Category Archives: Mathematics

Air Server In Kindergarten!

Prior to our winter break I was introduced to Air Server.  Wow!  What I am finding out is how easy it is to use as well as how my students are also benefiting from this neat, wireless tool!  What is so amazing is that I can now and my students can remotely access our Smartboard through an iPad.  What an inspirational tool that helps me and my students think, interact and reflect with our ideas.

Now every time I have a new app to share, I can do this remotely!  I can be anywhere in my classroom.  The value of this is now I can be flexible about where I am and also my students can easily interact with the SMARTboard, but are also able to remotely share their observations as well about what we are exploring.air1

For example; During our “Number Corner” time the children use iPads to create patterns, write numbers that come before, after and count using iPads.  Now the leader of the day is able to use their iPad remotely.  So what this means is that the leader displays the number patterns, numbers, etc. and others create what is being asked on their iPad and then they “check in”.  When my students “check in” they are checking their understanding with what the leader of the day is sharing.  This is a wonderful way for all children to be empowered by using a technology that helps others reflect on their own thinking.

So this is what I notice(keep in mind that I have only had 3 days with this tool)

1.  My students are able to make decisions about where they are, physically in the classroom when sharing and checking their understanding.  This encourages all learners to facilitate what they understand.

2.  I notice how excited and engaged my students are about what we are exploring.  This is contagious with all learners in kindergarten.

3.  I see how easily my students can begin to take on leadership roles about what they want to share.  A great self esteem experience for all my students.

4.  Air Server seems to be a pathway for me, my students and others to connect and collaborate with in regards to what we are learning.

5.  The access of what I have on my ipad is available for everyone and everyone has an opportunity to investigate the possibilities of the apps we use.

6.  My students take risks with making observations and connections about their understanding.

7.  What another great way to help promote the idea of being a safe, kind and responsible digital citizen.

8.  I already noticed how a couple of my students began to problem solve “how to” get back on line, when Air Server delayed.  Really!  Just the idea of looking for a way to problem solve a problem in a collaborative way.  Critical thinking happening here for sure!air2

I look forward to blogging more about Air Serve.  I have only used this tool for 3 days!  Looking forward to discovering more using Skype and other tools that enhance learning opportunities for my students.

Math Studio In Kindergarten!

What is math studio?  How did it evolve?

I have just completed my first year of math studio.  The studio provided 4 opportunities throughout the school year to collaborate, plan, produce, create and design math lessons that helped me and my colleagues develop how to get at the deeper meaning and concepts of a math lesson.  Phew!  Overall the experience was rigorous, but relevant.  I really enjoy the new learning and how much it can impact and improve student learning.  It is for this reason that I continue to create different on-line ways for others to read, collaborate and connect using the work that I have just begun to understand around “how to” teach, expose, experience  mathematics with young children.

Our school made a commitment to take a professional 5 day class through the Teachers Development Group.  This professional development has been amazing and very rewarding.  After taking the 5 day intensive course, we, the teachers at my school all began to work in collaborative teams to plan math lessons based on best practices.  A huge task!

What happens in math studio?

Math studio is a time when all the kindergarten teachers spend a day together to teach, observe, plan and talk about best practices for teaching math.  It is a great opportunity for teachers to share, collaborate and design math lessons that incorporate best practices.  We have had math studio 4 times this school year to work together as a kindergarten team to support each other in becoming strong math teachers, help our children think deeply about math(and ourselves) and to assist our students to develop mathematical habits of the mind. These math habits have been amazing and the learning that has developed is ongoing, never-ending and becoming almost seamless.  I mention this because children are now recognizing these math habits in all areas of Kindergarten!  For example; I put up blank paper all different sizes in our dramatic play area where many manipulative items are kept including blocks, tiles, etc.  A group of children created a blue print of a structure they created.  Using labels, symbols and numbers to represent their thinking.

My own experience with this professional opportunity has been endless. By using the different MHOM I have given myself and the children daily opportunities to practice and experience what these math habits can do for their understanding of mathematical concepts.  Through explicit teaching, role modeling and various technologies the children have been able to think more deeply about the math they are involved with.

The MHOM(math habits of mind) that we worked on this year were; making connections, justification, changing our thinking, how, multiple representations, conjectures and generalizations and private think time.

My post below is taken from my math wiki I created 2 years ago which focuses on mathematics in Kindergarten.  I hope to be able to collaborate, share and connect with others who are also interested in making learning engaging, exciting, relevant and fun!

Below I will share photos, video and reflections about the learning that occurred for me, my students and their families this year in Kindergarten.

In the beginning(fall)…

Children justify their thinking when they can talk and show their ideas about why something worked or not.

Children make connections when they see a connection between math ideas, representations and situations from everyday life.

We also learned about what a mathematical dyad was.

A dyad is structured so that children always have thought time about the task.

Always focuses on each child’s mathematical reasoning, justifications, and/or generalizations.

Always ends with an opportunity to share why their mathematical ideas are the same/different

Always follow a structure that provides children “practice” to talk to each other about what they heard and what they understand.

(This is taken from the teachers development group about How Math Teaching Matters)

“Mathematical Habits of Interaction”

Private Think Time is a very important time when thinking mathematically.  The children have an opportunity to think about their ideas before they share them.  This idea is a mathematical interaction because the children and myself think about our ideas and then share our ideas through interacting with others.  There are many Mathematical Habits of Interaction.

In the mathematical dyad the children all had some private think time first, before they shared their ideas, observations, and/or thoughts.

Multiple Representations

The children are becoming keen observers when it comes to making mathematical observations. Habit of Mind, Multiple Representations.  The ten frame cards represent numerals 11-18.  A great interactive game for children to begin to subitize and recognize the many ways numerals can be represented.

The children discovered that the number 14 can be made different ways using the Rekenrek.  Later we talked about what they saw and how we could write it.  The children discovered many different ways to represent numbers.  This is a great example of the Math Habit of Mind Multiple Representations.

Another Math Habit of Mind ……..Changing My Thinking!

Children love to create number patterns and look for patterns using a variety of objects.  As the children created different number patterns they began to solidify their thinking and understanding.  When they miscounted, they were able to “change their thinking” to the amount of sea creatures they needed to represent the number accurately.

 The children are beginning to discover that mathematicians change their thinking a lot!  Mathematicians do this when they have a different idea for a solution to a pattern, problem or an idea!  We make mistakes often and we have discovered that when we do make mistakes, we have a deeper understanding of what we were thinking!  This is when all the learning takes place.

 My reflections about the technologies I have used…………….

As a kindergarten teacher I have many opportunities to engage in productive math thinking.  My eyes have really been opened this year in terms of what young children(5 & 6-year-old children) are capable of!

I have also discovered numerous technologies that have helped in the engagement as well.  Podcasting has given young children an opportunity to use”math talk” to help develop and share their mathematical ideas.  Voicethread is another web tool that has given children a chance to interact and reflect on their mathematical ideas as well connect with others outside of our classroom!  Video has provided endless opportunities for children to reflect on their understanding as well as to use as a model of “what it might look and sound like”.  Children have just recently asked to use our flip camera to record some of their learning too!  Another great way of how technology can be part of a learning culture in a way that provides and encourages authentic learning and opportunities to grow from.  Photographs are easy to take and display.  In this photo you see how easy it is to show a mathematical understanding of children making a connection and justifying their thinking!

A wonderful thing happened during our “REST” time. The children collaborated together to make a row of chairs!  Later on the children continued to make rows using lots of different materials in Kindergarten!  Some of the comments were; “We know this is a row because(their justification) the chairs go from left to right in a horizontal way.”  A discovery; “Hey, It could be a column if you look at it this way.” A child stood looking”down” at the chairs.