How to Teach Your Child to Solve Problemsrightstartmath.com/wp-content/...to-Solve-Problems... · Helping Young Children Solve Problems • Ask young child to decide between two options.!

© Joan A. Cotter, Ph.D., 2015

How to Teach Your Child to Solve Problems!

Sioux Empire Christian Home Educators Homeschool Conference

Sioux Falls, SD Saturday, May 2, 2015 3:00 p.m.– 4:00 p.m.

Joan A. Cotter, [email protected]!


Math Education is Changing •  Mathematics is doubling every 7 years.

•  Math is used in many new ways. We need analytical thinkers and problem solvers.

•  Brain research is providing clues on how to better facilitate learning, including math.

•  Increased emphasis on mathematical reasoning, less on rules and procedures.

•  Educators and parents are learning that rote memorizing is not effective.


What is a Problem? Dictionary says:

“a matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome”

Oops! That’s not what we’re looking for!


Math Problems •  Computation drills are actually exercises. •  A true math problem: solution is not obvious. •  Two types of math problems:

1.  Story problems and 2.  Other problems involving math.


Problem Solving

•  is NOT rote memorizing.

•  is NOT following rules blindly.

•  is NOT passive learning.

•  is the major reason we study math.


Problem Solving Problem solving is not about:

•  trying to remember a similar problem •  or looking for key words, •  but thinking carefully about the situation, •  discovering what is given, •  figuring out what is needed, •  and deciding on methods to get there.


Chinese Checkerboard

How many dots are there?



Twelve 10s plus 1 in the middle gives 121.



Six 6s plus 21 fours plus lone 1 gives 121.



Nine 9s plus four 10s gives 121.



(13 × 14)/2 plus three 10s gives 121.


Some Barriers to Solving Problems

•  Trying to remember what rule to apply.

•  A superficial understanding of math in general.

•  Difficulty in reading.

•  Thinking you’re not good in math.

•  A fear of failure (math anxiety).

•  Expecting instant success without hard work.


Helping Young Children Solve Problems

•  Ask young child to decide between two options. Do you want to wear blue socks or red ones? Which book shall we read for bedtime tonight?

•  Jigsaw puzzles are good for learning persistence. •  Encourage by praising effort. •  Speak positively about problems you have solved. •  Ask child to explain how they solved the problem. •  Encourage children to make up their own problems.


Problem Solving in Japan

•  Japanese teachers discuss one problem in depth rather than four problems superficially.

•  They encourage multiple solutions. It is a check on correctness.

•  Wrong solutions are discussed.

•  The students do not look for “key” words.


Braid Model of Problem Solving

•  Understanding the problem/Reading the story

•  Planning how to solve the problem

•  Carrying out the plan/Solving the problem

•  Looking back/Checking


Some Solving Problems Strategies •  Read the problem at least twice. •  Draw a sketch. •  List what is known and unknown. •  Use smaller numbers. •  Estimate before calculating. •  In algebra try numbers in place of variables. •  Expect some frustration. •  Take a break and come back.


After Solving a Problem •  Did you answer the question?

•  Does the answer make sense?

•  Is the answer properly rounded and labeled?

•  Explain your work. (Not show computations.)

•  How else could the problem be solved?

•  Which method is most efficient?

•  Think how this problem leads to other problems.


Part-Whole Circles

Whole

Part Part


Part-Whole Circles

What is the whole?

3 2


Part-Whole Circles Missing addend problem

Lee received 3 goldfish as a gift. Now Lee has 5. How many goldfish did Lee have to start with?




Is 3 the whole or a part?

3




5

3

Is 5 the whole or a part?




2

5

3

What is the missing part?




2

5

3

Write the equation. 2 + 3 = 5 3 + 2 = 5 5 – 3 = 2


Part-Whole Circles

•  Research shows part-whole circles help young children solve problems. Writing equations do not.

•  Do not teach “key” words.


Part-Whole Circles Compare problems

larger set

smaller set

difference



Alex has 4 apples. Morgan has 7 apples. How many more apples does Morgan have?

Is 4 the larger, smaller, or the difference?

4




7

4

Is 7 the larger, smaller, or the difference?




What is the difference?

3

7

4


Rows and Columns

Good games can provide a chance for children to think of alternatives and make decisions to improve their chance of winning.


Rows and Columns Objective: To give the players practice in adding up to 15. Object of the Game: To collect the most cards in

rows or columns that add up to 15.


Rows and Columns 8 7 1 9

6 4 3 3

2 2 5 6

6 3 8 8


Rows and Columns 1 9

6 4 3 3

6 3 8 8


Rows and Columns 7 6 1 9

6 4 3 3

2 1 5 1

6 3 8 8


Rows and Columns 1

6 4 3 3

1 5 1

3 8 8


Math Balance

10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10


Math Balance

10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

7 = 7"


Math Balance

10 = 2 + 8"

10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10


Math Balance

10 9 8 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

8 + 6 = 14"

7


Equation Puzzles

1 2 3 4

Write equations using mathematical symbols, such as +, –, =, ×, ÷. (The order of the digits cannot change.)


Equation Puzzles

1 2 3 4 =" ×"



1 2 3 4

Equation Puzzles

–"+"=



1 2 3 4

Equation Puzzles

–"= –"



1 2 3 4

Equation Puzzles

= ÷"



Remainder Problems

Problem 1. Thirteen children are going on a

field trip. If 4 children can ride in a car, how many cars are needed?

[4 cars]


Remainder Problems

Problem 2. Pauline has 13 petunias to plant. She

wants exactly 4 in a row. How many rows can she plant?

[3 rows]


Remainder Problems

Problem 3. Four children have $13 to split

evenly. How much does each one receive?

[$3.25]


Remainder Problems

Problem 4. Four children divide 13 candy bars.

How much does each one receive?

[3 bars] 1 4


Remainder Problems

Problem 5. Jack packages 13 cookies with 4 per

bag and eats the leftovers. How many does he eat?

[1 cookie]


Remainder Problems

Five division problems with the same numbers, but different answers.

[4 cars] [3 rows] [$3.25]

[3 bars] [1 cookie]

1 4


Some Problems 1.  Chris and Pat have 100 cubes together. Chris

has 6 more than Pat. How many does Chris have?

2.  Use four 4s to equal 1, 2, . . . , or 10.

44 44 = 1 4 4

4 4 + = 2


A Geometry Problem

What is the area?


A Geometry Problem

What is the area?

w1

w2

h


A Geometry Problem

What is the area?

w1

w2

h

w1


A Geometry Problem

What is the area?

w1

w2

h


A Geometry Problem

What is the area?

w1

w2 – w1

h


Tens Fractal

How many little black triangles do you see?


Good Mathematical Practices 1.  Make sense of problems and persevere in

solving them. 2.  Reason abstractly and quantitatively. 3.  Construct viable arguments and critique the

reasoning of others. 4.  Model with mathematics. 5.  Use appropriate tools strategically. 6.  Attend to precision. 7.  Look for and make use of structure.


How to Teach Your Child to Solve Problems!

Sioux Empire Christian Home Educators Homeschool Conference

Sioux Falls, SD Saturday, May 2, 2015 3:00 p.m.– 4:00 p.m.

Joan A. Cotter, [email protected]!

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How to Teach Your Child to Solve Problemsrightstartmath.com/wp-content/...to-Solve-Problems... · Helping Young Children Solve Problems • Ask young child to decide between two options.!