Report

“BIG IDEAS” & “PROBLEM SOLVING” IN JUNIOR MATH INSTRUCTION Ms. Teighlor Marin BIG IDEAS • Programs that emphasize the big ideas allow students to make connections, to see that mathematics is an integrated whole, and to gain a deeper understanding of the key concepts • Big Ideas represent the key mathematical concepts • Effective math programs demonstrate understandings of the Big Ideas and or key concepts • The “Big Idea’s” or “Strands” within Mathematics are: • Number Sense & Numeration • Measurement • Geometry & Spatial Sense • Patterning & Algebra • Data Management & Probability BIG IDEAS The “Big Ideas” demonstrates concepts found in each strand. The “Big Ideas” act as a lens for: • Making instructional decisions • Identifying prior learning • Looking at students’ thinking & understanding in relation to the mathematical concepts addressed in the curriculum • Collecting observations and making anecdotal records • Providing feedback to students • Determining next steps • Communicating concepts & providing feedback on students’ achievement to parents BIG IDEAS • Mathematical processes that help aid in effective learning are: • Problem Solving • Reasoning & Proving • Reflecting • Selecting Tools & Computational Strategies • Connecting • Representing & Communicating *******Mathematical processes are all interconnected and help students acquire and apply math skills with knowledge. PROBLEM SOLVING APPROACHES Creating a Learning Environment Using Manipulatives Promoting Communication Teaching Through Problem Solving Assessing Effectively Central Themes Big Ideas of Mathematics PROBLEM SOLVING APPROACHES • Problem Solving is “the process of applying prior knowledge, experience, skills, & understandings to new and unfamiliar situations in order to complete tasks, make decisions, or achieve goals.” • Individuals in todays society need to be able to think critically • To prepare students for the real world, teachers are responsible to promote problem solving processes into their classroom • When students are taught math concepts through problem solving, they are exposed to problems and problem solving on a daily basis, even though the problem might not be formally identified • Problem solving is an integral part of the mathematics curriculum because it: • Helps students become more confident mathematicians • Allows students to use the knowledge they bring to school and helps them connect mathematics with situations outside of the classroom • Allows students to reason, communication ideas, make connections, and apply knowledge and skill CORRELATION BETWEEN PROBLEM SOLVING & BIG IDEAS • Students who are able to problem solve are more likely to understand the “BIG IDEAS” because they can use prior knowledge, skills, and understandings to figure out solutions • When teachers use Problem Solving to teach mathematics they make math make sense. They allow the students to make sense of what they are learning and focus on the Big Ideas • • • • The 4 Step Problem Solving Model Understand the Problem Make A Plan Carry out the Plan Look Back & Reflect on Solution PROBLEM SOLVING & CLASSROOM • Key concepts are introduced & explored through problem solving • There is no formal problem solving, instead students develop & share their own problem solving processes • Teachers model problem solving with the class and walk through the mental processes that happen while solving a problem • Students solve problems together • Problem solving solutions are shared as a class during discussions or sharing times • Perseverance in problem solving is modeled by the teacher and encouraged in students • Students explore math ideas in a way to developing their own understanding of concepts “Helping students become good problem solvers is like helping them learn how to ride a bike; tips can be helpful, but its impossible to master the process without actually trying it” (Baroody, 1998) Classroom Opportunities for Problem Solving: • Daily Challenges • Problem Solving Corner • Activity Centre Questioning Computation Collaboration Classroom Structures that Support Problem Solving Daily Challenges Manipulative Scaffolding PROBLEM SOLVING & COMMUNICATION • Oral communication is integrated into all mathematical learning concepts and ideas • Class discussion are incorporated throughout lesson to encourage students to talk about strategies, solutions, and growing understandings • Teacher Prompt Questions are used throughout the lesson • Teacher should constantly be asking “How do you know?” or “What’s your reasoning?” • Encourage students to think aloud • Different strategies are incorporated to promote communication • Think/Pair/Share • Word Wall • Journals • Class Discussions Nonverbal Speaking Thinking Listening RESOURCES & STRATEGIES • Ontario Curriculum Grades 1-8: Mathematics http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf • Leading the Way: Instructional Leadership in Elementary Mathematics http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/pdfs/e6.pdf • Teach Using Big Ideas http://fcit.usf.edu/mathvids/strategies/tubi.html • A guide to Effective Instruction in Mathematics https://faculty.nipissingu.ca/danj/DOCUMENTS/MATHEMATICS/GUIDES/GR ADES%20K-6/GEIM%20K-6.pdf