Analytical Reasoning

What is good thinking?What is involved in good problem

solving?

Good thinkers Develop logical, sequential pattern

of working through complex material.

Work persistently, believing they will find the answers.

Draw on old knowledge to solve new problems. Relate, interpret, & integrate.

Poor thinkers Merely collect facts Unaware of relationships Cannot put old and new information

together to draw conclusions No logical problem solving method.

Problem solving is a skill Good analytical reasoning is a skill that applies

to all fields of study. The skills you develop by struggling through

and figuring out a difficult mathematics problem are much the same ones used to struggle through and figure out a difficult literary passage, or solve a problem at the office.

The act of thinking through complexities of biology make it easier to think through other kinds of complexities.

Thinking is a skill that requires practice.

Beware of shortcuts Finding answers through help from

others can solve immediate problems, but it doesn’t help you build the skill.

Examples? Internet searches Copying instead of paraphrasing Classes to help you pass tests Teachers giving the answers Fill in the blank with prescribed words

Unsuccessful Students:

1. Have no method of attacking new material.2. Misunderstand or skip directions.3. Fail to keep goals in mind. 4. Are unable to apply knowledge to new

situations.5. Answer questions based on few clues.6. Use impressions and feelings to answer.7. Are careless, jumping from detail to detail.8. Give up easily and guess.

Successful Students:

1. Solve problems systematically.2. Read directions & know how to start reasoning.3. Keep goals in mind. 4. Pull out key terms to simplify material.5. Break problems into smaller sub-problems.6. Apply relevant old knowledge.7. Are persistent and careful.8. Are active and aggressive in seeking meaning

Arthur Whimbley did a study:

Poor college readers have two main features

One-shot thinking Rather than extended, sequential understanding of

the material An attitude of indifference

Too willing to allow gaps of knowledge to exist Don’t care about knowing accurately

Analytical reasoning skills can be learned through practice

Logical Problem Solving Skills

Break Problems into Small Parts. Use Logic to Arrive at a Solution. Break Complex Word Problems

into Sequential Steps for Solution.

Problem Solving Exercise Mary is shorter than

Carol but taller than Kathy. Sue is taller than Mary but shorter than Carol.

Which girl is tallest?

CarolMary

CarolMary Kathy

CarolSueMaryKathy

Problem Solving Exercise George and Scott are

the same age. Beth is younger than George, and Jack is older than Scott. Tom is older than Scott but younger than Jack.

Who is the oldest?

G = S

JG = SB

J TG = SB