Embedded Files
"Embedding the problem-solving information within a real-world context helps students activate their conceptual knowledge when presented with a real-life problem-solving situation (Gagne, Yerkovich, & Yerkovich, 1993) and improves student motivation, participation, and generalization (Polloway & Patton, 2001)."
(Sliva, Teaching Inclusive Mathematics to Special Learners K-6, 2004)
Considerations:
Considerations:
provide purposeful and authentic open-ended explorations
create responsive and flexible groups
engage in accessible thinking and reasoning routines
provide access for all learners through starting points in tasks that are low floor, high ceiling
incorporate student choice and voice
consider students’ strengths and interests when designing tasks and investigations
Resources:
Resources:
Math tasks should allow all students to engage meaningfully with rich problems. Equity and inclusive practice mean developing learning opportunities where all learners can contribute and engage in productive struggle.
Math tasks should allow all students to engage meaningfully with rich problems. Equity and inclusive practice mean developing learning opportunities where all learners can contribute and engage in productive struggle.
Inclusive Practices
Inclusive Practices
Shelley Moore: One Without the Other: Stories of Unity Through Diversity and Inclusion
NCTM Position: Access and Equity in Mathematics Education
Access_and_Equity.pdfProvide purposeful and authentic open-ended explorations
Provide purposeful and authentic open-ended explorations
Jenise Sexton gives a presentation on purposeful explorations
6 Bricks for foundational math literacy.pdfIllustration of characteristics of a "solid foundation" for an inquiry exploration in mathematics lessons.
In Dan Meyer's NCTM 2016 Annual Meeting talk, Beyond Relevance & Real World: Stronger Strategies for Student Engagement, he offers some strategies for "deleting the textbook" in order to open up questions and provide an entry point for student exploration.
Math for Love
Math for Love
Dan Finkel's free professional development videos on rich tasks.
Mathematical Mindsets: Jo Boaler
Mathematical Mindsets: Jo Boaler
Chapter 5 of Jo Boaler's book Mathematical Mindsets, focuses on the development of rich mathematical tasks and provides a framework to transform and open any task.
Each resource in this series offers a collection of low floor, high ceiling tasks around big ideas that help students make connections with math concepts through visualization, play and investigation (leveled by Common Core grade levels).
Visual-Math-Paper-vF.pdfJo Boaler's paper on the importance of visual mathematics for our brain and learning.
Thinking Classrooms
Thinking Classrooms
Peter Liljedahl's website has numerous resources and ideas.
Building-Thinking-Classrooms-Feb-14-20151.pdfPeter Liljedahl describes the background to his concept of a thinking classroom and the research that supports it.
An example of a thinking classroom in action!
Create responsive and flexible groups.
Create responsive and flexible groups.
Visible Random Groupings
Visible Random Groupings
Every student has something to add to the conversation, and so grouping should be random. Keeping the randomness visible allows students to know that they are all a valued part of the group. With regular random grouping, students are given an opportunity to work with a variety of people, and are exposed to different ways of thinking. If a student grouping doesn't work one day, chances are those students will be in a different group the next day. Along the way, students learn that random doesn't always feel that random.
Targeted, Small Group Instruction
Targeted, Small Group Instruction
In response to student needs or interests, guided math groups allow students to focus on a specific concept or skill in to develop or expand further understanding.
"The Guided Math framework developed by Laney Sammons provides teachers with a flexible instructional format that allows them to meet the diverse needs of their students."
Dr Nicki Newton's Guided Math in Action books provide teachers with support towards providing effective guided math lessons, scaffolding learning in small groups, and assessing student learning.
Provide access for all learners through starting points in tasks that are low floor, high ceiling.
Provide access for all learners through starting points in tasks that are low floor, high ceiling.
"One of the main reasons we like LTHC [low threshold high ceiling] tasks is because they provide opportunities for all children to work like mathematicians".
"One of the main reasons we like LTHC [low threshold high ceiling] tasks is because they provide opportunities for all children to work like mathematicians".
Rich questions to support all learners.pdfPresentation by Marion Small about rich questions, providing entry points for all students.
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