WERKLUND SCHOOL OF EDUCATIONGALILEO EDUCATIONAL NETWORK

LEARNING IN MATHEMATICS (K-6)A CBE RESEARCH & PROFESSIONAL LEARNING SERIES

In partnership with Werklund School of Education, University of CalgarySession 2: Friday November 3, 1:00-4:00 p.m.

The agenda, working documents and other materials for each session can be accessed on Galileo’s Professional Learning website http://galileo.org/plFocus:  Concepts related to Number: Concept of magnitude and multiplication.

Magnitude: a property which determines whether the object is larger or smaller than other objects of the same kind

Multiplication: a numerical operation that corresponds to a very general form of scaling

Conceptual understanding refers to an integrated and functional grasp of mathematical ideas. Students with conceptual understanding know more than isolated facts and methods. They understand why a mathematical idea is important and the kinds of contexts in which it is useful. They have organized their knowledge into a coherent whole, which enables them to learn new ideas by connecting those ideas to what they already know. Learning Outcome:  Recognize the leap from additive reasoning to multiplicative reasoning is significant developmentally.

Participant Agenda

Time Activity Learning Intentions/ Outcomes

1:00

1:10

Welcome & OverviewApplied Learning Individual reflection to prepare

for sharing (page 3) In triads, review the evidence of

learning Questions for further discussion

with colleagues (page 4)

Intention: Individual and collective knowledge building.Analyze student work product in terms of the mathematical concept.Outcome: The set of real numbers is infinite and each real number can be associated with a unique point on the number line.

1:50 Discuss key insights Large group discussion

Intention: Building collective and expansive

2

understanding of number line as the most complete representation of number.Outcome: Deepen teachers’ awareness of number.

2:00 What is multiplication? Generate word cloud

www.menti.com code 67 448Multiplicative Reasoning - Dr. Paulino Preciado Baab Grouping Cycles Multiplication Matrix (page 5)Revisit: What is multiplication? www.menti.com code 95 1304

Intention:  Individual and collective meaning making regarding the various meanings of multiplication and connection to multiplicative reasoning.Outcome: Consider words used to describe multiplicationOutcome: Identify critical features of multiplicative reasoning starting in early years.

2:40 Break

2:55 Multiplicative Reasoning: Working with Arrays Use the numbers that have

been placed on your table to construct as many different rectangles as possible. Use the cubes and graph paper provided.

Outcome: Identify critical features of multiplicative reasoning starting in early years.

3:20 Evaluating and Appraising Different Methods of Multiplication – Dr. Sharon Friesen Use of representations to model

and reason about procedures

Intention: Examine different methods of multiplication and procedural reasoning to identify gaps in understanding/errors.Outcome: Recognize multiplicative reasoning begins in Kindergarten. Analyzing errors can support differentiated learning designs.

3

3:50 For next session:1. Introduce your students to multiplication arrays in ways

that are developmentally appropriate to your grade level.2. Bring back evidence of the task you enacted, and

samples of student work. Examine the errors in reasoning that your students encountered and bring one or two examples of this.

Individual Reflection

1. Describe how you used the number line with students (what was the teacher doing? what were the students doing?).

2. Which properties of the number line (order, density, continuity, infinite extension) were involved in the task? Explain.

3. What does the artifact you brought forward and/or the observations you made indicate about the learning of your students?

4

Applied Learning: Questions for discussion with colleagues

1. Review the problem or activity that you introduced related to your interesting number.  What happened when you had your students work through it?

2. Examine the supportive and non-supportive representations of number that you were able to find from within your math resources

5

Multiplicative Reasoning: Multiplication MatrixWhat might students notice as they engage in the act of completing their own multiplication matrix?

X 0 1 2 3 4 5 6 7 8 9 10 11 12

0

1

2

3

4

5

6

7

8

9

10

6

11

12

Multiplicative Reasoning: Working with ArraysUse the numbers that have been placed on your table to construct as many different rectangles as possible. Use the cubes and graph paper provided.

Number Arrangement(s)

7

Principled PracticeGuiding

Principles

Domains of Practice

Attending to the integrity

of the mathematics

Committing to the

learning & achievement

of each student

Establishing and

managing a productive learning

environment

Learning from &

systematically improving

practice

Leading a whole class discussion

Representing mathematical ideas

Assessing students’ knowledge, skill, and dispositions

8

Planning math lessons

Evaluating and Appraising Different MethodsWhich of these students is using a method that could be used to multiply any two whole numbers?

9

Using Representations to Model Reasoning

10

Analyzing Error

11

Explaining

Why do you multiply before you add? Explain.