making the case for how the numbers work things to think about: as educators we should be judged...

MAKING THE CASE FORHOW 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 FORHOW 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 byREFLECTION 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 DISCOURSEI’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)