When addressing material that cannot be illustrated or is too complex to learn through discovery, a deductive approach can be used. In Texas, the direct teach model is deductive. The teacher relates new learning to prior learning, models, demonstrates or illustrates new material, the student practices learning and then demonstrates their mastery of it. 

DEDUCTIVE EXAMPLE: The teacher is focusing on the nature of change within a country and the class has just finished learning about Westward Expansion. The teacher reviews with the students the reasons and cause for this migration. She then states that they will be learning the cause of WW I today and by the end of the lesson, they will compare and contrast factors which instigated Westward Expansion in the US to the causes of WW I in Europe. She presents information about WW I and its causes through a short video, oral reading by the students from the text, and a discussion about Europe in the early 20th century. Then the students break into small groups and are provided three sets of questions, each focusing on one point of view illustrated in the video. Each group takes turns rotating through two CD-ROM encyclopedias in the classroom, looking for corroboration of the answers they are providing in their questions. The teacher monitors this activity, making sure students are referencing the video they have just watched as well as their text. Each response must have two sources to support it. Finally the students work in their groups to compare and contrast Westward Expansion to WW I, using their prior knowledge and the answers they have just discovered. This is recorded on a matrix and discussed in a large group once all have finished. 

Inductive approaches to teaching reflect how many of us learn things in real life. We notice patterns of objects, events or phenomenon and we categorize these and then label them. In this approach, the teacher is providing examples of concepts (either physical, pictorial or textual) to the students who then make inferences from these examples and either come up with a concept definition or a generalization.

INDUCTIVE EXAMPLE: The students have been investigating reasons for the Westward Expansion as well as barriers that were met by the pioneers as they traveled west. One of those barriers was weather which changed dramatically throughout the journey, as did the terrain. The students wonder what causes weather patterns across the US. The teacher provides students with US weather maps, collected over the year and which document air currents and weather phenomenon. The students carefully analyze the maps as the teacher focuses their attention to geography, air currents and climatic phenomenon. Students conclude that there is a relationship between these features. After the lesson the class is divided into groups. Each group focuses on a different section of the United States, determining climatic characteristics of each. The groups illustrate this by creating a weather guide for the pioneers, using a word processing program with draw functions, identifying location and likely weather for each month of the year. Graphs of amounts of rainfall and temperature changes are generated, on a spreadsheet program which re-formats data into graphs, and are included in the guide. 

Inquiry approaches to teaching place the student in the role of researcher and are based on questions from which the students can pursue answers through hypothesizing, predicting, collecting data, analyzing and drawing conclusions. This model is best used when focusing on generalizations that can be drawn from analysis of available materials and information.

INQUIRY EXAMPLE: As the students are reading The Diary of Ann Frank, they are also looking at the statistics of WW II: number of bombings on given cities; number of dead in various time periods; and change in economic conditions in Germany, the US and England. The wonder what it must have been like living in this period and how people changed between WW I and WW II. To explore this the teacher asks them how thought living in France, Germany, England or the US in the 1940's might have been like. The students hypothesize the US and England would have been the least changed, since the ground fighting was primarily in Germany and France. The class discusses what aspects of life may or may not have changed: daily activities, school, shopping, travel, media, clothes, etc. The students are divided into groups and each group is assigned one of the four countries. Each group is then provided photographs, in books on each country, taken during this time period, and groups take turns searching through a CD-ROM encyclopedia. Each group looks for the state of the factors discussed. When they are finished, the class as a whole records their findings on the board in a matrix and find that all of the countries are effected, in different ways, to different degrees. They conclude that proximity to battle does mean that more basic needs are deprived, but that allies in a war may also suffer in order to provide resources and manpower. Students then script and program a HyperCard stack that illustrates a day in the life of a child living in one of the countries during the war.