So, at the start of class today I put up the slides from yesterday. Then I had students write down their observations, what they noticed, and what questions (that may have something to do with math) they had. I gave them about 2 minutes to look at the first slide, had them share with the class and repeated for the second slide. I also told them to continue writing questions and observations as we talked, especially if they saw something while someone was talking so they wouldn't forget it. We then bowled a 3rd game today.

**3rd Period**

3rd Period Data

__Their observations:__

What they wrote:

- We had a low score but our skill level was higher. Team 1 beat Team 3 by 1. Team 1 had 1 strike
- Team 4 had 5 strikes but didn't win. Teams 2, 3, and 4 cheated. Team 1 had no strikes but should've won anyways. High skill level than our score. Team 4 had 1 open frame.
- Skill level and score is different. Team 3 had more strikes but didn't win.
- My team came in 3rd. All teams scores are different. We had the most strikes. We had 7 open frames. Every skill level went up.
- Scores are between 100-200. This student copied the information off the board.
- Why is the score lower than the skill level?
- Team 3 had a turkey. Different scores. Scores between 100 and 200. This student wrote the scores down.
- In the second game both Teams 2 and 4 had 6 spares.
- We had the most strikes but didn't win. Teams 1, 2, and 3 got smashed.
- (1st game) 2 teams had the most strikes but still did not win. Team 1 had no strikes and still won. All the scores were different. Skill level went up for everyone. The scores were between 100 and 200. Team 3 got a turkey. (2nd game) Team 4 got the most strikes and won. Everyone's skill level went up. Team 2 set a record. Team 3 beat Team 1 by 1 point.
- Teams 2, 3, and 4 cheated. Team 1 had no strikes but should of won.
- All the scores different. All skill levels different. Number of 0's different. Strikes are different. Teams 1 and 4 had the most spares. Open frames were different. Skill level went up for everyone. Team 3 got a turkey. 1st 3 frames spake strike Team 4. Teams 2 and 4 had most strikes. Team 3 had most open frames. Team 2 set record.
- (Game 1) Team 3 had more open frames. Team 2 their skill levels high then their score. Team 1 had no strikes. Team 4 won. Team 4 had 1 open frame. (Game 2) Team 1 had 6 open frames. Team 2 had 2 strikes. Team 3 score 117. Team 4 had 0 number of 0s. How is this math? I know there's numbers but I am confused!

__My notes from class discussion:__

(These are the observations and questions they shared)

Game 1:

- Higher skill level than your score
- All scores were different
- Teams 1 & 4 most spares
- Team 1 no strikes
- Team 4 1 open frame
- Skill level went up for all
- Scores 100-200
- Team 3 had a turkey
- Team 4 spare/strike/spare/strike

- Team 2 set a record (higher score than before)
- A lot of individual team observations

- Some are really close
- Some averages went down
- 2 teams in the 200s, 2 teams in the 300s
- Going up by 100s for right now
- Maybe they'll increase by 200s

- All skill levels will go up.
- If you do worse than you did before it will go down.
- Maybe it won't go up as much.
- Depends on how bad you do.
- Maybe if you got less than before - might drop a few points.

3rd Period Data Day 2

**5th Period:**

5th Period Data

Their observations:

__What they wrote:__

- I noticed that team four only had 4 strikes and they still one. I also noticed that Team 1 was winning most of the time except for the end. How did team 4 come back at the end/ How did Team 1 have the lead the whole game?
- (Game 1) Team 4 had the highest score. Team 2 had the lowest score. Why did Team 2 have 2 strikes and Teams 1 and 3 have 1 each? (Game 2) Team 4 had the highest score again. Team 2 had the lowest score again. Why did Team 2 and 4 have the same amount of strikes?
- (Game 1) Team 4 had the lowest score. Team 1 had the lowest skill. Team 2 had the lowest score. (Game 2) Teams 1 and 2 had the same number of open frames and zeros. Team 3's scores were all even. All over 100 points.
- Strikes help a lot. Open frames hurt. Even with a similar score Teams 3 and 2 didn't have (he crossed this out - I think he meant similar skill levels). 2nd game Teams 3 and 4 got better and Teams 1 and 2 got worse. Teams 1 and 2 had a lot of open frames. Team 2 could've won if they had more spares. Skill level didn't go up much for Team 4 even with the new record.
- (Game 1) Team 4 had 2 more strikes than Team 2. Team 4 had 68 more skill level points than Team 1. (Game 2) Teams 1 and 2 had 7 open frames. They all had above 100 points.
- 1st game teams had no skill level, and in the end it jumped up by hundreds. The skill levels jumped by a lot in the second game. The open frames from Teams 1 and 2 are the same but different the first game.
- The more open frames the less the score. Team 2 had most strikes but the number of open frames is the highest and tied the number of 0s.
- Teams 2 and 3 had a higher skill level than Team 1 but Team 1 had a higher score. teams 1 and 2 had the same amount of open frames.
- Why did Team 1 have the lowest skill level but they came in second?

__My notes from class discussions:__

I prefaced this discussion with something about not getting into comparing teams (so I wouldn't have the comments about my team was the best, etc.).

Game 1:

- Strikes help a lot, open frames don't help
- Why did Team 1 have the lowest skill level but came in 2nd?
- Team 4 had 68 more skill points than Team 1
- Team 2 had the most open frames and 0s.
- Kids had started to pull this out, but I also pulled it out of them - Teams 2 and 3 are 1 point apart but 5 points apart in skill level (1 less zero)

- All over 100 points
- Teams 3 and 4 had better scores; Teams 1 and 2 had worse scores
- Skill level did not go up much for Team 4 even with record
- Team 2 had most strikes, tied for highest number of open frames and zeros

Their Game 3:

5th Period Data Day 2

**So where does this leave our heroine?**

Well... when I left school, I felt pretty dejected. I had not read the student papers - I didn't have time (had to get registration completed for NCTM's Reasoning and Sense Making Workshop done so I could hand the school credit card back). The kids, while they enjoyed Wii Bowling, were getting rather silly at times (something about it being May 3rd and I have classes that are almost all freshmen boys) and I did not feel the discussion went well at all. 3rd period, the students who were willing to contribute were so focused on the competitive aspect that it was so difficult to get anything out of them of substance. Other students weren't willing to contribute to the discussion. I definitely see from today that I have to learn how to ask the right questions to get good discussion going. I also recognize that it is May and this is the first time I have really asked them to think about information in front of them.

5th period, the discussion went better. I have a student who has a rather strong interest in this. He plays Wii Bowling frequently (it sounded like almost daily) and you can tell he has put some thought into it. Also, I think my 5th period class is stronger academically than my 3rd period class (however, I also have bigger discipline issues in that class). While they were bowling, I was talking with the student who Wii bowls often and a couple of other students casually about it and I shared with them I have been thinking about this on and off for a year. I also shared with them that my first thought was wondering how the skill level was determined. Wii Bowler said that he had the same first thought. My guess is, he had that thought so long ago and since he bowls so often, he really doesn't think about it anymore.

I also left school discouraged because I felt that class was as chaotic as usual. I didn't feel like the students were engaged. Well, some students were, but very few. I don't know if I have unreasonable expectations here with it (a) being their first time doing this and (b) it being May, but I guess I felt like I had enough of a hook to get their attention. I just don't feel like they're focused on the math at all.

**What next?**

At this point, I am planning on starting into our next unit. I have no idea where to take it from here. In addition, I am out on Thursday and I'd like to start into something so I can leave an assignment for Thursday. I also want some time to step back from it and think through where this is heading. The kids aren't heading where I thought they would so it's time to re-evaluate.

Any thoughts? I feel like I'm at such a loss at the moment. Frustrated that it doesn't seem to be clear. I thought I had a good idea to start with and now I'm questioning that. Any advice is greatly appreciated. Thanks.

## 1 comment:

I had fun looking at your data today, and while I wasn't able to come up with a rule or formula I'm confident with, I can say that it looks like the better you bowl, the higher you have to score to keep raising your skill level, and that if you don't keep bowling consistently your skill level seems to go down.

The way I looked at the data was to graph each team on the same axis and measure the slope from (0,0) to (game1points, game1skill), then from (game1points, game1skill) to (game2points, game2skill), and finally from (game2points, game2skill) to (game3points, game3skill). I noticed that at first most of the slopes were above 1 (your skill level was slightly higher than your points) and then it was closer to 1, and then it was under 1 if you didn't improve enough.

After that, I went on Google and looked to see if Nintendo had explained the scoring everywhere. I learned that Wii skill levels might be affected by the skill levels of the people you beat or lose to (complicated) and that when playing against the computer at least, the formula is probably based on points + K*(actual points - expected points). But no one knows how expected points are calculated... is it just linear?

I also learned from Google that a lot of people have your question (how is skill level calculated?) and no one has the answer! Some other guesses were that it was based on the number of strikes, or the ratio of strikes to spares...

I noticed that your students are doing more thoughtful analysis than a lot of the people who posted on Yahoo answers...

I wondered if, since this is probably not going to end up being data that works that well with a linear model (especially as you bowl more games), it might be a chance to practice describing patterns in data? Maybe your student teams could post something to Yahoo answers saying what they saw in the data they collected and how they think the skill level is being calculated?

Also, I'm be happy to share my graphs with you if you'd like to use them to show your kids that someone else out there in the real world cares about the math they're doing! They're here: http://screencast.com/t/Gm4h7mmg (pd 3) and here http://screencast.com/t/zozr3wTGOxZO (pd 5).

I'm wondering what it would take for you and your students to end up feeling proud for having taken some time to explore math that no one (except some secret keepers at Nintendo) have been able to answer! You've practiced some problem-solving skills (noticing and wondering about patterns in data, describing patterns, generating and organizing data) and have some opportunities to contribute your thoughts to a conversation that lots of people online seem to care about.

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