## Provoking Exploration in Mathematics

Provocation can be defined as the act of causing someone to feel, think or begin to do something.  In the Reggio Emilia approach to learning they involve the teacher creating invitations/ displays that provoke students to begin to explore an idea or concept with materials that spark thinking. Provocation materials can be loose parts, natural items, children’s literature, photographs, inquiry questions or all of the above.  The goal is to find something that sparks curiosity and leads to new learning.

Within mathematics, provocations can lead to inquiry and discovery of mathematical concepts and initiate mathematical thinking.  I am currently working with a group of four exceptional kindergarten teachers to develop opportunities for our elementary teachers to explore the idea of using provocations as a tool to provoke mathematical inquiry, creativity, and discussions.  Together we initiated the first ever Kindergarten Mathematics Learning Community in which kindergarten teachers come together to discuss ways to provoke their young mathematicians in thinking and growing mathematically.

Our first provocation focused on the question How do Numbers Help Me Tell My Story?  This question and the materials we deliberately put together can serve as a starting point for developing a deeper understanding of numbers and counting concepts in Kindergarten.

Some of the Big Ideas of Counting that can be explored through this provocation are:

• You say one and only one number for each object (one to one correspondence)
• The last number spoken tells how many. (cardinal principle)
• You can represent a number in a variety of ways.
• The quantity of a group does not change if the objects are rearranged. (stability)
• There is a consistent set of counting words that never changes. (stable order principle)
• You say one number name for each object tagged. (synchrony)

Our How do numbers help me tell my story? provocation included a variety of loose parts (shells, buttons, rocks, glass beards, pipe cleaners etc.) as well as tree cookies with numbers printed on them and wooden numbers.  We used felt squares to delineate the space and added round cork pot holders.  Looking in the mirror students could study themselves to recreate what they see using the loose parts.  They can also think about numbers that connect to themselves and represent those numbers using the loose parts on the counting place mats as a guide.

Using high quality children’s literature to connect mathematical concepts, and cultural perspectives is an important consideration for us in every provocation we design.  The Colors of Us  was our inspiration for our How do numbers help me tell my story? provocation. Other literature connections can include The Best Part of Me,  and Every Buddy Counts.

For those of you wanting to provoke the thinking of our young mathematicians I am including a freebie to get you started.  Here are the counting mats I created in French and in English as well as the Number Formation Cards.  Enjoy!!

This exploration of Provocations in mathematics is has become a wonderful learning journey for me.  I am so honored to have an opportunity to learn with some fantastic teachers within my school division and around the world.  If you are looking for inspirations from leaders in this area make sure to check out the work of Janice Novakowski.

## Subitizing- A Fundamental Skill for Primary Mathematicians

Subitizing is the ability to instantly see how many in a small collection of items without counting.  Dots on a die, shapes on a playing card, number of fingers held up on a hand, are all examples of subitizing in action.  In order to subitize successfully students need to see the whole as a collection of objects as well as the individual units.  Subitizing is considered to be a fundamental skill for supporting students understanding of number and ability to perform number operations.

In the primary years students should be given regular and consistent opportunities to subitize in order to build their skills, improve number sense and lay the foundation for future mathematical learning.  In kindergarten numbers to 5 should be focused on for instant recognition.  Once students are familiar with familiar representations of 1 to 5, larger collections can be used to encourage students part-part-whole thinking.   For example, on the card below students may instantly recognize a three and a four and then add the numbers together to know that there is a collection of seven dots on the card.

As the collections get larger students can be encouraged to use their estimation skills to think about “how many” and “how do you know”.  Our Saskatchewan Curriculum refers to this fundamental skill through several outcomes from Kindergarten to Grade 2:

• Kindergarten- NK.2 Recognize, at a glance, and name familiar arrangements of 1 to 5 objects, dots, or pictures.
• Grade 1- N1.2 Recognize, at a glance, and name familiar arrangements of 1 to 10 objects, dots, and pictures
• Grade 2- N2.1 Demonstrate understanding of whole numbers to 100 (concretely, pictorially, physically, orally, in writing, and symbolically) by:
• representing (including place value)
• describing skip counting
• differentiating between odd and even numbers
• estimating with referents
• comparing two numbers
• ordering three or more numbers.

This video is an excellent example of a kindergarten teacher who is using Quick Images to build on her students subitization skills, and create opportunities for mathematical conversation.

Subitizing-What is it? Why Teach it?

Pinterest Board on Subitizing

###### Resources to support teaching Subitizing

Dot Cards and Ten Frames

Sparklebox Dot Cards