This document contains an introduction to a presentation on mathematics cognitive domains by Muhammad Yusuf from Sargodhians' Institute for Professional Development. It includes examples of questions classified into three cognitive domains: Knowing, Applying, and Reasoning. The presentation aims to discuss how focusing on developing conceptual understanding through problem solving and reasoning can help students learn mathematics more effectively than just memorizing procedures and facts.

1. Welcome in
“Mathematics Cognitive Domains”
by
Muhammad Yusuf
Sargodhians’ Institute for Professional Development (SIPD)
Rashidabad
Thursday, July 2, 2020
Muhammad Yusuf

2. Approach Us
Web: www.sipd.org.pk
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Professional-Development-101446921620638/
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Friday, July 24, 2020

3. Mathematics Learning
should focus on
practicing procedure and
memorizing basic
number combinations.
Mathematics learning
should focus on
developing
understanding of
concepts and procedures
through problem solving,
reasoning, and discourse.
For which side of the definition, would you like to be:
Side A Side B

4. Students can learn to
apply mathematics only
after they have mastered
the basic skills.
Students can learn
mathematics through
exploring and solving
contextual and
mathematical problems.
For which side of the definition, would you like to be:
Side A Side B

5. to being able to apply a
series of steps without
knowing why they are being
applied in that way, or what
they mean – 'rules without
reasons'.
to knowing both what to do
and why – an understanding of
all of the parts, how they relate,
and why they are applied in the
manner they are.
For which side of the definition, would you like to be:
Side A Side B
Skemp, 1976
Example: Changing the sign on
numbers moved from one side
of the equals sign to other
Example: Explaining the equals sign
means both sides are equal so to
remove a negative number from 1 side,
we add the number to both sides.

6. 1
6
of
1
2
1
6
×
1
2
=
1×1
6×2
=
1
12
Find
1
6
𝑜𝑓
1
2
. 𝐷𝑟𝑎𝑤 𝑦𝑜𝑢𝑟 𝑎𝑛𝑠𝑤𝑒𝑟 𝑎𝑛𝑑 𝑒𝑥𝑝𝑙𝑎𝑖𝑛 𝑦𝑜𝑢𝑟 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
First I draw a rectangle and shade the half of it.
Then I take
1
6
of the half. So, I divided the half
into 6 parts which would be 6 small rectangles. I
only needed
1
6
so that would be one small
rectangle. Then I needed to figure out what part
of the whole rectangle was and it was 1 out of
12. So
1
6
𝑜𝑓
1
2
is
1
12

7. Instrumental teaching and learning mathematics involves
following rules and procedure without reason, relational
teaching and learning mathematics allows and
encourages students to apply to reason to their learning of
mathematics.
So, it can be concluded

8. Mathematics Cognitive Domains
Knowing
covers the facts, concepts, and procedures students need to know.
Applying
focuses on the ability of students to apply knowledge and conceptual
understanding to solve problems or answer questions.
Reasoning
goes beyond the solution of routine problems to encompass
unfamiliar situations, complex contexts, and multistep problems
40%
40%
20%
Adopted: TIMSS Framework 2019

9. 7532 + 275
Cognitive Domain: Knowing

10. Q. No. 10: Which of these fractions is larger than ½
a) 3/5 b) 3/6 c) 3/8 d) 3/10
Ans.: a) 3/5
Cognitive Domain: Knowing

11. Draw the shape which shows the position of the
shape above after a half-turn or 1800 rotation.
Ans.:
Cognitive Domain: Knowing

12. Tahir ate ½ of a cake, and Jamila ate ¼ of the cake. How
much of the cake did they eat altogether?
Cognitive Domain: Knowing
Ans.: 3/4

13. If the string in the diagram above is pulled straight, which of these
is closest to its length?
a) 5cm b) 7cm c) 8cm d) 9cm
Cognitive Domain: Applying
Ans.: 7 cm

14. Farzana wants to send letters to 12 of her friends.
Half of the letters will need 1 page each and the
other half will need 2 pages each. How many pages
will needed altogether?
Ans.: 18
Cognitive Domain: Applying

15. The school playground is a square. The playground is 100
meter long. Rashid walks all the way around the edge of
the playground. How far does he walk?
Ans.: 400 Meter
Cognitive Domain: Applying

16. A bell rings every 30 seconds, another every 60 seconds.
At 8.00 pm the two ring simultaneously. At what time
will the bells ring again at the same time?
Ans.: 8:02 PM
Cognitive Domain: Applying

17. Fawad left Karachi and rode at the same speed for 2 hours. He reached
the following sign. He continues to ride at the same speed to Thatta.
How many hours will it take his to ride from the sign to Thatta?
Ans.: 3 hours
Cognitive Domain: Reasoning

18. In a Hockey tournament, teams get:
0 points for a loss, 1 point for a tie, 3 points for a win
Flower-land has 11 points.
What is the smallest number of games Flower-land could
have played?
Ans.: 5 games (3 Win + 2 tie)
Cognitive Domain: Reasoning

19. A Sequence of four figures is shown below
If the figures were continued, how many circle would there be in figure 10?
Answer: 19
Cognitive Domain: Reasoning

20. Has 4 Sides Does not have 4
sides
All Sides are the
same length
A
All sides are NOT
the same length
Has 4 Sides Does not have 4
sides
All Sides are the
same length
A, S D
All sides are NOT
the same length
C,E B,
Cognitive Domain: Reasoning

21. Mr. Javed invited 21 students at a dinner party. 13 are involved in
cricket and 11 play football. Of these students, 5 are involved in
both cricket and football. How many students play neither cricket
nor football?
Cognitive Domain: Reasoning
58 6 8+5+6=19
Ans.: 2