Interview with a Post Secondary Mathematic Instructor

Interview Except	Analysis
Can you give an example when you use technology and when you don't in your teaching? Please explain why you use or not use technology in each case. Use technology for computer demonstration of computer graphics, demonstration of calculations using Excel. Demonstration of other concepts using computers. Appropriate to use Excel to do the calculations to avoid tedium of calculation, and chart results. Computer graphics and algorithm course – demonstrate change in appearance, students can see the outcomes and effects. Don’t use Powerpoint. Used only rarely. On handouts, if you give them handouts, students believe handout is equivalent to learning. If you don’t give them handouts, they don’t make notes effectively, no matter how slow you go. Stay away from overhead projector, use white board, because it is more interactive.	The instructor uses technology judiciously. He is aware of the changing attitudes of his students and picks the appropriate technology, mainly to demonstrate the effects of mathematical concepts, rather than using technology to explain the details and derivation of these concepts. The instructor also prefers using the whiteboard to present mathematical concepts rather than using Powerpoint which is more static. By working out the mathematics on the board with the students, the students are able to follow the reasoning and the procedure behind the concepts and the derivation.
How has your teaching changed or not changed in the last X years with new technologies being introduced in the classroom? Does it reduce preparation time or increase it? Are the students more engaged? Less time on derivations and more time on demonstration. The effect can be seen on the changing characteristics of the class. Mathematic students tolerate derivation much less than before. Not big change in how to teach, but can do more demonstration better now. 20 years ago, computer graphics course emphasized on computer algorithms. Students nowadays will not benefit from that approach. They are less detail oriented, they click buttons to see what will happen. They learn less.	One of the advantages of technology is that it can easily captivate student attention through its multimedia presentation. The side effect is that the students are so used to the razzle and dazzle of these demonstrations that detailed analysis of the inner workings of the mathematical derivations, which are much more “mundane”, is not as well received.
How has the student's learning changed or not changed in the last X years with new technologies being introduced in the classroom? Do they do better? Do they ask more questions? Are their critical thinking skills improved? The students will not learn on their own. The existence of user interfaces in electronic equipment, whether telephone or computer screen, has changed. Strategy to solve problems is to put something down, and see if it gives the right answer. You may not know the answer but if it doesn’t look right, try something else. User friendliness does not promote stop and analysis learning. Strategy is to try a solution, if it doesn't work, try something else, and see if it works. Hacker mentality. It makes the trial and error. Hard to engage students in hard problem solving, with or without technology.	The result of using technologies in the classroom is that the students actually learn less with technologies, and the effect is exacerbated by the “user-friendliness” of available technologies in the classroom. Instead of promoting critical thinking and analysis, students can try different guesses to get at the solutions of their math problems, rather than logically reason out the steps to solve the problems. Instructors may also rely overly on technologies to grade student assignments, such as the use of Scantron, or simply checking the final answer rather than the steps to solve a problem, which is not available using current technology.
Imagine that your school had an unlimited budget and it offered the Mathematics Department the opportunity to completely revamp its classrooms and course contents. The Director of the Mathematics Department is looking for suggestions on how to spend that money. What would be your top three suggestions to spend those funds? (Damian) Used Maple TA to set up a testing system – enormous use of technology, took 8 months to set up the questions. Expense is not in equipment, but in developing the content, and creating the question templates. Potential use is to give every student equivalent work to do, but the questions are different. Students cannot just copy from other classmates. Good for co-op learning. Alternatives are generated by the random number generator. Used in a remedial class with high failure rate. Co-op learning does not work with one set of questions. Students will find out who the brightest student is and that student do the work and others will just copy from that student, and have little idea how to do the assignment. Students at XXXX have too much work to do. One student will do the work in one class for everyone, and another student will do the work for another class for everyone. Unique assignment will force each student to do the work. If done on the internet, the template can also generate hints for the students but these must be prepared by the instructor. Takes a lot of time to prepare.	Technologies need to be carefully evaluated before they are adopted in the classroom. The pros and cons of using technologies must be weighed upon carefully to ensure student learning is not affected negatively. Even learning methods without the explicit use of digital technologies, like co-op education, is found to be unsuitable for certain learning environments.
What kind of learning curve do your students experience with educational technology in your class? (PATRICIA) Are they pretty quick in picking up the new technologies? Not really a learning curve especially in demonstration. Students use Excel a lot. 25 years ago, they had to use calculators. Now they use Excel and they struggle with it. Not so much for computing students who probably learned from other courses. Other students take about 25% of course to learn Excel, included in course outline.	Learning to use technology in the classroom does take up extra time. This should be factored into the regular schedule without having students to learn them outside of class.
What limitations do you see with respect to using technology in your educational environment? (WANDA) Are there any support? Do you have enough preparation time? Consumes time. Support: it takes time to write programs to develop demonstration. Other instructors use Powerpoint to develop slides.	With the limited time and support for teachers, it is difficult to explore the use of technology in the classroom, and to critically evaluate their advantages and disadvantages. Powerpoint is popular and easy to use because presentations can be easily put together, and some textbooks already come with these presentations as part of the teacher’s resource kit. It also helps the teacher to organize the material to be presented.
Final comments on technologies in the classroom: Technology is not a panacea. Educational activity still takes place between people. Technology is just a tool. Technology is still very passive for the moment. Information is provided but the students have to figure it out themselves. As a tool to remove tedium of calculations, give variety and demonstration and visual in the classroom, technology is great. Not sure if the real contact between a machine and a student will ever happen. Not sure if a machine will pick up the thinking process of the students. Students still talk to the instructors because they can’t just learn from the book themselves.	Technology has not matured, and may not ever mature, to a state where learning can be tracked by a machine to effectively guide a student in the learning process. This instructor’s use of Maple TA is a step in the direction in that the templates he put together do project what the students may or may not do in the solution of the math problems. In case the student does take the wrong step, the program can question the student’s reasoning.

Video Clips

I watched the videos on Learning Environment 1 (graphing calculator) and Learning Environment 2 (high school physics).

Teacher F sees the calculator as a mini computer. He sees the potential of the calculator to be more than just a tool to ease the drudgery of manual calculation, but he uses the calculator to empower the students to attempt problems beyond those that are normally covered in class. Technology thus augments the students’ natural abilities to allow them to explore and make advances in mathematics. I think this is a good use of technology in that students are empowered to make the leap from a learner to an explorer or researcher.

Teacher F is obviously a good planner in his teaching in that he knows what the scientific calculator can do and the type of problems that are suitable for his students. He is also very resourceful in the purchase and use of calculators to motivate his students rather than depending on the limited resource of computers in the school. His continuous use of calculators from Grade 8 to 11 allows the students to become familiar with this technology and this familiarity, in turn, allows them to make use this technology with comfort and without fear. Good use of technology also involves good classroom management where Teacher F uses teams to allow students to help each other.

One area that I like to explore is how to come up with good exploratory problems for the students that are appropriate for the technology that is available in the classroom. I am not sure if this is based on intuition or whether there is any scientific methods for doing so?

Teacher A in the science classroom uses technology beyond the technical lessons that he wants to teach. He also emphasizes on the transferable skills. I think he actually organized his class such that these transferable skills can be learned because of the technology used. Thus his labs are done in teams, where they have to set goals, manage time and resources, etc. One area I like to explore further is the type of transferable skills that different technology best promotes, and to experiment how this can be incorporated in the classroom.

Teacher B realizes that good use of technology requires good support so teaching and learning can be conducted smoothly. She also sees that both computer simulation and manual, hands on lab have their advantages and disadvantages. It is not clear which method is better under what circumstances or topics to be covered. One area I like to explore further is to do a comparative study on the use of the two methods for different scientific experiments.

Good Use of Technology in the Classroom

What is a good use of technology in the math and science classroom? What would such a learning experience and environment look like? What would be some characteristics of what it is and what it isn't?

Having only taught one semester of math using no technology other than the whiteboard, and having no experience in teaching general science, I am not sure if I can really answer these questions. Anyway, here are my thoughts. I think a good use of technology in the math and science classroom is one that helps the students to construct their knowledge that closely resembles to either absolute truth (objectivist view) or a reality based on the experiences and interactions with the environment (constructivist view). For me, math is an abstract discipline. We can’t really touch and feel mathematical objects, like numbers, algebra, graphs, sets, etc. Similarly many scientific concepts are abstract in nature. Although we can do experiments in science, it is difficult really understand chemical reaction, biological growth, or physical interactions just by observation (Steele, 2002). So any tools or technologies that can help students have a better grasp of such abstract concepts are useful in the classroom.

For math, I can think of the graphing calculator or the bigger computer version, Maple program are examples of good uses of technology in the math classroom (http://www.maplesoft.com/). These technologies allow the students to visualize mathematical concepts through graphs and different ways of mathematical formula manipulations. Through interacting with the mathematical objects, and their transformations and being able to visualize the effects, e.g. in graphs, the students may come to a better understanding of the mathematical concepts.

Similarly, in science, simulations on the computer play an important role in helping students to associate abstract concepts with mental constructs. A realistic simulation provides the students the ability to experiment and manipulate an artificial world that closely resembles the reality and thus allowing her to have better understanding and predictions of the physical world.

The selection of mathematical tools and scientific simulations must be carefully made for the students so they don’t get overwhelmed. Even for scientific calculators, there is a wide range of selections out there. Some simulations can be too detailed while others are too simplistic.

What makes this a good use of technology? Is this a vision or is it possible in real classrooms? What makes this vision a challenge to implement and what might be needed to actualize it?

Simulations and mathematical tools like graphing calculators and Maple are commonly used in the science and math classrooms. Good and realistic simulations are not easy to come by though although there seems to be quite a number of them around. In my son’s high school, there are a number of scientific calculators that the students can borrow. However, such technologies can be expensive to produce and be purchased.

References

Steele, B. (2002). Why are some scientific concepts difficult to grasp? Retrieved on May 12, 2007 from http://www.pitt.edu/utimes/issues/34/020321/12.html

del.icio.us

This is amazingly delicious ... del.icio.us. I use a number of computers, at work, at home, and on the road. It is so difficult for me to keep track of my bookmarks since each computer has a different set of "favorites". When I upgrade a computer, it is so troublesome to store all the bookmarks from the old computer and reload them into the new computer. All this is history when I came across del.icio.us. It is so simple to have all the bookmarks stored somewhere in the virtual land. Now all my computers have del.icio.us installed and I can tag webpages anywhere and can access them anywhere else! Amazing!

I can't help but think how del.icio.us makes money. There is a "your network" link that allows me to connect to other people, and share my bookmarks. I suppose the more people you are connected, the network grows and as the user base increases, it has more power of influence. But I am still not sure what is the catch!

Down Memory Lane - First Encounter with Technology

My first memorable experience with digital technology in education setting, as far as I can remember, has to be the programmable scientific calculator. The year was 1975 when I was in Grade 10. (Yes, you may pause to figure out my age.) Basic function calculator that could only do simple arithmetic was pretty common back then. It had been around for a few years then and, in fact, I was quite unimpressed when my father first brought home one of these calculators. It was huge and heavy and all I could do with the calculator was add, subtract, multiply and divide. I don’t think it even had a memory function. I could do anything and everything that basic calculator could do .. although perhaps slower and I would make more mistakes. But in terms of functionality, I did not perceive the calculator as an extension to what I could do and that it could benefit me much.

But when one of my friends in Grade 10 showed me his TI SR-52 calculator (see http://www.thocp.net/hardware/ti_calculators.htm), I knew I had to get one. I was totally fascinated by the many colored keys and funny symbols, as well as the myriads of functions built into the calculator. I suddenly realized that here was a machine that was more intelligent than me. I had the idea that if I could own one of these little machines, I would be so much more intelligent. So after calling a number of stores in the lower mainland, I finally tracked down the last calculator available at the Bay and immediately went and bought it.

I then spent many hours pouring through the manual and experimenting on the calculator, and learning the different features of the calculator. I learned mathematics which I had not been taught in school before such as statistical functions, polar / rectangular coordinates, radian / degree conversions, etc. I was also fascinated by the RND key – it generated random numbers. I could not really understand why I was so fascinated by this function until recently, and that is I had always thought of the calculator as a deterministic machine and there was supposed to be a one to one correspondence between input and output. There was supposed to be no randomness in mathematical functions. The fact that this calculator seemed to violate this deterministic behavior caused me to think that this machine might have more power than I realized. (I said “seemed to” because I know now that there is really no such thing as random numbers. Random numbers are really generated by a function that generates numbers that “look” random.)

The TI SR-52, however, was more than just a scientific calculator, it was also programmable. This was my first exposure to programming. Once again, I was fascinated that by punching in a sequence of instructions, I could get the calculator to perform a series of complex calculations at the touch of one or two keys. Then as I explored further, the calculator turned out to be an amazing game machine. I started with some simple games, like high-low game, memory game, and then I learned how to program the calculator to play more sophisticated games like Blackjack, Mastermind, Lunar Lander, etc. The amazing thing was that all these games were played using one line of digital display. Others who watched me as I played these games must have wondered what I saw in those numbers. The programmability feature allowed the calculator to be transformed from one with a finite number of built in functions to one that could compute almost anything, limited only by the amount of memory inside. Again the sense of power in knowing what the calculator was capable of doing and how to program it was extremely exciting and satisfying for me then. It was an interplay between discovering the inherent power of the calculator with all the built-in functions and enhancing the calculator capability to give it additional functions that have captured my interest since then, and even now. Last year, I purchased what I believed to be the most advanced scientific programmable calculator on the market nowadays, the HP – 50G. The screen is a lot bigger now, and one can play Lunar Lander and Blackjack with much better graphics, and it boasts 2300+ built-in functions! One can hardly stop learning, discovering, and exploring with one of these marvels!