Critical Thinking in First-Year Math Courses

A type of reasoning that uses a general principle or premise to draw conclusions. The conclusions are valid if the premise is true.

A type of reasoning that uses evidence to support a conclusion. As more evidence is added, the conclusion becomes more likely to be true.

The ability to analyze information and form judgments based on evidence and reason. It involves critical thinking skills such as analysis, evaluation, and interpretation.

Evaluations in math and math-based sciences typically focus on problem-solving but may also assess understanding of concepts and theories.

Increasing the number of different ways to represent information (e.g., visually, verbally, or audibly) helps learners retain information better.

A way of knowing that involves applying knowledge to new situations and solving problems. It's about taking what you know and using it in a practical way.

This level of learning requires breaking down information into its components and examining the relationships between parts. It involves comparing, contrasting, and analyzing information.

This level of learning goes beyond analysis. It involves creating something new by combining different elements or ideas. It requires creativity, problem-solving, and critical thinking.

A verb that often indicates a synthesis-level learning objective. It implies creating something new by combining existing information or ideas.

A verb often used for analysis-level learning objectives. It suggests comparing and contrasting different elements to understand their similarities and differences.

Investigating alternative explanations for an observed phenomenon.

Two events may appear related, but one doesn't actually cause the other. They might be influenced by a separate factor.

Failing to recognize that two events are connected due to a shared underlying cause.

Oversimplifying causal relationships by assuming only one factor is responsible for an outcome.

Assuming that because event B happened after event A, then A must have caused B.

A hierarchical system categorizing learning outcomes based on complexity, from basic knowledge to complex application.

The simplest level of Bloom's Taxonomy, focusing solely on recalling information.

Understanding concepts and being able to explain them in your own words.

The ability to apply knowledge and understanding to new situations and solve problems.

Unconscious attitudes, reactions, stereotypes, and categories that affect behavior and understanding.

Assumptions made based on one's own cultural values, perspectives, attitudes, and behaviors.

A conscious preference or aversion toward a person or group of people, based on deliberate thoughts that can be identified and communicated.

The tendency to assume that all people think, feel, and act the same, regardless of their cultural background or time period.

The attempt by imperial powers to spread their culture and dominate others. It assumes a universal way of thinking and acting.

The tendency to treat people who are different as fundamentally and irreconcilably "other" based on their background (e.g., race, ethnicity, gender).

Implicit and explicit biases affect how we argue and interpret arguments by introducing opinions and assumptions, not logical reasoning.

Bias, whether implicit or explicit, can impact academic settings by leading to assumptions about students' abilities and potential.

Claims that can be proven or disproven through evidence and verifiable information.

Using personal feelings, experiences, or opinions as evidence, often problematic due to subjectivity.

Making decisions based on limited evidence or 'gut feeling', useful for individuals but limited in generalization.

Using personal experiences as evidence, can be compelling but prone to hasty generalizations.

Testimonials are accounts from others about their personal experiences, similar limitations to personal experiences.

Using information from someone considered an expert in a field, reliable if current and relevant.

Directly observing and monitoring subjects, influenced by observer's biases and motivations.

Detailed information about a specific group or instance, not always representative of the wider population.

A mental shortcut or rule of thumb that allows for quick decision-making, even with limited information.

The tendency to generalize from a single experience, potentially leading to biased decisions.

Our natural tendency to avoid risk, especially when potential losses are significant.

Exploiting social norms of reciprocity, where people feel obliged to return favors, even in situations where it's inappropriate.

The tendency to rely on emotions and social influences, even when they conflict with logical thinking.

The idea that there are limitations to logic, and emotions play a crucial role in human cognition.

The part of the brain responsible for processing emotions.

The part of the brain associated with logic, language, and reasoning.

The ability to think and feel, highlighting the complex interplay of logic and emotion in human nature.