MAKING THE CASE FOR
HOW THE NUMBERS WORK
Things to Think About:
• As educators we should be judged more by who
we are than by what we know. Will Durant
• We can’t give away what we don’t have…And
we are destined to give away what we do have.
MAKING THE CASE FOR
HOW THE NUMBERS WORK
• Welcome
• Thanks for coming today! We need you!
• Introductions
• Agenda/House-Keeping
• Loose schedule
• Tools on the tables
WORKING AGREEMENTS
• Make the Learning Yours
• All Voices in the Room
• Balanced Participation
• Take Care of Yourself
• Have Fun!
RESPONDING
• Plickers from Katie!
• Use the same card all day
• Posters on the Wall
• One comment per sticky note
• Posters on the Table
• Hold up when appropriate
• ½ composition book
• Brief written response/visual on each page
PLICKERS
• Are we satisfied with the current math scores in
our school, district, country?
• Do we want/need better math scores?
• With CCSS, the Standards of Mathematical
Practice, and the Teacher Evaluation Rubric,
how can we make sense of it all?
TEACHER STANDARDS
• Quality Standard 1 – Teachers demonstrate
mastery of…the content they teach, the
elementary teacher is an expert in …math…
• Element C: Teachers responsible for teaching
math
• The Teacher: Focuses math instruction beyond:
• Recall of facts, computational skills and rote
procedures
• Balances conceptual understanding and
procedural fluency
TEACHER STANDARDS, CONT.
• The Teacher establishes an effective
mathematics environment by:
• Challenging students to think deeply…
• Requiring students to explain their solutions
• Posing questions/stimulate students’
curiosity…
• Actively engaging students…
• Using real-world examples for problems…
TEACHER STANDARDS, CONT.
• …and STUDENTS:
• Solve problems in a variety of ways.
• Demonstrate mathematical thinking by
explaining their thinking…
• Recognize when they make procedural errors
and…correct them
• Expand their learning by using mathematical
concepts in other subjects
MY DESIRED OUTCOMES
• That today’s work will:
• challenge your thinking about math instruction
• refine your practices in math instruction
• provide you with new ideas, strategies, and
resources
• enable your students to develop deeper
understanding of the math you teach
REFLECTIVE WRITING
• What are your desired outcomes from today’s
work?
What are your best hopes, worst fears?
• Record them in your ½ Comp Book
WARM UP
Respond in your ½ comp book first, then on the
posters, then using PLICKERS!
• How did you feel about math as a child?
• What is the highest level of mathematics you
studied?
• What do the results tell us?
UNDERSTANDING
• What do we know when…?
• What is deep understanding? In math?
Dewey cautioned that the practice of teaching without
understanding damaged students’ ability to reflect and
to make sense of what they were doing. (1910)
Deep understanding is gained by
REFLECTION and COMMUNICATION!
Taken from, Making Sense: teaching and learning mathematics with understanding
DOING SOME MATH
• A Lesson with Lance
When we memorize rules for moving symbols
around on paper we may be learning something,
but we are not learning mathematics.
Taken from, Making Sense: teaching and learning mathematics with
understanding, (1997, p. 2.)
DOING SOME MORE MATH
• Something to ponder…
• What if you didn’t have any algorithms to use?
• The Inverses: +, - and *, /
• The Operations: 4 corners
• Using the Tools: composing and decomposing
BREAK
Is our instruction enabling the
understanding or inhibiting it?
CRA & DIFFERENTIATION
• Concrete
• Representation
• Accessible Algorithm
• Abstract
• Learning Path
ACCESSIBLE ALGORITHMS
• Expanded Notation or Decomposing Numbers
• Partial Sums
• Partial Differences
• Partial Products
• Partial Quotients
• New Groups Below
• Efficient Procedures and Mental Math
• Traditional (American) Algorithms (ccss)
USING TOOLS AND THE 3 F WORDS
• Number lines
• Number grids
• Hundreds Charts
• Mental Models
• Bar Model
• Dot patterns
POINT TO PONDER
Understanding breeds confidence and
engagement; not understanding leads to
disillusionment and disengagement.
Taken from, Making Sense: teaching and learning mathematics with understanding,
(1997, p. 2.)
LUNCH
When does the math reveal itself,
become obvious?
GAMES AND PRACTICE
• Sticky Note Hundreds Chart Game
• Greater Than, Less Than Game > < =
• Set Game
SET GAME – THE RULES
• Lay cards out face up in rows (9 or 12)
• Take turns; find sets of 3 cards with only one
aspect in common
• Take those sets of 3 cards as your points
• Lay out 3 more cards – refill the cards you took
• Continue until all sets are found
• Most sets found WINS!
SKIP COUNTING
Finding the patterns
All of math is patterns!
FACE THE FACTS
• Fact Families
• Strategies and Fingers
• Fact Grids
• Fact Games
FRACTIONS, DECIMALS, PERCENTS
•
•
•
•
•
1/4 of 1/3
Representations
Common Denominators
Improper Fractions
Clock Circle Math Lesson
• 1/12 of 60
• Fractions, percents, decimals, degrees (45’, 90’, 180’, 270,
360’)
• Which protractor? 180’ or 360’? Why?
BREAK
If I can’t picture it, I can’t understand it.
Einstein
MATHEMATICAL DISCOURSE
I’m starting to understand this. What does it look
like in the classroom?
• Grade 1 and Teacher Interview Sec 2/T3 - F
• Grade 3 and Teacher Interview Sec 2/T4 - F
• Grade 5 and Teacher Interview Sec 1/T1 – S
• Teacher Interview Sec 2/T2
• Classroom Structure White Papers
TABLE BOOKS
• Circle a table (in back of room, 129)
• Sit when the signal is given
• Choose one book of the 3 in front of you
• Read it to yourself
• Summarize it for your table
• Generate/share ideas for use in your classroom
• Take the three books in front of you!
YOUR TURN
• What Else? Did we meet our goals?
• Evaluations:
• 3, 2, 1
• 3 = things you learned (1/2 comp book)
• 2 = things you will use in your classroom (1/2
comp book)
• 1 = Suggestions for next time/Plus Delta (index
card)
• D11 form
• Credit
THANKS FOR COMING!
Students’ understanding is built up gradually,
over time, and through a variety of experiences.
Understanding usually does not appear full-blown
after one experience or after completing one task.
The primary goal of mathematics instruction is the
development of conceptual understanding.
Taken from, Making Sense: teaching and learning mathematics with
understanding, (1997, p. 6)