An understanding of number, specifically the idea of sets of quantities of things, begins in infancy and develops long before formal schooling. So…
• What does mathematical thinking and reasoning look like in infants?
• How do thinking and reasoning change after infancy?
• How might parents/families/caregivers influence the development of children’s mathematical thinking and reasoning?
• What are some things that adults can do to support children’s mathematical development?
Check out our interview with Dr. Melissa Libertus, Associate Professor, University of Pittsburgh Department of Psychology and Research Scientist, Learning Research & Development Center, who sat down with us to share her research and provide answers to these questions and so much more.
Six Strategies That Can Lead to More Equitable Online Mathematics Instruction
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.
Translating Accountable Talk® Practices Between In-Person and Virtual Teaching
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.
Principals Leading with a Coaching Lens
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.
Amplifying the Academic Rigor in Math Classrooms: Butler Area School District’s Journey
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 Principles of Learning in Action
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).
Engagement vs. compliance: Looking closely at criteria charts
Criteria charts that spur students to engage with the content matter actively are more likely to align with the Principles of Learning, so analyzing the criteria is critical. We have to consider if the combination of expectations results in active engagement with mathematical ideas that leads to deep understanding or simple compliance of learned procedures and rules.
Utilizing Small Tests of Change and High-Leverage Practices in PLCs
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.
Using PLCs to Build Teacher Capacity to Implement High-Leverage Practices
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.
Weighing Teacher Choices to Maximize Student Contribution
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.
Implementing Accountable Talk® discussions in math
“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 & Coaches Requires Setting Clear Learning Goals
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.
Focusing on the Instructional Approach Nurtures Agency
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?
Agency and Voice: A Push for Greater Equity and What it Looks Like in Math
In her article “Framing Equity: Helping Students ‘Play the Game’ and ‘Change the Game’” (2009), Rochelle Gutiérrez lays out the four key dimensions of equity: Access, Achievement, Identity, and Power, which sit on two axes. Access and Achievement create the dominant axis, and Identify and Power create the critical axis.
Tests of Change Lead to Meaningful Student Engagement in Mathematics
There is no shortage of professional development (PD) available to teachers, but PD alone is rarely enough to result in a change of practice.
Differentiation Across Tiers of Math Instruction
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.
District Uses Improvement Science Principles to Increase Math Scores
When a district successfully shifts their trajectory of students’ performance, many people ask how they did it. New Brunswick Public Schools’ use of strategic decision-making, grounded in improvement science principles, and greater collaboration across role groups resulted in impressive gains in mathematics scores across the district.
Working Toward Rigor: Implementing High-Level Math Tasks
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.
Math, a Journey of Understanding
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.
Coaching Moves Practice
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.
Building a Coaching Model that Works
Through a three-year Institute of Education Sciences (IES) grant with the TN Department of Education, the Institute for Learning (IFL) and researchers at the Learning Research and Development Center explored and studied coaching in mathematics.
Collaborative Work is the Key to Gaining Broad Perspectives to Complex Problems
Humans are problem solvers by nature, and educators are no exception. Whether we are working to improve student comprehension, or striving to improve low math scores, once a problem has surfaced, we often rush to find solutions – to our detriment. Trying to fix a problem before we know its true cause is a problem in and of itself.