1. Curriculum Integration Why and How? Jeff Froyd Texas A&M University froyd@tamu.edu

2. Outline What is it? Why? Underlying Ideas Curriculum Integration

3. Curriculum Integration: What is it?

4. Concept Map A concept map is a set of nodes that represent concepts connected by a labeled links that describe a link between concepts. Concept A Concept B Describe how concept A and concept B are related?

5. Concept Map Concept A Concept B Link between concept A and concept B Concept C Link between concept A and concept C Concept D Link between concept B and concept D

6. Form groups of 4 Start with the concepts on the following page and construct a concept map that shows the concepts you have selected and how they are related. Exchange concept maps and share insights Team Exercise Building a Concept Map

7. Function Derivative Second Derivative Position Velocity Power Slope Curvature Energy Potential Energy Force Acceleration Electrostatic Potential Electrostatic Field

8. Curriculum Integration: What is it? Strong Version –To help students build a small set of powerful concepts/abilities/skills instead of a large set of relatively weak concepts/abilities/skills Weak Version –To help students build connections across disciplines

9. Curriculum Integration: What is it? Complete Integration Coordinated Integration Solo Integration

10. Complete Integration Clustered Students Regular meetings of all faculty teaching in the cluster Conscious interweaving of topics and examples between and among the courses Integrated examinations (preferably with interdisciplinary problems) Other?

11. Coordinated Integration Coordinate syllabi to align related topics Some homework for mathematics from the dynamics and controls text, etc Revisit exam problems from one class as examples or homework in another class Discuss impact of current research in engineering and science on possible solutions to class examples...

12. Solo Integration What could you do without assistance or cooperation from any other instructor to provide an integrated experience for your students?

13. Curriculum Integration: Why?

14. Why might integration promote improved learning? Understanding the transfer problem Remembering words Linkages: remembering people’s names Qualitative study at Berkeley Gender differences in approaches to problem solving Evolution in cognitive science

15. Challenge of Transfer Researches posed this problem to people. "Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. It is impossible to operate on the patient, but unless the tumor is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumor. If the rays reach the tumor all at once at a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity the healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor either. What type of procedure might be used to destroy the tumor with the rays, and at the same time avoid destroying the health tissue?"

16. Challenge of Transfer Consider the following story "A small country was ruled from a strong fortress by a dictator. The fortress was situated in the middle of the country, surrounded by farms and villages. Many roads led to the fortress through the countryside. A rebel general vowed to capture the fortress. The general knew that an attack by his entire army would capture the fortress. He gathered his army at the head of one of the roads, ready to launch a full-scale direct attack. However, the general then learned that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely, since the dictator need to move his troops and workers to and from the fortress. However, any large force would detonate the mines. Not only would this blow up the road, but it would also destroy many neighboring villages. It therefore seemed impossible to capture the fortress. However, the general devised a simple plan. He divided his army into small groups and dispatched each group to the head of a different road. When all was ready he gave the signal and each group marched down a different road. Each group continued down it road to the fortress at the same time. In this way, the general captured the fortress and overthrew the dictator."

17. Challenge of Transfer After the subjects read and summarized this story, they were asked to solve the tumor problem under the guise of a separate experiment. Given the clear analogy, you might think that performance would be near ceiling. Surprisingly, only 30% of the subjects offered a convergence solution. Moreover, when these same subjects were given the suggestion that they should use the General story, 80% provided a convergence solution. This finding demonstrates that half the subjects could apply the General story to the tumor problem when they were instructed to but did not do so on their own.

18. Recalling Words/Images fMRI studies can show what part(s) of the brain are active during a particular task. Place subjects in fMRI tunnel and show them a list of words (images). Can you predict from the fMRI scan taken during the presentation of a word (image) whether a subject will recall the word (image) Yes! Activity in two regions is important. –One region is in the inner part of the temporal lobe: the parahippocampal gyrus in the left (right) cerebral hemisphere. –The other region is in the lower left (right) part of the frontal lobes, where apparently links are being made to existing information.

19. Recalling Names Have you ever been talking to someone and said, “Someone was telling me about X and her name is …….. I can’t remember.” However, you can remember what the person looked like, where she lives, her occupation, etc. If you imagine a giant concept map within the brain, it appears that names (or other proper names) are often weakly connected to other concepts as opposed to common nouns. Without intention, instruction on a new concept may create a map in which the concept is weakly connected to other ideas.

20. Student Perspective Researchers at the University of California Berkeley interviewed about 70 mechanical engineering students about their learning experiences in college. Although the researchers were aware of various integrated curricula that had been implemented across the country, they were interested in the student perspective of integration, as well as the pedagogical perspective. Data from the interviews tended to support the value of linking concepts. For example, “Of the 70 students interviewed, 60% commented on the benefit of linking concepts across disciplines.”

21. Gender Differences Rosser and Sandler both report a difference between how men and women approach problems. Men tend to handle problems with a single correct or concrete answer comfortably Women are better able to deal with complex problems and problems that are ambiguous. Rosser asserts that many of the first year courses are more directed to single correct or concrete answers, which favor the learning style of men. This is one of the reasons, she believes, that women with high GPAs may leave the major in the first year.

22. Evolution in Cognitive Science Domain Independent  Domain Dependent Phase 1: Domain Independent –Taking Latin, mathematics, etc. as gymnastic exercises Phase 2: Domain Independent –Simon and Newell: General Problem Solver Phase 3: Domain Dependent –Focus strongly on domain-specific knowledge Phase 4: New Synthesis –General skills (metacognitive skills, problem formulation, study skills, etc.) embedded in domain- specific contexts

23. Phase 1: Domain Independent Mental fitness curriculum –Latin, Greek, arithmetic, grammar, geometry, etc. Edward Thorndike conducted studies around 1900 that suggested that the mental fitness curriculum did not build mental strength Singley and Anderson (1985) showed that learning a line editor did not improve the rate at which people learned to use a screen editor.

24. Phase 2: Domain Independent Emphasis on general cognitive strategies instead of mental fitness Simon and Newell: General Problem Solver –Means-end analysis –Early successes in games and formal logic didn’t generalize to knowledge-rich areas Schools: emphasis on thinking skills and study skills “there is no strong evidence that students in any of these thinking-skills programs improved in tasks that were dissimilar to those already explicitly practiced” (Bransford et al., 1985, p. 202)

25. Phase 3: Domain Specific Experts acquire deep knowledge of their area of expertise and organize in ways peculiar to their area of expertise. –Chess –Physics Studies of novices and experts showed that experts organize their knowledge very differently than novices. [Bransford et al., 1999] Acquisition of world-class expertise requires about 10 years of continuing dedicated practice [Ericsson, 1996]

26. Phase 4: New Synthesis “On the frontiers of [knowledge] everyone is a novice in the sense that prior knowledge is not directly applicable.” [Bruer, 1993, p. 74] Potentially Applicable General Skills –Metacognitive Skills –Problem Formulation –Problem Solving Skills –Learning Strategies –Self-Assessment Processes

27. Strategy Instruction What: include explicit descriptions of a strategy Why: include information describing why the strategy should be effective When: include explicit descriptions on when the strategy might be useful Context: provide instruction on a strategy in a domain-specific context where it will be useful

28. Bransford on Learning Physics An awareness of the difference between understanding and memorizing material and knowledge of which mental strategies to use in each case [learning strategies] Ability to recognize which parts of the text were difficult, which dictated where to start reading and how much time to spend [resource allocation] Awareness of the need to take problems and examples for the text, order them randomly, and then try to solve them [self-assessment process] Knowing when he didn’t understand, so he could seek help from the expert Knowing when the expert’s explanations solved his immediate learning problem “the behavior of intelligent novices contrasted markedly with that of the less skill.” [Bruer, 1993, p. 71]

29. Underlying Ideas

30. Properties of Electronic Materials Electromagnetic Engineering Wave Phenomena Electrical Engineering @ ASU Ron Roedel and Bob Grondin, Arizona State University

31. Multidisciplinary Applications of Spectral Analysis Dynamic Data Acquisition And Spectral Analysis Sally McInerny (AE), Harold Stern (EE) Tim Haskew (EE) University of Alabama Digital Signal Processing Vibrations Acoustics Electric Machinery Communications

32. Mathematical Ideas Measurement Measurement in the presence of structure Equivalence and equivalence classes Transform –go somewhere else, do something, return Gary Sherman, Professor of Mathematics Rose-Hulman Institute of Technology

33. Conservation and Accounting Framework Unified Approach to Engineering Sciences System Concept Extensive Properties Time Conserved Properties Accounting Principle

34. Six Ideas That Shaped Physics Conservation Laws Constrain Interactions The Laws of Physics are Universal The Laws of Physics are Frame-Independent Electromagnetic Fields are Dynamic Matter Behaves Like Waves Some Processes are Irreversible http://www.physics.pomona.edu/sixideas/

35. First-Year Science, Engineering, and Mathematics Rate of change Accumulation Conservation Materials