Documentation of My Math Voice

using technology to document mathematical thinking

Supposition Statement

"If documentation of mathematical thinking and strategic questioning using technology is provided then students are able to self-reflect on their learning.”


"How does documentation of mathematical discourse using technology provide a venue for metacognition of student learning"

Overview

This paper explores the notion that documentation of mathematical discourse using technology provides a venue for metacognition of student learning. A Case Study in Peel District School Board elementary classrooms involving 4 schools and 6 classrooms documented via Ipads, students interactions with mathematical problems during `Three Part Lessons’, allowing educators and students to inform their learning and practice, analyze their thinking patterns, and substantiate assessment `as` learning to promote higher metacogntive abilities. A Student Work Study Teacher (SWST) conducted the research and examined the data.

Literature Review

This study was grounded in research around Pedagogical Documentation and Asking Effective Questioning Monographs from LNS's Capacity Building Series, in addition to Educational Resources.

Pedagogical Documentation

"When pedagogical documentation is used as an assessment 'for' and 'as' learning than it is not only our students thinking that becomes visible through pedagogical documentation, but our thinking as educators become visible as well, opening up the possibility for shared reflection on the learning process"

Five Features of Documentation

1. Documentation involves a specific question that guides the process, often with an epistemological focus (focus on questions of learning).
2. Documentation involves collectively analyzing, interpreting, and evaluating individual and group observations; it is strengthened by multiple perspectives.
3. Documentation makes use of multiple languages (different ways of representing and expressing thinking in various media and symbol systems).
4. Documentation makes learning visible; it is not private. Documentation becomes public when it is shared with learners-whether children, parents, or teachers.
5. Documentation is not only retrospective, it is also prospective. It shapes the design of future contexts for learning.


Giudici, C., Krechevsky, M., & Rinaldi, C., (Eds.) (2001). Making learning visible: Children as individual and group learners. Reggio Emilia, Italy.


Take a look at this video on Reggio Emilia Inspired Documentation.

Mathematical Thinking

When students talk about mathematics in a purposeful way it reveals their understanding of concepts and the thinking behind their reasoning. Research shows that “asking students to talk (or use Talk Moves) about mathematical concepts, procedures, and problem solving helps students understand more deeply and with greater clarity” according to Chapin, O`Connor and Anderson.


Talk Moves are described as six key moves to help students engage in meaningful math talk;

1) Say More, ask students to elaborate

2) Revoicing, teacher repeats part or all of the students explanation and asks for verification of interpretation

3) Repetition, teacher ask students to restate someone else`s reasoning

4) Press for reasoning, teacher asks student to explain how or why they came to their solution

5) Do you Agree or Disagree, teacher asks students and also asks to justify why

6) Wait time, teacher allows quiet thinking time to develop responses

Asking Effective Questions

Students engaged in math talk with peers and teachers and when provided strategic questions can deepen their understanding of how they arrived at a solution and the process that drew them there. According to Dr. Marian Small “teachers can prompt students with probing questions to elicit more mathematical thinking”.


There are Eight Tips for Teachers to Ask Effective Questions:

1. Anticipate student thinking

2. Link to learning goals

3. Pose open ended questions

4. Pose questions that actually need to be answered

5. Incorporate verbs that elicit higher level of Bloom's Taxonomy

6. Pose questions that open up the conversation to include others

7. Keep questions neutral

8. Provide wait time

Technology

According to Ruben Puentedura’s SAMR model, technology can impact teaching and learning at these four levels “Substitution”, as a direct tool substitute with no functional change; “Augmentation” a direct tool substitute with functional improvements; “Modification”, allows for significant task redesign; “Redefinition”, allows for the creation of new task, previously inconceivable.

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Methods

School #1 is a French Immersion K-6 school

Grade 2 classroom of 20 students

16 boys and 4 girls



School #2 is a K-5 school

Grade 5 classroom of 24 students

13 boys and 11 girls


Visited once a week for 3-4 hours


Observed in small group settings, in pairs, individually

Evidence

Key Learnings

Embracing 21Century Learning supplements Student Engagement


Pedagogical Documentation allows students metacognitive abilities to become visible for all


Pedagogical Documentation allows teachers learning to become visible and practice to become reflective

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Salima Ibrahim-Khan

Student Work Study Teacher, Peel DSB