Bringing It All Together
Math Class Needs a Makeover
In this TED Talk, middle school mathematics teacher Dan Meyer makes a strong argument for mathematics lessons that engage students in solving the kinds of rigorous non-routine mathematics problems and tasks that require them to read, write, speak, and listen like mathematicians. He talks about what it takes to create these kinds of problem-centered mathematics lessons.
Why We Need Common Core Math
On this site, Jo Boaler of Stanford University discusses four ways to strengthen mathematics instruction, including 1) focusing on learning rather than performance, 2) emphasizing multidimensional approaches that support thinking and reasoning, 3) encouraging student engagement in rich tasks with “low floors and high ceilings” that students can take to different levels, and 4) focusing on depth rather than speed. She supports these recommendations with research and student performance data. She provides a number of examples of rich tasks throughout that can be used to support student learning.
The Teaching Channel: Common Core
This site provides video of teachers working with CCSS tools and resources including those available through Achieve the Core, the Partnership for Assessment of Readiness for College and Careers, and the Smarter Balanced Assessment Consortium.
Implementing the Mathematical Practice Standards
This site provides illustrations of the Standards for Mathematical Practice for Grades 5–10 that consist of a mathematics task, a student dialogue based on that task, a mathematical overview that addresses the mathematical thinking and reasoning that arises during the student dialogue, and student materials that can be used to support the use of these tasks in classrooms.
Thinking Through a Lesson: Successfully Implementing High-Level Tasksby Margaret S. Smith, Victoria Bill, and Elizabeth K. Hughes. This article identifies a Thinking Through a Lesson Protocol (TLLP) that can be used to plan task-centered mathematics lessons that place students’ mathematical thinking at the center of instruction. The protocol includes selecting and setting up a mathematical task, supporting students’ exploration of the task, and sharing and discussing the task. It includes a discussion of how to create questions that assess and advance student thinking as they work on these tasks.
Orchestrating Discussionsby Margaret S. Smith, Elizabeth K. Hughes, Randi A. Engle, and Mary Kay Stein. This article identifies five practices that constitute a model for effectively using student responses to high-level mathematics tasks during whole class discussions. The five practices include 1) anticipating student responses to challenging mathematics tasks; 2) monitoring students’ work on and engagement with the task; 3) selecting particular students to present their mathematical work; 4) sequencing the student responses that will be displayed in a specific order; and 5) connecting different students’ responses and connecting the responses to key mathematical ideas.
Classroom Discussions in Math: A Teacher’s Guide for Using Talk Moves to Support the Common Core and More (3rd ed.)by Suzanne H. Chapin, Catherine O’Connor, and Nancy Canavan Anderson. This resource provides support for strengthening classroom discourse across Grades K–6 as a way to deepen the engagement of all students in the mathematics content they are learning. It identifies “talk moves,” provides guidelines as to how these might be used, and offers videos of teachers and students engaged in these talk moves together. While the focus is on the elementary grades, there are also implications for secondary grades; a version of this book is currently being developed to specifically address secondary mathematics classrooms.
Strength in Numbers: Collaborative Learning in Secondary Mathematics by Ilana Horn. This resource provides guidelines for organizing small-group collaborative work in secondary mathematics classrooms. In particular, it identifies guidelines for identifying “groupworthy” tasks, makes recommendations for fostering “positive interdependence” so all students are engaged and learning, discusses the teacher’s role while students are working, and addresses important questions about status and “equitable mathematics teaching.”
Five “Key Strategies” for Effective Formative Assessment. This resource discusses the research on effective formative assessment and makes recommendations regarding how these effective formative assessment strategies play an important ongoing role in mathematics instruction. These have important implications for how lessons are structured and planned.
Recommended Resources for Rich Mathematics Problems and Tasks
Dan Meyer’s Three-Act Math Tasks
Dan Meyer provides a collection of “Three-Act Math Tasks” that he describes as “the three acts of a mathematical story.” The first act introduces a mathematical challenge in the form of a central conflict; the second act engages students in overcoming obstacles, looking for resources, and developing new tools as they address the conflict; and the third act involves resolving the conflict and setting up a sequel or extension.
Mathematics Assessment Resource Service (MARS)
The Mathematics Assessment Program (MAP) is a collection of rich non-routine assessment problems and tasks that align with the expectations of the CCSS. It reflects a collaboration between the University of California, Berkeley, and the Shell Center team at the University of Nottingham, with support from the Bill & Melinda Gates Foundation. The team works with the Silicon Valley Mathematics Initiative and school systems across the US and UK to develop improved assessments.
SERP Poster Problems
This site provides a number of “Poster Problems” addressing grades 6 and 7 mathematics content that are designed to engage students in thinking and reasoning. Included are suggestions for designing mathematics lessons around these kinds of problems, explanations of the rationale for these kinds of approaches, and discussions about how these kinds of problems can be used for “diagnostic teaching” that supports student learning.
This site contains “real-world” lessons designed to help middle school and high school mathematics teachers address the CCSSM while challenging their students to think critically about the world.
PARCC: Partnership for Assessment of Readiness for College and Careers
This site contains descriptions of the PARCC assessment system, including professional development modules about the PARCC Performance-Based Assessments and End-of-Year Assessments, sample items, practice tests, and links to videos on the Teaching Channel that address how teachers can use these assessments to strengthen their instruction.
Smarter Balanced Assessment Consortium
This site contains a description of the Smarter Balanced Assessment system, including sample items, practice and training tests, and resources such as a digital library on formative assessment available to teachers from member states.
Recommended Tools and Other Resources
The Illustrative Mathematics Project
This site provides instructional and assessment tasks aligned to CCSS content and practice standards by grade level, course blueprints and lesson plans, and other print and video resources for mathematics teachers. There are also opportunities for virtual conversations for teachers and teacher leaders around a specific task, called “Task Talks,” as well as a virtual lecture series with monthly presentations addressing such topics as “Incorporating the Mathematical Practices into the Middle and High School Classroom.”
Achieve the Core
This site is full of materials designed to help mathematics teachers understand and implement the CCSS in mathematics and ELA. The site includes rich tasks and assessments with explanations and supporting commentary, sample lessons with annotations, an instructional practice guide intended to support lesson planning and reflection, and resources designed to support reflection on the expectations of the CCSS including readings and a discussion forum.
This site is designed to be a professional resource for mathematics teachers. The site includes CCSS resources that focus on content and practice standards, classroom videos that address these standards, problems of the month, performance assessment tasks, and tools for leadership.
This link contains resources collected and created by James Tanton of the St. Mark’s Institute of Mathematics, an outreach program promoting joyful and effective mathematics education. He is currently a visiting scholar at the Mathematical Association of America (MAA).
Principles to Actions: Ensuring Mathematical Success for All by NCTM. This resource lays out a set of strongly recommended research-informed principles and actions that are essential to strengthen mathematics teaching and learning for all students. These include planning and implementing effective instruction as described by the eight Mathematics Teaching Practices; developing socially, emotionally, and academically safe environments in which all students feel secure and confident as they engage in mathematics learning; identifying and accessing resources that are aligned with the CCSS; incorporating tools and technology as an everyday part of the mathematics classroom; providing students with descriptive, accurate, and timely feedback including strengths, weaknesses, and next steps; and working collaboratively with colleagues to plan instruction, solve common challenges, and provide mutual support through which collective responsibility for student learning is addressed.
Common Core Mathematics in a PLC at Work, Grades 6–8 by Diane Briars, Harold Asturias, David Foster, and Mardi Gale. This teacher's guide illustrates how to sustain successful implementation of the CCSSM for grades 6–8. Discover what students should learn and how they should learn it at each grade level. Acquire strategies for addressing the rigor of the grades 6–8 standards, including the unique content around ratios, proportions, and relationships at grades 6 and 7. Get insight into the new expectations for grades 6–8 assessment as well as the readiness required for the high school standards. There is attention to important supports for student engagement in disciplinary literacy practices throughout.
Common Core Mathematics in a PLC at Work, High School by Gwen Zimmerman, John Carter, Timothy Kanold, and Mona Toncheff. How do you help your students demonstrate mathematical proficiency, reflecting the learning expectations of the Common Core State Standards (CCSSM)? This teacher's guide illustrates how to sustain successful implementation of the CCSSM for high school. Discover what students should learn and how they should learn it, including deep support for the mathematical modeling conceptual category of the CCSSM. Comprehensive and research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency. You’ll also learn how fundamental shifts in collaboration, instruction, curriculum, assessment, and intervention can increase college and career readiness in every one of your students. Extensive tools to implement a successful and coherent formative assessment and RTI response are included. There is attention to important supports for student engagement in disciplinary literacy practices throughout.
Common Core Mathematics in a PLC at Work, Leader’s Guide by Timothy Kanold and Matthew Larson. How do you help your students demonstrate mathematical proficiency reflecting the learning expectations of the Common Core State Standards (CCSSM)? This leader companion to the grade-level teacher's guides illustrates how to sustain successful implementation of the CCSSM for mathematics. School leaders will discover how to support and focus the work of their collaborative mathematics teams for significant student achievement and improvement. Readers will receive explicit guidance and resources on how to lead and exceed the assessment expectations of the common core. There is attention to important supports for student engagement in disciplinary literacy practices throughout.