Category Archives: Dan Meyer

Review of Math Tutor

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Dear Kevin,

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?

 

 

The Problem with Standards

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Some people suggest that the medium in which we present mathematics is the problem. And I think that is true. However, as with all things that is only one part of the problem.

The Department of Education sees a lack of high standards in schools as the main problem in education.

Politicians, parents, schools boards, and millions of other people see unified standards as a method of solving this problem.

It certainly is tempting. The idea that if everyone would just teach that same stuff then at least we all have a base of knowledge to build upon, to depend on.

If we raise standards by requiring schools to teach specific standards how do we make sure this is being done? The obvious answer of course to raising standards in the quality of education is to set standards and then measure whether we are meeting those standards.

 

Let’s follow the logic:

When people think that a test is the way to measure a students mastery of a standard we think it is a good idea to develop a better test.

When we try to develop a better test that measures specific standards we spend a lot of time looking at those standards.

We write questions with those standards in mind.

It is very hard to write a question that meets a specific standard and only that standard.

We modify the question so that it only includes information or questions for that specific standard.

These modifications change the question from a fair description of real life into some mutant cyborg that scare little children.

Mutant Cyborg Costume front

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Algebra

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Algebra Tiles
I think most people have heard of these, but not everyone knows what they are and how to use them.  I’m not really going to explain that here. I have however found a great power point that is very easy to explain. A direct link to the power point is here. The Alliance for the Improvement of Mathematics site is here http://www.delmar.edu/aims/
What I will do is explain how to make your own set of tiles.
Start with four different colors of paper. Card stock would probably be best. Red, blue and yellow green is suggested.  The x tiles will be red and blue and the y tiles will be yellow and green.  One color will be for positive and one color for negative. I would also laminate when done if you can.
When making the tiles the important part to remember is that the long side of the tile should be immeasurable.  This is easily enough to figure out by simple using any sort of diagonal on graphing paper. Make the short side 1cm in length. Make two different size tiles. This is important because the immeasurable length means that the tile is an unknown.  When introducing the tiles to the students for the first time let them measure all they want and eventually they should come to the determination that the length of one is x and the length of the other is y.
The next two tiles to make are squares that are x2 and y2. Finally you will want 1cm by 1cm squares of white. (You can substitute centimeter cubes for this) If you want you can also include 10cm long strips.
The tiles can be used for everything from adding and subtracting integers to multiplying and dividing polynomials.
Finally, I want to end with a great video from Dan Meyer. He is sharing his application video for Apple’s Distinguished Educator Program. It’s a fun watch and because he uses Vimeo it is visible on school computers.
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Algebra

Posted on by
Reply
Algebra Tiles
I think most people have heard of these, but not everyone knows what they are and how to use them.  I’m not really going to explain that here. I have however found a great power point that is very easy to explain. A direct link to the power point is here. The Alliance for the Improvement of Mathematics site is here http://www.delmar.edu/aims/
What I will do is explain how to make your own set of tiles.
Start with four different colors of paper. Card stock would probably be best. Red, blue and yellow green is suggested.  The x tiles will be red and blue and the y tiles will be yellow and green.  One color will be for positive and one color for negative. I would also laminate when done if you can.
When making the tiles the important part to remember is that the long side of the tile should be immeasurable.  This is easily enough to figure out by simple using any sort of diagonal on graphing paper. Make the short side 1cm in length. Make two different size tiles. This is important because the immeasurable length means that the tile is an unknown.  When introducing the tiles to the students for the first time let them measure all they want and eventually they should come to the determination that the length of one is x and the length of the other is y.
The next two tiles to make are squares that are x2 and y2. Finally you will want 1cm by 1cm squares of white. (You can substitute centimeter cubes for this) If you want you can also include 10cm long strips.
The tiles can be used for everything from adding and subtracting integers to multiplying and dividing polynomials.
Finally, I want to end with a great video from Dan Meyer. He is sharing his application video for Apple’s Distinguished Educator Program. It’s a fun watch and because he uses Vimeo it is visible on school computers.
Enhanced by Zemanta