Dr. April StromScottsdale Community College

Dr. Ted CoeGrand Canyon University

Dr. Trey CoxChandler-Gilbert Community College

NCTM Las Vegas10-24-13

This work was supported in part by MSP grant #1103080 through the National Science Foundation. Opinions expressed are those of the authors and not necessarily those of the NSF.

ARIZONA MATHEMATICS PARTNERSHIP

• TARGETED MSP• 5-YEAR, $8.7M

• PARTNERS• 3 COMMUNITY

COLLEGES• MATH ED

FACULTY/RESEARCHERS

• MATHEMATICIANS

• MASTER’S AND DOCTORAL STUDENTS

• UNDERGRAD RESEARCHERS

• PRE-SERVICE TEACHERS

• 7 SCHOOL DISTRICTS• 300 MIDDLE SCHOOL

TEACHERS (EXPANDED TO 5TH-9TH GRADE)

• CURRENTLY 63 TEACHERS IN COHORT 1

• 20+ SCHOOL ADMINISTRATORS

• RMC RESEARCH

• ARIZONA STATE UNIV

TEACHER QUALITY, QUANTITY, & DIVERSITY

FOCUS ON…

• MEANINGFUL PROFESSIONAL DEVELOPMENT (SUMMER INSTITUTES, SATURDAY WORKSHOPS, CCOLS)

• ENHANCING PRE-SERVICE TEACHER EXPERIENCES IN CCS, DEVELOPING SERVICE LEARNING FIELD EXPERIENCES

• IMPROVING DEVELOPMENTAL MATHEMATICS

CHALLENGING COURSES & CURRICULA

• Number/Operations• Geometry• Problem Solving

Year 1

• Probability/Stats• Patterns/Functions• Problem Solving

Year 2

LeadershipYear

3

Institutes/Workshops

In Years 1 & 2…• Summer Institute I & II (1 week each)• Saturday Workshops (4 each year)• CCOLs

In Year 3…• Leadership Institute

(1 week)• Facilitate CCOLs

WHAT IS A COLLABORATIVE COMMUNITY OF LEARNERS (CCOL)?

• A “TYPE” OF PROFESSIONAL LEARNING COMMUNITY (PLC)

• A COMMUNITY OF TEACHERS THAT SELF-DIRECTS ITS INVESTIGATIVE FOCUS AND COLLABORATIVE EFFORTS TOWARD MATTERS THAT THE PARTICIPANTS FIND PROBLEMATIC IN THEIR OWN TEACHING ENVIRONMENT.

• THE GOAL OF A CCOL IS TO ENHANCE CLASSROOM INSTRUCTION SO THAT STUDENT LEARNING IS IMPROVED.

THE CCOL IS ULTIMATELY ABOUT THE STUDENTS! 

WHAT IS A COLLABORATIVE COMMUNITY OF LEARNERS (CCOL)?

• A "BETTER" FORM OF PROFESSIONAL DEVELOPMENT (WORKSHOPS, CONFERENCES, MEETINGS, COACHING, ETC.) 

• SAME: CURRICULUM, STUDENTS, STANDARDS, DISTRICT/SCHOOL ASSESSMENTS, PARENTS, SOCIO-ECONOMIC CLIMATE, ETC. 

• DIFFERENT: FOCUSES ON DIFFERENT IDEAS AND HAS CONTROL (WITH FACILITATOR INPUT/VETO) OF DIRECTION OF INVESTIGATION 

• ONGOING LEARNING 

TEACHER EXPECTATIONS

• 18 FACE-TO-FACE HOURS 

• 12 "HOMEWORK" HOURS

• (PLUS THE SUMMER INSTITUTE AND SATURDAY WORKSHOPS)

• COLLABORATIVE VENTURE/EQUAL PARTICIPATION

• ENCOURAGEMENT AND CONSTRUCTIVE CRITICISM IN A SAFE ENVIRONMENT

• IMPLEMENT NEW IDEAS AND TECHNIQUES 

• ONGOING ASSESSMENT AND REVISION 

• MAKE PRACTICE PUBLIC - OPEN CLASSROOM DOOR TO VISITORS 

• INSTRUCTIONAL ROUNDS

• SHOW-N-TELL PRESENTATION 

FACILITATOR EXPECTATIONS

• INSURE EFFECTIVE USE OF TIME - RELEVANT TO CLASSROOM TEACHERS 

• ESTABLISH COLLABORATIVE VENTURE/EQUAL PARTICIPATION

• BECOME EXPERT IN THE CCSS CONTENT STANDARDS AND MATH PRACTICES

• OBSERVE TEACHER CLASSROOMS AND PROVIDE INPUT/SUGGESTIONS

• SET MONTHLY AGENDAS AND ACTION ITEMS

• ATTEND QUARTERLY TRAINING SESSIONS

• BE FLEXIBLE, PROVIDE ENCOURAGEMENT, SUPPORT, AND APPROPRIATE CHALLENGES TO CCOL TEACHERS

• FACILITATORS ARE A MAJOR KEY TO SUCCESS 

A MULTIPLICATIVE THREAD

•WAYS OF DOING

•WAYS OF THINKING

•HABITS OF THINKING

BROOMSTICKS ACTIVITY

You have three broomsticks:

The RED broomstick is 3 feet longThe YELLOW broomstick is 4 feet longThe GREEN broomstick is 6 feet long

LEARNING TRAJECTORIES IN MATHEMATICS: A Foundation for Standards, Curriculum, Assessment, and Instruction, pp48-49.

• SEQUENCING:

LEARNING TRAJECTORIES IN MATHEMATICS: A Foundation for Standards, Curriculum, Assessment, and Instruction, pp48-49.

What do we mean when we talk about “measurement”?

MEASUREMENT

•“TECHNICALLY, A MEASUREMENT IS A NUMBER THAT INDICATES A COMPARISON BETWEEN THE ATTRIBUTE OF AN OBJECT BEING MEASURED AND THE SAME ATTRIBUTE OF A GIVEN UNIT OF MEASURE.”•BUT WHAT DOES HE MEAN BY “COMPARISON”?Van de Walle (2001) Elementary and Middle School Mathematics: Teaching Developmentally, 4th ed.

HOW ABOUT THIS?

•DETERMINE THE ATTRIBUTE YOU WANT TO MEASURE•FIND SOMETHING ELSE WITH THE SAME ATTRIBUTE. USE IT AS THE MEASURING UNIT.•COMPARE THE TWO: MULTIPLICATIVELY.

From Fractions and Multiplicative Reasoning, Thompson and Saldanha, 2003. (pdf p. 22)

The circumference is about how many times as large as the diameter?

The diameter is about how many times as large as the circumference?

http://tedcoe.com/math/circumference

ANGLES

• WHAT ATTRIBUTE ARE WE MEASURING WHEN WE MEASURE ANGLES?

CCSS Grade 4 p. 31

RADIAN MEASURE

http://tedcoe.com/math/trigonometry/radius-unwrapper

A measure of the area of whole square is 4r^2

A measure of the area of red square is 2r^2

A measure of the area of circle is…

SIMILAR TRIANGLES

2

3

THE PYTHAGOREAN THEOREM

http://tedcoe.com/math/geometry/pythagorean-and-similar-triangles

CONSTANT RATE

http://tedcoe.com/math/algebra/constant-rate

SIMILAR TRIANGLES & TRIGONOMETRY

• RIGHT TRIANGLE TRIGONOMETRY

http://tedcoe.com/math/geometry/similar-triangles

BANK ACCOUNTS

• CONSIDER A BANK ACCOUNT THAT GREW FROM $95 TO $120 OVER THREE YEARS.

• USE AN ADDITIVE COMPARISON FOR THESE TWO NUMBERS. WHAT DOES YOUR ANSWER MEAN?

• USE A MULTIPLICATIVE COMPARISON FOR THESE TWO NUMBERS. WHAT DOES YOUR ANSWER MEAN?

what?

what?

BANK ACCOUNTS

• IF THE TERMS OF GROWTH REMAINED CONSTANT, ($95 TO $120, 3 YEARS)

• WHAT IS THE ANNUAL ADDITIVE GROWTH FOR THIS ACCOUNT? WHAT DOES YOUR NUMBER MEAN?

• WHAT IS THE ANNUAL MULTIPLICATIVE GROWTH (FACTOR) FOR THIS ACCOUNT? WHAT DOES YOUR NUMBER MEAN?

what?

what?

EXPONENTIAL FUNCTIONS…

WHAT’S NEXT?

• WHERE COULD YOU GO NEXT?

• WHAT OTHER MATHEMATICAL IDEAS CAN BE BUILT UPON MULTIPLICATIVE THINKING?