common core state standards ncctm western regional conference joyce gardner [email protected]...
TRANSCRIPT
Common Core State Standards
NCCTMWestern Regional
Conference
Joyce [email protected]
Region 8 Professional Development ConsultantNCDPI
As much as you love math, what would you do if you weren’t here today?
Find someone you don’t know well and tell them all about it. Be ready to introduce your
new friend.
Norms
• Explore and Share ideas.
• Collect/locate ideas and resources to share with colleagues who are not here.
• Make a new math friend.
04/20/23 • page 3
Outcomes
• Explore the need for change in mathematics teaching and learning for our 21st century students.
• Explore and Bookmark resources.
• Know where to find evolving DPI updates.
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Math Assessment Item Types:Gridded Response
•Grades 5 through 8
•Algebra I/Integrated I End-of-Course
•multiple-choice items and approximately 20 percent gridded-response items.
• A gridded response item requires the student to record a numerical answer into a field rather than select an answer from several choices.
•Guideline documents and examples posted on the testing website at http://www.ncpublicschools.org/accountability/testing/.
•Additional examples of new online item types in the Online Assessment Tutorial (http://go.ncsu.edu/nctdemo).
Released Test Forms for 2012-13
• Available in an online assessment version and in a paper-and-pencil version
• Online released forms and Online Assessment Tutorial forms are presented in the same interactive environment as the actual online assessment and are available at http://www.ncpublicschools.org/accountability/testing/releasedforms.
Scoring Module for Elementary and Middle School Common Exams
ReleasedThe Scoring Module:
•begins with an introduction to Common Exams and the state's educator effectiveness model
•Includes content-specific sections for science and social studies.
• provide access to certificates of completion for the different sections.
Access the module here:
Common Exams: Elementary and Middle
The module can also be accessed through NC Education.
In the mathematics world…
We…•are all about problem solving and critical
thinking. •Hone best practices•Develop the Standards for Mathematical Practices•Build our classrooms around 21st century skills•Believe that all students can learn math •Provide tools and opportunities that help students develop their own mathematical understandings•Move beyond the traditional teaching model.
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Australia Czech Republic Hong Kong J apan Netherlands United States
Using ProceduresMaking Connections
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Australia Czech Republic Hong Kong J apan Netherlands United States
Using Procedures
Making Connections
Types of Math Problems Presented
How Teachers ImplementedMaking Connections Math
Problems
• Examined the relationship between the cognitive demands of mathematical tasks and student achievement
• 100 8th grade mathematics classes in six countries
• Australia, the Czech Republic, Hong Kong, Japan, the Netherlands, Switzerland each performed significantly higher than the U.S. on the TIMSS 1995 mathematics achievement test for eighth grade
• 17% of the problem statements in the U.S. suggested a focus on mathematical connections or relationships. This percentage is within the range of many higher-achieving countries (i.e., Hong Kong, Czech Republic, Australia).
Higher-achieving countries implemented a greater percentage of making connections tasks in ways that maintained the demands of the task
These countries used a greater percentage of “making connections” tasks in ways that maintained the demands of the task.
Virtually none of the making-connections problems in the U.S. were discussed in a way that made the mathematical connections or relationships visible for students.
The US tended to reduce these tasks into procedural exercises or into problems in which even less mathematical content was visible (i.e., only the answer was given).
Students in U.S. classrooms “rarely spend time engaged in the serious study of mathematical concepts” (Stigler & Hiebert, 2004, p. 16).
Lesson ComparisonUnited States and Japan
The emphasis on skill acquisition is evident in the steps most common in U.S. classrooms
The emphasis on understanding is evident in the steps of a typical Japanese lesson
•Teacher instructs students in concept or skill
•Teacher solves example problems with class
•Students practice on their own while teacher assists individual students
•Teacher poses a thought provoking problem
•Students and teachers explore the problem
•Various students present ideas or solutions to the class
•Teacher summarizes the class solutions
•Students solve similar problems
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US Data / Hong Kong
• Hong Kong had the highest scores in the most recent TIMSS.
• Hong Kong students were taught 45% of objectives tested.
• Hong Kong students outperformed US students on US content that they were not taught.
• US students ranked near the bottom.
• US students ‘covered’ 80% of TIMSS content.
• US students were outperformed by students not taught the same objectives.
8 + 4 = [ ] + 5•Think for a minute about your answer to this problem.
•Predict what students in 1-6 grade might give as the answer.
Children’s Mathematics: Cognitively Guided Instruction (CGI), by Carpenter, Fennema, Franke, Levi & Empson, 1999
8 + 4 = [ ] + 5Percent Responding with Answers
Grade 7 12 17 12 & 17
1st - 2nd
3rd - 4th
5th - 6th
Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.Carpenter, Franke, & Levi
Heinemann, 2003
8 + 4 = [ ] + 5Percent Responding with Answers
Grade 7 12 17 12 & 17
1st - 2nd 5 58 13 8
3rd - 4th
5th - 6th
Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.Carpenter, Franke, & Levi
Heinemann, 2003
8 + 4 = [ ] + 5Percent Responding with Answers
Grade 7 12 17 12 & 17
1st - 2nd 5 58 13 8
3rd - 4th 9 49 25 10
5th - 6th
Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.Carpenter, Franke, & Levi
Heinemann, 2003
8 + 4 = [ ] + 5Percent Responding with Answers
Grade 7 12 17 12 & 17
1st - 2nd 5 58 13 8
3rd - 4th 9 49 25 10
5th - 6th 2 76 21 2Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.
Carpenter, Franke, & LeviHeinemann, 2003
Estimate the answer for (12/13) + (7/8)
A. 1B. 2C. 19D. 21
Only 24% of 13 year olds answered correctly. Equal numbers of students chose the other answers.
NAEP
1. 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.
Standards for Mathematical Practices
Overarching habits of mind of a productive Mathematical Thinker
When planning, ask
“What task can I give that will build student understanding?”
rather than
“How can I explain clearly so they will understand?”
Grayson Wheatley, NCCTM, 2002
Announcements
The North Carolina ElementaryMathematics Add-On License Project
For more information on EMAoL offerings contact:
ASUKathleen Lynch Davis [email protected]
UNCSusan Friel
NCSUPaola Sztajn
ECUSid Rachlin
UNCCDrew Polly
UNCGKerri Richardson
UNCWTracy Hargrove
