# Exercises Offer Different Approach to Teacher Tests

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Most multiple-choice tests for teachers emphasize generic skills that can be applied to many teaching situations and subjects.

In contrast, Stanford University's Teacher Assessment Project is based on the assumption that effective teaching varies depending on the content and the students being taught.

The research team's emphasis on the relationship between subject-matter knowledge and pedagogical skills--often called "pedagogical content knowledge''--has generated a series of exercises that look very different from existing teacher tests.

During field tests, elementary-school teachers participated in 10 exercises on the teaching of equivalent fractions to 4th- and 5th graders, and high-school teachers participated in nine exercises, primarily on the teaching of the American Revolution.

Below are descriptions of several of these exercises from the research team's 15-month summary report to the Carnegie Corporation:

• Math Lesson Planning (90 minutes). The examiner provides the candidate with a lesson on simplifying fractions from a widely used 5th-grade arithmetic text. Following an instruction sheet, the candidate takes 30 minutes to review the section of the textbook and to plan a lesson on the topic. The lesson need not follow the textbook.

In the following hour, the candidate explains the lesson to the examiner and answers questions about it, such as what an appropriate homework assignment would be. Finally, the candidate responds to brief vignettes involving possible student misconceptions about the lesson, such as "You have the students simplifying 8/18 at their seats. You discover that one student has tried to divide numerator and denominator by 4. What would you say and do?''

• Math Topic Sequencing (45 minutes). The examiner gives the candidate 17 cards bearing a set of topics usually covered in a unit on fractions in the upper elementary grades. The examiner asks the candidate to arrange the cards "into groups and subgroups in the way that you think they best fit together mathematically, that is, as a set of mathematical ideas.'' The examiner asks the candidate to explain his rationale for the arrangement.

The examiner then gives the candidate 8 of the 17 cards, and asks him to arrange them "in the order they should be taught.'' Again, the candidate provides his rationale. The examiner also asks the candidate to discuss difficulties that students might have with the topics, and to discuss whether switching the order of 2 of the 8 topics would be a legitimate way to teach them.

• Math Opportunity Box (45 minutes). The examiner gives the candidate two boxes containing such items as a bag of poker chips, a package of white paper plates, a ball of string, a pad of graph paper, a clock, a set of measuring cups, a ruler, an empty egg carton, and a set of socket wrenches. The candidate selects from each box two items that might be used to help teach the equivalence of fractions. The candidate takes 20 minutes to think about how he would use the items in teaching. The examiner then asks such questions as, "What are some ideas for using this item to teach the equivalence of fractions?'' or "What are the main drawbacks of using this item?''
• Documentary History (90 minutes). The examiner gives the candidate a textbook summary, several documents, and three pictures concerning the Battle of Lexington, April 19, 1775. Most of the documents contain sworn testimony, collected at the time, regarding the events at Lexington. Some of the testimony conflicts. The three pictures were painted or engraved at different times; generally, one may discern the evolution of a myth in these pictures. The candidate has 30 minutes to examine all these materials. In the remaining hour, the examiner asks a variety of questions concerning both the use of the documents and pictures in a historical interpretation of the events at Lexington and the use of those same documents and pictures in history teaching. One question is, "How could you capitalize on the differences among the three pictures?''
• History Videotape Critique (90 minutes). After an introduction, the candidate views a 22-minute videotape of a teacher giving a lesson for 11th graders on the Spanish-American War. The candidate then is asked for general observations about what he has seen. The examiner then plays the tape again, stopping at three predetermined points to ask more specific questions, such as "Describe the quality and accuracy of the material you saw. How would you present the material to students?'' In closing, the examiner asks a few more questions, such as "If you could give this teacher two or three pieces of advice, what would you tell him?''

Vol. 07, Issue 37

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