Hots

SME 3023
TRENDS AND ISSUES
IN EDUCATION FOR MATHEMATICAL
SCIENCES
NAME NO MATRIK
ATINA HASANAH BINTI MOHD
RAZALI
D20121058406
NUR SHUHADA SURIA BINTI
SHA’ARI
D20121058472
FATIN AMIRA BINTI YUNUS D20121058529
GROUP : A
LECTURER : Dr. MOHD FAIZAL NIZAM LEE BIN
ABDULLAH

Introduction
Higher order thinking skills include critical, logical, reflective, metacognitive, and creative
thinking. They are activated when individuals encounter unfamiliar problems, uncertaint ies,
questions, or dilemmas. Successful applications of the skills result in explanations,
decisions, performances, and products that are valid within the context of available
knowledge and experience and that promote continued growth in these and other
intellectual skills. Higher order thinking skills are grounded in lower order skills such as
discriminations, simple application and analysis, and cognitive strategies and are linked to
prior knowledge of subject matter content. Appropriate teaching strategies and learning
environments facilitate their growth as do student persistence, self-monitoring, and open-minded,
flexible attitudes. An important but challenging part of mathematics teaching is
providing students with opportunities to engage in Higher Order Thinking. These include
students asking thoughtful questions, participating in student-student and student-teacher
substantiate conversations, applying existing knowledge, understanding and skills to
closed and open problems or investigations and learning activities that deepen
understanding of concepts.

BLOOM’S TAXONOMY
One of the most important aspects of setting tasks and asking questions is to know what
level of thinking you are requiring from your students.
In 1958, Benjamin Bloom created his thinking taxonomy for categorizing the level of
abstraction of questions that commonly occur in the classroom.
Remember
Student is able to recall information
Understand Student is able to explain information
Apply Student is able to carrying out or using a procedure
through executing or implementing
Analyze Student is able to breaking material or concepts into
parts, determining how the parts relate or interrelate
to one another or to an overall structure or purpose
Evaluate Student is able to Making judgments based on
criteria and standards through checking and
critiquing.
Design Student is able to create new products, ideas or ways
of seeing things.

Differences between HOTS and NTS
A main goal of educators today is to teach students the skills they need to be critical
thinkers. Instead of simply memorizing facts and ideas, children need to engage in higher
levels of thinking to reach their fullest potential. Practicing Higher Order Thinking (HOT)
skills outside of school will give kids and teens the tools that they need to understand, infer,
connect, categorize, synthesize, evaluate, and apply the information they know to find
solutions to new and existing problems. Consider the following example to distinguis h
between memorization of facts and actually engaging in thoughtful ideas:
‘After reading a book about Martin Luther King or studying the Civil Rights era, you could
choose to ask a child a simple question such as “Who is Martin Luther King, Jr.?”. When
answering this question, the child can simply provide facts that s/he has memorized.
Instead, to promote critical thinking skills, you might ask them “Why do you think that
people view Martin Luther King, Jr. as a hero of the civil rights era?” to elicit a more well
thought-out response that requires them to apply, connect, and synthesize the informa t ion
they previously learned.
In Bloom's taxonomy, for example, skills involving analysis, evaluation and synthesis
(creation of new knowledge) are thought to be of a higher order, requiring different learning
and teaching methods, than the learning of facts and concepts.
Higher order thinking involves the learning of complex judgmental skills such as critical
thinking and problem solving. Higher order thinking is more difficult to learn or teach but
also more valuable because such skills are more likely to be usable in novel situations (i.e.,
situations other than those in which the skill was learned).

High Order and Lower Order Applications
“Technology alone cannot move learners to higher order thinking skills, but some
applications are more suited for this task than others” (Burns, 2006). Burns classifies
applications into “Lower-Order and Higher-Order Applications”. How an application is
used by an educator determines whether it is a lower or higher order application. An
example of this is the use of the Internet. If used as an electronic textbook it would be a
lower order application as only lower order skills are used if the learner does not validate,
question, or evaluate, the information obtained. When learners engage in online
collaboration they would be using higher order thinking skills and therefore the Internet
would be used as a higher order application (Burns, 2006).
Lower order applications offer few opportunities for the development of higher order
thinking skills. Educators should avoid using presentation software all the time. When
using power point to present research the information has to be reduced to “sight bite”
(Burns 2006) and the focus is on the attractiveness of the presentation. At high school level
a Power point presentation does not necessarily lead to deep complex learning. It is
important for educators to be aware of all these pitfalls when they plan to integrate
technology and computers into the curriculum.
Higher order applications are developmentally appropriate and challenging tools.
These applications offer opportunities to analyses, evaluate and solve problems and
therefore offer more opportunities to practice analytical and critical thinking skills.
Spreadsheets and databases are two examples of such applications. Database design can
help learners methodically organize, assemble and order data according to recognized
criteria (Adams & Burns, 1999). Another example is Geographic Information Systems
(GIS). GIS was brought into the new grade 10 Geography Curriculum with the purpose of
developing higher order thinking skills. Learners can study change over time using a free
GIS tool like Google Earth (Burns, 2006).
According to Wilson (2000) lower order skills, such as reading and writing are
taught very well at schools. These skills are used to build higher order thinking skills.
Today the labor market demands people with higher order thinking skills. These skills are
of vital importance because it is impossible to remember all the information we need for

future use. Today information grows exponentially and therefore individuals need to learn
to navigate all this information. Many educators believe that detailed knowledge will not
be as significant to tomorrow's workers and citizens as the ability to learn and make sense
of new information. According to Resnick (1987) all individuals, not just the elite, have
the ability to become adept at thinking.
Education Reform
It is a notion that students must master the lower level skills before they can engage in
higher order thinking. However, the National Research Council objected to this line of
reasoning, saying that cognitive research challenges that assumption, and that higher order
thinking is important even in elementary school. Including higher order thinking skills in
learning outcomes is a very common feature of standards based education reform.
Many forms of education reform, such as inquiry-based science, reform mathematics and
whole language emphasize HOTS to solve problems and learn, sometimes deliberately
omitting direct instruction of traditional methods, facts, or knowledge. HOTS assumes
standards based assessments that use open-response items instead of multiple choice
questions, and hence require higher order analysis and writing. Critics of standards based
assessments point out that this style of testing is even more difficult for students who are
behind academically. The Texas Republican Party expressed their opposition to the
teaching of certain HOTS by including the following item in their 2012 Party Platform:
"Knowledge-Based Education – We oppose the teaching of Higher Order Thinking Skills
(HOTS) (values clarification), critical thinking skills and similar programs that are simply
a relabeling of Outcome-Based Education (OBE) (mastery learning) which focus on
behavior modification and have the purpose of challenging the student’s fixed beliefs and
undermining parental authority."

Definition of Thinking
The second edition of the dictionary hall states think is working with brain to make a
decision. According to the fourth edition of the dictionary hall, thinking is to use common
sense to solve something. According to Fraenkel, JR, 1980, however, states that thinking
is the formation of ideas, remodeling experience and organizing information in a particular
form. According to Nickerson, Perkins and Smith, 1985, think is a collection of skills or
mental operations used by an individual. According to Beyer, BK, 1991 defines thinking
as the human ability to form concepts, to reason, or to make the determination.
Different Types of Thinking
Critical thinking is the term that most people associate with higher-order thinking skills
and is characterized by careful analysis and judgment. According to the National Council
for Excellence in Critical Thinking (Scriven and Paul 1987), “Critical thinking is self-guided,
self-disciplined thinking which attempts to reason at the highest level of quality in
a fair-minded way. People who think critically consistently attempt to live rationally,
reasonably, empathically”. In other words, when a critical thinker is posed with a problem,
his or her learning is prompted. The thinker is committed to thinking logically about a topic
and refuse to jump a conclusions. He or she struggles to put away the biases that come so
naturally and endeavors to look at a situation in a new way so that it can be analyzed and
evaluated in a logical manner. And, the thinker reflects on what he or she learned. John
Dewey (1916) described reflective thinking as an active, persistent, and careful review of
something that is believed. The active learner does not just accept information passively;
he or she looks for evidence to support the information. If no evidence is found, the piece
of information cannot be believed. Instead of being told what to think, a person must think
for himself or herself and give good cause for the conclusions that are reached. Reflective
thinking is critical thinking. It is taking control of learning and being continually conscious
and committed to asking why.
Creative thinking is also a higher-order thinking skill and is equally as important as critical
thinking. In the book Curriculum 21: Essential Education for a Changing World, Heidi
Hayes Jacobs (2010) says that curriculum should go beyond giving tools for reasonable
and logical thinking. Curriculum should also nurture creativity in all learners. Inventing

and synthesizing characterize creative thinking. Create means to bring something valuable
into existence that was not there previously. It is the process or bringing about a new idea.
Michael Michalko (2006), author of Thinker toys: A Handbook of creative-Thinking
Techniques, says, “Creativity is not an accident, not something that is genetica lly
determined. It is not a result of some easily learned magic trick or secret, but a consequence
of your intention to be creative and your determination to learn and use creative-thinking
strategies” (Introduction XVII). Creative thinking is active work.
Convergent/Analytical thinking involves bringing facts and data together from various
sources and then applying logic and knowledge to solve problems or to make informed
decisions. Convergent thinking involves putting a number of different pieces or
perspectives of a topic back together in some organized, logical manner to find a single
answer. The deductive reasoning that the Sherlock Homes used in solving mysteries is a
good example of convergent thinking. By gathering various bits of information, he was
able to put the pieces of a puzzle together and come up with a logical answer to the question
of “Who done it?”
Answer
Fact
Fact
Fact
Fact
Fact
Fact

Divergent / Creative thinking, on the other hand, involves breaking a topic apart to explore
its various component parts and then generating new ideas and solutions. Divergent
Thinking is thinking outwards instead of inward. It is a creative process of developing
original and unique ideas and then coming up with a new idea or a solution to a problem.
Inductive thinking is the process of reasoning from parts to the whole, from examples to
generalizations. This type of thinking is something we are rather good at, especially as it is
our main mechanism for learning about the world. According to S. Ian Robertson (2013)
Inductive thinking refers to the extent to which we can make reasonable generalizat ions
from our specific experiences. This thinking is an extremely powerful thinking mechanism
since it underpins almost all learning. It allows you to learn fairly quickly to make new
types of inference that you have never made before.
Deductive thinking is the type of reasoning moves from the whole to its parts, from
generalizations to underlying concepts to examples. It is the process of reasoning from one
or more general statements regarding what is known to teach a logically certain conclusion
(Johnson-Laird, 2000). It often involves reasoning from one or more general statements
regarding what is known to a specific application of the general statement. This type of
thinking is based on logical propositions which is basically known as an assertion, which
may be either true or false. It is very useful because it helps people connect various
propositions to draw conclusion.
Closed questions are questions asked by teachers that have predictable responses. Closed
questions almost always require factual recall rather than higher levels of thinking. It is
involved a statement or question that followed by a rating scale. Robert D. Reid (2009)
said, closed questions provide a "don't know" or "no opinion" response where appropriate.
Closed question provides the respondent with options from which to select a response. It
is much easier to collect and analyze information in this type of question.
Open questions are questions that do not have predictable answers. Open questions almost
always require higher order thinking. Which is David C. Bojanic (2009) said, open question
does not provide the respondent with any options, categories, or scales to use in answering
this question. These questions ae valuable fo obtaining information for exploratory
research, o in instances when the researcher is not sure what the response might be. This

type of questions are used to build a rapport and obtain information that is easy for the
respondent to provide.
Lateral Thinking Technique
A set of techniques used to stimulate creative or "out of the box" thinking. Applying lateral
thinking techniques is a deliberate strategy to interrupt normal, linear thought patterns, to
facilitate the transition between patterns, and to widen the range of possibilit ies.
Base on Edward DeBono’s concepts of lateral thinking include the follow ing
characteristics:
1. The nature of thought should be provocative, non-sequential, and non-logica l.
2. The process of lateral thinking should seek additional options, exploring unlikely paths,
and does not have to be “correct”.
3. The process of lateral thinking should attempt to escape from established patterns, labels,
and classifications.
4. The results of lateral thinking are unpredictable and/or probabilis t ic.
Other techniques are available to stimulate creative or lateral thinking. These include
checklists, attribute analyses, games or exercises and metaphors and analogies.
The purpose of using lateral thinking technique is to stimulate creative thinking during
brainstorming, visioning, and reengineering sessions while helping project teams relate to
One another and affiliate. The benefit of using lateral thinking technique is that it stimula tes
out of the box thinking in group sessions.

Strategies in Higher Thinking Skills
These following strategies are offered for enhancing higher order thinking skills. This
listing should not be seen as exhaustive, but rather as a place to begin.
 Take the mystery away
Teach students about higher order thinking and higher order thinking strategies. Help
students understand their own higher order thinking strengths and challenges.
 Teach the concept of concepts
Explicitly teach the concept of concepts. Concepts in particular content areas should be
identified and taught. Teachers should make sure students understand the critical features
that define a particular concept and distinguish it from other concepts.
 Name key concepts
In any subject area, students should be alerted when a key concept is being introduced.
Students may need help and practice in highlighting key concepts. Further, students should
be guided to identify which type(s) of concept each one is — concrete, abstract, verbal,
nonverbal or process.
 Categorize concepts
Students should be guided to identify important concepts and decide which type of concept
each one is (concrete, abstract, verbal, nonverbal, or process).
 Tell and show
Often students who perform poorly in math have difficulty with nonverbal concepts. When
these students have adequate ability to form verbal concepts, particular attention should be
given to providing them with verbal explanations of the math problems and procedures.
Simply working problems again and again with no verbal explanation of the problem will
do little to help these students. Conversely, students who have difficulty with verbal
concept formation need multiple examples with relatively less language, which may
confuse them. Some students are "tell me" while others are "show me."

 Teach steps for learning concepts
A multi-step process for teaching and learning concepts may include (a) name the critical
(main) features of the concept, (b) name some additional features of the concept, (c) name
some false features of the concept, (d) give the best examples or prototypes of the concept
(what it is), (e) give some non-examples or non-prototypes (what the concept isn't), and (f)
identify other similar or connected concepts.
 Go from basic to sophisticated
Teachers should be sure that students have mastered basic concepts before proceeding to
more sophisticated concepts. If students have not mastered basic concepts, they may
attempt to memorize rather than understand. This can lead to difficulty in content areas
such as math and physics. A tenuous grasp of basic concepts can be the reason for
misunderstanding and the inability to apply knowledge flexibly.
 Expand discussions at home
Parents may include discussions based on concepts in everyday life at home. The subject
matter need not relate directly to what she is studying at school. Ideas from reading or
issues in local or national news can provide conceptual material (for example, "Do you
think a dress code in school is a good idea?").
 each inference
Students should be explicitly taught at a young age how to infer or make inferences. Start
with "real life" examples. For example, when a teacher or parent tells a child to put on his
coat and mittens or to get the umbrella before going outside, the adult may ask the child
what that might mean about the weather outside. When students are a little older, a teacher
may use bumper stickers or well-known slogans and have the class brainstorm the
inferences that can be drawn from them.

 Clarify the difference between understanding and memorizing
When a student is studying, his parents can make sure that he is not just memorizing, but
rather attempting to understand the conceptual content of the subject matter. Parents can
encourage the student to talk about concepts in his own words. His parents can also play
concept games with him. For example, they can list some critical features and let him try
to name the concept.
 Elaborate and explain
The student should be encouraged to engage in elaboration and explanation of facts and
ideas rather than rote repetition. His teachers and parents could have him relate new
information to prior experience, make use of analogies and talk about various future
applications of what he is learning.
 A picture is worth a thousand words
Students should be encouraged to make a visual representation of what they are learning.
They should try to associate a simple picture with a single concept.
 Make mind movies
When concepts are complex and detailed, such as those that may be found in a classic novel,
students should be actively encouraged to picture the action like a "movie" in their minds.
 Teach concept mapping and graphic organizers
A specific strategy for teaching concepts is conceptual mapping by drawing diagrams of
the concept and its critical features as well as its relationships to other concepts. Graphic
organizers may provide a nice beginning framework for conceptual mapping. Students
should develop the habit of mapping all the key concepts after completing a passage or
chapter. Some students may enjoy using the computer software Inspiration for this task.
 Make methods and answers count
To develop problem-solving strategies, teachers should stress both the correct method of
accomplishing a task and the correct answer. In this way, students can learn to identify
whether they need to select an alternative method if the first method has proven
unsuccessful.

 Identify the problem
Psychologist Robert Sternberg states that precise problem identification is the first step in
problem solving. According t o Sternberg, problem identification consists of (1) knowing
a problem when you see a problem and (2) stating the problem in its entirety. Teachers
should have students practice problem identification, and let them defend their responses.
Using cooperative learning groups for this process will aid the student who is having
difficulty with problem identification as he/she will have a heightened opportunity to listen
and learn from the discussion of his/her group members.
 Cooperative learning
Many students who exhibit language challenges may benefit from cooperative learning.
Cooperative learning provides oral language and listening practice and results in increases
in the pragmatic speaking and listening skills of group members. Additionally, the National
Reading Panel reported that cooperative learning increases students' reading
comprehension and the learning of reading strategies. Cooperative learning requires that
teachers carefully plan, structure, monitor, and evaluate for positive interdependence,
individual accountability, group processing, face to face interact ion, and social skills.
 Think with analogies, similes, and metaphors
Teach students to use analogies, similes and metaphors to explain a concept. Start by
modeling ("I do"), then by doing several as a whole class ("We do") before finally asking
the students to try one on their own ("You do"). Model both verbal and nonverbal
metaphors.
 Reward creative thinking
Most students will benefit from ample opportunity to develop their creative tendencies and
divergent thinking skills. They should be rewarded for original, even "out of the box"
thinking.

 Teach components of the learning process
To build metacognition, students need to become consciously aware of the learning process.
This changes students from passive recipients of information to active, productive, creative,
generators of information. It is important, then for teachers to talk about and teach the
components of the learning process: attention, memory, language, graphomotor,
processing and organization, and higher order thinking.
 Use resources
Several resource books by Robert Sternberg are available on higher order thinking. The
following books should be helpful and are available at local bookstores or online.
 Successful Intelligence by Robert J. Sternberg
 Teaching for Successful Intelligence by Robert J. Sternberg and Elena L.
Grigorenko
 Teaching for Thinking by Robert J. Sternberg and Louise Spear-Swerling
 Consider individual evaluation
Many students with higher order thinking challenges benefit from individual evaluation
and remediation by highly qualified professionals.
 Make students your partners
A teacher should let the student with higher order thinking challenges know that they will
work together as partners to achieve increases in the student's skills. With this type of
relationship, often the student will bring very practical and effective strategies to the table
that the teacher may not have otherwise considered.
Examples of Question in HOTS
(a) Function and Decimal
1. How can I use fractions in real life?
2. How can decimals be rounded to the nearest whole number?
3. How can models be used to compute fractions with like and unlike denominators?
4. How can models help us understand the addition and subtraction of decimals?

5. How many ways can we use models to determine and compare equivalent fractions?
6. How would you compare and order whole numbers, fractions and decimals through
hundredths?
7. How are common and decimal fractions alike and different?
8. What strategies can be used to solve estimation problems with common and
decimal fractions?
9. How are models used to show how fractional parts are combined or separated?
10. How do I identify and record the fraction of a whole or group?
11. How do I identify the whole?
12. How do I use concrete materials and drawings to understand and show
understanding of fractions (from 1/12ths to 1/2)?
13. How do I explain the meaning of a fraction and its numerator and denominator, and
use my understanding to represent and compare fractions?
14. How do I explain how changing the size of the whole affects the size or amount of
a fraction?
(b) Function and Algebra
1. Are patterns important in the world today?
2. What is the unknown?
3. Why do we use variables?
4. How can a variable transform itself?
5. How would you describe the order of operations?
6. What are the tools needed to solve linear equations and inequalities?
7. Are you able to solve a linear inequality by graphing?
8. When are algebraic and numeric expressions used?
9. How do we create, test and validate a model?
10. Do mathematical models conceal as much as they reveal?
11. What patterns or relationships do we see in each type of mathematics?
12. What are the different ways to represent the patterns or relationships?
13. What different interpretations can be obtained from a particular pattern or
relationship?

14. What predictions can the patterns or relationships support?
15. How can we use or test our predictions? Are they valid? Are they significant?
16. Where in the real world would I find patterns?
17. Why is comparing sets important?
18. Why are variables used?
19. What strategies can be used to solve for unknowns in algebraic equations?
(c) Data, Statistics and Probability
1. Are patterns important in the world today?
2. What is the unknown?
3. Why do we use variables?
4. How can a variable transform itself?
5. How would you describe the order of operations?
6. What are the tools needed to solve linear equations and inequalities?
7. Are you able to solve a linear inequality by graphing?
9. How do we create, test and validate a model?
10. Do mathematical models conceal as much as they reveal?
11. What patterns or relationships do we see in each type of mathematics?
12. What are the different ways to represent the patterns or relationships?
13. What different interpretations can be obtained from a particular pattern or
relationship?
14. What predictions can the patterns or relationships support?
15. How can we use or test our predictions? Are they valid? Are they significant?

Differences between Higher Order Thinking Skills (HOTS) and Lower Orde r
Thinking Skills (LOTS)
Higher Order Thinking Skills (HOTS) is the ability to think beyond rote memorization of
facts or knowledge. Rote memory recall is not really thinking. Higher order thinking skills
involve actually doing something with the facts that we learn. When students use their
higher order thinking skills that means they understand, they can find connections between
many facts, they can put them together in new ways and they can manipulate them. Most
importantly they can apply them to find new solutions to problems.
Lower Order Thinking Skills (LOTS) is the foundation of skills required to move into
higher order thinking. These are skills that are taught very well in school systems and
includes activities like reading and writing. In lower order thinking information does not
need to be applied to any real.
There are several differences between HOTS and LOTS which are:
 According to Bloom ,element of LOTS are the acquisition and comprehension of
knowledge while the elements for HOTS are evaluation, synthesis, application and
analysis .
 LOTS are used to understand the basic story line or literal meaning of a story ,play
or poem while HOTS are used to interpret a text on more abstract level and
manipulate information and ideas in ways that transform their meaning and
implications
 HOTS can make the student to think more creatively and think out of the box while
LOTS , the student only think and just recall back on the topic that they had learnt.

Bloom’s Question Starter
There are 6 levels of questions. The first three levels are considered lower order questions
and the final three levels are considered higher order. Higher order questions are what we
use for Critical Thinking and Creative Problem Solving.
Level 1: Remember – Recalling Information
List of key words:
Recognize, List, Describe, Retrieve, Name, Find, Match, Recall, Select, Label, Define, Tell
List of Question Starters:
• What is...?
• Who was it that...?
• Can you name...?
• Describe what happened after...
• What happened after...?
Level 2: Understand – Demonstrate an understanding of facts, concepts and ideas
List of key words: Compare, Contrast, Demonstrate, Describe, Interpret, Explain, Extend,
Illustrate, Infer, Outline, Relate, Rephrase, Translate, Summarize, Show, Classify
• Can you explain why...?
• Can you write in your own words?
• Write a brief outline of...
• Can you clarify...?
• Who do you think?
• What was the main idea?

Level 3: Apply – Solve problems by applying knowledge, facts, techniques and rules
in a unique way
List of key words:
Apply, Build, Choose, Construct, Demonstrate, Develop, Draw, Experiment with,
Illustrate, Interview, Make use of, Model, Organize, Plan, Select, Solve, Utilize
• Do you know of another instance where...?
• Demonstrate how certain characters are similar or different?
• Illustrate how the belief systems and values of the characters are presented in the
story.
• What questions would you ask of...?
• Can you illustrate...?
• What choice does ... (character) face?
Level 4: Analyze – Breaking information into parts to explore connections and
relationships
List of key words:
Analyze, Categorize, Classify, Compare, Contrast, Discover, Divide, Examine, Group,
Inspect, Sequence, Simplify, Make Distinctions, Relationships, Function, Assume,
Conclusions
• Which events could not have happened?
• If ... happened, what might the ending have been?
• How is... similar to...?

• Can you distinguish between...?
• What was the turning point?
• What was the problem with...?
• Why did... changes occur?
Level 5: Evaluate – Justifying or defending a position or course of action
List of key words: Award, Choose, Defend, Determine, Evaluate, Judge, Justify,
Measure, Compare, Mark, Rate, Recommend, Select, Agree, Appraise, Prioritize,
Support, Prove, Disprove. Assess, Influence, Value
• Judge the value of...
• Can you defend the character’s position about...?
• Do you think... is a good or bad thing?
• Do you believe...?
• What are the consequences...?
• Why did the character choose...?
• How can you determine the character’s motivation when...?
Level 6: Create – Generating new ideas, products or ways of viewing things
List of key words: Design, Construct, Produce, Invent, Combine, Compile, Develop,
Formulate, Imagine, Modify, Change, Improve, Elaborate, Plan, Propose, Solve
• What would happen if...?
• Can you see a possible solution to...?
• Do you agree with the actions? With the outcomes?

• What is your opinion of...?
• What do you imagine would have been the outcome if... had made a different choice?
• Invent a new ending.
• What would you cite to defend the actions of...?
I-Think
I-Think is an education program that created by Malaysian Ministry of Education
together with Agensi Inovasi Malaysia (AIM). The aim of this program is to equip
Malaysia’s next generation of innovators to think critically and be adaptable in preparation
for the future. Besides, Thinking School International (TSI) team works together with
Malaysian government in I-Think project. TSI is a team established in 2010 and focused
on student’s thinking skills across the globe that are committed to develop 21st century
learning.
According to Richard Cummins (CEO of TSI) and Nick Symes (Global Trainer of
TSI), i-Think program has three main objectives:
 Nurture and develop innovative human capital
 Increase thinking skill amongst children
 Equip future generations with Higher Order Thinking Skills
I-Think program is conducting in schools based on these objectives. I-Think program have
eight types of thinking maps. They are:
1. Circle Map
Thinking Process : Defining in context
Aim : Help people brainstorm and list everything they know
about a particular thing or idea.
Key Question : How we can define this thing or idea?

Key Words and Phrases : List, define, tell everything you know, brainstorm,
identify, relate prior knowledge, describe, explore the
meaning
Design : The topic is in the middle, smaller circle. Everything
you know about the topic is in the larger circle. A box
that may be included, around the entire map is a “Frame
of Reference” that is used to answer the question “How
did I learn this?” (The frame of reference can be used
around any of the maps.
Example : What are the topics under Mathematics?
Algebra
Integration
Statistics
Probability
Percentage
Whole Number
Multiplication
Factorization
Matrix
Calculus
Form 4 Text Book
KPM Website
Form 5 Text Book
Journal
Topics in
Math’s

2. Bubble Map
Thinking Process : Describing qualities or characterization
Aim : Help people to list down key adjectives (qualit ies,
properties or attributes) about a particular thing or idea
so that can describe and understand it better.
Key Question : How are you describing these things? What adjectives
best describe it?
Key Words and Phrases : Describe, describe feelings, observe using five senses
Design : The topic being described is in the center bubble. The
outer bubbles contain adjectives and adjective phrases
describing the topic.
Example : Characteristics of a Mathematics teacher
Math’s
Teacher
Patience
Clever
Confident
Loving
Discipline
Knowledgeable
Strict
Hard-working

3. Double Bubble Map
Thinking Process : Comparing and contrasting
Aim : Help people list down similarities and differences
between two things or idea so that can differentiate the
two by comparing and contrasting.
Key Question : What are the similar and different qualities of these
things?
Key Words and Phrases : Compare/contrast, discuss similarities and differences,
prioritize essential characteristics
Design : In the center circle are the words for the two things
being compared and contrasted. In the middle bubbles,
use terms to show similarities. In the outside bubbles,
describe the differences. If there are too many
similarities or differences, student should prioritize and
keep only he most important.
Example : Differentiate square and trapezoid
Sides
(4)
Square Trapezoid
Shapes
Vertices
(4)
No
right
angles
No
equal
sides
Only top
& bottom
sides
parallel
4 equal
side
2 sets of
parallel
side
All vertices
from right
and left
angle

4. Tree Map
Thinking Process : Classifying
Aim : Help people organize information into different groups
so that can understand the big picture in a
comprehensive way.
Key Question : What are the main ideas, supporting ideas, and details
in information?
Key Words and Phrases : Classify, sort, group, categorize, give sufficient and
related details
Design : The category name is on the top line, subcategories on
the second level, details under each category
Example : Classify equation of straight lines
E quation of Straight Lines
If two points are
given:
푦 − 푦1 = 푚(푥 − 푥2)
Equation in the
gradient form:
푦 = 푚푥 + 푐
If the gradient and a
point are given:
푦 − 푦1
푦=
2 − 푦1
푥 − 푥1
푥2 − 푥1
If the x-intercept and
y-intercept are given:
Equation in general
form:
푎푥 + 푏푦 + 푐 = 0
푥
푎
+
푦
푏
= 1

5. Brace Map
Thinking Process : Whole Part Relationship
Aim : Brace maps help people break thing apart so you can
understand how thing work.
Key Question : What are the parts and subparts of this whole physica l
object?
Key Words and Phrases : Part of, take apart, show structure
Design : On the line to the left, the name of the whole object is
written. On the lines within the first brace, list the major
parts. The subparts are listed in the next set of braces.
Example : Decomposing of RM 1.00
RM 1.00
RM 0.25
RM 0.25
RM 0.10
RM 0.05
RM 0.25
RM 0.25
RM 0.10
RM 0.05
RM 0.05

6. Flow Map
Thinking Process : Sequencing
Aim : Flow maps help people list down the steps involved in
a process so you can understand what needs to be done
to achieve something.
Key Question : What happened? What is the sequence of events? What
are the sub-stage?
Key Words and Phrases : Sequence, put in order, recount, and retell, what
happens next, cycles, patterns, describe processes
describe change, solve multi-step problems.
Design : Each stage of the event is in the larger rectangles. The
sub-stages are smaller rectangles below the larger ones.
Not all flow maps will have sub-stages.
Example : Describe the process to round off a number.
Identify the
number to be
rounded
Go to the right if
the number
If the number is
5 or greater,
increase the
number to be
rounded
If the number is
4 or less, do not
change the
number to be
rounded

7. Multi-Flow Maps
Thinking Process : Cause and effect
Aim : Multi-flow maps help people map the cause and effect
of an event so you can understand the results of actions,
and how the can be changed.
Key Question : What are the causes and effects of this event? What
might happen next?
Key Words and Phrases : Causes and effects, discuss consequences, what would
happen if, predict, describe change, identify motives,
and discuss strategies.
Design : The event is in the center rectangle. On the left side,
causes of the event. On the right side, effects of the
event.
Example : How do we achieve good grades in mathematics and
what are the benefits?
Good Grades in
Mathematics
Practice more
exercises
Focus during study
and doing
exercises
Create a study
group
Score Grade ‘A’ for
Mathematics
Award
Become tutor for
mathematics
subject

8. Bridge Map
Thinking Process : Seeing analogies
Aim : Bridge maps let people list down several pairs of items
that relate to each other. So you can understand things
in the world that have similar relationship (analogies).
Key Question : What is the analogy being used?
Key Words and Phrases : Identify the relationship, guess the rule, and interpret
symbols.
Design : On the far left line, write the relating factor. On the top
and bottom of the bridge, write in the first pair of things
that have this relationship. On the right side of the
bridge, write the second pair with the same
relationship. The line of the bridge represents the
relating factor between the pair of things.
Example : Coordinate plan
Quadrant I Quadrant II Quadrant III Quadrant IV
as as
Relating Factor: Any points located in _____________ will always have ________
coordinates.
as
(+,+)
(-,+) (-,-) (+,-)

Conclusion
Thinking is the heart of all learning. Thinking makes things that have yet to be perceived
possible, thinking facilities and enhances our ability to perform and produce and pass on
such vital information to others who would then do the same. There many types of thinking,
students should choose the best method to solve their problem. Students need to make
significant academic gains only to catch up with other students and have more life
opportunities. One way to help students is to provide the opportunity to lead, engage, and
motivate students toward higher-order thinking. Malaysian Education System helps
students gain knowledge, but now we need a transformation create thinking generation.
With i-Think program, students will become lifelong learners, equipped with the right skill
sets to take on the challenges of the 21st century. As a conclusion, HOTS is an alternative
that can improve the Malaysia education quality and all parties must take part in order to
gain the best outcome of this program.

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