dr. april strom scottsdale community college dr. ted coe grand canyon university dr. trey cox
DESCRIPTION
Dr. April Strom Scottsdale Community College Dr. Ted Coe Grand Canyon University Dr. Trey Cox Chandler-Gilbert Community College NCTM Las Vegas 10-24-13. - PowerPoint PPT PresentationTRANSCRIPT
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?