3. Effective mathematics instruction:  foster positive mathematical attitudes;  focus on conceptual understanding ;  includes students as active participants in their learning;  is based on problem solving and investigation of important mathematical concepts;  has students communicate and investigate their thinking through ongoing discussion;  includes all students, whether in the choice of problems or in the communicating of mathematical ideas;  encouraging the belief that everyone can “do” mathematics – emphasizing effort, not innate ability;  capitalizing on the “math moments” that occur naturally at home and in the classroom.

4. Big Ideas-“The interrelated concepts that form a framework for learning mathematics in a coherent way………”  Develops conceptual understanding and students recognize meaningful relationships in numbers and make connections interacting with the problem, develop the active construction of mathematical representations, and metacognition.  Engage students actively in problem solving using investigation and inquiry to explore problems can build a repertoire of reasoning skills and strategies, stimulating their interest.  Promotes collaborative learning as students learn from one another as they demonstrate and communicate their mathematical understanding.  Activates their prior knowledge, integrates new ideas and apply knowledge. Thinking is stretched to solve more complex and real world problems and can be connected to future learning.  Provides opportunities to gain thorough and deeper, knowledge and understanding of the key concepts.

5. Big Ideas-The key principles of Math  Encourage students to reason their way to a solution or to new learning;  Encourage students to make conjectures and justify solutions;  The process of problem solving helps all students to see the problem from different perspectives and opens the door to a multitude of strategies for getting at a solution;  Develop and extend their intuitive strategies;  Reflect on and monitor their own thought processes;  Represent mathematical ideas and model situations, using concrete materials, pictures, diagrams, graphs, tables, numbers, words, and symbols;  Participate in open-ended experiences that have a clear goal but a variety of solution paths;  Formulate and test their own explanations.

6. Problem solving is central to learning Mathematics…………….  helps students become more confident mathematicians;  helps students find enjoy ment in mathematics;  increases opportunities for the use of critical-thinking skills (estimating, evaluating, classifying, assuming, noting relationships, hypothesizing, offering opinions with reasons, and making judgements).

7. Help students make sense of what they are learning…… GETTING STARTED…THINK 1. engage students in the problem-solving situation; 2. discuss the situation; 3. ensure that students understand the probl em; 4. ask students to restate the problem in their own words; 5. ask students what it is they need to find out; 6. allow students to ask questions ; 7. encourage students to make connections with their prior knowledge.

8. By learning to solve problems and by learning through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding. SELECT A PLAN  encourage brainstorming ;  use probing questions ;  guide the experience (give hints, not solutions);  clarify mathematical misconceptions;  answer student questions but avoid providing a solution to the problem;  observe and assess.

9. Providing opportunities for students to reflect on a problem at the beginning, in the middle, and especially at the end of a task. Reflecting and Connecting ………… EXECUTE AND CHECK  be open to a variety of solution strategies;  ensure that the actual mathematical concepts are drawn out of the problem;  highlight the big ideas and key concepts ;  expect students to defend their procedures and justify their answers;  use a variety of concrete, pictorial, and numerical representations to demonstrate a problem solution;  relate the strategies and solutions to similar types of problems to help students generalize the concepts;  always summarize the discussion for everyone, and emphasize the key points or concepts.

10. “A positive classroom climate is essential to build children’s confidence in their ability to solve problems.” (Payne, 1990)  Daily challenges - Provide a meaningful challenge every day, or every other day, to engage students when they arrive in class first thing in the morning, or during a specific time of the day or whenever they have an opportunity throughout the day.  A problem-solving corner or bulletin board that provides a place in the classroom where interesting problems can be posted. Students are given time throughout the day or the week to visit the corner and solve the problem. At some point, the whole class is brought together to discuss the problem, share their strategies, hear and see strategies used by other students, evaluate solutions, and at times cooperatively solve the problem;  An activity centre that can be included as part of a rotation of centres in which students participate during the consolidation phase of a unit. The teacher provides a problem for students to solve collaboratively. (e.g., with a partner or group).

11. Problems that are organised around big ideas and focus on problem solving provide cohesive learning opportunities and explore mathematical concepts in depth…………  different methods of solving problems are welcomed and shared;  mistakes are looked upon as opportunities for learning;  teachers are flexible in their understanding of how students develop their own strategies for solving problems;  different ways of thinking and reasoning are viewed as valuable insights into students’ minds;  problem solving, Mathematical reasoning, communication and arguments are highly valued;  interest in mathematical ideas, even when they are not related to the curriculum, is encouraged and promoted;

12. The secret to successful teaching is being able to determine what students are thinking and then using that information as the basis for instruction.  promote mathematical tasks that are worth talking about;  model how to think aloud, and demonstrate how such thinking aloud is reflected in oral dialogue or in written, pictorial, or graphic representations;  model correct mathematics language forms (e.g., line of symmetry) and vocabulary;  provide “ wait time ” after asking questions, to allow students time to formulate a response;  give immediate feedback when students ask questions or provide explanations;  encourage students to elaborate on their answer by saying, “Tell us more”; ask if there is more than one solution, strategy, or explanation; ask the question “How do you know?”

13. Resources  The Guide to Effective Instruction in Math, Kindergarten to Grade 6, Volume 1 The Guide to Effective Instruction in Math, Kindergarten to Grade 6, Volume 1  http://eworkshop.on.ca/edu/resources/guides/ ExpPanel_456_Numeracy.pdf http://eworkshop.on.ca/edu/resources/guides/ ExpPanel_456_Numeracy.pdf  http:// www.edu.gov.on.ca/eng/literacynumeracy/inspire/ research/WW_problem_based_math.pdf http:// www.edu.gov.on.ca/eng/literacynumeracy/inspire/ research/WW_problem_based_math.pdf  Number Sense and Numeration, Grades 4 to 6.: Ministry of Education, 2006. Web. 23 Oct. 2015.