Use each of the digits
1,2,4,and 8 once to
make a number
sentence that equals
zero. You may use
any operation (add,
subtract, multiply, or
divide) as many times
as you wish. You may
use parentheses in
your solution.
Parkston, January 19, 2007
SD Math Science Partnership
Project
Jan Martin - SD DOE Math Curriculum Specialist
Parkston, January 19, 2007
South Dakota Counts is a three year elementary
math initiative focused on implementing researchbased instructional practices to improve student
learning in mathematics.
It is not a curriculum or a quick fix.
Parkston, January 19, 2007
GOALS:
To build broad-based expertise and
leadership for improving student
achievement in elementary mathematics.
Develop a statewide educational
community with a cadre of skilled
professionals to serve as resources and
trainers in the ongoing effort to improve
elementary mathematics instruction.
Parkston, January 19, 2007
• Suppose everyone in
this room shakes
hands with all the
other people in this
room. How many
handshakes will that
be?
Parkston, January 19, 2007
What was good enough for us in learning
mathematics is not good enough for our
children. Despite the reality that learning math
was a bust for so many of us, we have pressed
on with ineffective teaching approaches that
clearly don’t work.
The way we have traditionally been taught
mathematics has created a recurring cycle of
math phobia, generation to generation, that has
been difficult to break. (M. Burns, 1998)
Parkston, January 19, 2007
Why elementary math?
1. Data sources indicate gaps at the elementary
levels
NAEP data
DSTEP data
gaps between all students and Native
American students, low socioeconomic status
2. Elementary teachers need to broaden their
knowledge base about math content, math
pedagogy, and student mathematical thinking.
Parkston, January 19, 2007
• Selling a Horse
A man bought a horse
for $50 and sold it
again for $60. He
then bought back the
horse for $70 and
sold it again for $80.
What was the
financial outcome of
the transactions?
Parkston, January 19, 2007
Nationally, the negative attitudes and beliefs
that people hold about mathematics have
seriously limited them, both in their daily
lives and in their long-term options. (M.
Burns, 1998)
It is culturally ok to say that you are not good
in math while most of us would not admit
to not being a good reader.
Parkston, January 19, 2007
Best Practices in Teaching Mathematics
Making Sense – elements of classrooms
Adding It Up – five strands of mathematical
proficiency
Relearning to Teach Arithmetic
NCTM Process Standards
Cognitively Guided Instruction
Parkston, January 19, 2007
Making Sense
• Nature of Classroom
Tasks
• Role of Teacher
• Social Culture of
Classroom
• Mathematical Tools
• Equity and
Accessibility
Parkston, January 19, 2007
• What is a good problem?
• A good problem or task is any task or
activity for which the students have no
prescribed or memorized rules or
methods, nor is there a perception by the
student that there is a specific “correct”
solution method.
Parkston, January 19, 2007
How can you make this typical “naked
number” problem a good problem?
• 26 4 = 
Parkston, January 19, 2007
Adding It Up
Five strands of
mathematical
proficiency
•
•
•
•
•
Adaptive Reasoning
Strategic Competence
Conceptual Understanding
Productive Disposition
Procedural Fluency
Parkston, January 19, 2007
Adaptive Reasoning
Example
If a student solved this problem
correctly.
How many bows could you make from
12 yards of ribbon if each bow used
1/3 yard of ribbon?
Answer: 36 bows
An example of adaptive reasoning
would be understanding that you would
make fewer bows if you used 2/3 yard
per bow.
Parkston, January 19, 2007
Strategic Competency
Non-Example
• At ARCO, gas sells for $1.13 per gallon.
This is 5 cents less per gallon than gas at
Chevron. How much does 5 gallons of
gas cost at Chevron?
$1.13
- .05
$1.08
$1.08
X 5
$5.40
Parkston, January 19, 2007
Conceptual Understanding
Non-Example
9.83 X 7.65 = 7519.95
A student with conceptual understanding of
place value using decimals would know
the answer is under 80.
Parkston, January 19, 2007
Productive Reasonsing
Students are saying “Don’t tell me the
answer. I want to get it by myself.” Rather
than, “I don’t get it!”
Parkston, January 19, 2007
Procedural Fluency
Non-Example
62
- 48
26
Parkston, January 19, 2007
National Council of Teachers of Mathematics
Content and Process Standards
• State standards aligned to NCTM Content Standards
• Instruction should incorporate the process standards:
•
•
•
•
•
Representation
Communication
Connections
Reasoning and Proof
Problem Solving
Parkston, January 19, 2007
Relearning to the Arithmetic
• Key concepts:
– Building students' procedural fluency in
computation based on children's conceptual
understanding.
– Use of number talks as part of daily
instruction.
– Use of mental math to develop fluency and
flexibility.
Parkston, January 19, 2007
Solve this Problem
701
- 499
Parkston, January 19, 2007
Cognitively Guided Instruction
CGI is not a set of procedures to implement but rather a
philosophy or a way of thinking about teaching that starts
with the students’ thinking.
In the past I thought children didn’t understand subtraction
with regrouping, when what they didn’t understand was
how to use the process that I was insisting that they use,
rather than really understanding the concept of
subtraction that might encompass regrouping.
Kerri Burkey, second-grade teacher
Parkston, January 19, 2007
(CGI continued)
Based on more than 20 years of research, greater
understanding of how children come to
understand basic number concepts. From this
research, a framework of problem types and
strategies have emerged which enables
teachers to strategically guide learning in a
mathematics classroom.
Parkston, January 19, 2007
Problem Types
• Join *
• Separate *
• Part-Part-Whole
• Compare
• Multiplication
• Measurement
Division
• Partitive Division
Strategies Students
will naturally use
• Direct modeling *
• Counting strategies
• Using derived number
facts and known
number facts
Parkston, January 19, 2007
• Change is easier together than alone.
• Never doubt that a small group of
thoughtful, committed citizens can change
the world; indeed, it is the only thing that
ever does.
Margaret Mead
Parkston, January 19, 2007
Trains of Five
Using two colors of unifix
cubes, determine how
many unique trains of
five cubes you can make.
Determine a way to
represent your results
visually and numerically.
Parkston, January 19, 2007
• What do you think?
Some people say that to add four
consecutive numbers, you add the first
and the last numbers and multiply by 2.
What can you find out about the
statement? Agree or disagree? Why?
Parkston, January 19, 2007
• Change – go slow to go fast.
• What is one thing you can do differently in
your classroom to make mathematics
more problematic for your students?
Parkston, January 19, 2007
Eric the Sheep
• Eric the sheep is lining up to
be shorn before the hot
summer ahead. There are 50
sheep in front of him. Eric can’t
be bothered waiting in the
queue properly, so he decided
to sneak towards the front.
Every time 1 sheep is taken to
be shorn, Eric sneaks past 2
sheep. How many sheep will
be shorn before Eric?
Parkston, January 19, 2007
• CGI Problem
– The class baked 84
cookies. We want to
put them into boxes at
the school bake sale.
If we put 12 cookies
into each box, how
many boxes can we
fill?
Parkston, January 19, 2007
Partners
• SD Department of Education
• CAMSE (Center for the Advancement of
Mathematics and Science Education) - BHSU
• TIE
• Grant Awardees – ESA 1 – 7, Sioux Falls
• Sub-Grantees – participating school districts
• External Evaluator – Inverness Research
Associates
Parkston, January 19, 2007
Professional Development Components

Summer Institute (1 week each summer)

On-going coaching – math specialists and
teacher leaders

Regional workshops during school year

Lenses on Learning workshops for principals

On-going collaborative planning to ensure
implementation of research-based math
instruction at the school and classroom levels
Parkston, January 19, 2007
Project Objectives:
 Increase student academic achievement as measured
by the state mathematics standards.
 Train and place one Mathematics Specialist in 8 different
sites in SD. Status: ESA 1 – 7 and Sioux Falls
 Provide training for one Mathematics Teacher Leader for
potentially each elementary building in South Dakota.
Status: 149 teacher leaders 06-07 with plans for 50 more
to be added in 07-08
 Support work in each participating district to train
additional K-5 teachers.
 Provide training for building principals to support the
work of the Teacher Leaders.
Parkston, January 19, 2007
Elementary Principals role:
Participate in professional development designed
to help administrator, as instructional leaders in
their schools, to understand and support
effective mathematics instruction.
Support participating staff in the implementation of
grant activities.
Collaborate with math specialist and teacher
leader to develop implementation plans for their
school.
Parkston, January 19, 2007
Math Specialist role:
Collaborate with SDDOE, CAMSE, and TIE to
coordinate and deliver professional development
components
Collect data, data analysis, and reporting of data to
SDDOE and Inverness
Attend professional development centered on
mathematics content, mathematics pedagogy,
student mathematical thinking, and educational
leadership.
Support the work of the teacher leaders.
Parkston, January 19, 2007
Math Teacher Leader role:
Attend professional development centered on mathematics
content, mathematics pedagogy, student mathematical
thinking, and educational leadership
Utilize professional development content in mathematics
instruction to impact student achievement
Upon completion of one year of training, provide training for
other K-5 teachers in building
Create a model classroom as one component of the
training for other teachers in building
Parkston, January 19, 2007
Year 1 Courses
Math Specialists
•
Leadership Institute
•
Cognitively Guided Instruction
•
Best Practices
•
Summer Institute - Foundations
Teacher Leaders
•
Summer Institute – Foundations
•
Cognitively Guided Instruction
Principals
•
Lenses on Learning
Parkston, January 19, 2007