Transcript Title subtitle - Twitter Math Camp

Number Talks
in Middle & High School Classes?
A discussion
Chris Harris
@CharrisMath [email protected]
TOSA Escondido Union School District California
a K-8 school District
Me
You
“The way I teach math ≠ the way I was taught
math.”
Avery Pickford @woutgeo
Why?
CCSSM
Mathematical Practice
Standards
CCSSM
Fluencies
1. Make sense of problems and
persevere in solving them.
K
2. Reason abstractly & quantitatively.
2Add/subtract within 20
1Add/subtract within 10
3. Construct viable arguments &
critique the reasoning of others.
4. Model with mathematics.
Add/subtract within 100 (pencil & paper)
3Multiply/divide within 100
Add/subtract within 1000
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for & make use of structure.
8. Look for & express regularity in
repeated reasoning.
Fluent in the Standards means “fast and accurate.” It
might also help to think of fluency as meaning the same
thing as when we say that somebody is fluent in a foreign
language: when you’re fluent, you flow. Fluent isn’t halting,
stumbling, or reversing oneself. Assessing fluency
requires attending to issues of time (and even perhaps
rhythm, which could be achieved with technology).
Add/subtract within 5
4Add/subtract within 1,000,000
5Multi-digit multiplication
6Multi-digit division
Multi-digit decimal operations
7
Solve px + q = r, p(x + q) = r
8 Solve simple 2X2 systems by inspection
Why?
CCSSM
Mathematical Practice
Standards
CCSSM
Fluencies
1. Make sense of problems and
persevere in solving them.
K
2. Reason abstractly & quantitatively.
2Add/subtract within 20
1Add/subtract within 10
3. Construct viable arguments &
critique the reasoning of others.
4. Model with mathematics.
Add/subtract within 100 (pencil & paper)
3Multiply/divide within 100
Add/subtract within 1000
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for & make use of structure.
8. Look for & express regularity in
repeated reasoning.
Add/subtract within 5
4Add/subtract within 1,000,000
5Multi-digit multiplication
6Multi-digit division
Multi-digit decimal operations
7
Solve px + q = r, p(x + q) = r
8 Solve simple 2X2 systems by inspection
When?
Whenever
10-15 minutes whenever you have time. Could be a
warm up.
Doesn’t have to be what you’re teaching at the moment.
Review/reinforce past skills.
Who?
Everyone!!
- language learners
- SPED
- advanced learners
- intervention students
- shy students
- ‘not so’ shy students!
Where?
Anywhere!
All you need is some chart paper, markers and
students!!
Why Number Talks in Elementary
Classes?
How?
This is the book & method
most commonly used in
elementary school
“Simply defined, number talks are five- to fifteen-minute
classroom conversations around purposefully crafted
computation problems that are solved mentally.”
Sherry Parrish, Teaching Children Mathematics October 2011
This is the book for grades 4 10
“Making Number Talks Matter is about helping students take
back the authority of their own reasoning through a short
fifteen minute daily routine called Number Talks, in which they
reason mentally with numbers.”
Teach students hand signals
Get rid of pencils & paper
Present problem
Accept all answers, non-judgmentally
Have students justify their answers
Make a written record
(Don’t forget to stop!!)
BUT let’s look at dot cards
Why Dot Cards?
•
•
•
•
numbers represent quantities
you can use dots flexibly (& numbers too)
students can be successful
almost always guarantees several correct
answers
• useful introduction to Number Talks
For the teacher












wait time
gently probe their thinking (whether it is right or wrong)
look for multiple strategies
listen – don’t explain a student’s words
continue to do Number Talks – it gets better!!
expect precision of language
record the thinking – in a correct mathematical fashion
get students to talk to each other
multiple answers are great!
students should ‘present’ their answers
sometimes you can share your way of thinking
nudge students beyond the algorithm
Let’s give it a try