Critical Thinking Math Eye Level Critical Thinking Math takes students through a curriculum of study areas covering advanced mathematic concepts, skills and applications. Each level emphasizes critical thinking through reasoning skills, such as sequencing, comparing, planning, hypothesizing, analyzing, critiquing and developing of deep perception-- that can all be applied in the student’s everyday life. Critical thinker students can develop, therefore, greater concentration, better study habits and increases self-confidence and self-esteem.

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Critical thinking definition

The concept of critical thinking is derived from ancient Greek Kritikos meaning “discerning judgment based on standards”.

Then it can actually be defined as “thinking explicitly aimed at well-founded judgment, utilizing appropriate evaluative standards such as logic in attempt to determine the true worth, merit or value of something”. When we think, we bring a variety of thoughts in some order. When the combined thoughts support each other and make sense together, the thinking is logical. Critical thinking tradition seeks ways of understanding the mind and training the intellect so that such “errors, blunders & distortions” of thought are minimized.

the thinker - creative thinking - critical thinkingReversibility, Conservation & Classifications: essential ingredients of logic
Reversibility: Can a child mentally trace back his route home and tell you without hesitating?
Conservation: Can a child tell you that the amount of water in the short and tall beaker respectively is the same?
Classification: Can a child classify objects into their groups? Can children understand relationships between objects and people?

How do you know that children have mastered critical thinking skills?

  • Mastering ciritical thinking takes years of practice.
  • Critical thinkers are not dependent on instructors to tell them how well they are doing. This self-assessment ability should be something should be able to do comfortably at they higher levels of critical thinking Mathematics.

The following are qualities of students who have mastered critical thinking:

  • Raise important questions and issues with instructors
  • Analyze key questions and problems clearly and precisely
  • Distinguish relevant from irrelevant information
  • Recognize key assumptions and clarify key concepts
  • Reason carefully from clearly stated premises
  • Note important implications and consequences

Background concept wordcloud illustration of critical thinking strategy Stock IllustrationHow can critical thinking be applied to daily life?

Critical thinking is important wherever the quality of human thinking significantly impacts the quality of life. A well cultivated critical thinker (Paul, R. and Elder, 2006):

  • Raises vital questions and problems
  • Formulating them clearly and precisely
  • Gathers and assesses relevant information
  • Using abstract ideas to interpret it effectively
  • Comes to well-reasoned conclusions and solutions
  • Testing them against relevant criteria and standards;
  • Thinks open-mindedly within alternative systems of thought
  • Recognizing and assessing, as need be, their assumptions, implications, and practical consequences
  • Communicates effectively with others in figuring out solutions to complex problems.


Eye Level Critical Thinking Mathematics

The Eye Level Critical Thinking Concept in based on teaching of the following curriculum:


  • Relationship Analysis: Classification, relation, similarities, differences, irrelevances.
  • Geometry and spatial Sense: Spatial placement of directions, distances & location of figures and objects. The geometry and spatial sense ability helps to improve students’ skills in conservation, visualization and estimation
  • Problem solving strategy: Data Analysis, tree diagram, pattern recognition, alternative methods, drawing diagrams, reverse calculation, deduction, trial and error.
  • Reasoning: Reasoning, which is a higher order thinking skill, is a necessary skill in higher education and in working environment as students are required to critically evaluate statements and to make logical judgments. They will be able to understand and integrate a procedural process to reach a solution. With a developed reasoning skill, students will be able to show inferencing power that goes beyond factual information, and they will not easily be influenced by vague and ambiguous language.

When Eye Level instructors teach students, they ask questions to guide them and avoid spoon feeding, so that the students can come up with a solution with minimal assistance.

Memorizing the solution to a problem will lead to mastery of the specific problem short term. Critical thinking is a skill that Eye Level would like to nurture in students. At Eye Level, a good (or strong) critical thinker is equipped with the tools to solve effectively unfamiliar problems on a long term basis.