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?
What questions can you come up with for this picture? Do you see any patterns, shapes or groups? (This image comes from the ebook Mother Goose Math (free samples below), along with math questions and phonics/fluency worksheets that correlate to Mother Goose nursery rhymes.) 
Teaching creatively means we are being both adaptive and flexible, imaginative and motivating...all while looking for resultsbased outcomes.
What are the indicators educators can use to guide teaching math creatively?
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:
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:

Buy Mother Goose Math and see for yourself the difference it makes with your class!
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).
There are more mental math ideas at this page (great tips for adding large numbers!)
