california mathematics council november 2, 2013 ivan chengjaspreet sandha...
TRANSCRIPT
![Page 1: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/1.jpg)
California Mathematics CouncilNovember 2, 2013
Ivan Cheng Jaspreet [email protected] [email protected]
Lina [email protected]
The Right Answer Is NOT Enough
![Page 2: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/2.jpg)
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
![Page 3: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/3.jpg)
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
![Page 4: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/4.jpg)
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?
![Page 5: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/5.jpg)
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?
![Page 6: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/6.jpg)
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
![Page 7: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/7.jpg)
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?
![Page 8: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/8.jpg)
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
![Page 9: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/9.jpg)
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
![Page 10: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/10.jpg)
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
![Page 11: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/11.jpg)
“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
![Page 12: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/12.jpg)
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
![Page 13: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/13.jpg)
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
![Page 14: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/14.jpg)
Claim 1–Concepts and Procedures
![Page 15: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/15.jpg)
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)
![Page 16: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/16.jpg)
Claim 2–Problem Solving
![Page 17: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/17.jpg)
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
![Page 18: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/18.jpg)
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
![Page 19: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/19.jpg)
Claim 3–Communicating Reasoning
![Page 20: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/20.jpg)
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
![Page 21: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/21.jpg)
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
![Page 22: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/22.jpg)
From Smarter Balanced Assessments, MAT.06.SR.1.000EE.F.072
Sample Selected Response Item
![Page 23: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/23.jpg)
From Smarter Balanced Assessments, MAT.07.CR.1.000EE.D.165
Sample Constructed Response Item
![Page 24: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/24.jpg)
From Smarter Balanced Assessments, MAT.06.ER.2.000EE.C.172
Sample Extended Response Item
![Page 25: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/25.jpg)
From Smarter Balanced Assessments, MAT.HS.TE.1.0AREI.I.088
Sample Technology Enhanced Item
![Page 26: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/26.jpg)
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
![Page 27: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/27.jpg)
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?
![Page 28: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/28.jpg)
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?
![Page 29: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/29.jpg)
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
![Page 30: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/30.jpg)
Assessment Planning Matrix
![Page 31: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/31.jpg)
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
![Page 32: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/32.jpg)
Creating Assessments with the APM
From Smarter Balanced Assessments, MAT.06.SR.1.000EE.F.178
![Page 33: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/33.jpg)
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
![Page 34: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/34.jpg)
Creating Assessments with the APM
![Page 35: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/35.jpg)
Creating Assessments with the APM
![Page 36: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/36.jpg)
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
![Page 37: California Mathematics Council November 2, 2013 Ivan ChengJaspreet Sandha icheng@csun.edujxs9368@lausd.net Lina Kim lina.n.kim@gmail.com The Right Answer](https://reader037.vdocument.in/reader037/viewer/2022103122/56649ce65503460f949b4aaf/html5/thumbnails/37.jpg)
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
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Thank You
Ivan Cheng Jaspreet [email protected] [email protected]
Lina [email protected]
The Right Answer Is NOT Enough