Problem Solving

What’s the problem?

“If it can be solved using a procedure or an

algorithm, it is not a problem. It’s an

exercise.”What is a problem at one time to one child, may be an exercise to another.Ex. Sharing cookies to a student in grade 1 could be a problem but to a child in grade 4…it’s very likely an exercise.

Why teach through problem solving?

• The math makes more sense.• Provides the teacher with more

understanding of the student’s mathematical thinking.

• A challenge can be very motivating• Problem Solving builds perseverance

• Builds confidence, maximises the potential for understanding, allows for differences in learning styles and approaches

• Practice with concepts and skills• Provides students with a stronger

understanding of what math is about• Students needs to practise problem

solving

Before• I took a handful of M&Ms. 1/3 of them

were red. Draw the handful.

During• You have ¾ of the pizza left. If you give

1/3 of the left over pizza to your brother. How much of the whole pizza will your brother get?

After• Pay attention to how you solved the

problem & share your ideas.

• To teach through problem solving, the teacher provides a context or a reason for the learning by beginning the lesson with a problem to be solved and later drawing out any necessary procedures. This approach contrasts with the more traditional approach of presenting a new procedure and only then offering a few problems for students to solve.

(P.38 Making Math Meaningful, Marian Small)

What is it?

Things have changed….

NowStep 1: Begin the

lesson with a problem

Step 2: Draw out the procedures used

ThenStep 1: Teach the

procedure

Step 2: Provide problems that use that procedure

•Think about the questions you just worked through.

•What do you think that lesson would have looked like “then”?

A Good Problem:

• is a question that cannot be answered immediately

• is challenging to the learner• holds the learners interest• might have several answers• might have 1 answer but many

different approaches• is often connected to real life

Before(Getting Ready)-20 minutes

Get students mentally ready to work on the task,Be sure all expectations for products are clear;

During(Students Work) – 20 minutes

Let go! Listen carefully,Provide hints,

Observe and assess;

After(Class Discourse) – 20 minutes

Accept student solutions without evaluation,Conduct discussion as students justify and evaluate results and

methods (reflection).

(Adapted from Elementary and MiddleSchool Mathematics:Teaching Developmentally   4th Ed., John Van de Walle)

3-part Lesson

I picked up a handful of M&Ms. One third of them where red. What might the drawing of the M&Ms look like?

Page 27, #4

During

#5

A Problem Solving teacher:

• Encourages risk taking• Provides enough time to students• Respects and encourages respect for

each others thinking• Provides opportunity for discussion

and challenge solutions• Values perseverance

How to teach problem solving?• Begin with the problem• Teach students the Three Read Strategy• Allow students to work on the problem• Draw out the different strategies used

Three-read strategy 1st Read →Visualise → set the context → get a general impression

2nd Read → listen for details → gather the facts → determine what question is being asked

3rd Read →Check the facts → check the understanding of the question

Solve!

Three-read strategy 1st Read →Visualise the context (ask students general questions)

2nd Read

→ gather the facts and decide what you’re being asked to find

---

3rd Read →verify your facts, clarify what you have to find.

Solve!

Problem Solving with Grade 5s

Making Math Meaningful Marian Small

Making Math Meaningful Marian Small

FERMI Questions• http://mathforum.org/workshops/sum96/int

erdisc/fermicollect.html

• Ex. How many piano tuners are there in Toronto?

• People crowd into London until all available open space within the city limits is covered with standing people. How many people would there be?

• How many hairs are there on a human head?

Some problem solving resources

• http://www.mystfx.ca/special/mathproblems/• http://mathcontest.olemiss.edu/currentproblems.php

• http://people.stfx.ca/lborden/

• Making Math Meaningful Marian Small

• Roads to Reasoning

• Puddle Questions

• NCTM website

• Math Makes Sense texts

Taken from Puddle Questions Grade 3

Joan Westley