Here are Five Signature Practices to Promote Math Modeling in Your Classroom
(1) The Practice of Problem Posing-What’s the “Math Happening”?
What’s the “Math Happening”? The art and science of asking questions is the source of all knowledge.
“To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science.” Albert Einstein
Children are natural at this- In fact, Steven Hawkins said, ” I am just a child who has never grown up. I still keep asking these ‘how’ and ‘why’ questions. Occasionally, I find an answer.”
Asking questions and posing problem is quite natural for children. In fact, that is how they naturally learn. This curiosity and inquisitiveness is sometimes squelched when students are only asked to find answers to problems. Math Happenings signature practice is encouraging children to ask questions and pose problems in their world.
(2) Tapping into Children’s Funds of Knowledge – What do we already know?
What do we already know that can help us?
Tapping to students’ funds of knowledge is the second signature practice. Children come with a lot of knowledge- could come from informal learning, home environment, peers or other experiences and background knowledge. Drawing knowledge they own and tapping into their existing schema can amplify the learning. For example, in estimating the number of people who can ride a bus, students might be bus riders themselves and have a good sense of estimation for the number of friends who ride their bus. In a problem about finding the best deals for planning a big family meal for a reunion, they may know of places for discounts, coupons, or bulk buying that can help with the problem formulation.
(3) Making Assumptions to Mathematize.- What do we need to know?
If I knew_______then, I can figure out_________. (Make assumptions.)
Real world problems are messy and has many variables that can be accounted for and not accounted for. The best way to tackle a problem is to draw on as much on the known variable and make assumptions that can lead to the best solution. This requires one to make some reasonable estimates or assumptions based on what they know. This may involve defining the variable and constraints in their problem. For example, in Planning a Family Reunion, and a Meal Plan, one will have to make some assumption about how big their Turkey should be for everyone to have a good portion.If I knew about how many pounds of turkey each person eats then, I can figure out what size to buy. (Make assumptions.) Would 1 pound of turkey per person be a good estimate? Or in my cases, how much Galbi (Korean bbq short ribs) should I prepare for our Family reunion?
4) Do the math! Solve!
Build a Math Model or General Rule
(What math can I use to solve the problem?)
5) Does the solution make sense?
(Think back to the problem statement. Does the solution work?)
How can you Revise, Refine and Report your solution? (What might you change?)
In addition, through many lesson studies focused on mathematical modeling, I have found that a math routine like ‘Math Happenings” introduces students to process of mathematizing their world and building a closer relationship with mathematics. Students to see themselves as math doers and thinkers. They see the utility of mathematics and the relevance to their lives. Empowers our students as they see that mathematics can serve them.
Mathematical modeling is a process of applying mathematics to real world situations.
BACKGROUND INFORMATION: Math happenings occur daily in all of our lives. The math happening lessons serve as a framework for teaching many mathematical concepts within the context of real-life math events. The teacher’s role in the math happening lesson is:
- to encourage students to share stories about events that actually happen to them
- to interpret, translate, and represent these stories mathematically, using multiple representations
- to introduce other math concepts for which students are ready.
OBJECTIVE: Model with Math
Share a real-life event (math happening) and pose a question that can be answered using the information given in a math event from everyday life.
Key Processes- Problem Posing, Making Assumptions, Solving a Problem, Look for Patterns and Generalizations and Reflect the solution back to the Real world phenomenon.
MATERIALS: real world math materials, artifacts, photos, letter or an email. Read The Math Curse by Jon Sciezca and Lane Smith. This is a great read-aloud for students to experience all the math they experience in a given day at school.
Getting Started: Teachers can start with a story that happened to them in their life.
- Math happened to me. Let me tell you about it. (Tell the story. Talk outloud what you are trying to find out. What information do I need? Ask the question to help simplify the real world problem.)
- What math happened to you? Tell us about it. Tell me what you did last night, yesterday, or this weekend. (Listen to the event. Probe to gain enough information to make a math story and ask a question.)
Use this organizer to unpack the math! As more “math happenings” are shared in class, students will be able to better connect the math they are learning to their everyday encounters. Soon students will be coming to school after a weekend and saying, “ I had a math happening this weekend….”
As more “math happenings” are shared in class, students will be able to better connect the math they are learning to their everyday encounters. Soon students will be coming to school after a weekend and saying, “ I had a math happening this weekend….”
Lead a math modeling chat- Math Modeling planning guide –
Math Modeling tasks use math to make decisions! Some of the types of modeling problems that we have had success in elementary grades include:
Descriptive models: Using real world data to describe a phenomenon
Predictive models: Using trends and data analysis to predict an outcome
Optimizing models: Using data to find the “best” by optimizing or in some cases minimizing some situation.
Rating and ranking: Using criteria and mathematical measures as a way to rate and rank options to make decision.
This template might help you get started!
Math Modeling Discourse Outline
Mathematical Modeling Challenge