Symposium for Teaching and Learning with Technology

Abstract:
A sample of interactive modules for liberal arts students will be presented in the areas of counting techniques, probability, logic puzzles, and deductive reasoning. These modules are designed with the aim of helping students construct their
knowledge starting with basic definitions, and their use in simple contexts. Students work on their own, outside of class, at their own pace. Class time is then used to work on more complex problems. After class, students work on additional more complex problems. Technology plays a crucial role in coordinating out-of-class and in-class activities, and in providing
immediate feedback both to the students and the instructor. In this way, students come well prepared to class, allowing for more interactive learning. In addition, students have greater control on their own learning process.

"A small and selective audience" this morning. :) Professor Jimenez is presenting materials that he has been working on for about a year. He is trying to learn the new version of Flash. He is very fascinated what can be done with Flash. He understands that Flash is a commercial product and used to create animations on the web.

He wants students to have control of what they do, and he wants to provide the structure so students are lost. He wants to provide materials that address the students' needs. He has the challenge of the background - the requisites of the class. He has the challenge of that students may not have the motivation to learn, and the challenge that some students don't have the abilities to do the mathematical problems. He wants students to learn something and see the ability that it can be applied somewhere else. He wants them to think quantitatively and to read and write mathematics - not just crunch numbers. Based on all of this he is trying to build the content to build on these skills instead of having them just learn the content.

The first component of the course is logic. He is trying to help the students to develop a sequence of arguments in a logical way and use deductive reasoning. He produces a series of logic puzzles in the form of modules that are opened in ANGEL. He uses Flash to create these modules. The example he is showing has cartoon characters that were designed by a former student. After the students attempt the sequence of the puzzle they are brought to a screen that tells them the number of correct answers, the number of times the problem was tried, and the time spent. He is produces a background for security purposes to prevent students from sharing the answers with each other.

The second module he shows us also involves deductive reasoning. Everything on the module is created from scratch. The students can practice at home. In class, he asks the students to present how they solved the puzzle by demonstrating the sequence they used. The modules are a required part of the course, because students wouldn't do them otherwise.

He thinks of mathematics as a language. He understands that students can have difficulty with this language, so he creates these small "stories" to help them. At the end of these stories he asks "simple questions" for the students to answer.

He is beginning to fear that he is having too much control of his students. He knows that the student who knows how to do it will be able to finish the module in about 20 minutes. Now he can say do these two modules and these problems, and that is the two hours that the students owe him for the week.

Inductive reasoning: Suppose that there are 25 people in the classroom. How many handshakes occur? If the students can't solve that, he starts smaller and develops a pattern to start a table. He also asks students the magic word - "abracadabra." How many words can you spell from "abracadabra?" Start small and develop the pattern. With 10 cards, how many ways can they be shuffled? The idea of all of this is so students can visualize things. Students can do these things at home. In class, he asks students as a group to fill out tables to find the patterns.

Venn Diagrams: He has several modules featuring Venn diagrams. He wants to eliminate the possibility of guessing and getting the problem right. Students develop the the ability to see that Venn diagrams can become a double value table. He wants students to make a connection between the language and the diagram. His students have difficulty dealing with sets - complements, intersections, etc. He has developed modules that deal with these issues as well.

Combinatorics: He wants students to understand two concepts - combinations vs. permutations. This is a complex assignment. He has a module dedicated to these concepts - what they are and where they are going to use it. Students work on these modules at home and then come to class where they work on solving problems - starting small and then expanding and increasing the values. His modules ask students to integrate their knowledge in a specific context.

Conditional Probability: These modules try to give students a visual demonstration to learn this concept.

Professor Jiminez's feels that these modules are a powerful tool to ask students to work at home without using class time to teach basic concepts. Class time can be spent on using these concepts to solve mathematical problems. Even though he puts the modules in ANGEL, he understands the differences between producing things in ANGEL and producing things in Flash. Quizzes created in ANGEL don't take as long as creating them in Flash, but once a quiz is done in Flash, it is more dynamic - he can create simple or complex problems, randomize questions, etc.

Even though Professor Jiminez has not used Flash to create animations, how he is using it in his classes is a unique way to teach. The stories that he creates enables the students to visualize the problems as well as gives them the convenience to do the problems on their own time and work through them multiple times. He has said the the response to this from his students has been very positive. He seems to want his students to actually have to work to understand these concepts.