Mathematics Happens Everywhere

A Kindergarten Inquiry

LE4 Etivity 11, ETFO Kindergarten Specialist, June 2017

Brenda Fowler

The Spark of the Inquiry

About a month ago, a Kindergarten colleague of mine came to me looking for some ideas surrounding her Math program. She was interested to hear how we ran Math Bins in our classroom. She came into my room to speak with me how we run Math Bins in our classroom. She was surprised to hear that we did not have an all Math centre time built into our schedule as Math happens all day in our classroom. Our discussion then lead to how putting intentional materials out for students to explore help support mathematical learning in the following ways:

Caring for mathematical materials. We chatted about the need to rotate in and out materials of the classroom on a regular basis and we try not to overcrowd shelves with all of the materials that we own.

We want mathematics materials easily accessible to the students and to be intentional. Students learn that materials are readily available and they have the choose to access them if they think their learning would benefit from using them

We both wanted to make sure we put out meaningful literacy and numeracy reading materials throughout the classroom. For example providing books around the room based on students’ interests, having out number cards to record attendance, having writing materials accessible around the room, and having labels at the block centre to name a few.

If we watch and document what we see the students doing, we can see what the students actually know and what they are interested in learning. We are able to have student data to help change our students’ math abilities. Giving the students choice in how they show us what they know.

We decided we would start with a number sense and numeration focus with our students.

My current interest in Mathematics

Teaching Mathematics in the Early Years is a passion of mine. I am a strong believer in the importance of following an inquiry-based program in Kindergarten. I try to integrate rich math resources and opportunities throughout the room and not just in a defined ‘Math Centre’ in order to encourage exploration. The children are investigating and finding solutions to questions or problems generated in the social interactions they have during learning time. Often I try to bring the students’ inquiry-based topics to the whole group for further discussion, specifically highlighting math and computation when applicable. Since children are highly invested in solving these problems, they will be more likely to work together to brainstorm various strategies for arriving at solutions. I have always wondered about how literacy resources could help drive mathematics learning in Kindergarten.

What is the impact of sharing mathematics picture books throughout different learning areas in the class to enhance student engagement in math?

Effective inquiry questions help to frame the work of collaborative educator groups. I feel this inquiry question will compel my small group inquiry including my teaching team as well as my coworkers to investigate the "how" and "what" when using picture books to engage students in mathematics.

The Inquiry Question

The initial thinking surrounding my inquiry started with a series of ETFO PLEY videos called “Math Happens in Kindergarten”

Math Happens in Kindergarten is a video divided into multiple segments which captures a conversation with mathematics educator, Dr. Douglas Clements. (http://etfopley.ca/projects/math-happens-in-kindergarten).

“Creating an Environment Where You

Bump into Math”, April 22, 2014

Dr. Doug Clements said, “Good Kindergarten classes experience Mathematics everywhere! In the sand table, water table, at the blocks”.

He suggested the ways to get Mathematics in classrooms is through play, literature and running small groups.

He stressed the importance of using intentional manipulatives to free explore as well as being given a task.

He also stressed that concepts are being built using materials and it is not just playing with the materials.

“Math Happens in Kindergarten: Play... Seeing the

World Through Mathematical Eyes”,

Dr. Doug Clements said, “Kids like to see the world through mathematical eyes”. He shared that Math happens even when teachers are not noticing it happening.

Clements made the comment, “If the teacher didn’t see the Math, they never make the kids intuitively aware of the Mathematics they are doing”.

This comment made me think about the importance of observing students in play and teachers needing to find out what young children already understand and help them begin to understand these things mathematical. Through observation, educators can see the initial engagement and build on this interest by adding intentional materials, asking open-ended questions to promote problem-solving and through small group activities such as mathematics games tailored to the individual students’ next steps.

The Research says…

Math is

Everywhere!!!

It is important that teachers capitalize on the everyday activities in the classroom and get students talking about math concepts. To be most effective, teachers should also intentionally integrate math exploration opportunities into math routines (p.34)

Plan Small Group Work

Small groups allow teachers to give support, observe, and assess.

One-on-one support can help children who struggle, give teachers opportunities to direct specific questions and ideas, and observe children's reactions and assess their progress

Support math play in all centres

Recommended by NAEYC & NCTM, "provide ample time, materials, and teacher support for children to engage in play, a context in which they explore and manipulate mathematical ideas with keen interest."

Select materials that build on children’s skills and interests and engage children’s in math conversations as they interact with the material (p.33).

Manipulatives and Patterning Materials: Manipulatives are small items used to sort, count, match, measure, categorizes and pattern (e.g. Items from nature such as stones, pinecones, shells, keys, buttons, bottle caps, craft supplies. Geometric Materials Support children's understanding of shapes and spatial sense (e.g. wooden blocks, Legos, simple puzzles, shape sorters, shapes including 3D). Measuring Materials: Invite children to measure distance, time, volume, and weight (e.g. Rulers and tape measures, egg timers and stop watches, measuring cups and spoons, scales) Dramatic Play: count play money, fill out deposit forms. Science Center: measure grass planted and record changes on chart Literacy Center: Look through books to find math concepts embedded in the story. Water Table: Scales, measuring cups, predictions

Math Is Everywhere! Tips for Mathematizing Preschool Settings

by Amy Shillady from Spotlight on Young Children: Exploring Math, July 31, 2012 (p.33-35).

NAEYC position paper (2010), “Early Childhood Mathematics: Promoting Good Beginnings.” A joint position statement of NAEYC and the National Council of Teachers of Mathematics (NCTM). www.naeyc.org/files/naeyc/file/positions/psmath.pdf

I had to check out this resource for my own interest as I have always wondered about this resource as it is often cited in many discussions about early years mathematics.

I found the section “Integrate mathematics with other activities and other activities with mathematics” to be a valuable reference for my inquiry question. It said, “Effective practice does not limit mathematics to one specified period or time of day. Rather, early childhood teachers help children develop mathematical knowledge throughout the day and across the curriculum. Children’s everyday activities and routines can be used to introduce and develop important mathematical ideas.

It was also suggested that it is important to weave mathematics into children’s experiences with literature, language, science, social studies, art, movement, music, and all parts of the classroom environment. For example, there are books with mathematical concepts in the reading corner, and clipboards and wall charts are placed where children are engaged in science observation and recording (e.g., measuring and charting the weekly growth of plants).

Finally, the NAEYC gave the final rationale for integrating mathematics throughout the day lies in easing competition for time in an increasingly crowded curriculum. Heightened attention to literacy is vital but can make it difficult for teachers to give mathematics and other areas their due.

I plan on using this research to implement a change in my practice by:

Reading a picture book with a numeracy focus during a whole group lesson. I will follow up this lesson by placing the book out at a centre around the room to see if the students show any interest in the book. I will also take notice of any activities or conversations which start based on the story. Through observation and questioning, I will start to plan any next steps (e.g. adding intentional materials based on the students’ interests, setting up a table top provocation to see if students show learning). I will repeat this procedure with at least 3 books.

My Plan of Action

I have chosen picture books based on my students’ interests which have some numeracy focus

surrounding them.

The Hungry Caterpillar

by Eric Carle

City By Numbers by

Stephen T. JohnsonOne Duck Stuck

By Phyllis Root

A handful of students are very

curious about caterpillars as

they have just been seen

around the playground.

I have an activity in which the

students will use mud gup. My

students are always interested in

sensory activities.

This book will be placed at

Blocks. I will also use this book

to inspire some learning at the

tinker trays (loose parts

activity).

How we documented the change in

practice and learning.

My Plan of Action Getting it Started Observations: For a week, I recorded the areas

of the classroom where each student spent most of his or her time learning. This ended up being my beginning frequency chart. Due to time constraints, I decided to take the four students who rarely changed learning areas over the week to observe for changes due to this inquiry.

We made anecdotal observations on individual student's use of materials or math concepts he or she are showing. We also made notes of the student’s personal Interests discussing student’s engagement during the activities. Pictures were taken to support the data which showed student engagement with learning.

At the end of each day, I meet with my teaching partners and went over our anecdotal notes, the images we captured, the conversations we recorded and to discuss the important events of the day. From this, we will also talk about and record what we would like to revisit or what we would like to do as our next steps.

Observations of student engagement: Observations were written on an-at-a-glance sheet. These written observations tracked the students’ on track behaviours while learning is occurring with respect to Mathematics particularly Number Sense thinking.

Student A: Blocks Centre and Lego Duplo only (Very interested in creating roads and a garage to park the cars) (520 minutes out of the 600 minutes of open learning were in building activities)

Student B: Equal split between Dramatic Play centre which is currently set up as the Toronto Rogers Centre and the Art Studio (340 minutes out of the 600 minutes of open learning were in Dramatic learning, 120 minutes at the Art Studio)

Student C: Dramatic Play centre and interest in outdoor learning with a focus on the caterpillars (450 minutes out of the 600 minutes of open learning were in Dramatic areas)

Student D: Art Studio with a focus on making drawings for his mother (480 minutes out of the 600 minutes of open learning were in building activities).

How we documented the change in

practice and learning.

Our team reviewed the observations on student engagement and written documentation and pictures of students’ learning and thinking to determine if our 4 students were showing more mathematics at their centres of interest. We also kept a frequency checklist showing how often the books were used to support any learning experiences including mathematics learning.

A documentation panel recorded our development of the Mathematics around the classroom from start to finish and the learning that occurred. Through the use of a slide show, the children will also be able to see some other samples of learning that took place. The slideshow was shown at reflect and connect whole group learning time and helped provide opportunities for further discussion amongst them and further documentation.

Data/documentation that supports major findings

After the first few days of observation, I found the picture books did seem to impact the students engagement in Mathematics learning based on the book "The Very Hungry Caterpillar" by Eric Carle. I've included the student comments which definitely related to demonstrating mathematics learning. I was so excited to see how a few student comments actually elicited students responding to another student's learning experience naturally and in one case actually inspired a student to recreate the learning opportunity for herself. This learning ties in with Dr. Doug Clements’ thinking around “Kids like to see the world through mathematical eyes”. When students saw the learning activities of others or heard the mathematical ideas of peers, the students were more likely to talk about what they were seeing and sharing what they thought about the mathematics.

Data/documentation that supports major findings

It was also suggested that it is important to weave mathematics into children’s experiences with literature, language, science, social studies, art, movement, music, and all parts of the classroom environment (NAEYC). This documentation shows how an illustration in a book can actually inspire mathematical thinking.

We found when students had access to these familiar picture books added to a learning centre, the students’ definitely noticed the books and more conversations about the books definitely happened. I was also pleasantly surprised by the recreating of the learning experiences which occurred on a few incidents when students saw other students using the books.

Data/documentation that supports major findings

Dr. Doug Clements made the comment, “If the teacher didn’t see the Math, they never make the kids intuitively aware of the Mathematics they are doing”.

This comment made me think about the importance of observing students in play and teachers needing to find out what young children already understand and help them begin to understand these things mathematical. As I documented the students’ learning through this learning story, I never noticed the students had actually numbered the rows of seats for their movie theatre. When I asked if I could watch what they were learning, one of the students told me to find the seat in the 4th row for my seat and my ticket. I was able to notice that this student has some experience with ordinal numbers. Through observation, educators can see the initial engagement and build on this interest by adding intentional materials, asking open-ended questions to promote problem-solving and through small group activities such as mathematics games tailored to the individual students’ next steps.

We found by adding picture books throughout different learning areas

to enhance student engagement in math…

Some students seemed to take on a more active role in showing their mathematical understandings as they might have be more comfortable in a learning centre likely due to their interests or their previous experiences at this centre.

The students did show more mathematical thinking at the activities they choose to learn with. We feel the students were more engaged in their learning as they were given the choice to make the learning experience more authentic to their interests. A few students definitely come up with ideas I never thought possible and most students did make connections with other areas of learning within the four frames on the Kindergarten Program (2016)

The students will easily show the mathematics behaviours as described in the Kindergarten Program (2016) providing the students are interested and engaged in the picture books which are added throughout the classroom. I believe the students will also be more engaged in showing mathematical behaviours providing their classmates show them some interesting ways to play based on the books.

Our Major Findings

We found by adding picture books throughout different learning areas to enhance student engagement in math…

We found when picture books, the students had previously heard read aloud by the teacher, where added to a learning centre, the students noticed them and more conversations about the books definitely happened. This finding is supported by the NAEYC position paper, “It was also suggested that it is important to weave mathematics into children’s experiences with literature, language, science, social studies, art, movement, music, and all parts of the classroom environment”.

When looking at our anecdotal notes, we found when students noticed another student using the picture book to help guide his or her learning, other students were much more interested in what the student was showing. Most of these students who noticed students learning with the books, spent more time observing or asking questions why the book was being used.

We found by adding picture books throughout different learning areas to enhance student engagement in math…

Research supports the understanding that mathematics experiences occur naturally as children play (The Kindergarten Program, 2016, p.75). During play, children sort materials into corresponding bins at cleanup time, explore patterns and shapes while creating at the art table, tell time while using the visual schedule, measure their height in comparison with others and so much more!

It has also been found that intentionally introducing ideas and materials connected with mathematics in the classroom can create a wide variety of opportunities for children to learn about mathematics (The Kindergarten Program, 2016, p.75). By adding picture books with a possible mathematic focus, our students showed these books could offer some inspiration for learning. I found when our students had access to open-ended mathematics manipulatives placed in easily accessible locations throughout the classroom, as describes by Amy Shillady in her article “Math is Everywhere”, our students were more engaged in math exploration and learning. A well-stocked math and manipulatives center includes found objects such as shells, rocks, glass beads and sticks, as well as open-ended purchased materials including tools for measuring, blocks, and materials to help represent their thinking (The Kindergarten Program, 2016, p. 86).

Next Steps

I would love to try this inquiry using familiar children’s songs and poems which contain mathematical messages to see if the same findings would happen. I will start by using songs that help familiarize children with counting “One, two, buckle my shoe” and “Ten little monkeys jumping on the bed.”

As Amy Shillady mentioned in her article running small groups is another way to have Math happen in a classroom, I would really like to do some inquiry on how small group math focused groups also impacts student engagement in mathematics. As Dr. Doug Clements has mentioned, “Although many children learn some math concepts on their own, it’s important for teachers to include math in authentic experiences, resulting in a deeper understanding by children”.

I would definitely like to spend more time to implement this inquiry and I would be very interested to see if this inquiry would have the same results with a different group of students in upcoming school years. I would also like to involve more coworkers in this inquiry, perhaps at different Grade levels, to see if the findings are representative for most students.

I have found that through this process, my understanding of the collaborative inquiry has deepened with the opportunity to collaborate with my coworkers and have the ability to be an active member in this learning, as opposed to just sharing what I have learned through this course.

I found the social benefits were amazing for my teaching practice and for building a community with my coworkers. I found we all embraced a shared knowledge about our students and shared a view about situations from others’ perspectives.

As a facilitator, I monitor student progress, provide helpful resources and encourage student problem-solving, which is an important goal in education today. I feel it is important we see each other as a community of individuals working together to achieve a common goal. As responsibility and knowledge are shared between my coworkers and myself, I find my role as facilitator helped us connect ideas or new information with our experiences.

My Personal Reflections on the

process of Collaborative Inquiry

My Personal Reflections on the

process of collaborative inquiry

One drawback I noticed at first, despite my efforts to be a facilitator, I did find my coworkers were often waiting for me to tell them what I was thinking and what I know. Once I acknowledged this idea and shared with them that we all play a part in co-constructing our own learning, I did notice more co-learning happening. I shared with them I was hoping to take on more of a facilitative role, rather than being a simple bearer of information. I did find this conversation helped and actually seemed to empower my coworkers to share more of their thinking surrounding the inquiry.

Following this inquiry, I have also found I am more confident students will show me Mathematics learning everywhere. If I let the students take the lead, knowing their questions and instincts will lead to great growth in their learning, students will be more engaged to try more Math everywhere in the classroom.

Finally, an A-HA moment to remember for future collaborative inquiries! Though change in practice can be uncomfortable, and sometimes stressful, rethinking practices allow for deeper understanding of strengths. As a facilitator of collaborative inquiry groups, all members’ emotional needs to be considered and understood by all involved through the change process to develop a comfortable and safe environment where everyone, including students, will thrive to learn!

Resources:

Carle, Eric (1994). The Very Hungry Caterpillar. Philomel Books

ETFO PLEY Video: Creating an Environment Where You Bump into Math, April 22, 2014 (2 minutes 34 seconds)

ETFO PLEY Video: Math Happens in Kindergarten: Play... Seeing the World Through Mathematical Eyes (3 minutes 41 seconds)http://etfopley.ca/projects/math-happens-in-kindergarten

Johnson, Stephen T. (2003). City by Numbers. Pufferin Books.

NAEYC position paper (2010), “Early Childhood Mathematics: Promoting Good Beginnings.” A joint position statement of NAEYC and the National Council of Teachers of Mathematics (NCTM). www.naeyc.org/files/naeyc/file/positions/psmath.pdf

Ontario Ministry of Education (2016). The Kindergarten Program. Government of Ontario. Toronto, ON: Queen’s Printer for Ontario

Root, Phyllis (2003) . One Duck Stuck. Candlewick Press

Shillady, Amy. Math Is Everywhere! Tips for Mathematizing Preschool Settings", Spotlight on Young Children: Exploring Math, July 31, 2012 (p.33-35).