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Making Math Fun and Meaningful
Avril de Souza
Research About BIG IDEAS
• Focus on a number of key content areas• Topics presented in a logical sequence and
explored in-depth • Students allowed to develop, construct, test
and reflect on their understanding of concepts• Teaching that uses big ideas enables students
to make connections instead of seeing Math as a set of disconnected ideas
Importance of Problem Solving
• Exploring problems provides rich challenges, relevance and engagement
• Helps support core processes such as the use of representation, communication and connection among mathematical ideas
• Students develop problem solving skills as a result of solving problems
• Problem-solving processes develop over time and can be significantly improved by effective teaching practices
Providing Appropriate and Challenging Problems
CriteriaSolution not immediately obviousProblem has more than one solutionProvides a learning situation related to a key concept or big ideasContext of problem is meaningful to students problem promotes the use of one or more strategies The solution requires decision making above and beyond the choosing of a mathematical operationReasonable time is provided for arriving at a solutionThe situation encourages collaboration in seeking solutions
1. Help with Understanding the Problem
Engage students in the problem-solving situation
Discuss the situation Ensure understanding
by asking students to restate the problem in their own words
Ask students what they need to find out
Encourage the making of connections with prior knowledge
Provide requested materials
Have manipulatives available
2. Guide Students to Develop a Plan.
Students must realize that all plans are tentative and can be changed throughout the process.
Students can consider different strategies they could use.
Students could use strategies from the Strategy Wall as well.
3. Students Work at Carrying out their Plan with some Support
encourage brainstormingUse probing questions redirect the group by asking questions that help them recognize their own errors clarify mathematical misconceptions observe and assess to determine the next instructional steps join as a participating member if a group is experiencing severe difficultyModel think-alouds encourage students to clarify ideas and pose questions for other students give groups a 5-10 minute warning before bringing them back to the whole group discussion in the next phase.
4. Encourage Reflection and Connection
bring students back together to share and analyze solutions 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 share only strategies that students can explain
TIP FOR TEACHERDon’t have students randomly volunteer to share their solutions.Solutions need to be strategically sequenced to scaffold learning.
Observe and Assess
The teacher observes whether students:• make conceptual connections between mathematical ideas• approach problem solving situations with ‐confidence• use self monitoring strategies‐• are flexible in using strategies and processes
Importance of Communication
Having students communicate mathematically helps teachers to:
• • gauge students’ attitudes towards mathematics;
• • understand student learning, including misconceptions that
• students have;• • help students make sense of what
they are learning;• • recognize and appreciate another
perspective.• Develop and reinforce their literacy
skills
How to Assess
Conceptual Understanding – comprehension of mathematical operations and relations
Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently and appropriately
Strategic Competence – ability to formulate, represent and solve mathematical problems
Adaptive Reasoning – capacity for logical thought, reflection, explanation and justification
Productive Disposition – habitual inclination to see Math as sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy
Getting Started – Organizing the Classroom Learning Environment
Have students sit in flexible groups: face to face in pairs or small groups with sufficient space for small-group writing and the use of concrete materials
Clear the board so there is ample space for posting student work and/or recording mathematical details throughout the three-part problem solving lesson.
Use co-operative learning strategies like Turn and Talk, Think-Pair-Share, Round Table, Think-Talk-Write and Place Mat, to organize student interaction and to provide wait time for students to formulate a response.
Develop a culture of listenership where students (and the teacher) listen to every student in a nonjudgmental, inquisitive and attentive way.
THANK YOU. GOOD LUCK.
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