Transcript Fractions Don`t Need to be Fatal - GAINS

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
¼ Coffee
¼ Sugar
½ Cream
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
7
What fraction would you use to
represent this?
Math For Teaching: Fractions
Why use multiple models?
Children who have difficulty
translating•aPictures
concept from one
representation
to another
are the
• Written
Symbols
same children
who
have difficulty
• Oral
Language
solving problems
• Real and
World
understanding
computations.
Connections
Strengthening the ability to move
• Manipulative
between and among these
Models
representations improves the
growth of children’s concepts.
Fractions across the grades
11
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
12
How can you name this?
6 green:4 yellow
Part-Part (set)
6 green:10 shapes
Part-Whole (set)
One fifth of the
total area is green
Part-Whole (area)
Math Knowledge for Teaching
Mark Hoover Thames and Deborah Lowenberg Ball
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
Horizon Knowledge –
‘mathematical
peripheral vision’
SCK – knowing more
math than CCK but
distinct from PCK
14
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
15
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
16
One Task
Which way would you cut the
cake so that you could share
it with a friend fairly. Explain.
17
Let’s talk about it
• Share your thinking.
• Let’s hear what the students did.
18
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
20