Hacking Mathematics

1. Reimagine the "Do Now": Engage Students with Thought-Provoking Warmups

It is time to move from Do Now to Think Now.

Rethink class openers. Traditional "Do Now" problems often fail to engage all students effectively. Instead, create an "I See Math" starter using a thought-provoking image and an open-ended question. This approach:

• Draws students into mathematical thinking regardless of their prior knowledge
• Encourages observation, analysis, and creative problem-solving
• Prepares students for the type of thinking required in the day's lesson

Implementation tips:

• Use Google Slides or PowerPoint to create a simple three-slide presentation
• Slide 1: Title
• Slide 2: Intriguing image
• Slide 3: Vague, open-ended question related to the image
• Allow time for discussion and diverse approaches to the question

By shifting from "Do Now" to "Think Now," teachers create a culture of inquiry and prepare students for deeper engagement with mathematical concepts.

2. Transform Homework: Practice in Class, Lag Assignments for Better Learning

Take back the homework review time from the start of class and move it to after a lesson.

Revolutionize homework practices. Traditional homework often reinforces mistakes and causes stress. Instead, implement a "Double Switch":

1. In-Class Practice: Dedicate class time for guided practice with immediate feedback
2. Lagging Homework: Assign homework on topics covered about a week earlier

Benefits of this approach:

• Students receive immediate feedback during practice
• Teachers can observe and correct misconceptions in real-time
• Delayed homework reinforces concepts over time
• Reduces stress and increases engagement

Implementation steps:

• Commit to teaching the statistics section in your curriculum
• Create an overarching question to connect the unit
• Keep homework assignments short and accessible
• Develop a schedule that aligns with this new approach
• Adjust assessment timing to match the lagged homework model

This method transforms homework from a stress-inducing task to a valuable tool for long-term learning and retention.

3. Join the Math Twitter Blog-o-Sphere (MTBoS) for Collaborative Growth

Harness the amazing connections you now have at your fingertips by becoming part of an exciting and caring group of educators.

Connect with a global community. The Math Twitter Blog-o-Sphere (MTBoS) is a vibrant network of math teachers who share ideas, resources, and support through blogs and Twitter. Joining this community can:

• Expose you to innovative teaching strategies
• Provide a platform for sharing your own ideas
• Offer support and motivation from like-minded educators

Steps to get involved:

1. Create a professional Twitter account
2. Search for #MTBoS and follow active users
3. Visit mtbos.org for directories, resources, and connection tips
4. Start a blog to share your own thoughts and experiences
5. Engage regularly by asking questions and sharing ideas

By actively participating in the MTBoS, you'll find inspiration, support, and a wealth of resources to enhance your teaching practice and professional growth.

4. Leverage Digital Tools for Student-Driven Mathematical Explanations

When you change the instruction from "show your work" to "explain your thinking," you offer students the opportunity to do this by whatever means they are most comfortable.

Embrace digital explanations. Instead of insisting on traditional written work, encourage students to use digital tools to explain their mathematical thinking. This approach:

• Allows students to communicate in ways that feel natural to them
• Develops clear mathematical communication skills
• Provides teachers with deeper insights into student understanding

Digital tools to consider:

• Flipgrid: Short video responses (30-90 seconds)
• Screen recording apps: Demonstrate problem-solving in real-time
• Audio recording: Verbal explanations of mathematical processes

Implementation tips:

• Start by allowing students to talk through their solutions in class
• Introduce digital tools gradually, starting with one or two options
• Encourage creative approaches to explaining mathematical thinking
• Use student-created explanations as teaching tools for the class

By shifting from "show your work" to "explain your thinking," and providing digital avenues for expression, teachers can gain deeper insights into student understanding and foster more engaging mathematical discussions.

5. Ask More Questions, Be Less Helpful: Foster Deep Mathematical Thinking

Every time you're ready to give a mathematical answer, or point to a mathematical procedure, or remind of a previous example, or begin reteaching a mathematical concept, stop. Ask a question instead, then give your students time to think about and answer it.

Cultivate inquiry-based learning. Instead of providing answers, guide students with thoughtful questions. This approach:

• Develops problem-solving skills
• Encourages deeper understanding of concepts
• Builds student confidence in their mathematical abilities

Types of questions to ask:

• "What have you tried so far?"
• "How can you tell if your answer is correct?"
• "What do you notice about this problem?"
• "Can you draw a picture to help you see the problem?"
• "Have you solved similar problems before?"

Implementation strategies:

• Plan questions in advance for common student inquiries
• Practice redirecting student questions with your own questions
• Teach students to ask themselves questions during problem-solving
• Reflect on the effectiveness of your questioning techniques

By shifting from giving answers to asking questions, teachers foster a classroom environment that promotes critical thinking and mathematical independence.

6. Make Math Relevant: Connect Curriculum to Real-World Experiences

We can make it real for our students.

Bridge the gap between abstract math and real life. By connecting mathematical concepts to everyday experiences and current events, teachers can:

• Increase student engagement and motivation
• Demonstrate the practical applications of mathematics
• Foster deeper understanding and retention of concepts

Strategies for finding relevant connections:

• Take photos of mathematically interesting situations in daily life
• Use current events, sports statistics, or popular trends as math contexts
• Investigate students' interests and hobbies for mathematical connections
• Employ the 3-Act Math task format for engaging, real-world problem-solving

Implementation tips:

• Start small, gradually increasing the use of relevant examples
• Document successful real-world connections for future use
• Encourage students to find and share their own mathematical observations
• Be flexible with curriculum timing to incorporate timely, relevant examples

By consistently seeking and incorporating real-world connections, teachers can transform students' perception of mathematics from an abstract subject to a practical, engaging tool for understanding the world around them.

7. Embrace Desmos: The All-in-One Calculator Solution for Modern Classrooms

Desmos is a four-function calculator, a scientific calculator, and a graphing calculator all in one. But it's much, much more than that.

Revolutionize calculator use. Desmos offers a comprehensive, free solution for mathematical exploration and learning. Benefits include:

• Accessibility across devices (computers, tablets, smartphones)
• Powerful graphing and calculation capabilities
• Interactive activities for student engagement and learning

Key Desmos features:

• Graphing calculator with intuitive interface
• Activity Builder for creating interactive lessons
• Teacher dashboard for real-time monitoring of student work
• Accessibility features for visually impaired students

Implementation steps:

1. Familiarize yourself with Desmos tools at desmos.com
2. Explore pre-made activities at teacher.desmos.com
3. Learn to create your own activities at learn.desmos.com
4. Gradually introduce Desmos in your classroom, starting with simple graphing tasks
5. Integrate Desmos activities into your curriculum, replacing traditional lessons where appropriate

By embracing Desmos, teachers can provide students with a powerful, versatile tool for mathematical exploration and understanding, while also gaining valuable insights into student thinking and progress.

8. Cultivate Statistical Thinking with Unanswerable Questions

Unanswerable Questions will develop statistical thinkers in your classroom.

Foster deeper statistical understanding. By posing open-ended, complex questions, teachers can:

• Encourage critical thinking about data and its interpretation
• Develop students' ability to design and conduct statistical investigations
• Prepare students for real-world data analysis challenges

Characteristics of effective unanswerable questions:

• Open-ended with no single correct answer
• Require data collection and analysis
• Involve real-world contexts or current events
• Encourage discussion and debate

Implementation strategies:

• Start units with an overarching unanswerable question
• Use media claims and statistics as springboards for investigation
• Incorporate sports statistics, unlikely events, or popular trends
• Focus on the process of statistical thinking rather than specific answers

By regularly engaging students with unanswerable questions, teachers can cultivate a deeper understanding of statistics and its real-world applications, moving beyond mere calculation to true statistical thinking.

9. Create a Wonderwall: Nurture Mathematical Curiosity and Inquiry

When our students see an object or concept in your classroom that sparks an interest and they say, "I wonder what that's all about?" it's our responsibility to open that world that our students just created.

Cultivate a culture of curiosity. A Wonderwall is a dedicated space for students to post questions and wonderings about mathematics and the world around them. This approach:

• Encourages students to ask questions and think critically
• Provides insight into students' interests and thought processes
• Creates opportunities for organic, student-driven learning

Implementing a Wonderwall:

• Designate a physical wall space or use a digital platform (e.g., Padlet)
• Encourage students to post questions and wonderings regularly
• Reference the Wonderwall in lessons and discussions
• Celebrate new wonderings and investigations of posted questions

Tips for success:

• Give students time to interact with the Wonderwall
• Model curiosity by adding your own wonderings
• Use student questions as launching points for lessons or projects
• Involve students in investigating and answering each other's questions

By creating a Wonderwall, teachers foster an environment where questioning and curiosity are valued, leading to deeper engagement with mathematical concepts and their real-world applications.

10. Bridge the Parent-Teacher Gap: Communicate Effectively with Two-by-Fours

Take two minutes each day for four days each week and talk about nothing BUT what's being taught in your classroom.

Enhance parent engagement. The "two-by-four" communication strategy involves sending brief, focused messages to parents about classroom learning. This approach:

• Keeps parents informed about current math topics and methods
• Provides a consistent, manageable flow of information
• Empowers parents to support their child's learning at home

Implementing the two-by-four strategy:

1. Choose a communication method (e.g., email, video, audio message)
2. Commit to sending four 2-minute messages per week
3. Focus on key concepts, not detailed lesson plans
4. Include student explanations when possible

Tips for success:

• Start with an engaging, big-picture message to hook parents
• Keep messages concise and consistent
• Solicit feedback from parents to improve communication
• Involve students in creating messages when appropriate

By implementing the two-by-four communication strategy, teachers can bridge the gap between school and home, fostering a supportive learning environment and reducing misunderstandings about modern math education methods.

Last updated: July 28, 2024