Fractions Don’t Need to be Fatal

Session Goals

Participants will understand:•Why the Focus on Fractions?•What are ‘fractions’?•Intro to KNAER (grounded in research and in classrooms) •Classroom dynamics

Ordering Coffee

½ Cream

¼ Sugar

¼ Coffee

Fractions Can Be Fatal…pediatricians, nurses, and pharmacists… were

tested for errors resulting from the calculation of drug doses for neonatal intensive care infants…

Of the calculation errors identified, 38.5% of pediatricians' errors, 56% of nurses' errors, and 1% of pharmacists' errors would have resulted

in administration of 10 times the prescribed dose. (Grillo, Latif, & Stolte, 2001, p.168)

(Bruce & Ross, 2009)

What the Research Says…

The mathematics education literature is resounding in its findings that understanding

fractions is a challenging area of mathematics for North American students to grasp (National Assessment of Educational

Progress, 2005). Students also seem to have difficulty retaining fractions concepts

(Groff, 1996). (Bruce & Ross, 2009)

Implications beyond Childhood

Adults continue to struggle with fractions concepts (Lipkus, Samsa, & Rimer, 2001;

Reyna & Brainerd, 2007) even when fractions are important to daily work related

tasks.

(Bruce & Ross, 2009)

Why a Focus on Fractions?

• Fractions are a difficult to learn concept because they require deep conceptual knowledge of

– part-whole – measurement – ratios

• the College Math Project identified fractions as an area requiring further attention

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What fraction would you use to represent this?

Math For Teaching: Fractions

Why use multiple models?

• Pictures• Written Symbols• Oral Language• Real World

Connections• Manipulative

Models

Children who have difficulty translating a concept from one representation to another are the same children who have difficulty solving problems and understanding computations. Strengthening the ability to move between and among these representations improves the growth of children’s concepts.

Why Focus on Content Knowledge?

“Teachers must understand their subjects deeply and flexibly, and skillfully represent them in intellectually honest ways to a wide

range of students.”

Deborah Lowenberg Ball and Francesca M. Forzan

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How can you name this?6 green:4 yellow

Part-Part (set)

6 green:10 shapesPart-Whole (set)

One fifth of the total area is green

Part-Whole (area)

Math Knowledge for TeachingMark Hoover Thames and Deborah Lowenberg Ball

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CCK – knowing if an answer is correct, knowledge of definitions and procedures

PCK – knowing the most useful ways of

representing and formulating the

subject in order to make it

comprehensible to others

SCK – knowing more math than CCK but distinct from PCK

Horizon Knowledge – ‘mathematical peripheral vision’

Some Background• Funded by Knowledge Networks for

Applied Educational Research (KNAER)• Collaborative Action Research Project

involving:– Teachers and administrators from KPRDSB,

OCDSB, SCDSB– Laurie Moher, Suhana Kadoura, Trish Steele– Dr. Cathy Bruce, Tara Flynn and Rich

McPherson of Trent University

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What did it look like in practice?

The teams•explored student and teacher fraction understanding •co-planned, co-implemented, and observed lessons•analysed student responses•sustained a focus on fractions

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One Task

Which way would you cut the cake so that you could share it with a friend fairly. Explain.

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Let’s talk about it

• Share your thinking.• Let’s hear what the students did.

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Fractions Can be Fun!

• We learned that:– fractions ARE complex– learning is struggle, and sense-making is both

challenging and rewarding– learning together alongside colleagues and

students is energizing– thinking about thinking results in

understandings that extend beyond fractions

For you in the near future…

• a Digital Paper on EduGAINS.ca entitled Professional Learning about Fractions

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