Fatimah ALsaleh

MSTE 502

Overview: o Purposeo Methodologyo Interview Questionso Resultso Questionso Strengths & Limitationso Implications

Purpose

� Students’ conceptual understanding within:

� Addition and Subtraction; Multiplication and Division; Proportion and Ratio

� Basic facts: Addition, Subtraction, Multiplication and Division

� The kind of strategies and the nature of any Misconceptions

� The preferred ways to solve mathematical problems:

� Mentally or recording with using pencil and paper

Participants

� 8 Studentsat (St Andrews Middle School),Year 8

� 11 - 12 Years old

� 4 Top Students& 4 Less able Students

� Half of the students were females and another half were males(randomly)

Procedure

� A clinical interview

� Working with the students individually, approximately30 Minutes

� A photocopiable item from NDP Book 2: The diagnostic interview(Ministry of Education, 2008)

� Audio-taped

� 19 Items in Four categories andThree general questions

1/Addition and Subtraction

53 – 26 =

394 + 79 =

5.3 - 2.89 =

2/Multiplication and Division

5 × 8 = 40 24× 6 =5 × 16 =

72÷ 4 =3× 20 = 603 × 18 =

3/Proportion and Ratio

Cake into thirds

¾ of 28 =

2/3 of = 12

4/Basic Facts

6 + 9 = 6 + 6 =

17 – 9 = 15 – 6 =

6 + = 10

5× 7 = 8 × 5 =

56 ÷ 7 = 63 ÷ 9 =

Addition and Subtraction

� Both groups solved these tasks Correctly

� Place-value partitioning

� Difficulty: James was confused about whether he needed to Add or Subtract while using Rounding and Compensation Strategy

� He used a round number (400) instead of 394, then added 79 to 400 and got 475, he then forgot to subtract what he had added to 394 to make it 400

� Difficulty of solving addition of decimals:

Eli: I never have done points before.

Vili: I forget how to do this.

Multiplication

� The ability to think multiplicatively:

o The substantial use of repeated addition

� Difficulties of solving multiplication problems:

� James:

20 in each basket

In 2 baskets 40, 40 + 80 +100

And count by his fingers 4 muffins for each basket

“I do not know”

Division

� Difficulty working out divisionproblem

� 3 Top students could solve thisproblem using:

o Reversibility combined with derivingfrom known multiplication facts

o Reversibility with times table

o Guessing

Proportion and Ratio

� This section was the most problematic

� Less able students were the most confused

� Examples of difficulties:

o Eli:Is ¾ a half?½ of 28 is 14

o James: “I am not very good at these”.

Basic Facts

� The Easiest part of the interviews

� All Students recalled different types of the facts

� Stuck on remembering division facts

NR = No Response

Basic Facts Top Students Less able Students

Nazeefah Serena Deepel Vili James Eli Shirley Tyrael

Addition

6 + 9 � � � � � � � �

6 + 6 � � � � � � � �

6 + = 10 � � � � � � � �

Subtraction

17 – 9 � � � � � � � �

15 - 6 � � � � 10 � � �

Multiplication

5 × 7 � � � � 42 � � �

8 × 5 � � � � � � � �

Division

56 ÷ 7 � � � � NR NR � 12

63 ÷ 9 � � � � � NR � 50

Attitudes

� Like or dislike� Maths is easy

� Preferred ways

� It easier to record all the steps on paper

� Two Top Students preferred think mentally:

o Deepel:I can figure in my head instead of on my paper

o Nazeefah:If you record in a paper, it takes more time

Abilities

o Vili (a top student), had only amedium capacity to respond todifferent tasks

o Shirley (a less able student), shewas nearly as good at solvingdifferent parts of the problems as

the top students

TASKSTOP STUDENTS LESS ABLE STUDENTS

Nazeefah Serena Deepel Vili James Eli Shirley Tyrael

ADDITION

&

SUBTRACTION

53 - 26 � � � � 26 � � �

394 + 79 � � � � 461, 475 � � �

5.3 - 2.89 NR � 2.51 NR 3.28, 2.25 NR 2.11, 2.40 �

MULTIBLICATION &DIVISIOPN

5 × 8 = 40 SO5 × 16 =

� � � � 55 NR � �

3× 20 = 60 SO3 × 18 =

� � � � � NR � �

24 × 6 � � � � NR � � 131

72 ÷ 4 � � � NR 60 NR 24, 40 8, 11

PROPOTIONS &

RATIOS

Cake into thirds

� � � � � � � �

¾ of 28 � � � 7, 9 12, 8 NR NR 12, 172/3 of = 12

� � � � 10 6, 3 6 7, 8, 5

NR = No Response

� Did students genuinely show rapid mathematical thinking? OR

� Were they familiar with the interview tasks?

� Does teaching style affect student achievements in maths?

� Would a different teacher get different results from the same students?

� Place-value partitioning was the most common mental strategy

# Thompson (2000): some students have difficulty using thisstrategy

� The least common strategies were bridging and rounding

= Thompson (2000 & 1999): both these strategies were not usedcommonly bychildren

� None of the participants used The Balancing Strategy to solvemathematical problems

� The room provided to conduct the interviews wasnot quiet

� Not familiar with using ‘mathematical mental strategies’ in English

� No sufficient knowledge about teaching from the maths curriculum in NewZealand schools.

� Teachers become aware of which mental strategies are most and leastcommonly used by students

� Recognise students’ difficulties in maths

� Teachers need to have real understanding of mathematical thinking

� A study of how teachers can support students’ mathematical understandingneeds to be investigated in Saudi Arabia comparing it to western countries.