1. Big Ideas & Problem Solving A look at Problem Solving in the Primary Classroom
Lindsay McManus

2. AGENDA What is a “Big Idea”?
How “Problem-Solving” helps with the understanding of big ideas
Classroom Structures that Support Problem-Solving;
The importance of communication in problem-solving;
FOUR STEP PROBLEM-SOLVING MODEL
Observing and Assessing Students as they Problem-solve
Suggestions for learning how to use the problem-solving process in the classroom

3. According to Van de Walle, "Big ideas are really just large networks of interrelated concepts...whole chunks of information store and retrieved as single entities rather than isolated bits."
Teaching that uses big ideas or key concepts allows students to make connections instead of seeing mathematics as disconnected ideas
Students are better able to see connections in mathematics and to learn mathematics when it is organized in big, coherent "chunks.“
What is a Big Idea?
In order for students to be successful in learning mathematics, they need opportunities to have deep and sustained interaction with key mathematical ideas. “A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades. An effective program focuses on a number of key content areas rather than on trying to cover every topic or skill with equal weight.” (NCTM,2000).

5. How Does Problem Solving Help?
is the primary focus and goal of mathematics in the real world;
helps students become more confident mathematicians;
allows students to use the knowledge they bring to school and helps them connect mathematics with situations outside the classroom;
helps students develop mathematical knowledge and gives meaning to skills and concepts in all strands;

6. How Does Problem Solving Help?
allows students to reason, communicate ideas, make connections, and apply knowledge and skills
offers excellent opportunities for assessing students’ understanding of concepts, ability to solve problems, ability to apply concepts and procedures, and ability to communicate ideas
promotes the collaborative sharing of ideas and strategies, and promotes talking about mathematics
helps students find enjoyment in mathematics
increases opportunities for the use of critical-thinking skills (estimating, evaluating, classifying, assuming, noting relationships, hypothesizing, offering opinions with reasons, and making judgments)

7. Classroom Structures that Support Problem-Solving
promotes positive beliefs and attitudes towards mathematics;
• values prior knowledge
• makes connections between that knowledge, the world of the child, and the strands and actions of mathematics; encourages the establishment of a community of mathematics learners;
• focuses on important mathematical concepts or big ideas;
• explores concepts through problem solving
• includes a variety of learning resources;
• is supported by the strong roles of teacher, principal, and senior administrator
• is supported by home

8. The Important of Communication in Problem Solving
Having students communicate mathematically helps teachers to:
gauge students’ attitudes towards mathematics
understand student learning, including misconceptions that students have
helps students make sense of what they are learning
recognize and appreciate another perspective.

9. Strategies for Promoting Oral Communication
Think-Pair-Share
Show and Tell
Math Reader’s Theatre
Math Forum
Cooperative Problem Solving
Catch the Mistake and Make It Right
Show and tell: have children hold up their papers and show the variety of ways in which they have solved the problem. Once students have verbalized their answers, they are able to clarify and solidify their thinking and the thinking of others as well.
Math readers theatre is like the regular Readers theatre except students read Math problems.

10. Strategies for Promoting Written Communication
Mind Mapping
Math Word Wall
Model Writing
Shared Student Writing
Think-Talk-Write
Group Solution Writing
Poster Projects
Graphic Organizers
Math Strategy Wall
Individual and/or Class Journals/Logs
Math Picture Books
Place Mat
Math Creative Writing
Gallery Walk

11. Four Step Problem Solving Model
Students should be encouraged to think and talk about the problem and to restate it in their own words before they go to manipulatives or to paper and pencil.
Students should be guided to develop a plan. They should realize that all plans are tentative and may be changed throughout the process. They can consider strategies they might use. Suggestions such as looking at the classroom strategy wall might be helpful. It is not necessary for students to record the plan in writing.
At this phase, students are carrying out their plan and using strategies such as drawing a picture or working with manipulatives. Teacher prompting at this time should focus on questions that elicit greater understanding but should avoid inadvertently solving the problem for the student. Perseverance at this stage should be encouraged. Suggestions to help the student become unstuck can be provided – for example: “Ask Natalie for an idea.” “Refer to the strategy wall for another approach.” “Can you think of a problem that is similar to this?”
During this “getting back together” phase, it is crucial that students share their ideas in the large group. As a result of the sharing, they can begin to discern that a variety of strategies can be used. They also begin to evaluate critically which strategy works best for them (e.g., is most efficient, is easiest to understand). Teachers should encourage students to discuss what they have learned through the problem-solving experience and to pose new problems that are related to the one just solved.

12. Ideas for Implementing the 4 Step Process
Use the Planning template
Watch the Problem Solving Video
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14. Observe Students and Assessing Their Work as They Solve Problems
providing appropriate and challenging problems;
supporting and extending student learning
encouraging and accepting students’ own problem-solving strategies;• questioning and prompting students
using think-alouds to model how a problem is tackled;
anticipating conceptual stumbling blocks, noticing students who encounter these blocks, and helping them recognize and address their misconceptions.

15. Some examples
daily challenges that can be utilized to engage students in regular problem solving
a problem-solving corner or bulletin board that provides a place in the classroom where interesting problems can be posted.
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).