Big Ideas and Problem Solving An overview by

Big Ideas and Problem Solving An overview by Natalie Lafave

Definitions and Background

From: The Guide to Effective Instruction in Math, Kindergarten to Grade 6, Vol. 1 From: The Ontario Curriculum Grade 1 -8 Mathematics Big Ideas An approach that allows students “to see that mathematics is an integrated whole, and to gain a deeper understanding of the key concepts. ” • Number Sense and Numeration • Measurement • Geometry and Spatial Sense • Patterning and Algebra • Data Management and Probability

“An effective mathematics program takes the approach of clustering expectations around a big idea and investigating effective teaching strategies for that big idea. ” From: “Module 4: Literacy / Math Programming. ” AQ Junior Course. Queen’s University, 2014. From: Principles Underlying Effective Mathematic Instruction Problem Solving “Problem solving is central to the learning of mathematics; teaching through problem solving is a sense-making approach to “doing math” that focuses on big ideas. ”

The Importance of Problem Solving with Big Ideas • “Helps students become flexible thinkers” • Allows students to find what “makes sense” to them • Explaining helps reinforces the Big Ideas • Allows students to use logic rather than memorizing steps • Develops the understanding that it is acceptable to be confused • Encourages different ways of thinking • Connects students to real-life probelms From: Marilyn Burns’ “ 10 Big Math Ideas”

Class Structures That Support Big Ideas and Problem Solving Approach

Classroom Set Up • A place for whole group instruction and presentations • Desks arranged in small groups or pairs • Manipulatives available for students to use • Anchor charts of mathematical concepts and problem solving skills • An inclusive environment where students feel comfortable taking risks

Lesson Outline Getting Started: Whole Class • • Students share their strategies Students reflect on their strategies Help students recognize their understandings and misconceptions Use probing questions • • Introduce task to students Ensure students understand task Review prior knowledge Provide manipulatives • Have a class discussion about key mathematical concepts Reflect on different methods to solve the problem Working on it: Pairs or Small Groups Reflecting and Connecting: Whole Class From: A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, Vol. 1 •

Teacher Support • Provide complex problems that have a variety of entry points which does not have a solution that is immediately obvious • Model how to approach problems • Create problems are appropriate yet challenging • Encourage different approaches • Listen attentively as students explain their method of solving the problem • Question or prompt students when explaining their thinking • Observe students and anticipate where they may come across obstacle From: A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, Vol. 2

Communication • Students need to explain their reasoning to their classmates as well as the teacher • Explaining the reasoning behind the thinking allows students a chance to organize their ideas • Interaction between students helps them clarify their own ideas as well as try another approach • Discussing ideas before writing give students a chance to organize and clarify their ideas From: Marilyn Burns’ “ 10 Big Math Idea”

Resources and Strategies • A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, Vol 1 • http: //www. eworkshop. on. ca/edu/resources/guides/Guide_Math_K_6_Volume_1. pdf • 10 Big Math Ideas by Marilyn Burns • http: //www. scholastic. com/teachers/article/marilyn-burns-10 -big-math-ideas • Number Sense and Numeration, Grades 4 to 6, Vol 1 • http: //eworkshop. on. ca/edu/resources/guides/NSN_vol_1_Big_Ideas. pdf • Edugains • http: //www. edugains. ca/newsite/math/ • Junior Mathematical Processes, Problem Solving and Big Ideas by Strand • http: //www. ncdsb. net/education/program_dept/junior/Program%20 Department%20 Created%20 Resources/Mathematic al%20 Processes%20&%20 Big%20 Ideas%20 by%20 Strand%20 in%20 the%20 Junior%20 Grades. pdf