Logic is the systematic reasoning process we use to comprehend the relationships between facts in order to reach conclusions. Logical thinking enables students to understand what they read and what they are told and helps them see relationships, understand sequencing, and make inferences. Students with good logical-thinking skills can take new information to build upon what they already know. Outside of the classroom logical thinking can help improve social skills.
Logical reasoning comprises two opposite types of thinking: deductive and inductive. Deductive reasoning begins with a general statement. When we use deductive reasoning, we begin with a general statement. We then examine specific premises to infer a conclusion. If all the premises are true, then the reasoning will be sound. Inductive reasoning, on the other hand, uses specific observations to make a generalization. Inductive thinking may result in a correct conclusion, but it is not reliable.
Example of Deductive Thinking
Premise 1. A dog is a mammal.
Premise 2. All mammals are warm-blooded animals.
Conclusion: Dogs are warm-blooded animals.
This conclusion is valid, and because the premises are correct, it is also true.
Example of Inductive Thinking
Premise 1. Jane’s dog has spots.
Premise 2. Jake’s dog has spots.
Premise 3. Jennifer’s dog has spots.
Conclusion: All dogs have spots.
This conclusion is not valid. Just because the three premises are true, it does not follow that the generalization—all dogs have spots—is true.
Logic Activities That Strengthen Deductive-Reasoning Skills
There are several types of logic activities that help build important deductive-thinking skills. Some of the most popular ones are analogies, syllogisms, verbal picture puzzles, and logic “grid” puzzles.
An analogy is a type of logic in which one thing is inferred to be similar to another in a specific way. The relationship between one set of things is compared to another set of things with the same relationship. Analogies are typically expressed in this way:
A : B :: C : D
The items to the left of the “::” should have the same relationship as the items to the right of it. Possible relationships include antonyms, synonyms, part to whole, whole to part, item to function, cause to effect, and so on.
Example of an Item to Function Relationship
__________ : dry :: soap : clean
Answer: towel : dry :: soap : clean
Unless a list of possible answers is provided, there are likely to be more than one correct answer when completing an analogy.
A syllogism is an argument in which a conclusion is supported by two premises: a major premise and a minor premise.
Also, when deciding whether or not a conclusion is valid, It is important to consider words like all, some, every, and sometimes. It is also necessary to remember that a conclusion can be valid logically but untrue if a premise is untrue.
Example of a Valid Syllogism
Premise A: All birds are vertebrates. (Major Premise)
Premise B: The parrot is a bird. (Minor Premise)
Conclusion: All parrots are vertebrates.
This conclusion is valid logically and it is also true because the premises are true.
Example of an Invalid Syllogism
Premise A: Some ten-year-old boys like to play basketball. (Major Premise)
Premise B: Zack is a ten-year-old boy. (Minor Premise)
Conclusion: Zack likes to play basketball.
This conclusion is invalid. The fact that some boys like basketball does not mean that all boys like basketball.
Verbal Picture Puzzles
Readers analyze the way in which words are written in terms of position, size, and direction in order to decipher the words, phrases, and expressions depicted.
Examples of Verbal Picture Puzzles
1. an afterthought
2. strength in numbers
Logic “Grid” Puzzles
In each puzzle, the student is given an equal number of categories and options within those categories. The goal is to use the list of clues provided to determine which options go together. This type of logic puzzle has only one solution.
To find the solution, the student must read the problem to determine the sets of options. If no grid is provided, then he or she should arrange them onto a grid or other visual. Depending upon the level of the problem, the grid might have two, three, or more axes. The number depends upon the number of sets of variables to be sorted out.
Students read all clues carefully and use stated information and inferred data to complete the cells on the grid.
Students test their conclusion by making sure that each part of the conclusion satisfies the clues given and the inferences that were made.
Solving Logic Mysteries and Logic Mysteries for Young Readers
These two books, published by Educational Books ’n’ Bingo, provide ready-made logic grid puzzles for elementary students:
* Solving Logic Mysteries is for grades 3–6.
• Logic Mysteries for Young Readers is for grades 2–4.
The logic problems in these books improve students’ deductive-reasoning and other critical- thinking skills. They also improve memory and reading-comprehension skills and encourage students to expand their vocabularies.
Each book is divided into three levels, with Level 1 containing the easiest problems and Level 3 containing the most difficult. A labeled grid is provided for each puzzle.
Detailed instructions on how to do these types of activities are provided. If the students are unfamiliar with this type of activity, I suggest that you go over this step-by-step explanation, even at the upper levels.
Students should work on most of these mysteries alone, in pairs, or in small groups. Groups can compete against each other to see which group can solve the problem first.
Students should read the introduction to each mystery carefully. Explain that some of the information given here may be needed to solve the mystery. Instruct them to use context clues to figure out any new vocabulary words that appear and to use their dictionaries if they still are not sure of the meaning.
An option you might try once the class is familiar with this type of activity is to do a few on the board as a whole-class activity. In this case it is probably best not to give students their own copies. Instead, have then listen carefully and perhaps jot down a note or two as you read the story and the clues.
Detailed, clue-by-clue solutions are provided for every puzzle.
Hints (Provided for duplication in the books)
The following should be kept in mind as students work on these mysteries:
• Names that are usually girls’ names can be assumed to be girls’ names.
• Names that are usually boys’ names can be assumed to be boys’ names.
• Important information in the introduction may not be repeated in the clues.
• Some clues may not be used to solve the mystery.
• Some clues may be useful later on when more facts are known.
• It sometimes helps to make a diagram or chart.
Verblers contains 339 verbal picture puzzles for grades 4 through adult. They build skills in these areas:
• spatial reasoning,
• visual memory,
• problem solving,
• analogies, and
All solutions are provided.
Your students will love doing these Logic Grid Puzzles and Verbal Picture Puzzles! And so will you
Barbara Peller, Author of Solving Logic Mysteries, Logic Mysteries for Young Readers, and Verblers, published by Educational Books ’n’ Bingo