5.4: Marilyn Burns' Strategy

Marilyn Burns is a highly respected mathematics educator, author, and founder of Math Solutions, an organization dedicated to improving math instruction. With over four decades of experience, Burns has significantly influenced the field of math education through her innovative teaching methods and commitment to making mathematics accessible and engaging for all students. Her work emphasizes the importance of developing a deep understanding of mathematical concepts rather than just memorizing procedures.

Burns' problem-solving strategy centers around the belief that students learn best when they actively engage with mathematical concepts. She advocates for a hands-on, inquiry-based approach where students are encouraged to explore, ask questions, and discover solutions on their own. This approach helps students develop critical thinking skills and a deeper understanding of the subject matter. Burns also emphasizes the importance of communication in mathematics, encouraging students to explain their thinking and reasoning, both verbally and in writing. This process not only reinforces their understanding but also helps teachers identify and address any misconceptions.

One of the key components of Burns' problem-solving strategy is the use of rich, open-ended problems that have multiple entry points and can be solved in various ways. These types of problems allow students of different abilities to participate and contribute, fostering a collaborative learning environment. Burns believes that presenting students with challenging problems encourages them to persevere and develop resilience, which are crucial skills not only in mathematics but in all areas of learning.

Additionally, Burns emphasizes the role of the teacher as a facilitator rather than a lecturer. She encourages teachers to create a classroom environment where students feel safe to take risks and make mistakes, as these are essential parts of the learning process. Teachers are guided to ask probing questions that stimulate thinking and to provide appropriate scaffolding to support students in their problem-solving efforts. By promoting a positive and supportive classroom culture, Burns' strategy helps students build confidence in their mathematical abilities and fosters a lifelong love for learning.

Overall, Marilyn Burns' problem-solving strategy is rooted in the belief that all students can be successful in mathematics if given the right opportunities and support. Her approach has had a lasting impact on math education, inspiring teachers to adopt more student-centered, inquiry-based methods that promote a deeper understanding and appreciation of mathematics.

Marilyn Burns' Problem-Solving Strategy

1. Engage Students with Rich, Open-Ended Problems
   • Select Problems with Multiple Entry Points: Choose problems that can be approached in different ways to accommodate diverse student abilities.
   • Encourage Exploration: Allow students to explore various methods and strategies for solving the problem.
   • Promote Collaboration: Facilitate group work where students can share ideas and learn from each other.
2. Encourage Hands-On, Inquiry-Based Learning
   • Use Manipulatives and Visuals: Incorporate physical tools and visual aids to help students understand abstract concepts.
   • Foster Inquiry: Encourage students to ask questions, make predictions, and test their ideas.
   • Guide Discovery: Allow students to discover solutions on their own rather than providing direct answers.
3. Emphasize Communication and Reasoning
   • Verbal Explanation: Have students explain their thinking and reasoning verbally.
   • Written Justification: Encourage students to write down their thought processes and solutions.
   • Class Discussions: Facilitate discussions where students can present and critique different approaches to the problem.
4. Support Perseverance and Resilience
   • Present Challenging Problems: Introduce problems that require sustained effort and critical thinking.
   • Encourage Persistence: Promote a classroom culture where persistence is valued and students are encouraged to keep trying despite difficulties.
   • Recognize Effort: Acknowledge and celebrate effort and perseverance as much as correct answers.
5. Create a Positive and Supportive Classroom Environment
   • Safe Space for Mistakes: Establish an environment where mistakes are viewed as learning opportunities.
   • Positive Reinforcement: Use positive reinforcement to build students' confidence and self-esteem.
   • Individual Support: Provide individualized support and scaffolding to help each student succeed.
6. Teacher as Facilitator
   • Ask Probing Questions: Use questions to guide students' thinking and deepen their understanding.
   • Provide Scaffolding: Offer hints and support without giving away the solution.
   • Observe and Assess: Continuously observe and assess students' progress to identify and address misconceptions.
7. Develop Deep Conceptual Understanding
   • Focus on Concepts: Ensure that students understand the underlying concepts rather than just memorizing procedures.
   • Connect to Real-World Applications: Relate mathematical concepts to real-world situations to make learning relevant and meaningful.
   • Encourage Reflection: Have students reflect on what they have learned and how they approached the problem.

Implementation Steps for Teachers

1. Preparation
   • Select appropriate open-ended problems.
   • Gather necessary materials and manipulatives.
   • Plan questions and scaffolding techniques.
2. Introduction
   • Introduce the problem to the class.
   • Explain the expectations for exploration and collaboration.
3. Exploration
   • Allow students to work on the problem individually or in groups.
   • Circulate the room to observe and ask guiding questions.
4. Discussion
   • Facilitate a class discussion where students share their approaches and solutions.
   • Highlight different strategies and reasoning used by students.
5. Reflection
   • Encourage students to reflect on their problem-solving process and what they learned.
   • Discuss how the strategies used can be applied to other problems.
6. Assessment
   • Assess students' understanding through their explanations, written work, and participation in discussions.
   • Provide feedback that reinforces conceptual understanding and problem-solving skills.

Example \(\PageIndex{1}\)

Maria has 3/4 of a chocolate bar, and she wants to share it equally between herself and her friend. How much of the chocolate bar will each person get?

Solution

Solving the Problem Using Marilyn Burns' Strategy

1. Engage Students with Rich, Open-Ended Problems
   • Select Problems with Multiple Entry Points: Present the problem of sharing 3/4 of a chocolate bar, which can be approached in various ways (e.g., visual models, fraction division).
   • Encourage Exploration: Ask students how they might share 3/4 of a chocolate bar equally.
   • Promote Collaboration: Have students discuss their ideas in pairs or small groups.
2. Encourage Hands-On, Inquiry-Based Learning
   • Use Manipulatives and Visuals: Provide fraction strips or chocolate bar models for students to physically divide 3/4 into two equal parts.
   • Foster Inquiry: Encourage students to ask questions like, "What does it mean to share equally?" and "How can we divide 3/4?"
   • Guide Discovery: Allow students to discover that dividing 3/4 by 2 gives each person 3/8.
3. Emphasize Communication and Reasoning
   • Verbal Explanation: Have students explain their reasoning for how they divided 3/4 equally.
   • Written Justification: Ask students to write down their steps and reasoning.
   • Class Discussions: Facilitate a class discussion where students share different methods they used to solve the problem.
4. Support Perseverance and Resilience
   • Present Challenging Problems: Encourage students to solve similar problems with different fractions (e.g., sharing 5/6 or 7/8).
   • Encourage Persistence: Praise efforts and strategies even if they aren't immediately correct, emphasizing the importance of trying different methods.
   • Recognize Effort: Celebrate students' perseverance and the process of problem-solving.
5. Create a Positive and Supportive Classroom Environment
   • Safe Space for Mistakes: Establish a classroom culture where mistakes are seen as learning opportunities.
   • Positive Reinforcement: Use positive reinforcement to build confidence.
   • Individual Support: Provide additional support to students who may struggle with the concept.
6. Teacher as Facilitator
   • Ask Probing Questions: Use questions like, "How did you decide to divide 3/4?" and "What does each part represent?" to deepen understanding.
   • Provide Scaffolding: Offer hints and support as needed, such as demonstrating how to use fraction strips.
   • Observe and Assess: Continuously observe students' work and provide feedback to address misconceptions.
7. Develop Deep Conceptual Understanding
   • Focus on Concepts: Ensure students understand that dividing 3/4 by 2 means finding how much each person gets when 3/4 is shared equally.
   • Connect to Real-World Applications: Discuss real-life situations where dividing fractions is useful (e.g., cooking, sharing food).
   • Encourage Reflection: Have students reflect on what they learned and how they solved the problem.

Example of Implementing Each Step

1. Preparation

• Select Problem: "Today, we have a problem to solve. Maria has 3/4 of a chocolate bar, and she wants to share it equally between herself and her friend."
• Gather Materials: Prepare fraction circles and a visual representation of 3/4 of a chocolate bar.
• Plan Questions: "How do you think Maria can divide 3/4 of the chocolate bar so that she and her friend get the same amount?"

2. Introduction

• Teacher: "Maria has 3/4 of a chocolate bar. How can she divide it equally between herself and her friend?"
• Discuss Objective: "Our goal is to find out how much each person gets when 3/4 is divided equally."

3. Exploration

• Teacher: "Let's use these fraction circles to represent 3/4 of the chocolate bar. How would you divide it so both Maria and her friend get the same amount?"
• Student A: "We can divide it into two parts."
• Teacher: "Great! How do we divide 3/4 into two equal parts using the fraction circles?"

4. Guided Discussion

• Teacher: "Let's see how Student A divided it. Can you show us?"
• Student A: Divides the fraction circles. "I split it like this. Each part is 3/8."
• Teacher: "Why did you split it like that?"
• Student A: "Because when you divide 3/4 by 2, you get 3/8 for each person."
• Teacher: "Exactly! Does anyone have a different way to solve this?"

5. Whole-Class Sharing

• Teacher: "Let's hear from another group. How did you divide 3/4 of the chocolate bar?"
• Student B: Shows a different method using fraction bars. "We divided it into fourths first, and then each person gets 3/8."
• Teacher: "Interesting approach! Did anyone else use a similar method or have a different way?"

6. Reflection and Justification

• Teacher: "Now that we've seen different methods, why does dividing 3/4 by 2 give each person 3/8?"
• Student C: "Because when you divide, you're finding out how much each person gets when it's shared equally."
• Teacher: "That's right! How can we explain our answer to someone who doesn't understand fractions well?"

7. Application and Extension

• Teacher: "Let's try another problem. What if Maria had 5/6 of a chocolate bar? How would you divide it equally between three friends?"
• Students: Discuss and use fraction circles to solve the problem.

8. Assessment and Feedback

• Teacher: "I'm impressed with how well you divided the chocolate bar today. You all did a great job explaining your reasoning. Let's continue practicing dividing fractions to become even better!"

By engaging students in this interactive and guided manner, teachers can effectively use Marilyn Burns' problem-solving strategy to deepen their understanding of fraction division while promoting collaboration and critical thinking in the classroom.

Marilyn Burns' problem-solving strategy offers a transformative approach to math education, emphasizing exploration, communication, and resilience. By engaging students with rich, open-ended problems and fostering a classroom environment that values inquiry and collaboration, teachers can help students develop a deep conceptual understanding of mathematics. This approach not only enhances students' problem-solving skills but also builds their confidence and love for learning. Through Burns' methods, math becomes a dynamic and interactive subject where all students have the opportunity to succeed and thrive.