october 1, 2010 1 making sense of change vctm fall academy october 1, 2010 making sense of change...
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October 1, 2010 1
Making Sense of ChangeMaking Sense of Change
VCTM Fall AcademyVCTM Fall AcademyOctober 1, 2010October 1, 2010
Making Sense of ChangeMaking Sense of Change
VCTM Fall AcademyVCTM Fall AcademyOctober 1, 2010October 1, 2010
Michael BollingMichael BollingMathematics Coordinator, VDOEMathematics Coordinator, VDOE
(and managing it)
October 1, 2010 2
Slide TitleSlide TitleSlide TitleSlide Title
October 1, 2010 3
Oil leaked from April 20 – July 15, 2010.
On July 15, the leak was stopped after releasing about 4.9 million barrels (7.8×105 m3) of crude oil.
It was estimated that 53,000 barrels per day (8,400 m3/d) were escaping from the well just before it was capped.
It is believed that the daily flow rate diminished over time, starting at about 62,000 barrels per day (9,900 m3/d) and decreasing as the reservoir of hydrocarbons feeding the gusher was gradually depleted.
The Deepwater Horizon was able to operate in waters up to 8,000 feet (2,400 m) deep and drill down to 30,000 feet (9,100 m).
BP estimated the worst case flow at 162,000 barrels per day (25,800 m3/d).
Internal BP documents estimated the flow could be as much as 100,000 barrels per day (16,000 m3/d).
October 1, 2010
Deepwater Horizon Oil SpillDeepwater Horizon Oil SpillDeepwater Horizon Oil SpillDeepwater Horizon Oil Spill
• What “What “I wonder…I wonder…” questions about ” questions about the mathematics would kids (or the mathematics would kids (or adults) ask?adults) ask?
• What jobs related to the spill What jobs related to the spill involve pertinent mathematics?involve pertinent mathematics?
• To which mathematics content To which mathematics content could this disaster be connected?could this disaster be connected?
• What “What “I wonder…I wonder…” questions about ” questions about the mathematics would kids (or the mathematics would kids (or adults) ask?adults) ask?
• What jobs related to the spill What jobs related to the spill involve pertinent mathematics?involve pertinent mathematics?
• To which mathematics content To which mathematics content could this disaster be connected?could this disaster be connected?
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October 1, 2010
Highlighted SOL ChangesHighlighted SOL ChangesHighlighted SOL ChangesHighlighted SOL Changes
• Awareness Awareness (curriculum and pacing guides, (curriculum and pacing guides, SOL Crosswalks, VDOE training institutes)SOL Crosswalks, VDOE training institutes)
• UnderstandingUnderstanding• Content Content (Curriculum Framework, technical (Curriculum Framework, technical
assistance documents)assistance documents)
• Connections Connections (Enhanced Scope and (Enhanced Scope and Sequence lesson, vertical articulation of Sequence lesson, vertical articulation of content)content)
• Awareness Awareness (curriculum and pacing guides, (curriculum and pacing guides, SOL Crosswalks, VDOE training institutes)SOL Crosswalks, VDOE training institutes)
• UnderstandingUnderstanding• Content Content (Curriculum Framework, technical (Curriculum Framework, technical
assistance documents)assistance documents)
• Connections Connections (Enhanced Scope and (Enhanced Scope and Sequence lesson, vertical articulation of Sequence lesson, vertical articulation of content)content)
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October 1, 2010 6
New from grade 8
Exponents/Squares/Square Roots
October 1, 2010 7
Comparing and Ordering
October 1, 2010 8
New from grade 7
New from grade 7
Expressions and Operations
October 1, 2010 9
New content
Modeling
New content
October 1, 2010 10
New content
Equations and Inequalities
October 1, 2010
What can you tell me?What can you tell me?What can you tell me?What can you tell me?
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Algebra IRelation or function?
Domain/range
Zeros
x- and y-intercepts
Function values for elements of the domain
Connections among representations
AFDA - addsLocal/absolute max/min
Intervals of increasing/ decreasing
End behaviors
asymptotes
Alg 2 - addsInverse functions
Composition of functions
October 1, 2010 12
New content New content
New content
New content
Technical Assistance Document for A.9 Published
Technical Assistance Document for AII.11 October 2010
October 1, 2010 13
New content
October 1, 2010 14
Each figure in the pattern below is made of hexagons that measure 1 centimeter on each side.
If the pattern of adding one hexagon to each figure is continued, what will be the perimeter of the 25th figure in the pattern? Show how you found your answer.
October 1, 2010
Perimeter ProblemPerimeter ProblemPerimeter ProblemPerimeter Problem
• In what situation would this task be In what situation would this task be used? used?
• In which course/level would you In which course/level would you use this task?use this task?
• How would you adjust it for another How would you adjust it for another course/level?course/level?
• In what situation would this task be In what situation would this task be used? used?
• In which course/level would you In which course/level would you use this task?use this task?
• How would you adjust it for another How would you adjust it for another course/level?course/level?
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October 1, 2010
Worthwhile task?Worthwhile task?Questions to ask yourselfQuestions to ask yourself
Worthwhile task?Worthwhile task?Questions to ask yourselfQuestions to ask yourself
• Does the problem challenge students Does the problem challenge students to use higher-level critical thinking to use higher-level critical thinking skills?skills?
• Is the problem clearly connected to the Is the problem clearly connected to the targeted mathematics?targeted mathematics?
• Are there multiple ways to solve this Are there multiple ways to solve this problem? problem?
• Is it accessible to all students?Is it accessible to all students?
• Does the problem challenge students Does the problem challenge students to use higher-level critical thinking to use higher-level critical thinking skills?skills?
• Is the problem clearly connected to the Is the problem clearly connected to the targeted mathematics?targeted mathematics?
• Are there multiple ways to solve this Are there multiple ways to solve this problem? problem?
• Is it accessible to all students?Is it accessible to all students?
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October 1, 2010
Worthwhile task?Worthwhile task?Questions to ask yourselfQuestions to ask yourself
Worthwhile task?Worthwhile task?Questions to ask yourselfQuestions to ask yourself
• Does the problem promote Does the problem promote mathematical communication?mathematical communication?
• What might students struggle with?What might students struggle with?
• This would be an appropriate This would be an appropriate problem if you were studying… or if problem if you were studying… or if you have already studied…you have already studied…
• Does the problem promote Does the problem promote mathematical communication?mathematical communication?
• What might students struggle with?What might students struggle with?
• This would be an appropriate This would be an appropriate problem if you were studying… or if problem if you were studying… or if you have already studied…you have already studied…
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October 1, 2010
Where can I get worthwhile Where can I get worthwhile mathematical tasks?mathematical tasks?
Where can I get worthwhile Where can I get worthwhile mathematical tasks?mathematical tasks?
NAEP released items NAEP released items http://nces.ed.gov/nationsreportcard/
PISA released items PISA released items http://nces.ed.gov/surveys/pisa/educators.asp
APEC Mathematics Assessment Database APEC Mathematics Assessment Database http://hrd.apec.org/index.php/Mathematics_Assessments
Heinemann Mathematics (not free, but cheap) Heinemann Mathematics (not free, but cheap) http://books.heinemann.com/math/
NAEP released items NAEP released items http://nces.ed.gov/nationsreportcard/
PISA released items PISA released items http://nces.ed.gov/surveys/pisa/educators.asp
APEC Mathematics Assessment Database APEC Mathematics Assessment Database http://hrd.apec.org/index.php/Mathematics_Assessments
Heinemann Mathematics (not free, but cheap) Heinemann Mathematics (not free, but cheap) http://books.heinemann.com/math/
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October 1, 2010
Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills
Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills
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8.11The student will solve practical area and perimeter problems involving composite plane figures.
PAST FUTURE
Find the area of
the shaded region.
October 1, 2010
Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills
Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills
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8.5 b) The student will find the two consecutive whole numbers between which a square root lies.
PAST FUTURE
Between which two square roots does 5 lie?
October 1, 2010
Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills
Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills
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A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots.
PAST
Which class had the most students scoring higher than 83?
FUTURE
Class A has 30 students and Class B has 20 students. Which class has more students scoring above 83?
October 1, 2010
Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills
Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills
• Increased levels of complexity Increased levels of complexity in analysisin analysis
• Increased levels of complexity Increased levels of complexity in expressions and equationsin expressions and equations
• Comparing and contrasting of Comparing and contrasting of functions during analysisfunctions during analysis
• Increased levels of complexity Increased levels of complexity in analysisin analysis
• Increased levels of complexity Increased levels of complexity in expressions and equationsin expressions and equations
• Comparing and contrasting of Comparing and contrasting of functions during analysisfunctions during analysis
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October 1, 2010
New SOL BlueprintsNew SOL BlueprintsNew SOL BlueprintsNew SOL Blueprints
Mega-categories combine reporting Mega-categories combine reporting categoriescategories
• Grade 6 – from 5 to 4Grade 6 – from 5 to 4• Grade 7-8 – from 5 to 3Grade 7-8 – from 5 to 3• Algebra I – from 4 to 3Algebra I – from 4 to 3• Geometry and Algebra II – from 5 to Geometry and Algebra II – from 5 to
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Mega-categories combine reporting Mega-categories combine reporting categoriescategories
• Grade 6 – from 5 to 4Grade 6 – from 5 to 4• Grade 7-8 – from 5 to 3Grade 7-8 – from 5 to 3• Algebra I – from 4 to 3Algebra I – from 4 to 3• Geometry and Algebra II – from 5 to Geometry and Algebra II – from 5 to
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October 1, 2010 24
Note: Asterisk indicates that the SOL will be assessed in the non-calculator section.
October 1, 2010 25
New Formula SheetsNew Formula SheetsNew Formula SheetsNew Formula Sheets
October 1, 2010
Technology Enhanced ItemsTechnology Enhanced ItemsTechnology Enhanced ItemsTechnology Enhanced Items
Interactive questionsInteractive questions• Hot-spotsHot-spots
• Drag and dropDrag and drop
• Creation of graphsCreation of graphs
• Short responseShort response
Practice ePAT available by February 2011Practice ePAT available by February 2011
Interactive questionsInteractive questions• Hot-spotsHot-spots
• Drag and dropDrag and drop
• Creation of graphsCreation of graphs
• Short responseShort response
Practice ePAT available by February 2011Practice ePAT available by February 2011
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Beginning in
Spring 2011
October 1, 2010
New SOL Assessment TimelineNew SOL Assessment TimelineNew SOL Assessment TimelineNew SOL Assessment Timeline
Spring 2011Spring 2011• All SOL tests (live test items) based on All SOL tests (live test items) based on
2001 SOL 2001 SOL
• Field test items will be based on the Field test items will be based on the 2009 SOL2009 SOL
• Technology enhanced items will be field Technology enhanced items will be field tested in grades 6-8 and EOC SOL teststested in grades 6-8 and EOC SOL tests
Spring 2011Spring 2011• All SOL tests (live test items) based on All SOL tests (live test items) based on
2001 SOL 2001 SOL
• Field test items will be based on the Field test items will be based on the 2009 SOL2009 SOL
• Technology enhanced items will be field Technology enhanced items will be field tested in grades 6-8 and EOC SOL teststested in grades 6-8 and EOC SOL tests
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October 1, 2010
New SOL Assessment TimelineNew SOL Assessment TimelineNew SOL Assessment TimelineNew SOL Assessment Timeline
Fall 2011Fall 2011• EOC SOL tests will be based on EOC SOL tests will be based on
2009 SOL2009 SOL
Spring 2012Spring 2012• All SOL tests will be based on All SOL tests will be based on
2009 SOL2009 SOL
Fall 2011Fall 2011• EOC SOL tests will be based on EOC SOL tests will be based on
2009 SOL2009 SOL
Spring 2012Spring 2012• All SOL tests will be based on All SOL tests will be based on
2009 SOL2009 SOL
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October 1, 2010
What is our goal as teachers of What is our goal as teachers of mathematics?mathematics?
What is our goal as teachers of What is our goal as teachers of mathematics?mathematics?
• What will tomorrow’s jobs look What will tomorrow’s jobs look like?like?
• Teach kids how to use their Teach kids how to use their critical thinking and reasoning critical thinking and reasoning skills to adapt and overcome in skills to adapt and overcome in unfamiliar settingsunfamiliar settings
• What will tomorrow’s jobs look What will tomorrow’s jobs look like?like?
• Teach kids how to use their Teach kids how to use their critical thinking and reasoning critical thinking and reasoning skills to adapt and overcome in skills to adapt and overcome in unfamiliar settingsunfamiliar settings
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