# Responsive Math @DixiePSchool

### Exploring Purposeful Tasks Selected to promote Number Sense

## A collaborative inquiry by the Primary Team at Dixie P.S., Peel District School Board

The Student Work Study Initiative provides an opportunity for documentation of the Collaborative Inquiry to take place.

## Theory of Action

## Purposeful! Use of Resources & Practice to consolidate Basic Facts & Operational Skills

## Grade 2/3

## Number Talks

Recording student thinking during Number Talks involved a learning curve for the classroom teacher, SWST and students. Everyone had to learn how to pay attention to the reasoning of others. The teacher had to learn how to record the students' reasoning.

Our reading in mathematics research revealed that number lines were a powerful thinking tool/model for students to use to help consolidate relationships between numbers. Alex Lawson in the clip below speaks of the power of the number line.

## Number Line Games To introduce number lines to students, we played guessing games from Van de Walle's Teaching Student-Centered Math. Students familiarized themselves with the number line and the concept of 'making jumps' | ## Explicit Instruction Some students needed explicit instruction that the jumps did not always have to be by the same amount. | ## Counting Up Strategy Students used a counting up strategy to make change. This representation helped students to visualize the concept instead of perhaps using a standard North American algorithm with little understanding. |

## Number Line Games

__Teaching Student-Centered Math.__Students familiarized themselves with the number line and the concept of 'making jumps'

## Explicit Instruction

Another student responded the teacher's recording of his thinking," “**I saw it as a number line, it made more sense to me then when you recorded it that way". **The student was illustrating Fosnot's statement that "the mathematics is not in the model to be seen -it develops in the learner's mind and is only then brought to bear on the models and representations."(Imm,Fosnot et al, 2012)

## Fosnot's Context For Learning Mathematics; Investigating Multiplication and Division

The focus of the unit titled Groceries, Stamps and Measuring Strips is on the introduction and early development of multiplication. Students are "encouraged to make groups (and groups of groups) to find efficient ways to deal with repeated addition and determine totals." (Fosnot, 2016)

We were able to use Fosnot's Landscape for Learning for Addition and for Multiplication. By using the landscapes, we were able to deepen our knowledge of the big ideas, models and strategies students were using in their mathematizing. Unique learner profiles emerged which allowed us to adapt our instruction for students.

## Fosnot Quick Image 'strings' "Quick images, count-aroud-the-circle activities, and pictures with built in constraints support the construction of efficient strategies" (Fosnot, 2016). Our class followed the Number Talk format while using these images as number strings. | ## A Learning community It is interesting to note that the student did not say she was to "...get the answer more quickly" as this is not the purpose of Number talks. Finding the answer quickly was not emphasized by the classroom teacher as Jo Boaler's research suggests speed leads to students shutting down in math. Instead, the learning goals for Number talks focused upon using each other's strategies to help each other learn together as a community. | ## An Array of Strategies The variety of strategies perhaps demonstrates that students were able to see that numbers could be related to each other in many ways. This understanding contrasts with memorizing isolated multiplication facts. |

## Fosnot Quick Image 'strings'

## A Learning community

## Fosnot stamps

The Classroom Teacher and Student Work Study Teacher engaged in many reflective discussions about the big ideas of multiplication. We were able to see unitizing, regrouping of repeated addition, commutative property and the distributive property through observations of student conversation and work.

Approaching the instruction of multiplication in this way enabled us to open up the math for ourselves and our students.

## Reflections & Continued Wonderings

Discussion of mathematical content between colleagues is a worthwhile and important pursuit. Collaborative learning leads to richer learning experiences for students *and * teachers.

Careful selection of tasks enables students to demonstrate their thinking. For example, the use of Number Talks in the classroom enabled students to listen and respond to each other's mathematical thinking. In this way, students were providing feedback to their classmates.

Teachers were able to observe, document and respond to students' thinking. We were able to use this information to respond to students to inform our instruction.

Our instruction is rooted in the Landscape of Learning which provided the content knowledge that framed our instruction and assessment.

We must honour our students as teachers in the classroom.

*Going forward, we wonder...*

How can we spread the learning culture developed by Number talks towards other parts of our math classroom?

What will the focused, consistent use of small groups and math partners reveal for our students? What does research say about math partners?

Will personalized math tool kits make a difference for students?

How can we incorporate descriptive feedback in mathematical content for students to propel their own learning?

## Student Work Study Collaborative Inquiry 2014/15

Janet D'Silva, Student Work Study Teacher