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Effective Planning in Mathematics

Published October 9, 2015 by Mrs. Malo

Part of being an educator is always continuing to be a learner.  This fall I decided to focus on my mathematics instruction in my Kindergarten room and start working towards by Mathematics specialist.  The first course on this path is P/J Mathematics Part 1 which I am currently taking online through ETFO.

As part of the first module I have created a series of blog posts on Effective Planning in Mathematics.  I chose to do this from a Kindergarten perspective.  There are four posts in this series:

Big Ideas in Mathematics

Thoughtful and Clear Planning

Daily, Unit and Long Range Plans

Cross-curricular Planning

I would love to hear perspectives of others.  Please post comments and links in the comment section.

Cross-curricular planning

Published October 9, 2015 by Mrs. Malo

Meaningful integration deepens children’s understanding of the skills and concepts in each of the subjects that are involved.  Through meaningful integration, children can be encouraged to generate new connections and to explained their existing understanding.  Integration also helps children see how the knowledge and skills developed in one area can be relevant to other areas.

The Full-Day Early Learning-Kindergarten Program Draft Version 2010-2011 page 17

Throughout this series of blog posts I have talked about how slight changes sometimes need to be made in thinking and planning in order for these structures to be used in Kindergarten.  When it comes to cross-curriculuar planning this is an area that Kindergarten often leads the way!  We integrate everything.  Rarely is anything ever taught in isolation.  To give you an idea of how this looks let me explain some of the things that took place in the past couple of weeks in our classroom.  Since the focus of these posts is mathematics I will start with our math unit on sorting.  We read a number of books to introduce us to sorting:  A Lost Button  chapter in Frog and Toad are FriendsThe Button Box, Pete the Cat and His Four Groovy Buttons, and Sort it Out!  Lots of manipulative were put out in our Loose Parts Centre including big box of buttons.  When students started describing things by colours we started to study the primary colours in the visual arts centre and combine colours to create secondary colours (we also learned these words and added them to our word wall).  In our music lessons we were describing famous pieces of music by tempo – fast and slow, which connected to our movement in PE.  We had some local newspapers delivered and while learning about what a newspaper is (Media Literacy) we cut out picture of pumpkins and faces and sorted them.  Finally in science we cut open those pumpkins and sorted different types of pumpkin seeds, squash seeds and sunflower seeds.  Every different subject in our class was integrated making it more meaningful and engaging for our students!

Day, unit and long-range plans in Kindergarten Mathematics Teaching

Published October 9, 2015 by Mrs. Malo

One of more difficult aspects in the move to the Full-Day Early Learning Kindergarten Program is the change in planning.  In the former program teachers use to select themes to base their year around and planned the entire year out.  Long Range Plans were done in a similar way to older grades.  In the new program the students are the leaders.  We follow their lead in their play and inquiry and it is our role as educators to guide them while making sure we are addressing the curriculum expectations.

The team should use inquiry-based learning to build on children’s spontaneous desire for exploration and to gradually guide them to become more focused and systematic in their observations and investigations.  pg. 15

Planning is still very important in Kindergarten, however built into the planning there needs to be flexibility.  The students are the leaders and often the best learning takes place when they are following their own questions and inquiries.

Long-range planning is helpful, especially for new teachers, to understand the ultimate goals for the end of the school year.  What knowledge and skills are students expected to know going forth into grade 1?  What knowledge and skills in the Kindergarten program need to be developed before other skills?  For example before estimating quantities students need to understand that quantity is greater when counting forward and less when counting backwards.

Note: In Kindergarten students are not coming from a previous grade so they come with a wide variety of background knowledge.  Teachers should be very aware of this when planning.

In some school boards a math alignment may be provide to aid with long range planning (Grand Erie Math Alignment).  This can be very helpful in seeing progression through the year and also through the grades.  In saying this flexibility is key and sometimes changes need to be made – this is OK.  Last fall we had a variety of different apples out at an exploration centre.  We didn’t expect students to start comparing the different weights of the apples.  We took this opportunity to delve into a unit on weight.  We normally would teach weight later in the spring but this was what the children were interested in so we got out the balances and scales and had a great engaging study of the measurement of weight.

Unit Planning in Kindergarten is important, but again flexibility is important.  It is very important throughout a unit to have a solid understanding of the curriculum and the Big Ideas.  An understanding of what knowledge needs to be covered is important, however, to ensure your math program is the most engaging for students it is important for teachers to be flexible in instructional tasks.  One example is the unit in our class we recently finished on sorting.  Much of our unit was planned around sorting buttons.  Part way through our unit our students showed an interest in the pumpkins growing in our community.  We continued our unit on sorting however instead of buttons we started sorting different types of seeds, including pumpkin seeds of course.  We were still developing the same skills of sorting and describing attributes however the specific tasks changed.

In planning daily math lessons it is important to use a variety of structures, teaching strategies and groupings.  Traditional lessons including teacher demonstrations and rote learning still have a role in math lessons.  Every day in our Kindergarten class we add a new number to our hundreds chart.  Through this 5 minute routine we are learning how to print our numbers, counting, and patterns in numbers.  Only by lots of practice do students learn number order and how to print and recognize numbers.

When developing more complex mathematical ideas structures such as three-part lessons help students create their own understanding.  A traditional 3-part lessons includes the following parts:

  1. Getting Started (10-15 minutes): Whole class lesson to introduce idea and problem.
  2. Working on It (30-40 minutes): Students actively engaged in a task
  3. Reflecting and Connecting (10-15 minutes): Students share ideas and understandings

In a Kindergarten classroom 3 part lessons can be valuable but they do need to be modified slightly.  With our youngest learners they are very limited in how long they are able to stay engaged in a task.  A large group / whole class lesson can be used to introduce a problem.  The largest change would be in the working on it section.  Sometimes students are given a small problem that can be solved in 10 minutes. Other times a problem is explored during exploration/play time as students choose to visit the centre.  There are even times that a problem is explored over a number of days.  The important part is that students are engaged in working through the problem.  As they are working on it, educators are documenting student work, observations and conversations.  This all is brought together in the reflection and connecting stage.  This can take place at the end of the same block of learning, at the end of the day or at the end of a number of exploration blocks.

In conclusion, effective and purposeful mathematics planning is very important in Kindergarten teaching but it always needs to be flexible and adaptable to student developmental needs and interests.

Big Ideas in Math – Focus on the Early Years

Published October 8, 2015 by Mrs. Malo

So what is all this hype about “BIG IDEAS” and is the hype worth it?

Let’s start by talking about what Big Ideas are.  Different researchers have different names for Big Ideas – they can also be called enduring understandings, key concepts or key ideas.  In the NCSM Journal in 2005 Randall I. Charles defines Big Ideas:

A Big Idea is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole.

You may need to read this quote a few times for it to really make sense.  At first the concept may seem like it is trying to make things more confusing but the heart of it is that it is trying to make thinking more succinct, more concise and easier to relate.  Think about all those specific expectations in a math curriculum.  When starting a school year it can seem very daunting when looking through everything.  Many new teachers wondering how they are ever going to get through it all!  Sometimes when we plan based on these specific expectations we can get very ‘hung up’ on the little details.  We worry that are students may not be meeting one very small specific expectation and that we are failing as a teacher.  Big Ideas help us take a step back and focus on the important understandings that we are in essence teaching our students.

Marian Small writes that by

Focusing the learning of each strand in mathematics around a few big ideas makes it easier for students to relate new knowledge to previously learned ideas.  In addition, it simplifies the teacher’s job of prioritizing what is usually a fairly lengthy list of specific curriculum expectations/outcomes by organizing them around a relatively small number of big ideas.

Making Math Meaningful to Canadian Students, K-8 pg. 18

OK did you catch that “simplifies the teacher’s job”!!!  Big Ideas are not only useful for building student understanding but make a teacher’s job easier.

I was sold, now the next step was to figure out – What are these Big Ideas?  That task proved to me a bit more difficult.  I started by looking in the 2010-11 Full-Day Early Learning – Kindergarten Program.

In the mathematics section it lists the Big Idea as:

Young children have a conceptual understanding of mathematics and of mathematical thinking and reasoning.

To me this is very broad and very big – it isn’t going to help me or my students.  I decided I needed to look a little further.  When looking at Small’s writing it didn’t clear anything up as she started by saying that different researchers look at big ideas in different ways.  Some big ideas sound like overall curriculum expectations while others are more specific.  If you can get a copy of Marian Small’s Making Math Meaningful to Canadian Students (2013) she has an excellent overview of different approaches to Big Ideas on page 18 to 24.  Personally I was starting to get a bit better understanding but not yet sure I had found something that was going to help be directly in my classroom so I turned to another source – the internet.

After a bit of searching I found the perfect resource for helping me in my Kindergarten classroom in Ontario.  It is was a resource called “Kindergarten Unit Plans Linked to the Big Ideas” and published by the Lambton Kent District School Board. Here are the reasons this resource jumped out at me:

  1.  This is a school board in Ontario so they are using the same curriculum/program document that I am using in my class.
  2. It connects with the Big Ideas in A Guide to Effective Instruction in Mathematics.
  3. It makes sense in language I can relate to and connect with my youngest learners!  For example under the idea of Quantity it outlines the big idea as: ” the “howmuchness” of a number and is a crucial concept in developing number sense.”

This is an idea I can use in my planning, I can use with my students, and I can use when explaining learning to the parents of my students.  We can all understanding this language and help move everyone forward in their understanding.

So in short I have personally reached the conclusion that Big Ideas can be extremely valuable in mathematics planning.  The exact wording of those big ideas may be a bit different for different educators but the important thing is that they are valuable for you and your students.

The Importance of Thoughtful and Clear Planning in Math

Published October 7, 2015 by Mrs. Malo

I started to write this post based around the title “The Importance of Thoughtful and Clear Planning Math” and was really struggling with how to start.  I got out all of my math resources and started going through them looking for resources on planning and it’s importance.  I was starting to get frustrated.  I had numerous publications from the Ontario Numeracy Secretariat about Pedagogical Documentation, Communication in the Mathematics Classroom, Student Interaction, and Asking Effective Questions amongst others.  I had books by Marian Small, curriculum documents and board policies.  As I flipped through Seven Foundational Principles for Improvement in Mathematics, it hit me!


Why do I have all these resources.  Yes I have collected them over the years but why have I kept them and why do I regularly refer to them.  It is because I am carefully planning out my lessons, my units and my year.  It all started because in Kindergarten we don’t have a math textbook.  There was no prescribed way to teach Kindergarten math.  I had to put it together myself.  It has been a journey and 5 years into this journey there a some things that I have done the same from the beginning and many that are very, very different.  Every year things change.  I change, my philosophies change, my knowledge and understanding changes but most importantly my students change.  I can’t just take a prescribed lesson and teach it the same way every year.  My students have different backgrounds, differing levels of understanding and different learning styles.  I may start a unit the same as previous years but it may go in different directions based on the needs of my students.

One of the big changes that happened when we moved from the traditional Kindergarten program in Ontario to the new Early Learning Kindergarten Program was that we were told we were not to do worksheets with our students anymore.  Some people took this very literally but I took a slightly different approach that I believe has made me a much better and more thoughtful teacher.  Every time I make a photocopy, create a lesson or design an activity I ask myself

“Is there a better way to do this?”

Much of the time the answer is yes.  Yes they may learn this better with hands on manipulatives, Yes this is redundant.  Yes this is not going to engage these students.  Sometimes the answer is no.  When students are learning numerals and how to print numerals I feel they do need some practice forming their letters properly using paper and pencils.  This doesn’t mean we sit for hours copying numbers down but it means that a number worksheet may be part of a balanced program.  Not everything was thrown out and changed but everything was looked at in a thoughtful and clear manner.

24 Books of Christmas – 2013

Published December 2, 2013 by Mrs. Malo

It has started again, for the 3rd year!  Our 24 books of Christmas Countdown.  This year I am really trying to keep it simple as my kids already have a pretty hectic life. I considered not doing it this year but they love it so much and started asking about it mid November.  I have compiled the list, collected most materials and we hit the ground running today.

As always our first book was “The Elf on the Shelf”.  You can check out what we did in 2011 and 2012, but we have to do this book the first of December every year as our elf Frankie comes back to visit.  My girls in particular have been very much looking forward to his return.  Kaitlyn was even invited to have a sleep-over at a friend’s last night but came home before sleep time because she wanted to wake up here in the morning to see Frankie.  In our house it is almost the excitement of Christmas morning.

To keep it ‘kid friendly’ and in the spirit of ELK Kindergarten I invited the kids to work together to make a house for Frankie.  I showed them a picture of an idea on spoonful.com and told them they could use whatever they wanted to make Frankie’s house.  I had been saving the boxes from all our winter boots so they picked their favourite and from there I let them use anything they could find in our craft centre and introduced them to the Christmas craft bin where I had put a collection of random Christmas craft supplies.

The most amazing part was how well they worked together.  For almost 1 hour my three children (aged 3, 5, and 7) work quietly together to build this house.  No one yelled, no one told someone they were doing it wrong, they were even complimenting each other – it was pretty amazing.  I gave no guidance and the only thing they asked me to do was glue the boxes together at the end.

Their finished project:


The Read-Aloud Handbook – Chapter 1: Why read aloud?

Published July 8, 2013 by Mrs. Malo


At a cottage in Muskoka this week, I enjoyed sitting in a screened porch looking out over the lake, as I read Chapter 1 last night.  I enjoyed reading the introduction a few days ago so I had no trouble getting in to the book.  Prior to starting I made sure to first read with my girls – Kaitlyn a chapter from The Wide Awake Princess and Eileen a story from her Cars anthology.  Michael was not sitting for a story last night but I was not too worried. There are a few distractions here at the cottage and at home where he can pick one of his hundred own books he always brings a book to “Family Reading Time”.  Trelease often writes of making reading enjoyable for children and this can’t happen by ‘forcing’ them to sit and listen to a story, to me that seems counterproductive.

Trelease starts chapter 1 with statistics, there are a lot of statistics in this book and a lot of research.  The first shows the decline in the number of students who read for pleasure as they age.

“We have 100 percent interest in kindergarten but loose three-quarters of our potential lifetime readers by the time they’re eighteen.”

Trelease has a a good discussion on his thoughts on electronic reading – tweets, email, facebook etc.  His points on vocabulary are important and became more concrete when you see the table on page 18 comparing the number of rare words per thousand in different forms of oral and written communication.  This kind of sums of the content of this chapter.  Trealease goes from discussing the reading problem, discussing what needs to be done to fix it, and then finishes with discussing why this is important (background knowledge and vocabulary).

Key thoughts that jumped out at me and what is rolling around in my head:

  1. The opening stats discusses not only if children are reading but what they are reading.  It states that children are reading less magazines and newspapers than they are books.  Do I need to have more varieties of print in my classroom?   I have a bin of magazines (Chirp and Highlights) but do I need to have enough variety.  Maybe I need to have a bin/area for ‘environmental print’.
  2. We read the newspaper online in our house – is this good enough modelling for our children?  My husband gets one magazine (The Economist) in print and the girls each get two magazines but we don’t have any print copies of the newspaper. Is this something we need to reconsider?
  3. I don’t need to abandon what I am doing now in my class, I just need to re-jig a few things. “You need the combination of know-how and motivation (pg. 10)
  4. Background knowledge!!! As a parent this is the one area I feel very confident, our children have lots of experiences and adventures but I teach children from a diverse SEC group that don’t have as rice of background experiences
  5. Types of vocabulary, I found the illustration on the different types of vocabulary on page 14 very helpful – listening vocabulary, speaking vocabulary, reading vocabulary, and writing vocabulary.

Final favourite quotes from chapter 1:

The one prekindergarten skill that matters above all others, because it is the prime predictor of school success or failure, is the child’s vocabulary entering school.  (page 15)

The least expensive thing we can give a child outside of a hug turns out to be the most valuable: words. (page 16)

The eventual strength of our vocabulary is determined not by the ten thousand common words but by how many rare words we understand.