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
Explicit Instruction
Counting Up 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 Quick Image 'strings'
A Learning community
An Array of Strategies
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
Location: Peel District School Board
Twitter: @janetdsilva