LEARNER-CENTERED MATHEMATICS

Close your eyes and picture quality mathematics instruction. Who is doing the math? Who is doing the talking? Who is doing the thinking?

A learner centered mathematics classroom amplifies student voice and leverages the power of inquiry through problem solving. Shifting to an inquiry approach represents a significance change for teachers nationally and the formative assessment process creates conditions for student ownership and agency.

Empowered Mathematicians are Learners who:

 
Believe they have the ability to learn and explore math


Expect mistakes are part of exploration


Take ownership of their exploration and regulate their learning

Good Mathematics is not about how many answers you know…it’s about how you behave when you don’t know.

 

– Unknown

LEARNER-CENTERED MATHEMATICS IN ACTION

Observe how learners take charge of their learning by engaging deeply in the learner-centered mathematics process.

LEARNER-CENTERED MATHEMATICS PATHWAYS

Shift to an inquiry-based approach to mathematics  with our three learner-centered pathways!

The New Art and Science of Teaching Mathematics

by Dr. Nathan Lang-Raad

 

Explore the New Art and Science of Teaching Mathematics Model by math thought leader, Dr. Nathan Lang Raad. Discover teaching resources, tools, and instructional strategies for inquiry-based math that will support teachers in:  co-constructing and communicating learning goals and success criteria, conducting inquiry based math lessons, tracking students’ learning outcomes, and more.

Explore! Amplifying Inquiry Based Mathematics

by Lori Cook

 

Instead of “telling and showing” students how "to do math”, students must be empowered to explore concepts, wrestle with complex ideas, and make sense of math. Join us as we investigate how to expand student ownership in an inquiry math setting using The Learning Cycle. The Learning Cycle is a practical framework to expand inquiry-based mathematics instruction for student empowerment. 

The Learning Cycle Framework has inspired mathematics teachers across the country to design inquiry-based cycles in an effort to empower mathematicians who problem-solve, persevere and explore math to make sense of it!

Math Makes Sense!

by Ivan Alba

Ivan Alba's enthusiastic style of facilitation inspires ALL to learn and believe that "Math Makes Sense" and "Everyone will be Good at Math". Using current best practices in mathematics education, the “Math Makes Sense” series is designed to support students to make sense of math through inquiry, reflection, mathematical discourse, modeling and problem solving. If students aren’t engaged in productive struggle and problem solving, they aren’t learning math!

 
THE NEW ART AND SCIENCE OF TEACHING MATHEMATICS

Discover teaching resources, tools, and instructional strategies for inquiry-based math in this series authored by Dr. Nathan Lang-Raad.

How do we know when students are learning and how do we respond when they don’t? A math workshop framework creates opportunities for teachers to differentiate instruction and support students in talking about their mathematical thinking and reasoning with each other through collaborative groups and independent learning stations. In this workshop, participants will explore different options and strategies for creating a new structure for math learning in their classroom.

  • Create learning processes that facilitate creativity, independence, and responsibility in their own math learning.

  • Design a classroom structure that utilizes an effective balance of whole and small group opportunities to foster student engagement.

  • Create independent learning experiences that amplify differentiation and personalization of learning for students.

Learner-Centered Math Workshop Design

Success in math learning begins with successful planning. How do we know what students should learn? Are there design elements that can create a consistent and safe structure of student problem solving and perseverance in math? In this workshop, participants will explore tools and apply strategies that will help them plan successful math learning experiences. 

  • Design innovative and formative learning processes that accurately measure proficiency of essential learning standards to promote student learning.

  • Design learning experiences that promote higher level cognitive thinking, reasoning, and problem solving for all students.

  • Plan and create tasks that ask students to think in complex ways.

Inquiry Based Lesson Design and Planning for Success in Math

Students own the learning when they are the ones that carry the conversation, and when they are asking the “why” questions.  This shift occurs when the teacher only guides from the periphery of the conversation. In this workshop, participants will apply and practice strategies that promote student discourse, where student-to-student talk is student initiated and led.

  • Design learning processes that help build discourse skills so that all students defend and justify their answers with little prompting from the teacher.

  • Design effective questioning techniques to help guide student discourse in collaborative and whole group settings. 

  • Explore strategies that allow students to discover their mathematical voice and make a bigger impact through higher level cognitive thinking.

Shifting from Teacher Questioning to Student Voice

Much of math instruction today is still teacher prompted. Many times students are being asked to memorize a strategy or algorithm without any meaningful mathematical connections. Deeper learning in mathematics occurs when students help shape and inspire the mathematical thinking and reasoning of others. In this workshop, participants will explore strategies that lead to successful cooperative learning groups where students support each other’s thinking in respectful and collaborative ways.

  • Design student learning protocols that promote active listening, reflection, and idea promotion through mathematical discourse conversations.

  • Construct frameworks that allow students to build skills to justify and evaluate their own solutions and strategies to mathematical tasks and scenarios. 

  • Empower students to create their own learning pathways through differentiation and personalization of math content, context, and processes.

Cultivating Student Leadership Capacity in Math

Research shows that our brains tend to think about math in a very visual way. We can enhance math instruction and learning when we’re able to create visual connections and representations between abstract and concrete concepts. In this workshop, participants will not only discover the power of visual math but will explore strategies to help students create visuals to represent their thinking. 

  • Promote mathematical engagement through innovative strategies that help students view problems in new ways and solve problems in different ways.

  • Create learning processes that leverage visual mathematics to promote higher-level thinking, effective communication, and creativity in mathematics.

  • Construct learning structures that inspire students to help shape the descriptions of their own math thinking and the thinking of others through math visualization.

Leveraging Visual Representations to Activate Mathematical Thinking

 
JUMP START YOUR LEARNING
book-new-art-and-science-of-teaching-mat

The New Art and Science of Teaching Mathematics

by Dr. Nathan Lang-Raad and Robert J. Marzano

Discover myriad math strategies, tools, and methods of teaching mathematics for every step of the process, from articulating learning targets and conducting math lessons to engaging students, tracking progress, and celebrating successes.

EXPLORE! AMPLIFYING INQUIRY BASED MATHEMATICS

Investigate how to expand student ownership in an inquiry math setting using the Learning Cycle Framework in this series, authored by Lori Cook.

Learn how to increase student ownership through problem solving. Learners co-construct success criteria for effective problem solving and use the criteria to guide their inquiry.

  • Leverage collaborative learning structures to develop student voice and mathematical discourse

  • Strengthen problem-solving structures to develop student confidence and stamina

  • Design problem-based instruction

Explore! Student Engagement and Problem Solving

"Number sense" refers to a child's fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another. Learn practical strategies to: 

  • Develop number sense

  • Improve procedural fluency

  • Expose and correct misconceptions through reengagement strategies

  • Foster math facts confidence

Explore! Number Sense and Procedural Fluency Routines

The formative assessment process is core to quality inquiry-based mathematics instruction.  Students must be involved in every aspect of the formative assessment process so students take ownership of their learning.  

  • Learn the impact of the formative assessment process on teaching and learning 

  • Engage learners in self-peer assessment to answer the questions: Where am I going? Where am I now? How do I get there?

  • Design lesson cycles developed around big ideas

  • Create conceptual units of study

Explore! Learner-Centered Mathematics Assessment

Lesson study affords teams the opportunity to focus on student learning and try out new strategies without pressure. Working together, teams will utilize their own expertise and knowledge to study content, plan instruction, teach, and reflect on student learning at their own pace while being supported by a peer facilitator.

  • Foster a collegial learning environment through established norms and protocols

  • Use formative assessment data to set goals and determine learning intentions

  • Elicit student voice to add more choice into lessons

  • Examine implications of a particular lesson and instruction from a big picture point of view

  • Set goals as an Impact Team and develop collective actions in order to increase clarity and impact in the classroom

Explore! Expanding Student Ownership Through Lesson Study by Carol Cronk

 
MATH MAKES SENSE

Support students to make sense of math through inquiry, reflection, mathematical discourse, modeling and problem solving in this series authored by Ivan Alba

Math educators and leaders will learn a straight-forward continuum of math concepts from kindergarten to middle school that will focus everyone onto the most important mathematical ideas for success in algebra.  Regardless of the grade level, each person will see how important teaching algebraically is in order to prepare students form higher mathematics in high school.  The course is fully aligned with current state standards and empowers everyone to understand their own mathematics in deeper ways.

  • Determine and Plot a progression of number concepts vital to student success in Algebra

  • Build a visual model of computation that strengthens student understanding and mastery of Arithmetic

  • Plan for content-based interventions focused on a progression of learning

Math Makes Sense Foundation: Building a School-Wide Perspective

In this interactive session, teachers from Kindergarten through Second Grade will explore ways to engage the young learner in research-based best practices that help solidify number sense concepts integral to their development.  Special emphasis will be placed on addition and subtraction strategies as well and basic number concepts that are difficult for young students to master.  The session will focus both on teacher-directed instruction, as well as student independent learning through hands-on activities.  Groups will explore their own curriculum and materials as well as others in order to maximize their students’ learning time in the classroom.

  • Design hands-on activities focused on the most essential number concepts and skills in primary grades

  • Determine and Plan for a progression of skills that ensures a conceptual understanding of number and operation

  • Organize a systematic approach to student practice that differentiates for the learner in a manageable and engaging way

Math Makes Sense: The Primary Approach to Number Sense

Educators from Third Grade through Fifth Grade will strengthen their conceptual understanding of number sense and how to best develop it with their grade levels in mind.  Special emphasis will be placed on multiplication and division strategies and how students learn these concepts and skills best.  Teachers will explore their own curriculum and materials as well as others in order to learn how to use manipulatives for deeper learning and higher retention.  During the session, teachers will explore mathematics through a problem-based approach that encourages multiple representations and accesses multiple modalities of learning.

  • Link computation of multiple number systems in ways that make learning accessible to all students

  • Identify and Plan for student learning based on visual models and multiple representations of upper-grade concepts

  • Design a problem-based approach to student exploration that builds upon natural curiosity and a solid understanding of upper-grade content

Math Makes Sense! The Upper Grade Approach to Number Sense

In this hands-on session, participants will engage in deep learning of how fractions, decimals, percents, and ratios work interdependently to strengthen student number sense.  Through a problem-based approach, each participant will learn innovative ways to build the concepts necessary to maximize learning in this domain.  Because students have such difficulty in this area, special emphasis will be placed on visual models and connections to whole-number concepts without reverting to tricks and mnemonics.  Participants will walk away with focused and usable strategies for students to compute fluently with rational numbers.

  • Determine the direct connections between computation in whole number with strategies for computation in rational number

  • Design learning tasks with fractions, decimals, and percents that make it easier for students to compute with mastery

  • Build a progression from whole number to ratios that ensures seamless connections in student thinking and problem solving

Math Makes Sense! Rational Numbers from Grade 3 through Middle School

In this two-day session, participants will learn how to implement Number Talks into their mathematics instruction in order to propel students learning or intervene where students have gaps in understanding.  Teachers will view video examples of Number Talks in various levels as well as learn to use data to design their own for intervention or enhancement.  If students are available, the presenter will model Number Talk lessons in which participants will learn the nuances of classroom management, questioning strategies, generalization, and enhancing discourse.  On day 2, teachers will develop their own Number Talks and receive expert coaching in order to become empowered to use this strategy on a regular basis.  

  • Design and Implement a Data-based approach to supporting struggling learners as well a as extending for successful students

  • Determine best practices for building discourse in mathematics while maximizing learning of concepts and skills

  • Construct a systematic approach to building mastery through intervention and practice

Math Makes Sense! Using Number Talks for Enhancement and Intervention for All Grades

Students in PreK-2 already come to school willing to learn math. Teachers already teach the standards in interactive, hands-on ways. But, what can happen when Primary Students are empowered to be agents of their own learning trajectory? What can be accomplished when students self-assess and actively build a path to deeper understanding with their peers and their teacher AS PARTNERS in all that they do? Learn how to invigorate your primary math workshop and help students set their own goals, independently work to achieve them, and use self- and peer-assessment on a daily basis. In our time together, we will focus on ensuring strong number sense as a backbone that will endure for the rest of students’ math career.

Math Makes Sense! Amplifying Mathematics Goal Setting with K-2 Learners

Bring Learner-Centered Mathematics to your School or System.
 
 
 
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The Core Collaborative

Tel: 619-432-CORE (2673)