Transcript Number Talks: Strengthen Students’ Mathematical Reasoning

Number Talks:
Strengthen Students’
Mathematical Reasoning
Robin Moore
K-6 Math Specialist
James Morris School, RSD#6
Sara Baranauskas
K-6 Math Coordinator
Regional School District #6
About Us….
Robin Moore
K-6 Math Specialist, James Morris School
12 years Grades 1 and 5,
2 years Math Specialist
Email: [email protected]
twitter: @rmoore628
Sara Baranauskas
K-6 Math Coordinator, Regional School District No. 6
15 years Grades 5 and 6,
3 years Math Coordinator
Email: [email protected]
twitter: @sarabara13
Today’s Purpose
To provide teachers with an instructional
strategy that is grounded in developing
students’ mathematical reasoning and
conceptual understandings rather than
just teaching rules and procedures
without understanding of numerical
relationships.
What is Mathematical Reasoning?
As one of the five Process Standards (NCTM 2000), reasoning (and proof ) is
an essential part of acquiring and using mathematics. More than a means by
which to confirm whether a solution is correct, mathematical reasoning
involves exploring the mathematics at hand; generating, implementing, and
evaluating conjectures; as well as justifying our thinking and actions as we
engage in mathematics.
Simply put, mathematical reasoning is about making sense of the
mathematics in our world as well as making mathematical sense of
our world.
Nurturing Mathematical Reasoning, Jennifer Thom, Teaching Children Mathematics, Nov 2011
Focus Questions
•
•
How can Number Talks develop students’
mathematical reasoning?
How do Number Talks align to the
Common Core Mathematical Practices
and Content Standards?
What is a Number Talk?
A number talk is a quick (10 min) classroom routine used
to develop computational fluency that promotes students
to:
• Clarify thinking.
• Investigate and apply mathematical relationships.
• Build a repertoire of efficient computational strategies.
• Make decisions about choosing efficient strategies for specific problems.
• Consider and test other strategies to see if they are mathematically logical.
• Build connections between key conceptual ideas.
Key Components of a Number Talk
• Classroom environment and community
• Classroom discussions
• The teacher’s role (facilitating vs. teaching)
• Purposeful computation problems
• The role of mental math
Classroom Discussions
 Problem is posted for all students to solve mentally.
 Wait time is critical!
 Multiple strategies are encouraged.
 Discrete signals to indicate solution and strategies.
 Students share, discuss, justify and critique strategies and solutions.
 Mistakes are an opportunity for learning- wrong answers are used as
springboards to address misconceptions.
Classroom Discussions cont’d
Benefits of sharing and discussing computation strategies
Students have the opportunity to:
 Clarify their own thinking.
 Consider and test other strategies to see if they are mathematically logical.
 Investigation and apply mathematical relationships (connections)
 Build a toolkit of flexible and efficient strategies.
 Make decisions about choosing efficient strategies for specific computation
problems.
Number Talks: Helping Children Build Mental Math and Computation Strategies, Sherry Parrish, 2010
The Role of Mental Math
The KEY COMPONENT of any Number Talk
 Focus on number relationships and use these relationships to develop
flexible, efficient strategies to develop accuracy (fluency!)
 Mental math allows students to rely on what they know and understand
about number and how they are inter-related.
 Leads to efficiency with numbers to avoid holding numerous quantities in
their heads.
The Role of Mental Math cont’d
 Strengthens understanding of place value, rather than the
discrete quantity of digits.
 Numbers initially written horizontally – encourages place
value understanding.
 Both formats should be used once students are comfortable
with flexible strategies.
Let’s Try It!!
59 + 13
Thumbs up indicates solution.
Fingers extended signify strategy.
Our Number Talk
What mathematical ideas did we share?
How do these strategies encourage
mathematical reasoning (number sense and
the use of number relationships)?
A Third Grade Number Talk
Watch the number talk.
Refer back to the Key Components. What do you notice?
- Classroom environment and community
- Classroom discussions
- The teacher’s role (facilitating vs. teaching)
- The role of mental math
- Purposeful computation problems
(Think-Pair-Share)
Let’s apply mathematical reasoning
1. These students share several addition strategies
 Adding up in chunks
 Decomposing by place value
 Making landmark or friendly numbers.
How are these strategies similar and different?
2.
How could you help students connect among strategies they
share?
Taken from Number Talks, Parrish
The Content Standards
Computational Fluency Number Talks are within the
domains of

Operations and Algebraic Thinking

Numbers and Operations in Base Ten

Numbers and Operations – Fractions
But Number Talks can also be within any domain of the
Common Core content standards.
What about the Practice Standards?
MATHEMATICAL PRACTICE 1
Make sense of problems and persevere in solving them
Mathematically proficient students
 explain to themselves the meaning of a problem and look for ways to solve it.
 apply a solution pathway rather than jumping right into a solution attempt.
 listen to the strategies of others and apply other approaches.
Common Core Standards Initiative (2010)
MATHEMATICAL PRACTICE 2
REASON ABSTRACTLY AND QUANTITATIVELY
Mathematically proficient students

make sense of quantities and their relationships to each other.
 connect quantity to written symbols.
 attend to meaning of quantity, not just how to compute them.
 know and flexibly compute using different properties of
operations and strategies.
CCSI (2010)
MATHEMATICAL PRACTICE 3
CONSTRUCT VIABLE ARGUMENTS AND
CRITIQUE THE REASONING OF OTHERS
Mathematically proficient students
 communicate clearly and articulate their ideas to others, their
thinking becomes visible and their understanding deepens.
 follow the thinking of others and communicate why they agree or
disagree their understanding often solidifies and strengthens.
Math Sense: The Look, Feel and Sound of Effective Instruction, Moynihan (2012)
CCSI (2010)
More Standards….
Mathematical Practice 6
Attend to precision
Mathematically proficient students
 communicate to each other with precision.
 attempt to use clear definitions and discussion with others and within their own reasoning
–their language is precise, their reasoning can be followed, their words and symbols are
clear.
 Calculate accurately and efficiently.
Math Sense: The Look, Feel and Sound of Effective Instruction, Moynihan (2012)
CCSI (2010)
Example of Number Talk Progression
Kindergarten- Subitizing/Partitioning Dot Images
K.CC.B.5, K.OA.A.3
Number Talk Progression
Kindergarten- Building to Ten using Ten Frames
K.CC.B.5
Number Talk Progression cont’d…
Grade 1- Making Friendly Numbers using Double Ten Frames
1.OA.B.4, 1.OA.C.5
1.OA.C.6
Number Talk Progression cont’d…
Grade 1- Friendly Number Number Strings
2+5+8
1.OA.A.2, 1.OA.B.4
1.OA.C.6
Number Talk Progression cont’d…
Grade 2- Making Friendly Numbers
9 + 14
13 + 8 + 7
49 + 27
2.OA.B.2, 2.NBT.B.5
2.NBT.B.9
Number Talk Progression cont’d…
Grade 3 - Making Friendly Numbers
126 + 38
899 + 25
3.NBT.A.2
Number Talk Progression cont’d…
Grade 4 - Making Friendly Numbers
4 x 49
16 x 25
4.NBT.B.5
Number Talk Progression cont’d…
Grade 5 - Making Friendly Numbers
840  25
756  24
5.NBT.B.6
Focus Questions
•
•
How can Number Talks develop students’
mathematical reasoning?
How do Number Talks align to the
Common Core Mathematical Practices
and Content Standards?
Resources
The Common Core State Standards Initiative (2010)
Moynihan, Christine (2012). Math Sense: The Look, Sound and Feel
of Effective Instruction. Stenhouse.
http://www.stenhouse.com/shop/pc/viewprd.asp?idProduct=9655
Parrish, Sherry (2010). Number Talks: Helping Children Build Mental
Math and Computation Strategies K-5. Math Solutions.
http://store.mathsolutions.com/product-info.php?Number-Talks-pid270.html
Thom, J (November 2011). Nurturing Mathematical Reasoning: do
students physical actions and interactions precede sophisticated
reasoning? Teaching Children Mathematics, 234-243.
Free Number Talks Resources
 Article - Number Talks Build Numerical Reasoning: strengthen
accuracy, efficiency and flexiblility….
http://www.mathsolutions.com/documents/NumberTalks_SParrish.pdf
 Teaching Channel videos
https://www.teachingchannel.org/videos/third-grade-mental-math
https://www.teachingchannel.org/videos/third-grade-math-solutions
 Math Perspectives
http://www.mathperspectives.com/num_talks.html
 Insidemathematics.com - Number Talks
http://insidemathematics.org/index.php/number-talks
 Implementing Number Talks Helpful Hints
http://www.mathperspectives.com/pdf_docs/num_talks.pdf
Digital Resources
Apps
Subitize Tree, $.99
Quick Images, $.99
Counting Together, $1.99
Websites
Math Coach’s Corner http://mathcoachscorner.blogspot.com/
Stanford Online - “How Children Learn Mathematics”, Spring
2014http://online.stanford.edu/
Free Formative Assessment Tools
• Show Me – records voice and actions; saves to website
for easy linking to websites, digital portfolios, etc
• Educreations & Screen Chomp
interactive whiteboard apps that records voice and
actions
• Three-Ring– take pictures, videos of students, write
notes, add to students’ folders.