# Communicating Thinking in Math

### Exploring the Impact of Number Talks and Math Manipulatives

## Collaborative Inquiry at Northwood Public School - The SWST Initiative

As part of the Student Work Study Teacher Initiative in Peel Northwood Public School in Brampton was selected to work as part of the collaborative model. Teachers are invited to connect with the SWST teacher and conduct a Collaborative Inquiry that will allow the SWST and the teachers to co-plan, co-learn and co-debrief in order to better understand student thinking and have a positive impact on student learning.

What is the SWST Initiative?

(Student Work Study Teacher)

__Inquiry Details__:

·SWST in classroom 2 days/week

·Collect student work

·Triangulate data-observation,conversation and products

·Observe and share findings

__Student Selection:__

· Collaborative process with host teacher

· "Students of mystery"

· Students working through level 2

· 2-3 students per host teacher

·Engage in collaborative inquiry to learn more about your students thinking

.Build trusting relationships that are open to wonderings

· Receive release time to co-plan, co- analyze, co- debrief and discuss student work

· Gain instructional resources for your school

## Introduction

September 2015 was an atypical start to the learning year. In Ontario, teachers were engaged in job action that affected the work and actions of elementary teachers. This job action also had a large impact of the role of the SWST in the Peel District School Board. This September also brought about large changes in staffing with reorganization process that affected many teachers and students across the board.

During this time I began my work at Northwood Public School in Brampton. I was invited into the learning environments of the grade 1, a grade 2/3 and a grade 3 teacher. The grade one teacher had been teaching at Northwood for several years. The grade one teacher actively used Number Talks to encourage math thinking and develop math communication. The grade 2/3 and grade 3 were both new to Northwood and were now teaching grades that were new to them due to reorganization. This late change in teaching assignment and new school environment set the stage for our work together. Both teachers had a very open Mindset and were seeking extra hands and resources to support them in their new assignments.

Although job action limited our ability to collaborate as a group or to engage in traditional documentation I was able to support students in the classroom and work with teachers one on one. I worked with students one on one and in small groups and shared resources with teachers in the area of literacy and mathematics. I also provided some initial grade level resources as well as was involved in reading with students, math support, working with small groups and support around the implementation of the daily 5 in the grade 2/3 and grade 3 classes.

In the grade 1 class I worked mostly with math and supporting students in sharing and developing their mathematical thinking. The grade one classroom had many math routines in place that encouraged math talk. Students required additional support when sharing their thinking in writing and practicing their skills.

## Emerging Themes

As our work progressed some common themes began to emerge around communication in general and specifically in math. As the fall progressed we noticed that the students were having trouble engaging in learning around math. There were many factors outside of the classroom that were inhibiting student engagement, students hesitated to share their thinking and take risks. We also noticed that students had difficulty sharing their thinking or working through math problems. Many learning opportunities were cut short due to behavioural issues, lack of engagement or peer conflicts. There were several students in all three classes that showed gaps in their learning that inhibited them from participating in math discussion and activities. Many students resisted sharing their thoughts and ideas.

As the political situation in Ontario settled our work was able to begin in a formal way. Due to the shortened time frame we were working in we decided to focus in on the grade 2/3 and the grade 3 teachers. We explored factors that maybe inhibiting success in math and the ability to share math thinking. Both teachers had done some significant work around building a stronger classroom climate and established stronger learning routines.

We had noticed that some students were beginning to share their thinking in math in more effective ways and felt that improving this ability and encouraging all students to share their thinking and communicate in a respectful and effective way would benefit all learners.

## Establishing a Community of Learners - Mindfulness

## The Zones of Regulation by Leah Kuypers This book integrates approaches and teaching tools to better help students understand their needs regulation and develop awareness of the "Zones" as they are referred to. "The goal of The Zones is to help students develop social, emotional, and sensory regulation." (Kuypers, 2011) | ## The Zones at Work In Grade Three The teacher was able to use this vocabulary and visual to refer to her own feelings as well as the feelings of others to foster a more caring and understanding learning enviroment. | ## Morning Meetings - Creating a Climate for Learning The teacher started her day with mindfullness breathing. Students were encouraged to clear their mind and stay present. They set a positive intention for the days learning. This happened daily before instructional time began. It helped students prepare for their day. Following mindfulness the climate for learning was reinforced through morning meetings where students shared their person feelings or discussed things that were important to them. |

## The Zones of Regulation by Leah Kuypers

## The Zones at Work In Grade Three

## Morning Meetings - Creating a Climate for Learning

## Theory Of Action - Our Initial Supposition

After sharing initial observations and seeing a common thread around communication in math the following supposition was co constructed.

If we regularly use manipulatives and practice Number Talks as a means of increasing math vocabulary students will be more engaged in learning and confident sharing their mathematical thinking.

## Resources To Support Our Planning

## Number Talks by Sherry Parrish This text served as a guide for our co-teaching. We worked together to develop our skills in facilitating Number Talks with students. We wanted students to have experience working with numbers and deepening their understanding | ## Ontario Math Curriculum Grades 1-8 revised 2005 We referred to the Ontario Math Curriculum and explored the Number Sense Strand where we felt students were struggling with their ability to perform on tasks. We focused in on the Mathematical Process Epxpectations found on page 54. We were particularly interested in reasoning and proving their thinking. We felt that they key to improving these skills would be to focus on the process of communication. | ## Making Number Talks Matter by Cathy Humphrey and Ruth Parker This book explores why Number Talks are such an important part of a mathematics program. It shares strategies for developing the "art" of numbertalks, and looks at strategies that make Number Talks tools for developing student thinking. |

## Number Talks by Sherry Parrish

## Ontario Math Curriculum Grades 1-8 revised 2005

## Lots of Opportunities to Explore Our Thinking

## Real Life Sorting and Organizing Manipulatives are all around us. Students were developing their understanding of sorting and attributes. Two hula hoops from the gym became a Venn diagram that helped students sort their shoes according to type of shoe. This hands on learning allowed all students to attach personal meaning to challenging vocabulary such as the word "attributes". This hands on experience was something they could understand and relate to. Students sorted their shoes based on Laces, Velcro or Laces and Velcro. Students with slip on shoes realized their shoe belonged outside of the diagram all together. This introduction to sorting and the use of Venn Diagram was an effective way to help students organize and sort data. | ## Patterns and T Charts Students explored their thinking and made connections to multiplication and patterns using an inexpensive and easily accessible manipulative. The text book question became interesting and real when students could manipulate their thinking and work towards a solution in a hands on way. | ## Developing Our Number Sense - Justify your Thinking Students used number lines and Wooden Dice with three digit numbers written on them to demonstrate their understanding of numbers. (two digit and one digit numbers were available to differentiate for a variety of learners) Students worked with a partner or the teacher to place numbers on the number line. This practice built a strong foundation before moving into patterning and word problems involving larger numbers. This small group instruction allowed students to deepen their understanding of number lines as a thinking tool and supported their development of language to describe concepts such as greater than and less than, as well as making links to their understanding of place value. |

## Real Life Sorting and Organizing

## Patterns and T Charts

## Developing Our Number Sense - Justify your Thinking

## An Ahhh Haaa Moment!

While working on making patterns using pattern blocks an ELL student was struggling to find the language to describe his patterns attributes. The student spoke to the teacher saying he needed the words big and small. The teacher asked him what the attribute would be. He answered,"size, humm, that's not it." Then through further conversation the student decided he needed the words thick and thin.

We had introduced the concept of math word walls and the students were beginning to use some math words from the word wall in their oral and written work. Without prompting he went to get index cards and asked how to spell the words. As his table group partner helpped him spell the words he wrote them on index cards.

It was amazing that the math word wall had now become his. The power of "co" creating this word wall and having students use it to explain their thinking was evident. When I asked him why he wrote the words on a card and put them on the wall he told me "so I can use the words later". This was a powerful moment.

## Student Generated Word Walls The power of "Co" arises here. The students asked questions and co generated word wall vocabulary that they needed to explain their thinking. The students used the word wall to support their learning in Number Talks, in group work and when working on individual tasks. The vocabulary that is student generated is more helpful to them and seems to have a far greater impact on student learning then when the teacher simply gives the students a list of words. | ## Students Use Posters to Prompt Thinking As students discovered math strategies during Number Talks the teacher would create a poster to place on the math wall to remind students of the strategies we had learned. Students would then refer to the posters when they were working on Number Talks or math activities. These poster helped to prompt their thinking and remind them of strategies they could use then they were "stuck". | ## Students "Co-Created" A List of Attributes Students were struggling to find vocabulary to describe their patterns. Together with the teacher they created a list of words and pictures that they can refer to when engaging in problem solving and describing patterns. This poster was then placed on the math word wall. The students then ended up adding some sentence starters as well to support their work. The poster had value to students as it was co-created with the information they needed to support their learning. |

## Student Generated Word Walls

## Students Use Posters to Prompt Thinking

## Students "Co-Created" A List of Attributes

## Happy and Proud This student is able to "describe, extend and create a variety of numeric patterns and geometric patterns" (Ont. Math Curriculum pg 61) Students were actively engaged in activities when they used manipulatives to explore their thinking and share their ideas. | ## Thinking Out Loud These students had the opportunity to use geometric blocks to create their patterns. They shared their pattern core and described their patterns to the group before and during the time they completed their written work. This sharing of ideas and oral discussion supported their ability to share their thinking on paper. Students also referred to their student generated word wall for vocabulary and ideas as needed. | ## The Paper Product The quality of communication on paper increased when students had the opportunity to share their ideas and use manipulatives and classroom visuals. |

## Happy and Proud

## Thinking Out Loud

## Math Games Using Dice Fun math games with dice and ten frames help students practice communication skills, reinforce understanding and practice addition facts. A welcome change for students rather than completing a timed math stencil. | ## Math Games Using Cards Using cards to build numbers, add them together and organize them from greatest to least all support Number Sense flexibility. Students using cards to represent a variety of digits in various places forced them to think about numbers and place value in a fun hands on way. | ## Number Talks We introduced Number Talks as part of weekly math lessons. Over time there was an increase in students ability to share their thinking, and increase in the variety and flexibility of students use of numbers and an increase in respectful listening and conversation about each other's thinking when students followed the Number Talk protocols regularly. |

## Math Games Using Dice

## Math Games Using Cards

## Number Talks

## Number Talks - What Are They?

Number Talks are a brief learning experience where students share ideas and solutions to a math question. The teacher guides the sharing and records student thinking which helps students see multiple ways to find a solution. Students learn from working through a problem to determine if a number is correct or incorrect.

By sharing their ideas, considering other answers and being given time to think students develop greater number sense and flexibility in solving mathematical equations. During a number talk students listen and communicate their stage of thinking by using hand signals which created a safe environment for thinking and reflecting about numbers.

“A brief daily practice where students mentally solve computation problems and talk about their strategies, as a way to transform teaching and learning” (Humphreys & Parker, 2015)

Humpheres and Parker say that Number Talks are important because they are “About helping students learn to work flexibly with numbers and arithmetic properties; and helping them build a solid foundation and confident disposition for future mathematics learning.” (2015)

## Number Talks - Why Do We Need Them?

In recent years brain researchers have found that the students who are most successful with number problems are those who are using different brain pathways – one that is numerical and symbolic and the other that involves more intuitive and spatial reasoning (Park & Brannon, 2013).

Additionally brain researchers have studied students learning math facts in two ways – through strategies or memorization. They found that the two approaches (strategies or memorization) involve two distinct pathways in the brain and that both pathways are perfectly good for life long use. Importantly the study also found that those who learned through strategies achieved "superior performance" over those who memorized, they solved problems at the same speed, and showed better transfer to new problems. The brain researchers concluded that automaticity should be reached through understanding of numerical relations, achieved through thinking about number strategies (Delazer et al, 2005). (Bollard, 2015)

Traditional methods of having students memorize math facts and complete speed tests is not meeting the long term students need for a mathematical education. In addition these methods have caused anxiety and a lack of desire to continue in math classes for many students. It is necessary to develop teaching practices that support student learning in a more positive way to produce lifelong learners of math.

In education have spent the past few years focusing on literacy and developing strong foundations around reading and writing. Now is the time to place the same emphasis on comprehension and understanding in our mathematic programs. Just as we would not accept students memorizing sight words and not being able to read sentences as a complete reading program; we cannot accept students memorizing times tables as a complete math education.

## Number Talks - Part of a Rich and Balanced Math Program

Traditional curriculum and instructional methods in the United States have left our students with fragile skills and a shallow understanding.(Hiebert, 1999)

The teaching of algorithms without understanding limits thinking and understanding. Students begin to treat numbers a place value neutral digits rather than understanding their true value. Number Talks bring students back to explore their understanding and solidify their knowledge and flexibility around numbers.

## Documentation During Number Talks

-the number of students who groaned and complained when math class started decreased with the use of Number Talks

-now only a few complained; and when a Number Talk ends several students asked to continue

-students asked for more numbers and harder numbers to work with

-students began to communicate using silent signals and stopped telling others they were wrong (most of the time) when they shared a variety of numbers, they began to wait to defend their thinking and prove their point

-more and more students offered to share thinking as time went on

-all students had something they could contribute

## What Student 1 Said

## Students said that...

Number Talks:

-I like doing number talks, they help me learn different strategies

-I like them because if you know everything one day and then another day its hard and if we don't know it we can think about it and try it and then we can finally do it

-they help my brain grow like the fantastic elastic stretchy brain

-I liked it because it helped me learn different strategies and it helped me with adding and subtracting and learning other things to help me think

-I like working together, I can use the strategies later

-I liked when it was wrong it wasn't really the wrong answer it was just on the way then I got the right answer

-I liked them because when I thought it was 20 but I found out that it was really 30, I could learn

-they made me think

-I like the word wall with the strategies because it can help me think if I don't know the answer at first

## Reflections About Our Work With Number Talks

When teachers gathered to reflect on what they had observed using number talks for a few weeks in their classes:

-students are enthusiastic and engaged

-at all times at least 90% of students are focused and listening

-I think it is already helping them to communicate their thinking

-they are excited to share

-they make connections to the Number Talk the day before

-this helps me really pause and focus on responding to student needs and student learning in the moment

-it is amazing to see them all engaged and wanting to use the vocabulary and think aloud, they want their peers to listen to their thinking

We wondered???

-If we continue to use Number Talks all year will their enthusiasm continue?

-What would happen if we use different types of problems, such as T-charts, patterns, word problems and apply the Number Talk protocols?

## Teachers said...

-an increase in student engagement

-an increase in math vocabulary during math talk

-an increase in confidence to disucuss math thinking

-students seemed to use a wider variety of strategies, they definitely began to use each other's thinking strategies

-when I don't make time for Number Talks students ask for them

## Learning To Remember - The Power of "Co" and Pausing to Focus on Student Learning

Through the eyes of the Documenter two main ideas have emerged from our work together.

Co Creating is a powerful contributor to student learning:

-co creating math strategies - Number Talks

-co creating solutions - using thinking tools, Number Talks, math games

-co-creating thinking- games with thinking tools and a partner, word problems

-co-creating word walls

-co-creating thinking

A powerful quote from a teacher:

Sometimes I have to change and adjust my practice. Its not just good enough to keep going. Using Number Talks helps me really pause and focus on responding to student needs and student learning in the moment. (Isla)

## Where Do We Go From Here?

The teachers at Northwood were happy with the initial observations we made. They saw a positive benefit to the increased use of manipulatives as teaching tools and were convinced that using Number Talks regularly was beneficial for their students.

They found the work with the SWST teacher was valuable and supported their practice.

They used a release days to come together and reflect and co-plan ways in which they can continue this work into the next term. This time together to reflect, share, discuss and plan was very rich and valuable to the teachers.

They refined their theory of action and plan to continue to invest in the use of Number Talks and thinking tools as a regular part of their practice. Their hope is that these strategies will lead to increased understanding of mathematics which will be evident in the students thinking and communication skills. I look forward to hearing how their learning journey continues and the impact is has on student learning.

## Written By: Deborah Cote; SWST Teacher PDSB.

@DebbieCote1

Sept-Dec 2015