It is common in ELA classrooms for students to leverage relational thinking around text-to-text, text-to-self, and text-to-world connections. What does this kind of relational thinking look like in math class and how can it benefit students? This article, the second in the series, uses classroom scenarios to look at how these connections provide opportunities for students to become stronger mathematicians and for teachers to implement more equitable teaching practice.
People of all ages and in all spaces use relational thinking on a regular basis. Relational thinking, generally speaking, involves using existing understanding to reason about and make sense of novel information or situations to deepen and/or construct new understanding. In recent years, the IFL math team has been exploring ideas related to relational thinking and its role in teaching and learning mathematics for understanding.
Check out four of our top ELA articles from the archives! They offer insights into why we advocate to make space for collaboarative instructional planning.
Check out four of our top math articles from the archives! They offer insights and practical suggestions for making math classrooms more equitable learning spaces for students.
Despite best intentions, test writing sometimes ends up being the formula that students never have to break. In this article, I advocate for teachers to teach test writing as a genre, inviting students to develop knowledge around the features, purpose, and audience of the writing required on standardized tests.
“Esto Si lo Puedo Hacer!”: Creating Opportuinities for Success when Teaching Academic Vocabulary in Mathematics
Too often we hear the suggestion to pre-teach math terms to multilingual students, an action that prefences memorization over meaning making. Though well intended, this approach limits opportunities for students to engage in sense making of the mathematical concepts and relationships they are studying. There is a better and more equitable way! This article shares four pedalogical choices that foster student success in the math classroom while positioning multilingual learners as leaders.
High-level comprehension tasks impact the depth to which students respond to analysis tasks. Check out this article in which two teachers share their stories about working with their students on comprehension tasks that support text analysis.
Are You “Wishing” Math Content Knowledge Into Your Students? 6 Questions to Ask Yourself to Find Out
What does it mean to “wish mathematical knowledge” into your students? If reading the title of this article makes you pause, you might be doing it. Take the quiz to find out!
Students are more engaged when they see themselves in the books they read. IFL partner, Syracuse City Schools, has worked to better represent all their students by expanding their multicultural libraries on a global scale.
Changing the system changes the outcomes is the premise by which one school approached reorganizing their resources to maximize mathematics interventions. This meant getting everyone on board to increase and improve mathematical understanding for all learners. This article is the second of a two-part series the explores one school’s efforts to change their system of mathematics intervention to better meet the needs of every student (and every teacher) across all tiers of instruction.
If you want the results to be different, then you must do things in a different way. For one school, this meant taking a hard look at the types of opportunities provided to students to think and reason about mathematics across tiers of instruction. They knew that wanting to increase and improve mathematical understanding for all learners, meant systemic changes related to the instructional materials, teaching practices, and school scheduling. It also meant that everyone had to be on board! This article is the first of a two-part series that explores one school’s efforts to change their system of mathematics intervention to better meet the needs of every student (and every teacher) across all tiers of instruction.
Working with numbers and mathematical representations! Read about the success that one of our partners is seeing in the land down under.
Comprehension work is critical work when we engage students with a text. Understanding and enacting the steps for planning a high-level comprehension task will help teachers provide students instructional opportunities that set every student up for success.
While there has been a tremendous amount of schooling loss, students maintain unique funds of knowledge valuable to math classrooms. This article looks at three practices that work in combination to foster safe, student-centered learning environments as students return to school having unique and varied lived experiences.
Examining ways that school systems can rethink preparation for high-stakes testing, so that it does not highjack the rest, can help establish a post-pandemic new normal. Based on our research-informed work in schools and classrooms, no matter how well-intended, the current system of rewards and sanctions tied to test scores has negatively impacted opportunities for meaningful, high-quality learning experiences that prepare learners for college, career, and community engagement. This has disproportionately impacted students of color, those impacted by poverty, and multi-language learners.
Have you ever left a classroom discussion and cannot remember what questions you asked? To reflect on practice and consequently to know what to continue and what to modify, teachers need evidence and data of their own facilitation of discussions. Talkmoves, an app that processes Accountable Talk® (AT) math classroom discussion and feeds back the data (typically in about an hour) can support teachers with enhancing their practice!
Creativity in mathematics abounds at the intersection of belief and practice! When the belief that all learners are doers of mathematics and enter the classroom with valuable lived math experiences intersects with the use of a lesson routine that offers space for students to do the thinking, learners become the creators and authors of the material from which they learn.
“If you cannot read the word problem, you cannot do the math.” This statement is false on many levels! Students who are receiving math instruction in a language other than their native language are doers of mathematics! And as teachers, it is our job to utilize specific strategies that allow every student in each of our classrooms to engage in thinking deeply about the mathematics. In this article we share four strategies for math teachers to use when working with multilingual students who are working on their English skills while also learning math.
Questioning the Author is a discussion-based approach that supports students in studying and understanding complex texts. Comprehension work is an essential piece of any text-based task. If students don’t get the gist of the text or grasp an author’s ideas, it becomes increasingly difficult for them to do deeper analytic and interpretive work. It is especially important for emerging readers and emergent multi-lingual (EML) students to be able to access the big ideas of a text while building their comprehension muscles.
Representations are windows into student thinking and reasoning. In a time of virtual classrooms, using visual representations is more complex, but as important as ever. If a teacher values students’ thinking, they need to consider how to make it possible for all students to represent that thinking. This article addresses the use of representations and the questions that help students connect representations to deepen understanding of math concepts.
Accountable Talk® Discussions: Solidifying Knowledge and Engaging in Rigorous Thinking Alongside Others in a Collaborative Community
Accountable Talk discussions require teachers and their students to support one another and mutually create a classroom community committed to using and building accurate knowledge and engaging in rigorous thinking. Everyone involved understands and is accountable for respecting each other and the learning community, as a whole. This begins with recognizing and honoring each person’s different lived experiences because every person brings vital knowledge and valuable assets to the learning community. This article provides a general understanding of Accountable Talk discussions and serves as a basis to begin exploring this high-leverage practice.
Teachers can use writing routines to support student writers by creating a sort of conversation between the student writer and the text. This article examines how a set of well sequenced student routines allows students to use writing to express what they know in connection with what they learn from the text.
As the need for virtual instruction continues, educators continue to look for ways to make mathematics instruction more equitable and honor students’ abilities and backgrounds. In this article, we examine three teaching practices that work in virtual spaces and offer six strategies for keeping every student invested and advancing in their conceptual understanding.
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. 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.
Every person is a “math person” and using learner-centered routines can support students in seeing themselves as doers of mathematics. This article, the second of a two-part series, shares how’s and why’s of four learner-centered routines that provide opportunities for students to build positive math identity by creating space for voice, agency, and actually doing mathematics.
Learner-centered routines are valuable tools for educators because the routines help to spur discussion based on student input, support students as they construct understanding, improve how students see themselves as mathematicians, and create opportunities for formative assessment. This article, the first of a two-part series, shares four learner-centered routines that work in-person and online during mathematics discussions. The second article, coming out on December 1, explores how these four routines can be used to create space for student voice and agency and support them in developing positive mathematical identities as doers of mathematics.
Remote Coaching for Rigorous and Engaging Online Classroom Discussions: Layering New Forums with Fresh Insights
Coaches have a critical role in assisting teachers in continuing, rather than abandoning, important pedagogies while teaching online. Read about what is being learned through 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.
A story about the art of teaching and the process of translating and refining practice to ensure rigorous learning opportunities for students through collaboration and productive talk.
Many school districts have moved to virtual or hybrid models of instruction and we recognize that using the typical Learning Walk routine, which asks district and school leaders to visit classrooms and provide targeted feedback, doesn’t quite fit in a virtual space. However, we also recognize the need to continue to support district leaders in helping teachers provide high-quality instruction to every student.
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.
When we visit classrooms that reflect a culture of Socializing Intelligence, we notice several commonalities. We see evidence of a highly rigorous curriculum, and we see all students engaging in productive conversations around cognitively demanding tasks that are grounded in complex texts and rich content.
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.
When teachers are working to acquire new instructional practices, particularly ambitious reforms, teachers tend to gravitate toward approaches that are congruent with their prior practices, or they focus on discrete activities, materials, or classroom organization (Spillane, 2009).
Refine Instructional Practices Through PLC Discussions That Relate Content, Student Thinking, and Pedagogy
Almost every school out there has tried to implement some sort of professional learning community, or PLC. Many of those schools started PLCs with the right intentions and provided time for PLCs to meet regularly to work collaboratively with the goal of increasing academic performance of students.
Propel Pitcairn, one of the Institute for Learning’s newest partners, went through the process of an organization-wide curriculum adoption for both math and English language arts last year. As a result, the teachers will now be regularly using high-level tasks, which dovetails with the network’s vision that students will do the thinking.
A growing number of schools focus on some form of communities of practice as a key to improving their performance. Schools typically refer to communities of practice as professional learning communities (PLCs). These work in a variety of ways and have different goals, but only some achieve their intended results.
Accountable Talk® discussions are discussions that promote learning. They are discussions that have evidence of accountability to the learning community, accurate knowledge, and rigorous thinking.
“It definitely makes my heart smile when I hear a teacher say, ‘I just stopped what I was doing because the student knew more than I did and just took over!’ or ‘I began to feel frustrated because we were not able to work through the content the way that I originally planned, but I learned so much about what they know and have experienced by re-framing some of my questioning and allowing them to create the questions too.
Conferring with teachers in advance of observing a lesson is a critical component of the Content-Focused Coaching® (CFC) cycle. These “pre-conferences” are opportunities for the coach and the teacher to reflect together about a teacher’s lesson plan, and thus are a rich opportunity for teacher learning. Lesson planning is specifically important for facilitating rigorous Accountable Talk® classroom discussions.
The Institute for Learning (IFL) and Schenectady City School District have worked collaboratively for several years, and this year, we continued our ongoing partnership with a focus on using improvement science methodology to “get better at getting better.” District-wide, there is a focus on using improvement science to work on persistent problems of practice.
Children are born with the innate capacity to reason beginning at a very young age (Carey, 2009; Gopnik and Wellman, 2012; Spelke and Kinzler, 2007). Very young children build explanatory systems—implicit theories—that organize their knowledge. These theories enable children to predict, explain, and reason about relevant phenomena and, in some cases, intervene to change them.
Many educators name student agency as something they want to work to develop within their schools and classrooms. But what is student agency? And, more importantly, what can we as educators do to foster student agency?
What does it mean to differentiate instruction to meet the needs of every learner in a mathematics classroom? Giving different students different tasks does not yield a common learning experience; therefore, the availability of holding rich mathematical conversations with the whole class is lacking.
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.
Designing for academic rigor in a thinking classroom starts with the choice of task with which students will engage. Likewise when striving to improve student achievement, we ask our school partners to begin by analyzing the tasks students experience. If we want students to truly understand mathematics, as opposed to a series of tricks, sayings, and acronyms, then we have to ensure they have a regular diet of high-level tasks that require thinking and reasoning about mathematics.
Recently, the Institute for Learning was selected to bring its expertise and extensive experience with instructional coaching to mathematics educators in the state of Tennessee. More specifically, IFL provided instruction around coaching moves that support high-quality teaching, resulting in improved student learning.
New Brunswick Public Schools (NJ) is a continuing partner with the Institute for Learning (IFL). Over the last 4 academic years, the district has seen definite growth across grades 3 – 10 in both English language arts and mathematics, as measured on the NJ state assessment tests.