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Collaborative Inquiry for Learning Mathematics for Teaching

Collaborative Inquiry for Learning Mathematics for Teaching. CIL-M. Co-Teaching in a Public Research Lesson – Process and Sample Key Learning DSBN and NCDSB. Collaborative Planning for the 3 part lesson. Key concepts come from an analysis of the curriculum expectations continuum

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Collaborative Inquiry for Learning Mathematics for Teaching

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  1. Collaborative Inquiry for Learning Mathematics for Teaching CIL-M

  2. Co-Teaching in a Public Research Lesson – Process and Sample Key Learning DSBN and NCDSB

  3. Collaborative Planning for the 3 part lesson • Key concepts come from an analysis of the curriculum expectations continuum • A developmental sequence comes from an analysis of the continuum of expectations across the grades, the Guide to Effective Instruction in Mathematics and other research including landscapes, learning trajectories, etc. • Focusing on the Big Idea • Knowing what math vocabulary to draw out and emphasize also comes from the curriculum expectations • Choosing a problem • DO the problem several ways  connect strategies and/or solutions to continuums, landscapes, or trajectories

  4. Before (Activation) Consistencies (Fundamentals) • Careful thought to the big idea in the lesson  mathematics is connected to the During part of the lesson • Students DO mathematics • Develop a context that is both engaging and grounds the mathematics • Relatively short (5 to 10 mins) • Activating student schema • Use of mathematical terms (used in a previous lesson) • Not an abstract review of the previous lesson - it builds on students’ knowledge • Record students’ thinking on the far left side of the board

  5. During (Working on it) • Pose and post the problem (working left to right) • Ask, “What is the important information we will need to solve this problem?” • Record and post students’ thinking • Students work to solve the problem • Teachers only ask questions to provoke students’ thinking • The purpose is to get the students’ existing thinking onto the paper  the solution is evidence of mathematical understanding at that point in time • Within the struggle is the new learning

  6. The 3-part After AFTER – Teaching and Learning • Focused on knitting ideas together from one solution to another towards the learning goal • Mathematical annotations - either on the board or on the student solutions to make explicit mathematical ideas, strategies, and tools and to show relationships between the solutions AFTER – Consolidation - Highlights / Summary • Focuses on the learning in the learning goal or Big Idea AFTER – Practice • Students solve a similar problem or problems independently using the work of the class that is still posted to guide their thinking

  7. Three key questions for analysis: What mathematics are evident in students’ communication (oral, written, modeled)? What mathematical language should we use to articulate the mathematics we see and hear from students? (e.g., mathematical actions, concepts, strategies, tools) What mathematical connections can be discerned between students’ different solutions? Analyse student work by: identifying the mathematics evident in student solutions to a lesson problem discern the mathematical connections between the solutions, Purpose - Plan next steps instruction during the lesson for the next day lesson (activation) Teacher Moderation of Classroom WorkAssessment for Learning

  8. After – Teaching and Learning Make the mathematical thinking in the room visible: • To get students thinking about their thinking (metacognition) as they solve problems • To make connections among the many different ways to solve a problem AND to the mathematical Big Idea through discussion and annotation • To allow young mathematicians to describe and defend their mathematical ideas and conjectures

  9. After - Consolidation Highlights/ Summary Preparing  revisit: • Key concepts that came from an analysis of the curriculum expectations • A developmental sequence that came from an analysis of the continuum of expectations across the grades and the Guide to Effective Instruction in Mathematics and other research including landscapes, learning trajectories, etc. • The math vocabulary to draw out and emphasize that also came from the curriculum expectations In the classroom: • Coordinate discussion based on student work • Record the highlights / summary based on student work in light of the Big Idea of the lesson

  10. After – Practice Pose one or two questions that are closely related to the problem just solved Students may use the work of the lesson as an anchor chart: • mathematical annotations - either on the board or on the student solutions to make explicit mathematical ideas, strategies, and tools and to show relationships between the solutions

  11. Co-Teaching Roles • Classroom teacher • 2 co-teachers – may ask questions of students but may not tell how • The other teachers are student observers • These teachers may not interact with the students but feed to the co-teachers information about the way students are learning.

  12. The Heart of our Learning • Even though it’s messy, we are engaging students deeply in mathematics • We are not telling them or showing them mathematics but are engaging them in mathematics; in other words… • We are not transmitting our mathematics to students but rather establishing conditions through which students construct their own mathematics • Research shows that students do better in all measures if they are activelyengaged in mathematical problem solving

  13. Let’s look at the math! • We focus on what the students DO KNOW, not on what the students don’t know or what we think they should know

  14. Students are playing a dice game. The red die is the numerator and the white die is the denominator. Plot the dice rolls on the number line to decide who got the highest fraction. As you walk around, you see these solutions. What is your response to the students in the class?

  15. Student Work • What do the students know? • What do we learn about the mathematics by looking at what students do know?

  16. Math We Noticed • The numbers were often ordered from smaller quantity of pieces to larger number of pieces • The whole number intervals were generally evenly spaced • Students seemed to use the number line 0-6 for some fractions and ‘saw’ the number line as 0-1 for others • the half-way point on the number line was correctly placed and was labeled as either ½ or 3 • The 1/3 point was correctly placed between 0 and 1/2 • The fractional intervals on the number line varied • Many students reflected an understanding of the relationship of the improper fraction to a mixed number

  17. Learning Goals for Next Steps and Further Classroom Discussion • Intervals on the number line should be equidistant • Placing of whole number quantities • Counting fraction manipulatives beyond 1 and representing of fractional quantities on the number line • Developing benchmark of 1/3

  18. Things we still wonder… • How many fractions is too many to place on a number line at the beginning? later on? • How much work should students have with the 0-1 number line before moving to a ‘0 – more than 1’ number line? • Are some fractions nicer stepping stones for developing understanding than others? • What is the impact of using area, set and linear models for fractions on this work with a number line?

  19. Sustainability • How has this informed OUR practice? • How will this influence our board improvement plans? • How will this help improve student learning in mathematics in our boards? • How will we use our learnings to build teacher capacity in mathematics

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