Responsive Math @DixiePSchool

Exploring Purposeful Tasks Selected to promote Number Sense

Part 2

This Collaborative Inquiry is part 2 of a two year long inquiry. More information about Part 1 can be found here. Part 3 explores the use of different structures in response to student need and can be found here.

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

Dixie Elementary school test scores, on the provincial EQAO assessment, have been steadily increasing since 2012. Analysis of the greatest area of need for students revealed that students had specific gaps in their numeracy skills. The local middle school indicated that students needed to develop a deeper conceptual understanding of the relationships between numbers. This feedback was taken into consideration as classroom teachers formulated their collaborative inquiry theory of action.

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

Theory of Action

If we use a balance of purposeful, focused activities in response to student need then students’ conceptual knowledge of number sense will be deepened, student engagement and communication of their thinking will be enhanced.

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

Resources were selected to respond to student need. The use of Number Talks was introduced to enable students to further develop and consolidate their mental math skills. Emphasis was placed on understanding why strategies made sense and building connections across math concepts. Purposeful practice enabled students to build a community where students listened to each other's mathematical thinking and compared it to their own thinking. Fosnot Contexts for Learning Mathematics kits were used to enable students to demonstrate their learning and thinking within a 'mathematized context'.
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Grade 2/3

Number Talks

Number Talks by Sherry Parrish are a "five to fifteen minute classroom conversation around purposefully crafted computation problems that are solved mentally". To learn more about Number Talks, visit Sherry Parrish's You Tube clip Number Talks: Building Numerical Reasoning..

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.

Representation of thinking Grade 2
In this video, a grade 2 student records his strategy.

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 stamps

Below is the chart where the teacher recorded the student strategies and a transcript of students sharing their methods for determining the total value of the 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.

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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?

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Student Work Study Collaborative Inquiry 2014/15

Suja Zacariah, Grade 3 Classroom Teacher

Janet D'Silva, Student Work Study Teacher