Number Talks: Strengthen Students’ Mathematical Reasoning Sara Baranauskas K-6 Math Coordinator...
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Number Talks: Strengthen Students’ Mathematical Reasoning Sara Baranauskas K-6 Math Coordinator Regional School District #6 Robin Moore K-6 Math Specialist James Morris School, RSD#6
Number Talks: Strengthen Students’ Mathematical Reasoning Sara Baranauskas K-6 Math Coordinator Regional School District #6 Robin Moore K-6 Math Specialist
Number Talks: Strengthen Students Mathematical Reasoning Sara
Baranauskas K-6 Math Coordinator Regional School District #6 Robin
Moore K-6 Math Specialist James Morris School, RSD#6
Slide 2
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: @[email protected] 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
[email protected]
Slide 3
Todays 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.
Slide 4
Slide 5
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
Slide 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?
Slide 7
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.
Slide 8
Key Components of a Number Talk Classroom environment and
community Classroom discussions The teachers role (facilitating vs.
teaching) Purposeful computation problems The role of mental
math
Slide 9
Classroom Environment and Community Setting up takes time and
MUST be initiated from day 1. Explicit modeling and reinforcement
Set Norms a common goal for learning and understanding for all
Safe, risk free environment. Students know that their trust in you
and their classmates is well founded. Increases self confidence
Risks often come with learning and learning ALWAYS comes with
risks. Predictable routines allow students to feel confident and
capable. Effective learning environment will maximize the
engagement of learners.
Slide 10
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.
Slide 11
Classroom Discussions contd 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
Slide 12
The Teachers Role Teacher as facilitator, questioner, listener
and learner NOT teller and explainer. Crafts purposeful problems.
Supports discourse to deepen mathematical understanding and
knowledge and keeps discussion focused on the important
mathematics. Assists students to learn how to structure their
comments and wonderings in a meaningful and natural manner. Asks
open ended questions from What answer did you get to How did you
get your answer? and Why did you choose your strategy?
Slide 13
Purposeful Problems Teachers choose and develop just right
mathematical problems and concepts based on student need and
objectives. Certain types of problems elicit certain strategies.
Random problems do not lend themselves to a common strategy. It
doesnt initiate a common purpose for a Number Talk discussion. Can
be differentiated for all students and used for small group
settings.
Slide 14
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.
Slide 15
The Role of Mental Math contd 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.
Our Number Talk What mathematical ideas did we share? How do
these strategies encourage mathematical reasoning (number sense and
the use of number relationships)?
Slide 18
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 teachers role (facilitating
vs. teaching) - The role of mental math - Purposeful computation
problems (Think-Pair-Share)
Slide 19
Lets 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
Slide 20
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.
Slide 21
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)
Slide 22
Teacher Questions to Foster MP 1 How would you describe the
problem in your own words? How would you describe what you are
trying to find? What do you notice about...? What information is
given in the problem? Describe the relationship between the
quantities. Describe what you have already tried. What might you
change? to this point. What steps in the process are you most
confident about? What are some other strategies you might try? How
might you use one of the previous problems to help you begin? How
else might you organize...represent... show...?
Slide 23
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)
Slide 24
Teacher Questions to Foster MP 2 What do the numbers used in
the problem represent? What is the relationship of the quantities?
How is _______ related to ________? What is the relationship
between ______and ______? What does_______mean to you? (e.g.
symbol, quantity, diagram) What properties might we use to find a
solution? How did you decide in this task that you needed to
use...? Could we have used another operation or property to solve
this task? Why or why not?
Slide 25
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 )
Slide 26
Teacher Questions to Foster MP 3 What mathematical evidence
would support your solution? How can we be sure that...? / How
could you prove that...? Will it still work if...? What were you
considering when...? How did you decide to try that strategy? How
did you test whether your approach worked? How did you decide what
the problem was asking you to find? (What was unknown?) Did you try
another solution that didnt work? Would it ever work? Why or why
not? What is the same and what is different about...? How could you
demonstrate a counter-example?
Slide 27
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)
Slide 28
Teacher Questions to Foster MP 6 How did you know your solution
was reasonable? Explain how you might show that you solution
answers the problem. What would be a more/the most efficient
strategy? How are you showing the meaning of the quantities? What
symbols or mathematical notations are important in this problem?
What mathematical language...,definitions..., properties can you
use to explain...? How could you test your solution to see if it
answers the problem?
Slide 29
Example of Number Talk Progression Kindergarten-
Subitizing/Partitioning Dot Images K.CC.B.5, K.OA.A.3
Slide 30
Number Talk Progression Kindergarten- Building to Ten using Ten
Frames K.CC.B.5
Slide 31
Number Talk Progression contd Grade 1- Making Friendly Numbers
using Double Ten Frames 1.OA.B.4, 1.OA.C.5 1.OA.C.6
Slide 32
Number Talk Progression contd Grade 1- Friendly Number Number
Strings 2 + 5 + 8 1.OA.A.2, 1.OA.B.4 1.OA.C.6
Number Talk Progression contd Grade 3 - Making Friendly Numbers
126 + 38 899 + 25 3.NBT.A.2
Slide 35
Number Talk Progression contd Grade 4 - Making Friendly Numbers
4 x 49 16 x 25 4.NBT.B.5
Slide 36
Number Talk Progression contd Grade 5 - Making Friendly Numbers
840 25 756 24 5.NBT.B.6
Slide 37
Focus Questions How can Number Talks develop students
mathematical reasoning? How do Number Talks align to the Common
Core Mathematical Practices and Content Standards?
Slide 38
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.
Slide 39
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
Slide 40
Digital Resources Apps Subitize Tree, $.99 Quick Images, $.99
Counting Together, $1.99 Websites Math Coachs Corner
http://mathcoachscorner.blogspot.com/http://mathcoachscorner.blogspot.com/
Stanford Online - How Children Learn Mathematics, Spring
2014http://online.stanford.edu/http://online.stanford.edu/
Slide 41
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.
