using visual representations as well as written and oral explanations to clarify and make visible mathematical reasoning. After engaging in this work on several occasions, students were given the opportunity to individually reflect on their areas of strength as well as the concepts they find challenging. 

    Following this self-reflection process, the class worked as a whole to brainstorm elements of a quality mathematical explanation. This, in turn, led to a class-generated criteria chart indicating the qualities of effective communication of mathematical reasoning upon which all students agreed. Each student used this checklist to self-assess one of their previously recorded mathematical explanations and then identified one area to set as their goal for better meeting the criteria for quality explanations. A copy of the chart was posted in the front of each student’s math journal and is being used independently by students as a guide when reviewing mathematical explanations and monitoring progress towards an identified goal. Teachers are able to reference this student-generated tool when conferring with students in order to better ask advancing and assessing questions that push students’ thinking around mathematical reasoning.

    Clear Expectations:
    The student-generated criteria chart is posted in front of a student’s math journal for easy reference.

    Tagged with: Leadership, Math, Partner Spotlight, Principles of Learning