Monday, October 27, 2014

A logic puzzle clue trading game

I've been on a logic puzzle binge recently (all in the name of research, of course) and I got to thinking about some games that could be built around the puzzles.

Just to review, here's a description from Wikipedia:
Another form of logic puzzle, popular among puzzle enthusiasts and available in magazines dedicated to the subject, is a format in which the set-up to a scenario is given, as well as the object (for example, determine who brought what dog to a dog show, and what breed each dog was), certain clues are given ("neither Misty nor Rex is the German Shepherd"), and then the reader fills out a matrix with the clues and attempts to deduce the solution. These are often referred to as "logic grid" puzzles. The most famous example may be the so-called Zebra Puzzle, which asks the question Who Owned the Zebra?.

Here are some potential rules:

1. Each clue is printed on a separate card;

2. An equal number of cards are dealt to each team. Remaining cards are turned face up for everyone to see;

3. Teams take turns filling in cells with x's and o's. There is no limit to the number of cells that can be filled in a single turn.Teams receive one point for every correct x and ten points for every correct o. Incorrect guesses cause a team to lose a turn. If the incorrect guess was an o and the cell was actually an x, the moderator fills in that one cell. If the incorrect guess was an x and the cell was actually an o, the moderator will fill in the o-cell and will put x's in the cells of the row and column containing the o.

4. After each turn, the team that just went will have a chance to trade cards with other teams. Teams must describe their cards honestly though they can withhold information. For example "Our card involves Alice and honey" could describe the clue "Alice ate the honey" or "Alice did not eat the honey" or "Either Alice ate the honey or Simon ate the jam."

5. Teams can copy clues before trading them away.

Still very much in the early stages. Let me know if you can come up with something better.

Friday, October 17, 2014

Hexagonal Reversi

Now that you have a hexboard, here's on of many games you can play on it. Hexagonal Reversi is very similar to regular Reversi (which is suspiciously similar to Othello, but that's a subject for another post).

Here are the starting positions:

Each player takes turns placing one of his or her pieces on the board so that at least one row of the opponent's pieces lie between the newly placed piece and another piece already on the board at which point the row of opponent's pieces are replaced with the player's pieces.

This figure above shows the possible initial moves if black goes first (B) or if white goes first (W).

Wednesday, October 15, 2014

Make your own hexagonal game board

After the standard 8x8 chess board, the 6x6x6 hexboard might be the most versatile piece of equipment an abstract strategy gamer can own. (Here are a few of the games you can play with this set.)

If you're serious about games you should probably buy one of the boards, but if money's tight or if you want to ease your way in, here's a good, high-res image that you can download and print off to make your own.

Tuesday, October 14, 2014

Positive steps: if we have to make tough choices then we need to be honest about them

A few years ago I taught at a small rural school in the Mississippi Delta. The old timers would talk at great length about how much better the school had been before I got there. They attributed the decline to the closing of the alternative school. In the "good old days," any student who caused trouble would be pulled out of class and sent to a special, highly structured school -- basically a glorified study hall -- run by an honest-to-God former Marine drill sergeant.

According to the version I was told, the program worked exceptionally well but was shut down in a discrimination suit because a disproportionate number of African-American students were being sent to there. This was a very conservative community (I doubt that there was a unionized teacher in the county let alone in the school), so it is not surprising that this was seen as another instance of the federal government interfering.

As you might guess, I saw things a bit differently. The government has not only the right but the obligation to step in in cases of racial discrimination. Furthermore, even if there had not been a civil rights issue here, I still have very mixed feelings about policies that potentially denied certain kids a quality education simply because they were difficult to deal with.

There is, of course, another side to the debate. In a world of fixed resources, educators frequently have to weigh the needs of the many against the needs of the few. If a small group of students is undermining the quality of education for the student body as a whole, there is a case to be made for removing the students. Just as importantly, sometimes that particular disciplinary action is the best thing for the kid being disciplined. For some, the structure and discipline of a boot camp environment really is the best educational setting. For others, there is a scared-straight effect. For these kids, a brief stay in the alternative school is enough to convince them to improve their behavior and work habits.

There are a lot of lessons to be learned here, but for me, the big one is that education is filled with tough choices and difficult trade offs. We need to acknowledge this difficulty. We need to have honest, well thought out discussions about the consequences of discipline and expulsion (both nominal and de facto). In particular, if we decide to sacrifice one student for the good of the many, we need to own up to that decision.

Today, in many schools, we have covert policies in place (particularly in the popular "no excuses" schools) that effectively mimic the alternative school approach of that small Delta town, including having a disproportionate impact on African-American males (often taking it to the next degree). But as much as that troubles me, what bothers me even more is the fact that we don't face up to what we're doing.

Sunday, October 12, 2014

A couple of Halloween themed word puzzles

Both of these puzzles are simple enough for elementary school students but can be surprisingly challenging, even for adults.

I'd recommend having kids work on the first individually and the second as a group.

From Classic Word Problems for the Classroom.

Friday, October 10, 2014

A note on creating geometric graphics

As you can see in the previous post, I've been working on a project involving the kind of problems you might see on the SAT or GRE. I've been focusing on geometry to start with which means I have to create lots of geometric drawings.

I recently started using Inkscape and I would highly recommend it for the following reasons:

It's a free, open-source program;

It works with  Scalable Vector Graphics (SVG). Scalability is a great feature;

It's easy.

Quick tip: you can draw circles and squares from a center point using the shift key.

Tuesday, October 7, 2014

A step-back SAT/GRE problem -- Circles

I've been thinking a lot about video learning, particularly video-assisted self-study. One of the ideas I've come up with is the step-back problem.

Sometimes, when you're trying to teach yourself a subject or study for a test like the SAT or GRE, you will run into a problem that still confuses you after you've gone through the explanation. If you have access to a live instructor,  you can always ask for a more detailed explanation but what do you do if you are trying to learn the subject from YouTube videos?

My thought is to pair up problems of medium to high difficulty with problems that use some of the same concepts but are much simpler.

Here's an example. The following is very similar to some problems you are likely to see on the SAT or GRE. Try it on your own then check below the fold for the answer. If you didn't get the right answer and still don't understand what you got wrong even after reading the explanation, try the second problem.

Circle 1

The radius of circle 1 is 5. Both line segments pass through the center of the circle. Find the area of the shaded region.

Monday, October 6, 2014

Friday, October 3, 2014

Advice to a student about online videos --too easy is better than too difficult.

I think as a general rule, there is a lot to be said for the idea of taking the time to get the basics down and understand the fundamentals before moving on. In the context of a confused student looking to catch up, however, this rule goes from generally good to absolutely essential. The kids who are likely to seek out this kind of assistance and, more to the point, those who really need it are almost without exception afraid of the material. This anxiety is usually one of the main obstacles to mastering their lessons

One of the great advantages of watching a math video is that it doesn't watch you back. The fear of looking dumb, of being judged, is perhaps the main reason struggling students are reluctant to ask for help. Being able to listen to an explanation or see an example in a safe and private place can be remarkably beneficial but those benefits go away quickly if that video makes the viewer feel stupid or confused.

The first requirement of any math video (or math lesson, for that matter) is that it be correct, not necessarily in the picky, get-the-jargon-right sense, but correct in the sense that the basic ideas are right and you end up where you're supposed to. A close second is that the video make the student comfortable with the material. If I'm explaining a problem to a student or group of students, I can adjust my presentation based on the reactions I'm getting. I can slow down, make an explanation more detailed, offer words of reassurance, even stop what I'm doing and switch over to a simpler problem. The video instructor can do none of these things.

That said, under the right circumstances, a video that walks a student through a problem and hits just the right level of difficulty can do a lot to build both skills and comfort level.

Here's a clip that does a pretty good job, particularly with the reassurance part.