What is the best way to expose our students to divergent ways of thinking and problem solving?How can we help them learn to explain, elaborate, defend and support?
By learning how to talk about math.
Look the picture below of the little boy stuck in the rain. He looks pretty happy, right?
Take a mathematical twist here for a moment and think what type of questions and discussions your students could have about math. Could you have a discussion about shapes and position of objects?
Would your more able students be able to talk about developing a variety of equations to describe the leaves on the flowers?
Teaching creatively means we are being both adaptive and flexible, imaginative and motivating…all while looking for results-based outcomes.
What are the indicators educators can use to guide teaching math creatively?
- Originality – unexpected responses
- Flexibility – different angles and playing with elements
- Fluidity – alternative ideas and combinations
- Elaboration – attention to detail and discoveries
Teachers are also beginning to understand how the development of mathematical thinking may change throughout the schooling years (it becomes more sophisticated), yet some things remain the same:
- Precision (good choices to solve problems)
- Assumptions
- Use of diagrams, graphs and examples
- Accurate use of math vocabulary and symbols
5 Ways To Get Students to Talk About Math
1. Math Pictures
Skilled problem solvers visualize what they are going to do. In other words, we create images to make sense of things.
However, sometimes kids need an image to even begin talking about math, and this is where math pictures come into play. We have to build their “Math Eyes.”
Images of familiar objects can be used to prod mathematical discussions. This is a prime opportunity to build academic vocabulary and become engaged in real life discussions about math.
Choose pictures that children know, can recognize and feel comfortable with. Nursery rhymes are a terrific example of this and can easily be part of a daily oral math routine.
Grab these Mother Goose Math free samples to start developing “math eyes” and oral math skills with your students.
Each sample includes:
- Nursery Rhyme
- Phonics and fluency worksheet
- Full color and b/w picture
- Math questions to guide discussion (Beginner, Intermediate, Challenge)
- Opportunity for students to color and develop their own math stories about the rhyme.
2. Mental Math Games That Use Daily Oral Math Skills
Bounce Count
Use a playground ball and bounce it around a circle as the children skip count forwards or backwards.
My Turn, Your Turn
Each child has a partner. They face each other and have a back and forth conversation about a math topic for one minute. For example, if they are studying shapes, the teacher says, “Quadrilateral!” and they students take turns saying properties of quadrilaterals. Studying fractions? Tell them to count by 1/4 from a number.
What’s My Question
Students work in pairs or small groups, and they have one whiteboard. The teacher gives a number and the students have one minute to write down as many ways they can think of to arrive at the answer using the four operations (idea: whole numbers for younger students, percents and square roots for older ones).
Talking about mathematics to develop math skills
The 6 Rs of Daily Oral Math
This is a short math starter to use at the beginning of each lesson. There is no book that can write this out for a teacher – it has to be done according to what is being taught, what has been previously taught in the math lessons, and the direction lessons have taken.
Too often these types of math activities drag on and become the entire lesson – don’t let that happen.
Keep them short and tightly focused. Setting a timer for one minute each time really helps.
Here are six “Rs” of developing daily oral math skills (one minute for each one):
- Rehearse
- Recall
- Refresh
- Refine
- Read
- Reason
Rehearse: Practice existing skills (calculations, using ten frames, etc.)
Recall: Names, properties, types of measurement, math vocabulary
Refresh: A return to recently taught lessons where children had difficulty (it has been taught but not yet mastered)
Refine: Extend mastered knowledge into a new area (applying a skill to new learning)
Read: Read and interpret/discuss a word problem, graph, puzzle, diagram, etc.
Reason: Predict, hypothesize and draw conclusions when the answer isn’t obvious or available
At first it seems overwhelming, but it isn’t. Soon it will become second nature. At first it can be done twice per week and gradually build up to daily use. The only “Rs” that need a bit of preparation really are the last three.
Often the teacher’s manual has great ideas and charts/diagrams that you can use on the fly.
4. Talk the Test
Group students of like abilities and let them take a math test orally. Here’s how to do it:
Choose 4-5 of the most important questions (the same number of questions as there are students). This is the hardest part for many teachers, but if you want a great discussion then you have to give fewer questions that are higher quality.
Allow the students to talk through all the questions within their groups. Then tell them they are to record their answers along with their reasoning for how they came up with it (use your classroom iPads, computers – anything that has voice recording capabilities).
Each student has to say an answer and discuss the process the group went through to arrive at it. That is why there needs to be the same number of students as there are questions.
Too often educators take on merely the logical and analytical side of mathematics. That’s a pity because there is so much creativity and imagination in math. There is also wonder and amazement.
Take this story about Carl Gauss. Nearly all students can relate to it.
Carl often was in trouble at school. This was because he would always finish his lessons before the other students and became bored.
One day he went a little too far and his teacher gave him a very difficult math problem to solve as punishment.
Carl was to add the numbers 1 to 100 and it should have taken him most of the next hour.\
It didn’t.
Carl was finished within a few moments, long before the teacher ever completed writing it on the board.
How was he able to solve this? Look up the Gaussian Pairing Method. But don’t tell your students. Have them figure out how he did it.
That is teaching mathematics through storytelling.
Story books for teaching math
If you are short on stories, there are hundreds of books out there you could use for teaching math.
If you are looking beyond the Scholastic book fair however, this book of stories will definitely intrigue and delight your students.
Oral Storytelling and Teaching Mathematics takes you into two case studies through enchanting stories: The Wizard’s Tale (grades 2-4) and The Egypt Story (grades 5+).
These are epic stories, which means they take a number of days to finish. Within each story math skills are taught and emphasized, but in a way that it doesn’t even feel like math. It’s just a part of the story.
This is really a teacher book, because it has notations and discussions of how to use stories in the math classroom. It goes into great detail about how oral storytelling helps students who struggle to learn math and problem solving.
Teachers will also learn how to use physical manipulatives and imagery while telling a story to clarify and enhance teaching mathematics objectives.
Math From Many Cultures Poster
Love, love, love this!
Even though it is geared towards middle school, the posters spark fascinating math conversations.
Teachers always have multicultural books that can be integrated with the poster topics:
- How the Days Got Their Names
- Where Our Numbers Came From
- Rock Art