SD Math Science Partnership Project Jan Martin - SD DOE Math Curriculum Specialist

Parkston, January 19, 2007

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.


SD Math Science Partnership Project

Jan Martin - SD DOE Math Curriculum Specialist


South Dakota Counts is a three year elementary math initiative focused on implementing research-based instructional practices to improve student

learning in mathematics.

It is not a curriculum or a quick fix.


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.


• Suppose everyone in this room shakes hands with all the other people in this room. How many handshakes will that be?


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)


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 status2. Elementary teachers need to broaden their

knowledge base about math content, math pedagogy, and student mathematical thinking.


• Selling a HorseA 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?


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.


Best Practices in Teaching Mathematics

Making Sense – elements of classroomsAdding It Up – five strands of mathematical

proficiencyRelearning to Teach Arithmetic NCTM Process StandardsCognitively Guided Instruction


Making Sense• Nature of Classroom

Tasks• Role of Teacher• Social Culture of

Classroom• Mathematical Tools• Equity and

Accessibility


• 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.


How can you make this typical “naked number” problem a good problem?

• 26


Adding It UpFive strands of

mathematical proficiency

• Adaptive Reasoning • Strategic Competence• Conceptual Understanding• Productive Disposition• Procedural Fluency


Adaptive ReasoningExample

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 bowsAn example of adaptive reasoning would be understanding that you would make fewer bows if you used 2/3 yard per bow.


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 $1.08- .05 X 5$1.08 $5.40


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.


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!”


Procedural Fluency Non-Example

62 - 48 26


National Council of Teachers of MathematicsContent and Process Standards• State standards aligned to NCTM Content Standards• Instruction should incorporate the process standards:

• Representation• Communication• Connections• Reasoning and Proof• Problem Solving


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.


Solve this Problem

701 - 499


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


(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.


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


• 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


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.


• 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?


• 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?


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?


• 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?


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


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


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.


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.


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.


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


Year 1 CoursesMath Specialists• Leadership Institute• Cognitively Guided Instruction • Best Practices• Summer Institute - FoundationsTeacher Leaders• Summer Institute – Foundations• Cognitively Guided InstructionPrincipals• Lenses on Learning

Documents

SD Math Science Partnership Project Jan Martin - SD DOE Math Curriculum Specialist