00:08good morning today i would like to show you how artificial intelligence can transform
00:17the way we study mathematics i will be presenting a model built around an interactive
00:27book that i created specifically for my students that's one you can see
00:37in this model learning take place through a dialogue between the student and the book content
00:46mediated by microsoft copilot in essence copilot acts as a highly qualified and freely accessible
01:01tutor i have implemented this approach across all the subjects i teach algebra trigonometry
01:16calculus and even more advanced areas of applied mathematics
01:21my goal is to demonstrate how artificial intelligence can make mathematical thinking
01:32more engaging more personalized and more effective
01:41let's see how the model works
01:45studying mathematics has never been this easy learn how copilot can help you understand concepts
01:52solve problems and enjoy math like never before dedicated to algebra students
02:08i must acknowledge that some colleagues have cautioned me about the potential risks of adopting
02:13these methods as certain students might rely on artificial intelligence to reproduce solutions
02:19mechanically thereby bypassing the genuine learning process while i partially share this concern i do not
02:26believe that the existence of dishonest practices should dictate teaching strategies instead such methods can be
02:34particularly beneficial for students who are genuinely motivated to learn as they allow them to
02:39verify their solutions formulate more advanced questions and ultimately deepen their understanding
02:46this method aims to raise the level of educational competence to the upper floor of learning
02:51learning and not to compare the performance of the students with the lower level of academic
02:55honesty or with skills that have stagnated regardless of the reason simply let's help them improve
03:02to compete not with the underperforming but with those who demonstrate high efficiency
03:08come on think think think why won't it stick
03:13to illustrate the method i'll use a partially interactive book i created for my students
03:20it is designed as both a lecture guide a framework for my presentations and a structured workspace where
03:25students can explore ask questions and practice extensively in the next minutes of this video
03:32i will illustrate the method not by delivering a traditional mathematics lecture but by working as a
03:38student who is learning calculus i will follow the guidance provided in lectures consult the textbook
03:45solve exercises and complete the assigned homework let's see how it works first locate the source in your computer
03:56then open the file and then open the authorized document this is an authorized pdf document
04:05now open it and check that that it is correctly opened reduce or enlarge to the
04:10dimension of your choice and arrange the browsers as preferred i used to open the book on the left side
04:17the next step is the most important open the copilot by clicking in the copilot symbol in your browser
04:24now you are ready to work individual study is recommended the student reads the book
04:30studies and takes notes in the blank spaces provided after each topic in the interactive book student
04:37manually solve some exercises and suddenly the student comes across something that don't understand well
04:45the student does not fully understand the relationship between the numerical solution and the graph
04:50and fears not knowing how to ask correctly so they simply ask for the solution and wait for the tutor
04:56to
04:56guide them the question should be asked politely it is necessary to establish a good and respectful
05:03relationship with copilot for example could you please help me with this question copy the example
05:10and paste it into copilot preceded by the question copy and paste very simple operation and then submit
05:21as you can see copilot produces a full answer to the question explaining the solution step by step and even
05:28providing multiple approaches using different methods you can also request voice commands which is a great
05:35advantage for students with visual disabilities
05:40would you check the solution by substitution
05:46I answered yes peas and now you can see full explanation
05:58also we can request graphic interpretation of the question let's see
06:11now you can download the graph to your computer you can copy and paste or you can request an explanatory
06:18document in word or pdf format
06:26be grateful and kind say thank you and ask copilot if it can continue helping you for your satisfaction touch
06:35the voice command
06:39of course
06:41you can continue working with me anytime I am here to help you with your math
06:47graph explanations or anything else you'd like to explore what would you like to work next
06:55please solve and explain this rational equation
07:04I don't understand why this equation do no have real solution or why the solution is no solution
07:18is no solution or a code that is a solution or what would you like to do
07:21expect that you can do with some of your own things
07:22it's also a solution that causes a solution that you can do with my understanding and
07:26you can do without any insight on doing it
07:26the most complete answer but the student can also ask for a simple as objective as possible answer
07:37copilot will rephrase the answer for a beginner in algebra
07:52For reasons of time, I think we can finish with one more example, although I would really like to solve
07:59many examples let's say one more, a word problem from chapter 4 on logarithms and exponential equations. The possibilities are
08:07practically limitless.
08:11Now we will look at something that is quite difficult in practice and that many intelligent online systems cannot solve,
08:18word problems. Let's choose one using exponential functions, mostly this is an algebra exercise, suppose that at the start of
08:27an experiment there are 10,000 bacteria. A growth inhibitor and a lethal pathogen are introduced into the colony. After
08:352 hours 2,000 bacteria are dead.
08:37If the death rates are exponential, a, how long will it take for the population to drop below 1,000?
08:46b, how long will it take for two-thirds of the bacteria to die?
08:57Notice how Copilot responds to your question in detail, even offering theoretical foundation of the topic.
09:16We can say that we are done, with those examples.
09:20I think it is enough to illustrate how to use Copilot to study mathematics.
09:25This way of studying is so pleasant that it seems to me that, from now on, I will like mathematics.
09:32I liked the method so much that now I am going to solve a difficult example, a system of equations,
09:38I copy it and again ask Copilot to teach me how to solve it.
09:44I increased the speed of the video 10 times to save time, basically looking for the solution.
09:55Copilot solve the problem using three different methods.
09:59Elimination, substitution, and matrix method.
10:02Also I requested graphic solution, I can download the graph and keep it in my computer.
10:20To finalize this lecture, I want to introduce my Copilot assistant, please pay attention.
10:28The best way to use Copilot overall.
10:31White heavy check mark use it after attempting the problem yourself.
10:35White heavy check mark use it to clarify, not replace, reasoning.
10:39White heavy check mark use it to learn how to think mathematically.
10:43If you use it well, Copilot will.
10:45Make hard topics clearer.
10:47Reduce frustration.
10:49Help you become more confident and independent.
10:51Final advice to students.
10:54Copilot works best when you work too.
10:56Ask good questions, think actively, and treat it like a patient tutor, not a shortcut.
11:04Students of Professor Preeto Valdez receive the book free of charge.
11:09However, the books for the different algebra options can be purchased on Amazon, and in digital format at lulu.com.
11:25Final thoughts.
11:27To use Copilot in this class, please be sure to follow the guidelines outlined in the syllabus.
11:33This includes reading the classroom AI policy, signing the Copilot use agreement, and submitting it to me.
11:41Completing these steps will give you permission to use Copilot as a learning tool in our course.
11:46I hope this presentation helped you better understand how artificial intelligence, especially Copilot, can support your learning and strengthen your
11:54understanding of mathematics.
11:56Thank you for your attention, your participation, and your willingness to explore new tools that can enhance your learning.
12:03Professor Juan Preeto Valdez.
12:06Professor Juan Preeto Valdez.
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