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.