california mathematics council november 2, 2013 ivan chengjaspreet sandha...
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California Mathematics CouncilNovember 2, 2013
Ivan Cheng Jaspreet [email protected] [email protected]
Lina [email protected]
The Right Answer Is NOT Enough
The proportion = can be used to solve
which of the following situations?
Situation 1: For every 1 teacher, there are 2 TAs at Some HS.If there are 10 teachers, how many TAs are there?
Situation 2: Abel is 1 year old and Betty is 2 years old.When Abel is 10 years old, how old will Betty be?
• Situation 1
• Situation 2
€
12
€
10x
C. Both Situations 1 and 2
D. Neither Situation 1 nor 2
Presented by Jimmy de la Torre at AERA 2013
Just for Fun – Try This Now
The proportion = can be used to solve
which of the following situations?
Situation 1: For every 1 teacher, there are 2 TAs at Some HS.If there are 10 teachers, how many TAs are there?
Situation 2: Abel is 1 year old and Betty is 2 years old.When Abel is 10 years old, how old will Betty be?
• Situation 1
• Situation 2
€
12
€
10x
C. Both Situations 1 and 2
D. Neither Situation 1 nor 2
Presented by Jimmy de la Torre at AERA 2013
The Right Answer is NOT Enough
The Right Answer is NOT Enough
Suppose on one test… Period 1 students averaged 75% correct
Half the class scored 100% and the other half scored 50%
Period 2 students averaged 75% correct Half the class scored 76% and the other half scored 74%
How do these two classes differ?
The Right Answer is NOT Enough
Suppose on one test… Two students both scored 75%
Sample problem: 12 – 2(3 – 5)
One student got –20 for an answer andanother student got 8 for an answer
How do their errors differ? What does this mean for our teaching practice?
Mathematical content Ratios & proportions, the number system, expressions & equations,
functions, geometry, statistics & probability
Mathematical practices1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
The Right Answer is NOT Enough
Depth of Knowledge (DOK)
Cognitive rigor for each type of thinking Remember (Level 1 only) Understand (Levels 1 – 4) Apply (Levels 1 – 4) Analyze (Levels 1 – 4) Evaluate (Levels 3 – 4) Create (Levels 1 – 4)
What is the DOK for current CSTs?
Depth of Knowledge (DOK)
DOK 3 DOK 4
Current CST <2% 0%
New SB Assessment 49% 21%
Yuan & Le (2012); Herman & Lin (2013), from Linda Darling-Hammond Assembly Testimony, 3/6/13
Depth of Knowledge (DOK)
DOK 3 DOK 4
Current CST <2% 0%
New SB Assessment 49% 21%
Yuan & Le (2012); Herman & Lin (2013), from Linda Darling-Hammond Assembly Testimony, 3/6/13
Smarter Balanced Blueprints
“Claims”
Assessment “Targets”
ELA Math
1 Reading Concepts and Procedures
2 Writing Problem Solving
3 Speaking/Listening Communicating Reasoning
4 Research Modeling/Data Analysis
“Claims” integrate content and practices
Assessment “Targets”
ELA Math
1 Reading Concepts and Procedures
2 Writing Problem Solving
3 Speaking/Listening Communicating Reasoning
4 Research Modeling/Data Analysis
Smarter Balanced Blueprints
Smarter Balanced Blueprints
“Claims” integrate content and practices
Assessment “Targets” specify what will be tested
ELA Math
1 Reading Concepts and Procedures
2 Writing Problem Solving
3 Speaking/Listening Communicating Reasoning
4 Research Modeling/Data Analysis
Smarter Balanced Blueprints
“Claims” integrate content and practices
Assessment “Targets” specify what will be tested
ELA Math
1 Reading Concepts and Procedures
2 Writing Problem Solving
3 Speaking/Listening Communicating Reasoning
4 Research Modeling/Data Analysis
Claim 1–Concepts and Procedures
Claim 1–Concepts and Procedures
Assessment Targets–Grade 8A. Numbers (NS.1, NS.2)
B. Radicals and exponents (EE.1, EE.2, EE.3, EE.4)
C. Proportional relationships and equations (EE.5, EE.6)
D. Expressions and equations (EE.7, EE.8)
E. Functions (F.1, F.2, F.3)
F. Modeling relationships (F.4, F.5)
G. Geometric relationships (G.1, G.2, G.3, G.4, G.5)
H. Pythagorean Theorem (G.6, G.7, G.8)
I. Volume (G.9)
J. Data analysis (SP.1, SP.2, SP.3, SP.4)
Claim 2–Problem Solving
Claim 2–Problem Solving
Assessment Targets–Grades 6–8, 11A. Applying mathematics to solve problems
B. Select and use appropriate tools strategically
C. Interpret results in the context of a situation
D. Identify important quantities in a practical situation and map their relationships
Claim 4–Modeling and Data Analysis
Assessment Targets–Grades 6–8, 11A. Apply mathematics
B. Construct chains of reasoning to justify models, solutions
C. State logical assumptions being used
D. Interpret results in the context of a situation
E. Analyze the adequacy of and improve models
F. Identify important quantities in a practical situationand map their relationships
Claim 3–Communicating Reasoning
Claim 3–Communicating Reasoning
Assessment Targets–Grades 6–8, 11A. Test propositions or conjectures with specific examples
B. Construct chains of reasoning to justify or refute
C. State logical assumptions being used
D. Breaking arguments into cases
E. Distinguishing correct logic
F. Base arguments on concrete referents
G. Determine conditions under which arguments apply
Claim 1Concepts & Procedures
Claim 2ProblemSolving
Claim 3Communicating
Reasoning
Claim 4Modeling & Data
Analysis
Selected Response (SR)
Constructed Response (CR)
Extended Response (ER)
Technology Enhanced (TE)
Performance Task (PT)
Item Types for SBAC Assessments
From Smarter Balanced Assessments, MAT.06.SR.1.000EE.F.072
Sample Selected Response Item
From Smarter Balanced Assessments, MAT.07.CR.1.000EE.D.165
Sample Constructed Response Item
From Smarter Balanced Assessments, MAT.06.ER.2.000EE.C.172
Sample Extended Response Item
From Smarter Balanced Assessments, MAT.HS.TE.1.0AREI.I.088
Sample Technology Enhanced Item
Mathematical content Ratios & proportions, the number system, expressions & equations,
functions, geometry, statistics & probability
Mathematical practices1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
The Right Answer is NOT Enough
Mathematical content Ratios & proportions, the number system, expressions & equations,
functions, geometry, statistics & probability
Mathematical practices1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
What Do We Need to Do?
Have clear objectives for each test item we make Use the standards and blueprints Specify precise learning goals
Create problems that reveal understanding Use SBAC samples as a guide Reveal mastery of specific concept or skill
Analyze student work for understanding Go beyond the score Look for patterns of errors and misunderstandings
What Do We Need to Do?
Have clear objectives for each test item we make Use the standards and blueprints Specify precise learning goals
Create problems that reveal understanding Use SBAC samples as a guide Reveal mastery of specific concept or skill
Analyze student work for understanding Go beyond the score Look for patterns of errors and misunderstandings
Assessment Planning Matrix
Assessment Planning Matrix
Have clear objectives for each test item we make Use the standards and blueprints Specify precise learning goals
Create problems that reveal understanding Use SBAC samples as a guide Reveal mastery of specific concept or skill
Analyze student work for understanding Go beyond the score Look for patterns of errors and misunderstandings
Creating Assessments with the APM
Creating Assessments with the APM
From Smarter Balanced Assessments, MAT.06.SR.1.000EE.F.178
From Smarter Balanced Assessments, MAT.06.SR.1.000EE.F.178
Claim 1 – Target F – Grade 6
Concepts & Procedures – Expressions & EquationsModel 1: SR (DOK 2) – Stimulus: The student is presented with a one-variable equation or inequality in
a problem and/or problem set. Prompt: The student is prompted to use substitution to identify the solution to one-variable equations and inequalities.
Model 2: SR (DOK 2) – Stimulus: The student is presented with a verbal expression in a real-world or mathematical problem involving a one-variable equation in the form x + p = q or px = q or a one variable inequality in the form of x > c or x < c. Prompt: The student is prompted to identify the variable equations or inequalities that correspond to verbal expressions in real-world and mathematical problems. Or the student is prompted to identify the solution to one-variable equations and inequalities in real-world and mathematical problems.
Model 3: SR (DOK 1, 2) – Stimulus: The student is presented with a one-variable inequality presented in a real-world or mathematical problem. Prompt: The student is prompted to identify a number line that represents the solution to a one-variable inequality presented in a real-world or mathematical problem.
Creating Assessments with the APM
Creating Assessments with the APM
Creating Assessments with the APM
Selected Response (SR) Constructed Response (CR) Extended Response (ER) Technology Enhanced (TE) Performance Task (PT)
Choose one sample as a model Note the Assessment Target and the DOK Note the type of stimulus and the prompt
Create a similar task
Creating Assessments with the APM
Online Resources
Common Core resources CA Common Core Standards
http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf
Smarter Balanced sample interactive problemshttp://sampleitems.smarterbalanced.org/itempreview/sbac/index.htm
Howard Countyhttps://secondarymathcommoncore.wikispaces.hcpss.org
MARS/Shellhttp://map.mathshell.org/materials/stds.php
Illustrativemathematics.org Schools.nyc.gov/Academics/CommonCoreLibrary Achievethecore.org Serpmedia.org
Thank You
Ivan Cheng Jaspreet [email protected] [email protected]
Lina [email protected]
The Right Answer Is NOT Enough