Comox Valley Professional Development Day

Comox Valley Professional Development Day

February 8, 2010

Richard V. DeMerchant

Agenda

• Background

• Examine the Mathematical Processes

• Questions

www.wncp.ca

Key Terms

WNCP – Western and Northern Canadian Protocol

CCF – Common Curriculum Framework: basis for K-12 mathematics in BC, YT, AB, NT, SK, NU, MB, NB, PEI, NF

Pathways – series of courses students take in high school

PLO – Prescribed Learning Outcomes: specific knowledge, skills and understandings that students are required to attain by the end of a given course

AIs – Achievement Indicators: how students may demonstrate their achievement of the goals of a specific outcome

Mathematical Processes – critical aspects of learning, doing and understanding mathematics

Demographics

7.1% 7.5% 8.2% 8.5%16.0% 17.2% 18.6% 18.1%

76.9% 75.2% 73.3% 73.4%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

2004/2005 2005/2006 2006/2007 2007/2008

Scho

ol Y

ear

Percentage of Students

Grade 10 Student Percentages

AM 10

EM 10

PM 10

Demographics

6.6% 8.7% 9.5% 9.9% 9.9% 11.0% 10.7%8.9%

24.0% 23.5% 23.2% 21.6% 21.5% 23.4%

84.5%

67.3% 67.0% 66.9% 68.5% 67.4% 66.0%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

2001/2002 2002/2003 2003/2004 2004/2005 2005/2006 2006/2007 2007/2008

Perc

ent

School Year

Grade 11 Student Percentage

AM 11EM 11

Demographics

3.2% 4.2% 4.6% 5.3% 5.4% 6.0%0.3% 1.0% 0.8% 0.7% 0.7% 0.7%

96.5% 94.8% 94.6% 93.9% 93.9% 93.3%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

2002/2003 2003/2004 2004/2005 2005/2006 2006/2007 2007/2008

Perc

ent

of S

tude

nts

School Year

Grade 12 Student Percentages

AM 12EM 12

Current Situation

Teachers

Too much content for the instructional time

Want to provide a deeper understanding of mathematics

Students are in the “wrong” pathway

Post Secondary

Students are not prepared well enough

Need a better understanding of “the basics”

Parents

Students are struggling

Do not want to “close doors”

Overview of Pathways

K to 9

Foundations of Mathematics

Pre-calculusApprenticeship and Workplace

Mathematics

GRADE 10

GRADE 11

GRADE 12

Foundations of Mathematics

Foundations of Mathematics and Pre-calculus

Apprenticeship and Workplace

Mathematics

Pre-calculusApprenticeship and Workplace

Mathematics

Majority of Trades and Workforce

Programs not requiring

theoretical calculus

Programs requiring

theoretical calculus

Intended for study in

Some Factors to Consider

Post-Secondary AdmissionsUBC Case Study

Math 1XX* No Math** Grand TotalCampus ProgVancouver BA (Arts) 688 1365 2053

BASC (Applied science/engineering) 731 8 739BCOM (Commerce) 510 37 547BDSC (Dental Hygene) 20 20BHK (Human Kinetics) 33 76 109BMUS (Music) 1 39 40BMW (Midwifery) 1 1BSAB (Bachelor of Applied Biology) 6 1 7BSAG (Agroecology) 12 5 17BSC (Science) 1560 77 1637BSCN (Nursing) 29 13 42BSCW (Wood products, Forestry) 14 14BSF (Forestry) 22 4 26BSFN (Food, Nutrition and Health) 162 18 180BSFS (Forest Sciences) 16 3 19Unclassified 3 3

Vancouver Total 3784 1670 5454Grand Total 3784 1670 5454* Students taking first year math at UBC (2009 Direct Entry)** Student did not take a first year math at UBC (including IB, AP, BC Calc 12)

Post-Secondary Admissions:UBC Case Study

UBC Student Population (2003-2006)

Total BC Grade 12 Students 170,000

UBC Entrants 10,303

PM 11 Entrants 991

Percent of UBC Entrants with PM 11 only 9.62%

Percent of Total BC Grade 12 Student Population 0.58%

Grade 12 Math (PM 12, IB, AP, BC Calculus 12) 9,312

Percent of UBC Entrants with Grade 12 Math 91.38%

Percent of Total BC Grade 12 Student Population 5.48%

Note: Only Arts, Dental Hygiene, Human Kinetics, Midwifery, and Music do not require PM 12 for admission

Post-Secondary Admissions

• UBC – Foundations of Mathematics 12 or Pre-calculus 11 for general admission (i.e. Arts, Dental Hygiene, Human Kinetics, Midwifery, and Music) all other programs will require additional mathematics courses

• Decisions from other post-secondary institutions pending

• Information will be posted on www.educationplanner.cawhen available

http://www.educationplanner.ca/

Overview of 10-12 Courses –The Blankets

Mathematical Processes –The Threads

Com

munication

Reasoning

Technology

Visualization

Mathematical Processes – Why?

“... three issues that make all the difference, according to our advisors, first year instructors, and the research I have seen:

•study skills ...•conceptual level ... •processes ...

- Walter Whitley - Chair Curriculum Committee for Mathematics for Education Program

Mathematics Processes – Why?

There is an underlying feeling among college/university instructors that overall the secondary mathematics curriculum, in the main, contains the content and topics with which a mathematics/ statistics student would need familiarity in order to succeed in most post-secondary environments. However, the success rates, especially in Calculus, are evidence that to judge student preparedness solely on the curricular content of a prerequisite course is unwise. In a full analysis of the reasons for student success, other influences and other mathematical proficiencies must be considered.http://bccupms.ca/document/Mathematics%20Proficiencies%20Project.pdf

Mathematics Processes – Why?

Calculus Statistics Elementary Education WNCP

Thinking Skills Thinking Skills Thinking Skills Reasoning / ME

Solving Word Problems Solving Word Problems Problem Solving / Technology

Multi-step Problems Problem Solving / Connections

Modeling Modeling Visualization/Connections

Integration of Topics Integration of Topics Integration of Topics Connections

Abstracting/Generalising

Connections / Technology

Symbolism Symbolism Symbolism Connections

Language Skills Communication

Positive AttitudeToward Math

Positive AttitudeToward Math

Affective Domain

How do the proficiencies align?

Rush Hour / Traffic Jam

Why is this important??

Can you see a solution?How would you solve

http://www.puzzles.com/products/RushHour/RHfromMarkRiedel/Jam.html

Rush Hour / Traffic Jam

Mathematics Processes -Communication

Frayer Model

With a partner pick one term and complete:

Equation, Expression, Polynomial, Linear, Inscribed Angles, Scale Diagram


Frayer Model


Classroom Instruction that Works- Robert Marzano, Debra Pickering, and Jane Pollock

1. Identifying similarities and differences2. Summarizing and note taking3. Reinforcing effort and providing recognition4. Homework and practice5. Nonlinguistic representations6. Cooperative learning7. Setting objectives and providing feedback8. Generating and testing hypotheses9. Cues, questions, and advance organizers

Mathematics Processes –Connections

“Wherever possible, meaningful contexts should be used in examples, problems and projects.”

CCF (pg. 17)


Course Organizer PLOGrade 9 Transformations • Demonstrate an understanding of line and rotation

symmetry

AWM 10 Geometry • Model and draw 3-D objects and their views.• Draw and describe exploded views, component parts and scale diagrams of simple 3-D objects.

FOM 11 Statistics • Demonstrate an understanding of normal distribution, including: standard deviation, z-scores.

PCM 11 Relations and Functions

• Analyze arithmetic sequences and series to solve problems.• Analyze geometric sequences and series to solve problems.


Course PLO summary

Grade 9 • line and rotation symmetry

AWM 10 • 3-D objects and their views,exploded views, component parts and scale diagrams

• Flat pack furniture

FM 11 • normal distribution, including: standard deviation, z-scores.

• Galton Box• Mr Tubbs

PM 11 • arithmetic and geometric sequences and series

• Spreadsheets to compare data models such as • Simple vs. Compound Interest

Mathematics Processes –Mental Mathematics and Estimation

“ Mental mathematics is a combination of cognitive strategies that enhance flexible thinking and number sense. It involves using strategies to perform mental calculations ....

WNCP (pg. 8)

Mathematics Processes –Mental Mathematics and Estimation

Estimation is used for determining approximate values or quantities, usually by referring to benchmarks or referents, or for determining the reasonableness of calculated values. Estimation is also used to make mathematical judgements and to develop useful, efficient strategies for dealing with situations in daily life. When estimating, students need to learn which strategy to use and how to use it.”

WNCP (pg. 8)

Mathematics Processes –Estimation and Mental Mathematics

Benchmark - A benchmark is something (for example a number) that serves as a reference to which something else (another number) may be compared. The most common use for benchmarks is in estimation. Benchmarks tend to not be personal.

e.g. 0, 0.5, ½, ¾, 1, 100%, 50%


Referent – A known quantity used to estimate or compare. Referents tend to be personal.

e.g. Metre and inch, litre and gallon


Pre-calculus 11


Apprenticeship and Workplace 10

Mathematics Processes –Problem Solving

“A problem can be defined as any task or activity for which the students have not memorized a method or rule, nor is there an assumption by the students that there is only one correct way to solve the problem”

Hiebert et al. 1997


A problem for learning mathematics also has these features:• The problem must begin where the students

are.• The problematic or engaging aspect of the

problem must be due to the mathematics that the students are to learn.

• The problem must require justifications and explanations for answers and methods.

Van de Walle 2006


In order to be successful, students must develop, and teachers model, the following characteristics:

• interest in finding solutions to problems

• confidence to try various strategies

• willingness to take risks

• ability to accept frustration when not knowing

• understanding the difference between

• not knowing the answer and not having found it yet

(Burns 2000)


A final word on problem solving ...

• both groups [calculus and statistics] stress the importance of problem solving abilities, particularly in the context of word problems. (BCCUPMS)

• Multi-step problems involve two or more stages to arrive at a solution. They are not necessarily word problems. (BCCUPMS)

Mathematics Processes –Reasoning


Examine the verbs in the PLOs and the AIs as they help interpret the breadth and depth of outcomes

http://www.psy.gla.ac.uk/~steve/best/bloom.html


Grade 9


Foundations of Mathematics 11

Mathematics Processes –Technology

The use of [ T ] in the PLOs does not include routine calculation.

Calculators and computers can be used to:

• explore and demonstrate mathematical relationships and patterns

• organize and display data

• generate and test inductive conjectures

• extrapolate and interpolate

• assist with calculation procedures as part of solving problems

• increase the focus on conceptual understanding by decreasing the time spent on repetitive procedures

• reinforce the learning of basic facts

• develop personal procedures for mathematical operations

• model situations

• develop number and spatial sense. (pg. 9)


Grade 8


Foundations 11

Mathematics Processes –Visualization

http://naungancinta.wordpress.com/2008/04/11/multiple-intelligences-which-one-your-learning-style/

Visualization is fostered through the use of concrete materials, technology and a variety of visual representations. It is through visualization that abstract concepts can be understood concretely by the student. Visualization is a foundation to the development of abstract understanding, confidence and fluency. (p. 10)


Apprenticeship and Workplace 11


Foundations of Mathematics 12

Visualization Canadian VS US National Debt

Canada United States

$100 $100

Images from istockphoto.com and pagetutor.com



$10 0001/2” thick

$10 000½” thick



$1 000 000 $1 000 000



$100 000 000 $100 000 000



$1 000 000 000 $1 000 000 000



Total $600 000 000 000March 2009

$1 000 000 000Not there yet



Total $600 000 000 000March 2009

$10 000 000 000 000March 2009

Questions

Contact Information:

Richard V. DeMerchantCoordinatorEducation Standards UnitBritish Columbia Ministry of EducationEmail: [email protected]: (250) 387-3907

Please include your phone number and email.

Comox Valley Professional Development Day

Documents

Transcript of Comox Valley Professional Development Day