Learning

I Am Here!

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One of the greatest and most unexpected gifts of my graduate studies has been that it has pushed me to reflect deeply on what I know, believe, and think.  I have always considered myself to be a reflective person but this has pushed me further.  Graduate studies has provided me with new constructs to think about, deeper understandings of theories, and learning that has challenged everything I thought I knew.  It has been and continues to be, a fantastic opportunity not only to learn more about education but to learn more about myself.

I equate this multifaceted opportunity to a journey.  I have embarked on a voyage across the landscape of academia with a destination of deeper understanding of my craft on the horizon.  As I navigate across the landscape there have been several places where I have stopped, investigated, and toured around.  Some of these stops have been brief; I took in the sights, snapped a few photos and carried on with my journey.  Other places have felt so comfortable, so right, so much like home that I find myself constantly going back to them only to discover new landmarks to visit.  These places have become a part of who I am as a learner, an educator, and a person that they now make up a part of who I am.

I am a Constructivist!

Constructivist belief is one such place on my journey.  I find myself constantly drawn to constructivist ideology and thinking.  It feels so right to me.  I believe in constructing knowledge for myself and providing the opportunities to support my learners in constructing their own knowledge.  I believe that there is not one “right” way to do anything.  Instead there are multiple paths that can take one to the destination.   I have always felt tension when knowledge has been presented to me as an absolute; with no exceptions, room for questioning and in a “one right way” fashion.

My constructivist epistemology has led me to several beliefs which I hold dear:

  • Learners need to be active participants in learning.
  • Learning and “truth” are unique to the individual.  Everyone constructs their own knowledge based on their schema, culture, and experiences.  I believe that knowledge is value dependent, subjective and highly contextualize.
  • Learning is socially constructed.  I learn best with others.  Talking, sharing, questioning, and analyzing with others helps me to create meaning for myself.

I have a Cultural Bias!

A few of years ago, I had an opportunity to discover the influence that my western culture has had on my ways of knowing, being, and doing.   I was standing with a friend looking at a photograph on the wall.  My friend, a consultant with our First Nations, Inuit and Metis Unit, and herself a Metis woman, asked me what I saw in the picture.  I paused, took a careful look and began to tell her what I saw.  My description was a list of items from the picture; rock, tree, man, car….on and on I went until she asked me to stop.  Then she began to share with me what she saw.  She saw the elements in the photo…earth, air, fire, water.  She connected the image with the wisdom the Elders had shared with her in regards to car.  She saw more than a steel mode of transportation.  She saw the metal as a part of Mother Earth, born from the rocks and minerals she created and nurtured.  She saw the asphalt on the street and wondered about the earth that lay underneath, trapped under tar.  In that single moment I realized that we did not see things the same way and that my truth was not hers.  She saw connections, she saw the whole, she saw much more than my laundry list of discrete items.  In that moment my mind was opened to a new way of seeing, knowing, and being.

I now believe that knowledge is not only socially constructed but it is highly dependent on cultural ways of knowing, being, and doing.  In First Nations and Metis cultures everything is interconnected, humans hold no more importance than worms in the ground and we are all connected to Mother Earth. Observations of relationships are a significant component of this epistemology.  (Kovach, 2009) In many ways my constructivist epistemology fits so well here.  I too see relationships but how I process and make sense of what I see continues to be different.

Another ideology I connect strongly to within First Nations and Metis culture is the ideas of ownership.  I believe that knowledge should be freely shared with others.  This spirit of generosity connects us with our community, allows us to contribute, and honors the generosity of others who we learn from.   We do not own knowledge…we are a part of it, just like we do not own the earth, or the animals in it.  We are all interconnected.

I am an Action Researcher!

I connect strongly with the ideas of Action Research.  I like to be an active participant in the work.   For me, the value in educational research lies in the day-to-day, minute to minute impact it can have on student learning.  In those moments I connect strongest with the purpose of the research.   I enjoy taking theory and putting it into practice, taking big ideas and making them work in the classroom.  The classroom continues to be the place where I feel most at home.

The Journey Continues!

As I continue to navigate my learning journey I know there will continue to be places I encounter that will encourage me to stop, think, connect and reflect.  Each place I visit shapes and changes me as a person and as a learner.  This personal impact has been the most amazing and unexpected surprise in this adventure.  The journey has not been about learning more educational “stuff”.  It has and continues to be about discovering myself.

Learning, Math, Saskatchewan Curricula

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.

dot 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 video

Information about Subitizing

Subitizing-What is it? Why Teach it?

Pinterest Board on Subitizing

Resources to support teaching Subitizing

Dot Cards and Ten Frames

Sparklebox Dot Cards