Different Problem Solving Strategies

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Different Problem Solving Strategies

• Russell Larson
• Elementary Math Coordinator
• Pflugerville ISD
• russell.larson_at_pflugervilleisd.net
• http//www.pflugervilleisd.net/curriculum/math/
• 512-594-0123
• CAMT 2010

Why problem solving is so important for students?
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What Peppermint Patty would say about problem
solving!
We must help students realize that there is
MORE to problem solving than just numbers and
answers!
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Examples of Student Problem Solving without
guidance
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Math Problem Solving
The primary goal of mathematics is to enable
students to develop their ability in
Mathematical Problem Solving.
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Why teach Problem Solving Skills

• Help students deal with problems creatively and
  effectively
• Stimulate students and help develop thinking
  skills and problem solving strategies in both new
  and unfamiliar situations
• Develop, reinforce, enhance, and extend
  mathematical concepts and skills in students
• Help students engage in imaginative and creative
  work arising from mathematical ideas

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What Research Says About Problem Solving
Strategies

• Mathematical problem solving skills are critical
  to successfully function in todays
  technologically advanced society
• Solving word problems requires understanding the
  relationships and outcomes of the problem
• You must make connections between the different
  meanings, interpretations, and relationships to
  mathematical operations
• Van de Walle, 2004

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Explicit Instruction Matters!

• Why teach different problem solving strategies?
• Explicit instruction with students who have
  mathematical difficulties has shown consistent
  positive effects on performance with word
  problems and computation
• Student receive extensive practice in use of
  newly learned strategies and skills
• Students are provided with the opportunity to
  think aloud, talk through decisions, and get
  immediate feedback
• National Math Panel Report 2008

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Chocolate Math

• Pick the number of times a week that you would
  like to have chocolate (more than 1, but less
  than 10)
• Multiply this number by 2
• Add 5
• Multiply by 50
• If you have already had your birthday this year,
  add 1756
• If you have not had your birthday this year, add
  1755
• Subtract the four digit year that you were born
• You should have a 3 digit number now
• The first digit is your original number.
• Why????

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7-9-11

• Walk 7 steps from where you are anddiscuss why
  with your partner why you think the Chocolate
  Math worked.
• Walk 9 steps from where you are anddiscuss
  the reasons your first partner gave.
• Walk 11 steps from where you are
  anddiscuss the combination of reasons

Why is math talk so important?
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What to say instead of I dont
know!

• May I please have some more information?
• May I ask a friend for help?
• May I have some to time to think?
• Where could I find that information?

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Importance on Vocabulary in Problem Solving

• A students math vocabulary level directly
  affects his/her conceptual understanding of
  mathematics, ability to communicate with peers
  about mathematical problems, and performance on
  high stakes tests
• Numbers and Operation
• Algebraic Reasoning
• Geometry
• Measurement
• Probability/Statistics
• NCTM, 1999

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Graphic Organizer for vocabulary development
Vocabulary Word
Student definition after table discussion
Teacher definition after table discussion
Picture
Picture
List Real World examples of vocabulary word
Picture
Picture
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2 x 2 Writing Grids !
Students write a total of 6 sentences from the
grid. 2 words from the row (2 sentences) 2
words from the column (2 sentences) 2 words on
the diagonal (2 sentences)
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3 Components of Mathematical Thinking

• Making meaning from mystery
• Making sense of symbols
• Sorting and classifying unorganized data

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What to do with word problems

• Focus on the Meaning of the problem, not just
  the numbers.
• Identify the numbers that are Important.
• Thinking leads to an Estimate of the answer-
  show reasonableness.
• TALK about all probable/reasonable answers.

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Keywords can lead to misunderstanding

• The association of keywords with the
  mathematical operation is problematic in that
  reliance on these translations cues can lead to
  systematic errors
• Misleading suggests the wrong operation
• Some problems dont have key words
• Sends the wrong message that the word problem
  doesnt have meaning and the structure of the
  problem is ignored
• Example Jose took the 26 baseball cards he no
  longer wanted and gave them to Brian. Now Jose
  has 71 baseball cards left. How many baseball
  cards did Jose begin with?

Typical answer 45 baseball cards. Why? 71 26
45 cards LEFT
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2009 TAKS example
4th GradeRobert and Julia collect stamps.
Robert has 54 stamps in his collection. He has 18
more stamps than Julia does. Which if the
following equations can be used to find s, the
number of stamps Julia has in her
collection? F s 54 18 G s 54
18 H s 54 x 18 J s 54 18
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Solving the Two-step problem issue

• Take a one step problem to ask a question
  about the answer without giving the answer.

It took 3 hours for the Jones family to drive 195
miles to Washington DC.
Tony bought three dozen eggs for 89 cents a
dozen. (How much was the bill?) How much change
did Tony get back from 5?
Now, think about the answer, and give another
question that uses the answer to solve another
part of a question.
If they drove for 7 more hours the next day at
the same rate, how many miles did the Jones
family travel the second day?
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2009 TAKS questions Two Steps
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Two-Step Problem Solving Writing

• With a partner
• Each partner writes a basic word problem
• Exchange
• Write the missing question
• You can begin to create a class set of multi-step
  questions.. Trade with other class

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Why teach Problem Solving strategies?

• We want the students to
• Understand the problem
• Choose a strategy
• Solve it
• Look back

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Different Strategies that will be introduced

• 4 cell matrix
• Detective Problem Solving
• See-Plan-Do-Reflect
• Group Approach to word problems

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Analyze Math Word Problems4 cell matrix approach
Do I know the vocabulary?
What are the skills required?
What prior knowledge do I need?
Are there any distracters?
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Lets Practice!

• Mrs. Evans wrote clues on the board to describe
  a mystery geometric shape. The fourth clue was
  erased. What clue is the most reasonable choice
  as the fourth clue?
• 1. It is a 3 dimensional object.
• 2. It has 6 faces.
• 3. It has rectangular shaped faces.
• a. None of the sides are equal
• b. It has 12 edges
• c. It has 5 vertices.
• d. It has 1 curved surface.

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Problem Solving Detectives Approach

• Read, Explain, Reflective Reasoning
• 2 3 students in a group
• Witness, Detective, and By Stander
• Witness Sees everything
• Detective Solves the crime
• By Stander Observes all

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Lets Practice!

• Get in groups of 3
• One will be the witness, one will be the
  detective, one the by-stander (silent partner)
• Each person gets the correct card for their part
• Listen for directions
• Witness and By-Stander will be the only ones to
  read the next slide.

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Witness Read this information and be ready to
answer questions from the detective.

• Maria and her family drove 1,236 miles on
  vacation. Monica and her family drove 376 miles
  on their vacation. What was the total number of
  miles both families spent driving on their
  vacations?

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Detective Ask all the questions you need. Write
down the responses from the Witness. By-stander
can take it all in.

• Research says you have to read the problem
  multiple times in order to get all the details
  and information.
• Allow the witness to review the problem several
  times, and the detective needs to write down the
  facts they learn.

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Sentence Stems to debrief/review

• Complete this sentence
• I think the Detective strategy was _________
  because it will allow _______________.

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SEE PLAN DO - REFLECT
PLAN Reflect on the
problem Select an appropriate strategy simplify,
draw, patterns, guess/check modeling, act,
organize, work backward
REFLECT Reread the problem for
reasonable solution Check your solution Justify
your solution Explain your process
SEE Read the problem
carefully Identify the unknown Draw pictures or
diagrams Consider relationship of the
problem Restate the problem in kid words
DO Implement a strategy Solve
the problem Check each step Answer the question
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SEE PLAN DO - REFLECT
PLAN
SEE
DO
REFLECT
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Group Approach to word problems

• Different steps to understand word problems
• Everyone in the group reads the problem
• Everyone in the group must share a fact about the
  problem
• Everyone in the group must ask a question about
  the problem
• Work as a group to solve the problem together

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Lets try it out together!
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Balanced Classroom with Problem Solving
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Why Different Problem Solving Strategies

• Make it Happen
• Make it Work
• Have the students explore MANY options!