Thinking Skills for Rich Tasks
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The Problem Solving Process

Seven Core Thinking Skills for Mathematics
And Any Other Rich Task Activity



Expectations:  The Student will:

  1. Describe seven key structured thinking skills and explain how these skills are used to apply and enhance the problem-solving process.
  2. Identify important prerequisites to becoming a good thinker.
  3. Synthesize (ie “output”) Portfolio entries connecting Thinking Skills, the Learning Process and the Mathematics Problem-Solving Process.
  4. Apply the seven key structured thinking skills to a problem in geometry.
  5. Summarize learning through organized reflection.


Assignment:  This is individual work. The questions are in Section 2 below. Sample good answers by the teacher are shown in Blue bold italics font.  

Mark:  ___  / 15     Due Date: Today or Homework Tonight

  Special Insight:

What is the single biggest difference between life and your personal computer? There is no “undo” command in life.  

This Sub-Module is Important Because:

  1. To keep or advance in a job you must be able to think clearly -- to propose better ways of doing something; to save your employer money; to be able to use new tools quickly… and so on…


Other Resources / Instruction Aids to Use -- Files Will be In Pickup Folder:

  • Note: The following files are not necessary for the assignment below, but are required for the Math ISU project:
    • Keywords_Structures_Geometry.doc
    • math_Problem_solving_Process.doc
    • Thinking_Geometry.doc


1         Thinking Skills In the Design, Problem-Solving and Learning Processes

1.1        Learning About Thinking

To be complete, the learning process must involve a great deal of “quality thinking”. After “doing”, “seeing” and “hearing”, the human mind must do a certain amount of processing in order for a module of learning, knowledge or skill development to be solidified. This is generally called “thinking”. Note that reflection “after the fact” is not sufficient (i.e. not good enough). The approach to the development of thinking skills must be radically improved. This is the purpose of the Seven Key Thinking Skills shown in Figure 1 below. Structured thinking will be rigourously “taught” by this teacher.

Seven basic forms of thinking (in order from simplest to most demanding) are: recall, translate, interpret, apply, analyze, synthesize, and evaluate. Recall (memory) is what many people mistakenly believe learning (and school) is “all about”. This is a very unfortunate perception. While most would classify thinking as a skill, to become a good thinker first requires the learner to develop sound attitudes such as persistence, flexibility and openness.

It is very important to recognize that the goal of making the Design and Problem-Solving Processes of paramount (crucial) importance in school today does not infringe on student imaginativeness and creativity. A good design process actually fosters (supports) creativity and the use of imagination by encouraging brainstorming, consideration of many varied inputs and generation of multiple alternate solutions.

Creativity drives improvements in our quality of life. Creative thinking is best used in multi-disciplinary efforts in very close connection with thorough critical thinking that reaches for a solid understanding of a sustainable social, economic or political system. Indeed, creative thinking can be used to improve the multifaceted (having many aspects) socio-economic-political environment which we all share.

Creative thinking is, very generally, a collection of skills, attitudes and concepts centred on the Synthesis form of thinking. Critical thinking is, very generally, a collection of skills, attitudes and concepts centred on the Analysis form of thinking. Skilled analysis, synthesis and evaluation are at the heart of any successful design project. “Reverse engineering” a piece of technology is a powerful tool for improving analytical skills.

The use of these seven thinking skills is very much a learning process or cycle. It may be seen that the design process and the learning process follow a similar and perfectly natural pattern -- input, processing, output and then, finally, evaluation of the output and another cycle of improvement. The cerebral cortex of the brain is dedicated to three functions known as sensory, integrative and motor. We could label Figure 1 below as follows:

  • Input =   Sensory  (Observe/experience the world around us using our senses)
  • Process =   Integrative  (Put / connect our observations into a bigger picture)
  • Output =   Motor   (Act or do something with our enhanced understanding; simplify if necessary)


1.2   The Seven Thinking Skills -- A Closed Loop Process



Figure 1: Information Processing Using Seven Structured Thinking Skills


All students must actively engage in the following forms of thinking where relevant to their assignments (in order from most complex to simplest). Note that the terms in brackets are merely approximations or “simplifications” of that thinking skill.

  1. Higher Forms of Thinking:
    1. Evaluate (judge against criteria).
    2. Synthesize (to output or put together; one aspect of creativity)
    3. Analyze (to break down or take apart; one aspect of critical thinking)
    4. Apply (use knowledge in a new situation)
  2. Lower Forms of Thinking:
    1. Interpret (summarize, sort, establish classifications, reveal relationships, make connections with other courses etc.)
    2. Translate (“do not copy”) (put into your own words) (transform from English words into a math equation)
    3. Recall (Memory)

Note that the higher thinking skills are beginning to develop at the age of 13 or 14 -- it is important to strategically exercise these skills at this age.

It is very important to note that, in using a higher form of thinking, you are also generally using some aspects of each lower form. Critical thinking is not just analysis as it involves the thinker having certain well-developed attitudes as well. Critical thinking speaks more to the quality of the thinking that is performed.

In reality, most forms of thinking are at work to some extent during most stages of this iterative problem-solving process -- and you should document your thinking as you generate evidence of understanding and learning.

Note that “copying” from a text or elsewhere is NOT evidence of learning or understanding. When “describing” something, you must “translate” into your own words, also using higher forms of thinking as much as possible depending on the question. Accurate translation coupled (along) with necessary interpretation and analysis is typically acceptable evidence of some degree of understanding or learning. You must practise, demonstrate and document all seven forms of thinking as you engage in the problem-solving process.

Note that thorough problem-solving involves cycling through all of the seven thinking skills several times.

1.3        Thinking Skills: Definitions and Applications

In the following table, column 2 lists some general characteristics of each form of thinking. The purpose of column 3 is for you to describe how you used this form of thinking on a particular assignment or project. The sample data in italics in column 3 relates to the grade 9 Integrated Technologies popsicle stick bridge project. Delete these samples and then describe your own applications of each thinking skill. This exercise is a relatively complete summary of or "reflection on" any assignment or project.





An Initial Definition


Student Translation / Application / Additional Context --- Describe Your Best Example of Using This Thinking Skill in (eg) Your Bridge Project


A set of mental skills that put humans above all other animals. We can use these mental skills to make the world a better place for all creatures. The following seven structured thinking skills comprise a simple yet powerful model of Thinking that is particularly useful in learning.



-Form of thinking -- Lowest -- the least effective form in terms of learning

-Recite, remember or pull pieces of knowledge or sequences from memory. Outputs may be a keyword definition or match, procedure, statement of a theory or law etc.

-These “recalled facts” may either be correct or incorrect.

-Several cycles through all seven thinking skills may be required before a “fact” is “correctly comprehended” or understood in a particular context or situation.

-Recall simply pulls information from memory without necessarily having any degree of comprehension or significance

-Use cues, mnemonics, concept maps etc. to trigger recall

-Paying attention to input you are given is very important

-The human brain continuously takes in feedback from the other forms of thinking in order to more completely develop some “understanding” surrounding a package of information

Delete this Teacher Sample Answer:

Before I started working on my bridge design I first pulled out of my memory some information from my science class in elementary school. The topic was structures and we learned about forces such as tension and compression. I will use this information as I continue to think about my bridge design.

I also recall from my Structure class in elementary school that the shorter the distance between supports or piers, the more force the structure can withstand.


-Form of thinking -- Second lowest

-Re-word the idea or statement

-Student translates input information into a meaningful sentence or paragraph using his or her own words

-Promotes learning by preventing the student from  copying input information

-Paraphrase a statement, law, procedure etc.

-Summarize a paragraph in your own words.

-Convert a verbal statement into a mathematical formula or a simple diagram.

-Focus only on the limited scope of the information piece that is in front of you -- don’t question the information itself

-Above all, engage with or “dive into” the input information that you are given -- don’t just read it

-Outputs may be another paragraph, combination of paragraphs, mathematical formula, concept map or mind map or other visualization etc.

-Note: DO NOT COPY from someone or somewhere.

-DO NOT translate one word at a time using synonyms.

Delete this Teacher Sample Answer:

The Bridge Design Scenario letter was not clear about the length of the span that the bridge had to cross. The letter said “maximum of 30.5 cm long”.  So I translated that sentence in the scenario letter into “the bridge must cross a 30.5 cm span from pier to pier” and showed it to my teacher for his interpretation.  My teacher agrees that my translation is a much more clear requirement.


-Form of thinking -- Third lowest

-Explore the input you have been given

-Student assesses the collection of input information and determines relationships and classifications within the information set(s)

-summarize a paragraph or a page or an entire article

-Look for the “essence” of the information set

-Look for patterns in the data

-“If I only remember one thing from this article, this is it…”

-Question the information by using the 80/20 principle -- “80% of the value of this article will be found in only 20% of the article’s information” -- find and then translate and re-organize that 20%

-sort, classify, categorize or group data sets

-make simple preliminary or initial connections with other courses or subject areas -- eg “how does the concept of structure relate to database programming?” -- this is the beginning of extra fact-finding that may prove useful

-transform some confusing but important input information into “a more useful to me right now” format -- eg a table of due dates for unit assignments

-Outputs may be a concept map, flow chart, table of structured information, written paragraph, summary of several paragraphs, prediction etc.

-Note: Recall, Translate and Interpret are generally mental processes but, of course, making a concept map is “doing”

Delete this Teacher Sample Answer:

I read about types of bridges on the internet. A beam bridge has a thick heavy member spanning the river. The top portion is in compression -- getting shorter when it bends under a load -- and the bottom portion is in tension -- getting longer. According to other web pages, a truss bridge is similar, but it has only slender top and bottom members that are connected by slender diagonal struts. I interpret a truss bridge as being a special case of a beam bridge, with the top member in compression and the bottom member in tension. I should probably verify my suspicion through a test of some kind.


-Form of thinking -- Middle

-Application of information to solve problems in new or unknown situations

-Use information, concepts, skills, procedures, scientific laws, principles and other learnings in a new concrete situation.

-“Transfer” your knowledge and skills to other areas of study

-This thinking skill focuses on “making connections” -- more detailed than the simple connections made using the Interpret thinking skill

-Explain how a familiar concept relates to a new topic

-Value-added fact-finding begins in earnest as an important component of “making connections”

-Outputs may be a performance, demonstration, physical product, procedure, essay, mathematical solution, concept map etc.

-Note: “Doing” may generally be thought of as beginning at the Apply thinking level

Delete this Teacher Sample Answer:

I remembered from last week that my teacher stressed that the glue joints are very important. I used my apply thinking skill as follows.  I made sure we used the best glue for our Popsicle stick truss joints. I did some tests on several kinds of glue. Carpenters glue was the strongest if some pressure is applied while it dried. I needed to use my evaluate thinking skill here too.



-Form of thinking -- Third highest

-An important aspect of “critical thinking”

-More complete and detailed than the Interpretation form of thinking

-Student “takes apart” collections of information using logic, intuition, emotion, deductive and inductive reasoning, lateral thinking and other formal and informal techniques (eg, “gut feeling”)

-Reverse Engineering is a very valuable form of analysis for Technological Studies -- “how does this contraption work?”

-Find gaps in the information set -- what other information do you need in order to fill those gaps?

-Where there is uncertainty, the good designer obtains more data -- this may require further physical experiments or detailed research

-Sometimes what is not stated is just as important as what is stated

-Respond to your own “what if” questions

-Be the “devil’s advocate” making initial checks for weaknesses and faults

-Expose logical interfaces between sub-systems

-Explore cause and effect patterns or relationships

-Compare and Contrast 2 concepts is a simple form of analysis

Delete this Teacher Sample Answer:

Going back to my interpretation that a truss bridge is maybe just a smart way to make a beam bridge, I decided to explore this idea in a rather formal, organized manner.



Here is my analysis.  I found the above visual model of a beam in bending in the Keywords-Structures document. The arrows pointing toward each other represent compression forces and the arrows pointing away from each other represent tension forces. Suppose I model compression as positive force and tension as negative force. Then I would say that there must be zero force at the horizontal central axis of the beam. So I now ask:  if the middle of a beam bridge has zero force on it, then why would I waste good material there? This mass of material in the middle of the beam cross section is just adding dead load to our bridge and not helping us at all!


-Form of thinking -- Second highest

-An important aspect of “creative thinking” within the context of a greater system or an integration of sub-systems

-More complete and detailed than the Application form of thinking

-Student uses the creative process to carefully render a product or other output

-Outputs may include a physical or written product, process, performance, demonstration or any other form of communication etc.

-A set of Requirements and other planning procedures for a possible product solution must also be synthesized in the early stages of product development

-Goal-setting is a strong consideration -- think about “how to get there”

-A list of possible alternative solutions may also typically be synthesized during a brainstorming session

-Propose alternative viewpoints and hypotheses

-Elaborate on a product design idea -- integrate further details that make the product more valuable

-Elaborate on the interfaces that emerged during analysis

-Create metaphors and analogies to underscore the importance of a concept or to assist you in transferring skills and knowledge to a new topic or subject

-Define the level of “control” that must be integrated into your product, procedure or process

-Combine seemingly independent concepts into a workable value-added idea

Delete this Teacher Sample Answer:

Here is where I “put it all together”.

The teacher said that truss joints are weak spots in any bridge -- the interfaces between Popsicle sticks in my truss bridge for example. I made a very strong pair of trusses using carpenters glue -- see “Apply” above.  So I reason that the interface between the entire truss and my floor deck could also be a weak spot. It sure would be if I just use glue to stick the floor deck to the underside of my pair of strong trusses! I want to avoid just having the strength of glue as the only thing keeping my floor deck from ripping away from the strong trusses. In my design, the trusses provide the strength function while the floor deck provides the transport function of my bridge -- getting people from point A to B. I simply laid my floor deck Popsicle sticks on top of the strong bottom members of my trusses. Just a little dab of glue will stop them from sliding around. The glue does not have to provide any strength at all.

To summarize, the synthesize thinking skill is vital to taking apparently isolated individual ideas and concepts and weaving them together in a unique or special way to yield a better solution.


-Form of thinking -- Highest

-Student makes judgements against various established standards and other criteria

-Synthesize your own scoring system to assist the evaluation process

-Decision-making -- what do we do next?

-Engineering Judgement is particularly important when safety is an issue.

-weigh the advantages and disadvantages of each alternative solution idea under a variety of clear criteria (eg risk, build-ability; test-ability; cost etc)


-Note: Several cycles through all seven thinking skills may be required before a “fact” is “correctly comprehended” or understood in a particular context or situation. Problem-solving also requires several cycles through the 7 thinking skills.

Delete this Teacher Sample Answer:

For version 2 of my bridge I will experiment with making some I-beams as the horizontal bottom members of my truss. This is because I think that the bottom members are not in pure tension. They actually bend under the traffic loading as well.

Table 1: Thinking Skills: Definitions and Applications


  2 Assignment: Checking Understanding, New Connections and Relationships


This is individual work.  Teacher’s sample answers are in blue font.

  1. In about 30 words, Interpret, or summarize section 1.1 “Learning About Thinking”. What is the “essence” of section 1.1? (3 marks)

The essence of Section 1.1 is to clearly point out that “learning to think” is crucial in school. Memory work is a very small part of learning. It is good analytical and creative thinking that will make our world a better place. The design process follows the same natural pattern as the learning process. The cerebral cortex of the brain works in much the same way as the design process -- input, process and output.


  1. What do you need to do before you can become a “good thinker”? Which thinking skill did you just use to answer this question? Using a different form of thinking, state some other examples of prerequisites to becoming a good thinker. (2 marks)

In order to become a good thinker you must first become good at being open-minded, flexible, persistent, inquisitive and curious. For example, it was only 2 years ago that I first even “thought about thinking”. I am now a better learner myself because I constantly question my own thinking.


  1. In 20 or so words, use your Interpret thinking skill to explain what this Special Insight means to you:

What is the single biggest difference between life and your personal computer? There is no “undo” command in life.  (2 marks)

You must think clearly before you act or speak. Your actions can hurt others and this hurt cannot be reversed. The computer’s undo command is teaching us to be careless.


Some things that you do can hurt others -- you cannot undo these actions. You have to constantly think about impacts and consequences of your actions -- before you act!


  1. At what Thinking Skill does “Doing” actually begin? Explain in about 20 words using examples from what you know so far. (3 marks)

“Doing” most typically begins when you start to Apply some knowledge to a new situation in order to solve a problem or secure an opportunity. For example, I know some things about a few special students. I know some things about a software program. I will apply what I know in order to start to develop a learning opportunity for these students using that software. This will ultimately involve my higher forms of thinking as well.


  1. In about 50 words -- your own -- compare and contrast the two thinking skills, Analyze and Synthesize. Explain with examples connected to your experiences in real-world problem solving assignments. (5 marks)

When you Analyze something, you break it apart in a logical sort of way in order to better understand what each part or sub-system “does”. Synthesize is much the opposite -- we put things together to make a new whole. To properly analyze a system or other examples is an important prerequisite to doing a good job of synthesizing something new. It is important to be critical during design, so you must carefully use your Analyze thinking skill. It is also important to be creative during design and this requires use of the Synthesize thinking skill.

When I translate a physical object into a 3 view orthographic drawing, I am also breaking up the object into 3 particular carefully selected views. Someone else could synthesize an isometric drawing (a single 3D representation) by “putting together” the information from those 3 orthographic views.


Safety Reminder:

If you will be working with some tools -- “Think Safety”.

Inputs / Knowledge / Understanding That I Still Need or Connections that I Want to Make For This Unit: (give each a #)



Peer Assessor’s Name and Notes:







 The Scarboro Heights Record V15 #1