Building a Math Community Christine Rowe Quinn FOS Math Coach for WR6 and WR7 christine.rowequinn@tdsb.on.ca

Our Goals for Today We will look at… An effective mathematics classroom environment in the Early Years Why teach through Problem Solving? Sharing of ‘Best Practices’ by taking an in depth look at 3 Part Lesson Framework and how to encourage accountable Math Talk in the mathematics classroom

Maximizing Mathematical Learning in the Early Years Identify and use everyday mathematics knowledge to plan instruction Encourage and foster ‘Math Talk” Facilitate experiences that allow for mathematization of everyday knowledge Model and nurture positive attitudes, self –efficacy and engagement

The Third Teacher: Your Classroom Spaces where students can use manipulatives to solve and record problems Wall space to display student work Wall space to display co-created success criteria that supports BIG IDEAS in current unit of study Manipulatives and tools organized in such a way as to provide easy access for all students

Manipulatives/ Math Area

Primary Math Walls

Kindergarten Math Wall

Student Work

Early Years Numeracy Skills Number Sense is defined as a good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms. (Van de Walle, 2001) We want to encourage flexible thinkers.

Where are your students on the continuum? Counting Principles Stable Order Order Irrelevance Conservation Abstraction Principle 0ne-to-One correspondence Cardinality Movement is Magnitude Unitizing Subitizing Counting on Where are your students on the continuum?

Math Games Supports students’ learning in Number Sense Students can play them independently Easy to gather the necessary materials- usually just dice or playing cards and scrap paper Fun for the whole family! Great way to send home Homework

Build Ten Materials: die, base ten rods, base ten cubes. Directions: Each student has one rod and 10 cubes. Each student takes a turn rolling the die. As they roll, they collect the corresponding number of cubes. They line them up along side the rod until they reach ten. Prompting Questions along the way: “How many more until ten?” “What is the sum of your first roll and second roll?” “I noticed you have ___ cubes. What numbers did you roll to get __?”

Addition Tic-Tac-Toe Materials: paper clips, counters/tiles, game board Directions: 2 Players Player 1 places 2 paper clips on two addends and then a counter over the sum. Player 2 moves only ONE paper clip to a new addend and covers a the new sum. The players continue until one player connects 5 spaces across, vertically or diagonally. Prompting questions along the way: “Why did you make that move?” “What will your next move be?” “What sum are you hoping to cover next?”

Why Teach Through Problem Solving? Encourages an increased level of mathematical dialogue between students The math makes more sense Provides the teacher with better insight into students mathematical thinking Builds confidence, maximizes the potential for understanding, and allows for differences in style and approach Provides practice, both with concepts and with skills Small, M. (2013). Making Math Meaningful p 97

3 Part Lesson Should be used daily from K-8 The framework is the same for every grade The timelines are significantly different based on the age of the students

Mathematics and Numeracy: Expected Practice Document

RICH, OPEN TASKS Problems that require students to have to figure out what to do Can be solved in more than one way Have multiple entry points for all learners

Rich Tasks Brandon and Vanessa went to their grandfather’s barn. When they got back to the house, their mom asked what they had seen. Brandon said they saw some chickens and pigs. Vanessa agreed and said that she had counted 18 animals. Brandon hadn’t noticed that, but he had counted 52 legs. If Brandon and Vanessa are correct, how many chickens and pigs were there?

How can we make this accessible to all students?

Accountable Math Talk 5 Practices for Orchestrating Productive Mathematics Discussions By Margaret Smith and Mary Kay Stein Anticipating Monitoring Selecting Sequencing Connecting

Anticipating What are the likely student responses to challenging mathematical tasks?

Monitoring Checking students’ actual responses to the tasks while students work on the tasks in pairs or small groups

Selecting Which students do you want to present their mathematical work during the whole-class discussion?

How will you sequence and display the student responses? Sequencing How will you sequence and display the student responses?

Connecting How will you connect students'’ responses to each other as well as to the key mathematical ideas of your lesson?

ASSESSMENT AND MONITORING WHAT’S NEXT? CO-PLANNING CO-TEACHING ASSESSMENT AND MONITORING