Thanks for asking readers of Dan’s blog to chime in on your website. http://blog.mrmeyer.com/?p=16514#comment-753923
What I don’t understand is how adaptive programs are better than a worksheet. Sure it’s nice to know where you went wrong when solving a math problem and a teacher can’t give every student the individual attention s/he deserves, but that can also be considered also be considered robbing the student of persistence in problem solving. (Individual v Personalized)
When a student comes to me, or a table mate, and asks for help we can backtrack his or her attempts. I can see the mistakes and make a quick guess at what s/he was thinking before asking a question.
I’ve often thought that for these adaptive computer programs each problem should have a list of common mistakes, and these mistakes should lead to questions the computer should ask after the student learns s/he is wrong. It’s just that students often have to input information into fields and the computer has to read the field and interpret what the student means. It become a huge AI problem.
I worked for a company that was paying teachers to write hints and clues along this manner. I thought it was a good idea, but I couldn’t seriously add the information I wanted to each question in the time allotted. I also thought it would be better idea to have teachers bounce ideas of off each other to make each problem better.
I also want to ask how we can incorporate different methods of solving a problem? (And perhaps that is my biggest problem with the last company and yours) Sure if I’m teaching multiplication I can give a 3 digit by 2 digit multiplication problem and check each step in the standard algorithm, but what if my student wants to use the lattice method? What if s/he wants to add repeatedly? What if s/he wishes to expand the numbers first then multiply? How do we write this into a computer program?
Ok you’re teaching students to use the most efficient procedure of multiplication (I would type it into Google or Wolfram Alpha) Where do we learn those other methods? Why are they valued less? If I can multiply do I understand? I get it this was all taught in class before we started using this method of practice (Why are we paying so much for a method of practice?). Is that the way the software will be used?
Yes, you are building software as an aid to teachers. A way for students to practice problems and be told immediately when and where they make mistakes so they can self correct. So I ask, “Is that the best way to practice?” “Will, that be the way your software is used in schools?” “How can students practice multiple ways of solving a problem?”
I get the temptation to use adaptive software to teach math. If you know certain sub topics then you can learn a specific new topic. Math of course is pretty well mapped out too. To multiply we need to know how to add, to add we need to know how to count, etc….. I don’t know how we can go from doing math to knowing math from a computer program, at least not without some quality guided discussions with real live human beings. Maybe Watson can do it, we should try?
What happens and what is happening on this website, at least in my opinion, is that the emphasis is on the skills and not the knowing.
Stills captures from https://mathtutor.web.cmu.edu/ using Skitch and the practice problems
Persistence is important in math. Many students will just type in numbers until they go green.
The second hint was better. It’s true though students don’t read the questions they just flop around until they hit upon the right answer. My three favorite questions as a teacher are: “Did you read the questions?” “Why are they asking you/?’ and “Why did you do that?”
I think your instructions are nice and clear, but they are teaching how to solve the problem, not teaching math.
What happens if I the student has a question that is not specifically about solving the problem, but is related to the fundamentals of the concept?