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Creating Active Thinkers
Taking the Ultimate Journey
Kitty Rutherford
Who’s in the Room”
Norms
• Listen as an Ally
• Value Differences
• Maintain Professionalism
• Participate Actively
04/20/23 • page 3
Let’s Define the Problem
We in the mathematics world are all about problem solving. If we want to follow best practices, develop the Mathematical Practices, help students develop 21st century skills, we have to move beyond the traditional teaching model.
High School
Rows of 5, all eyes on the chalk board, blue overhead marker smeared from palm to elbow….
Students asleep or praying for a fire drill.
First Grade
• The Leader
• The Ethics Police
• The “I’m Finished First” Winners
• The Do-Overs
Instruction Must Change
• TIMSS and other international measures
• Common Core State Standards
• N.C. Teacher Evaluation Process
61
77
84
41
57
69
15 1613
54
24
17
0
10
20
30
40
50
60
70
80
90
100
Australia Czech Republic Hong Kong J apan Netherlands United States
Using ProceduresMaking Connections
31
1618
20 19
59
8
52
4648
37
00
10
20
30
40
50
60
70
80
90
100
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
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
9
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.
Why is change necessary?
8 + 4 = [ ] + 5
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 to (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
How are you feeling?
Let’s Do Some Math!
The Famous Horse Problem
A farmer buys a horse for $60.
Later he sells it for $70.
He buys it back for $80.
Finally, he sells it for $90.
Shoe Store Problem A man walks into a shoe store and buys a pair of
shoes for $5. He pays with a $20. The store owner goes next door to the baker to get change for the $20, returns, and gives the customer his change. That afternoon the baker shows up with a police officer, declaring that the $20. was counterfeit, and he wants his money back. The shoe shop owner returns his money. How much did he make or lose?
Feeling Better?
More research
Students were given this problem:
168 204th grade students in reform math classes solved it with no problem. Sixth graders in traditional classes responded that they hadn’t been taught that yet.
Dr. Ben Klein, Mathematics ProfessorDavidson College
Research
Students are shown this number. Teacher points to the 6 and says, “Can you show me this many?”
16
Research
When the teacher points to the 1 in the tens place and asks,
“Can you show me this many?”
16
Research
By third grade nearly half the students still do not ‘get’ this
concept.
16
More research - It gets worse!
A number contains 18 tens, 2 hundreds, and 4 ones. What is that number?
1824
218.4
2824
384
We know“What” Students Need…
21st Century Skills, critical thinking and
problem solving, collaboration and leadership, agility and adaptability, oral and written communication, accessing and analyzing information.
Tony Wagner, Rigor Redefined
But Not “How” to Meet Their Needs
Common Core Standards for Mathematical Practice
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
Creating Active Thinkers
Do You Value Thinking?
Turn and Talk with your shoulder partner about your
Teacher Test.
The First Step
“Before all else, a classroom environment that fosters complex thinking must be predictable and safe.” Creating Active Thinkers, page 34
How do you know if your classroom is safe and predictable?
The Next Step
“Complex thinking is developed in students primarily through the careful planning and teaching of lessons.”
Creating Active Thinkers, page 37
What do you need to keep in mind when planning a lesson?
Jigsaw on Teacher Strategies
Let’s Jigsaw!
Find your Teacher Strategy #
Find your Teacher Strategies Color
Student Responsibilities
“The student takes his or her cues from the teacher.”
Include your students in the journey.
Meet some of your students
Creating Active Thinkers, page 97-99
Student Behaviors
Read the student behaviors on page 101.
Compare student behaviors to the Standards for Mathematical Practice.
Surprise?
Developing These Behaviors
The first step is to let students in on the game.
They must be explicitly taught about these nine behaviors.
Self Assessment
Students are amazingly honest when assessing themselves.
Creating Active Thinkers, page 117 – 121; 136-137
Self Assessment Doesn’t Always Work
The last pages contain Observation Forms, to help you see what your students and others see.
Creating Active Thinkers, Appendix C
For all you do for our students!
Kitty Rutherford
kitty.rutherford@dpi.nc.gov
Contact Information
Website: www.ncdpi.wikispaces.net
What questions do you have?
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