Manitoba Rural Learning Consortium Dianne Soltess Meagan Mutchmor August 2015

MATHEMATICS KNOWLEDGE

DOMAINS

Manitoba Rural Learning Consortium

Dianne SoltessMeagan Mutchmor

August 2015

Purpose: Connect to the Manitoba Curriculum, and other

related resources. The document compliments the mRLC

Essential Learning and Backward Planning Templates

Highlight methodology and pedagogy, content knowledge

Provide teachers with a conceptual tool that they can use to think constructively about mathematics.

What gets focused on flourishes…

We want learning to flourish.

Michael Absolum

Planning for Instruction

How does it all fit together?

Knowledge Domain Documents:

Counting & Place Value Addition & Subtraction Multiplication & Division Rational Number (Fractions, Decimals, Percent, Ratio)

* NOTE: Documents are created for K-8

Why Domains?

End of grade expectations are the curriculum outcomes

“Big Ideas” several “experts” have shared their thinking

Teachers need to understand the development of knowledge in mathematical domains

Effective teachers of mathematics have many things to consider…

Teacher Knowledge

There are three kinds of knowledge needed for the teaching of mathematics:Content Knowledge: understanding the

mathematics Pedagogy: knowing how to teach effectively Pedagogical Content Knowledge: Knowing how

to effectively teach mathematics.Models, manipulatives, questioning, math talk,

developmental progressions…

Layout

Each Document follows a similar approach:

IntroductionThings to considerCurricular outcomes associated with domainDevelopmental “Look Fors”GlossaryAdditional Resources/Further Learning

Getting to know the documents:

Find something that is new to you or provided you with an “Ah-ha” moment!

Find something that you would like to know more about.

Find something that is affirming for you and you think will help teachers.

Turn and Talk

Counting and Place Value

Please select this Knowledge Domain Document

Counting on the AlphabetWhat do students experience when they are learning to count?We chose letters because we all know the alphabet sequence well, just as many young children know the number sequence, but we may not have mastered the quantity that each letter represents.

A collection such as ♣ ♣ ♣would be described as having “C” objects.

When solving the problems please do not to translate the letters to numbers.

Try this:

Lucy has H fish. She wants to buy E more fish.

How many fish would Lucy have then?

Use of “Direct Modelling” to solve

H + E =

Janelle has G trolls in her collection.

How many more does she have to buy to have K trolls?

Use of “counting strategy” to solve:

G + = K

Use of “Direct Modelling” to solve:

G + = K

Use of a “Derived Strategy” to solve:

K- = C

Try solving the following:Tee Jay had M chocolate chip cookies. At lunch she ate E of them. How many cookies did TeeJay have left?

Max had some money. He spent I dollars on a video game. Now he has G dollars left. How much money did Max have to start with?

K children were playing in the sandbox. Some children went home. There were C children stillplaying in the sandbox. How many children went home?

Willy has L crayons. Lucy has G crayons.How many more crayons does Willy have than Lucy?

Place Value Article Share:

Get title from Dianne, insert visualDianne could you email me the article?

Addition and Subtraction

Please select this Knowledge Domain Document

Problem Types

This is where we thought we would highlight problem types and have them sort them…

Lets look at one together…

Multiplication and Division

Please select this Knowledge Domain Document

Explore the Document

Exploring a Concept: Multiplication K-10

What does it mean to understand

multiplication?

Multiplicative Thinking involves more than just models that can be grouped:

Three Plates with 5 cookies on each plate.

Multiplicative Thinking also involves array models:

Three rows with five carrots in each row.

Multiplicative Thinking also involves & area models:

3 rows with 5 in each row.

5 rows with 3 in each row.

Commutative property for multiplication. 3x5=5x3

Multiplicative thinking also includes rate and Cartesian products

Rate

Vinh travelled 3 kilometers in 10 minutes.How far will he have travelled in hour?

Cartesian Products

Mia has 3 tops and 4 bottoms. How many outfits can she make?

Understanding of arrays leads to the distributive property.

Students in the part whole thinking section of the pathway understand that 7 rows of 8 dots can be distributed by applying hTheir understanding of arrays.

Think:7 is the same as 5 + 28 is the same as 5 + 3So, (5x5) + (2x5) + (5x3) + (2x3)

Knowledge of the distributive property and understanding how to partition arrays leads to use of open arrays.

12 x 13

This can be directly linked to understanding of the multiplication algorithm.

13 13 X12 x12 6 0R 26 20 +130 30 156 + 100 156

Non-Standard Algorithm

Which can be further linked to use of algebra

tiles.

Mult.

Key:

(x+2) (x+3)=

(x+2) (x+3)=

= x2 + 2x +3x+ 6

= x2 + 5x + 6

Rational Number

Please select this Knowledge Domain Document

Problem Solving: Buttons

Whip Around

Now that you have been introduced to the Knowledge domain documents, how do you see their use with teachers, administrators, coaches?

What are you wondering?

Exit Slip:Reflection and Feedback

Problem Solving: Buttons

This article presents an activity using alphabet that one can use in pre- and in-service teacher training program. This alphabet activity is often used in professional development programs, such as Cognitively Guided Instruction and the activity is adapted for teacher training programs. The goal of the activity is to help teachers understand what children go through as they begin to learn the number sequence and to construct strategies for solving arithmetic problems. It takes a long time and plenty of experimentation and learning opportunities for children to develop number sense and proficient strategies for adding and subtracting small numbers. As adults tend to underestimate how much understanding children need in order to apply the knowledge in problem solving situations. The fluency of children in reciting the number sequence often leads to think that they have the same depth of understanding of quantities as one does. To get a sense of what children go through as they develop number sense and problem solving strategies, one introduces an activity where pre- and in-service teachers have to use the alphabet sequence instead of the number sequence to solve arithmetic problems.