Greenwood Primary School€¦ · • compare it to the thinking process in STAR approach ... thinking process in problem solving 4 Steps towards problem-solving: Step 1: Study the

“STAR”

Approach for

Mathematics

Problem Solving

Greenwood Primary

School

Tuning-in (Activity 1)

Work out the following problem:

Some motorcycles and cars are

parked at a car park. Tom

makes a count to find a total of

20 vehicles and 52 wheels. How

many cars are there?

Greenwood Primary School

What questions or thoughts

came to your mind while you

were working out the solution?

Jot them down.


Objective By the end of the sharing, participants should be

able to

• identify the four steps in the STAR approach.

• recognise the benefits of focusing on steps 1

and 2 in the STAR approach.

• apply the STAR approach to engage their child

in the thinking processes to ‘Study the problem’

and to ‘Think of a plan’ in mathematical

problem solving.







Action Research (AR)

Study the Effectiveness of

Step 1 (Study the problem)

and 2 (Think of a plan) in the

STAR approach towards

Mathematical Problem-

Solving


Background of the AR

Adopted Polya's four-phase approach

towards problem-solving

Pupils are overly enthusiastic in working

out the solution

Pupils' lack of thinking processes in

understanding and formulating a plan

to solve problem may be the root

cause of this issue


Timeline


Assessment

Pre- and Post-test on pupils’ ability

to

1) study the problem

2) think of a plan

Analytical rubric


Pre-/Post-test Sample


Analytical Rubric STEP 1:

Study the

Problem

Are pupils able to:

• rewrite the problem in their own words?

• identify all the important information given in the

problem?

• state the information they are required to find?

Step 2:

Think of a

Plan

Are pupils able to:

• Indicate the connection(s) between the information given in the problem and the

unknown?

• indicate the key concept(s) in the problem?

• state the strategy used to solve the problem?


Pre-test of Student A

Sample of

Pupils’ Work


Sample of

Pupils’ Work

Post-test of Student A










Sample of

Pupils’ Work

Pre-test of Student B


Sample of

Pupils’ Work

Post-test of Student B










Results: Combined


Results: High Progress


Results: Middle/Low Progress


Results Experimental group showed a 29.75%

improvement from Pre- to Post-test.

Results indicate that the explicit teaching on

Step 1 and 2 in the STAR approach towards

problem solving does improve pupils’ understanding of the problem and the ability

to formulate a plan.

Treatment was equally effective for both HP (30%) and MP-LP (28.9%) groups.


Question 1 Some motorcycles and cars are

parked at a car park. Tom makes

a count to find a total of 20

vehicles and 52 wheels. How

many cars are there?


Question 1 Step 1: Study the Problem

a) Can I find the important information given?

I can underline or highlight the key information.

b) Can I repeat the problem in my own words?

Can I relate the given information with each other?

I can rewrite the key information in relation to each

other.

c) What is the missing information? What do I need to

find?

I need to identify what the problem wants me to find.


Question 1 Step 1: Study the Problem

a) Can I find the important information given?

I highlight the following “Some motorcycles

and cars, total of 20 vehicles and 52

wheels, how many cars are there?”

b) Can I repeat the problem in my own

words? Can I relate the given information

with each other?

There are 20 motorcycles and cars

altogether.

There are a total of 52 wheels.


Step 1: Study the Problem

c) What is the missing information?

What do I need to find?

I need to find the number of cars and

the number of motorcycles that are

missing.

I need to find the number of cars.

Question 1


Step 2: Think of a plan

a) Do I have all the information to solve

the problems?

I know that there are cars and

motorcycles in the car park.

There are 20 vehicles altogether.

The total number of wheels is 52.

A car has 4 wheels and a motorcycle

has 2 wheels.

Question 1


Question 1 Step 2: Think of a plan

b) What are the possible headings for the

guess and check table?

I need to draw a table with 6 columns.

The first column is the number of cars.

The second column is the total number of wheels of cars.

The third column is the number of motorcycles.

The fourth column is the total number of wheels of motorcycles.

The fifth column is the sum of all the wheels.

The sixth column is to check if the sum of wheels matches 52.


Question 1 Step 2: Think of a plan

c) What are the strategies I can use to solve

this question?

I make logical guesses on the number of

cars and motorcycles (making up 20) and

check if the sum of their wheels matches the

total number of wheels (52 wheels) in the car

park.

I keep guessing and checking until I get the

correct answer.


Reflection (Think-Pair-Share)

• refer to your thoughts or questions

from Activity 1

• compare it to the thinking process in

STAR approach

• share with your partner!


Hands-on (Activity 2)

In a car park, there are a total of

14 cars and motorcycles.

Altogether, 44 wheels are

counted. How many cars and

how many motorcycles are there

in the car park?


Quick Check


Let’s look through the

solution for Activity 2.






How Can You Adapt these

Ideas for Your Child? Let’s take a few minutes to do Think-

Pair-Share with your partner!


Consolidation STAR approach focuses on improving the

thinking process in problem solving

4 Steps towards problem-solving:

Step 1: Study the Problem

Step 2: Think of a Plan

Step 3: Act on the Plan

Step 4: Reflect on the Solution

Applicable across different heuristics and

discipline as the emphasis is on the

metacognition (thinking about thinking)


Clarifications for Participants The emphasis of STAR approach is on

meta-cognition (thinking about thinking).

So, pupils can represent their thinking

process in diagrams or phrases.

STAR approach provides a structured

development to pupils’ thinking process.

As pupils internalize and become more

independent in problem-solving, studying the problem and thinking of a plan

become their way of thinking.


Reference

Polya, G. (1973). How to Solve It: A New

Aspect of Mathematical Model. (3nd ed.).

Princeton, N.J.: Princeton University Press.


Documents

Greenwood Primary School€¦ · • compare it to the thinking process in STAR approach ... thinking process in problem solving 4 Steps towards problem-solving: Step 1: Study the