Thursday, January 22, 2015

Interview Assessments

I've been experiencing some growing pains with flipped mastery.

Test security:

Yesterday when I went to grade the day's tests, in the pile there was a test that I didn't remember handing out.  It had neat creases in it as it had been folded into fourths, and I wondered if I gave that student the test on the previous day.  Did he really take the test home to finish it and then hand it in today?!?!  When I asked him if that was the case, he admitted to it.  I gave him another version of the test to complete.  It's now the end of the school day and guess what I noticed?  Yes, he didn't hand the test in.  He took it with him again.  

I've started dating the tests in pen as I hand them out.  Now I'll know if a student took a test home with them.  

In some of my larger classes, students are taking tests right next to people who are working on other things.  It's been challenging to notice who is taking a test and should not be talking or have their notes out vs. those who are not testing and should be collaborating and have their notes out.  In these large classes I don't have the space to create a testing area.  One solution is to print the tests on color paper to make it more noticeable.  

Students who are Falling Behind:

There are some students who are not motivated enough for this program.  They will do anything to avoid doing the work.  I suppose that happens in any program.  So I had this great idea (or so I thought).  I created a google sheet where the students would type in their plan for the week.  It worked great for the first few weeks.  Can you figure out why?  Because I was staying on top of the students.  I was nagging them to type in their plan.  And if they didn't, I went to them individually and then made them type it in.  This was just another form of babying the students.  And these same students would type in their plan and then not do it.  

Assessment Feedback:

While I'm grading tests I will notice that a certain student has this misconception or that misconception.  I write my comments on the test, file them away, and then they are never seen again.  Hold on.  That's not entirely true.  If a students asks to see his test, we will go over his mistakes, I'll tell his what to work on, then I'll send him on his merry way.  Effective right?  Bah!

Some Just Need a Little Push:

I sat with a student yesterday as he was taking a test.  His initial complaint was that he could correctly do all of the practice problems, but then he would fail the test. And he was right.  I sat with him before and he did amazing, I gave the test and he failed.  So this time I sat and watched.  I noticed a little error in the beginning of the test and from there he was fine.  Passed like a pro.

There's a Common Theme Here:

Do you see the common theme among many of these complaints?  Assessments.  

The other week my 4 year old son came home from pre-school with a DVD for us to watch.  The director of the pre-school took each student one by one into a room, assessed the child on the recommended skills for Kindergarten, recorded each session, and sent the DVD home for the parents to watch with their child.  As a parent I loved this.  It made my child's education so transparent.  I want to do this in my own classroom.  

Interview Assessments:

I've decided that I'm going to try assessment interviews with my students.  I will still have the paper and pencil tests available, but volunteers can chose to take their test with me.  This is how I see it in my head:  The student and I are sitting at a table with an iPad and using the educreations app to record our session. I write a question on the iPad, then the student answers it in writing and verbally.  During the recording I can tell the student where they need more work.  I can redirect them and clear up misconceptions immediately.  Students who are unable to prove that they possess all the skills necessary for that outcome can reassess.  Once the recording is over, I can email it to the student and his parents.  I can even post these recordings to my website.  Students who are not yet on that outcome can see what the assessment is like and what it looks like to have those necessary skills.  

Here is a skills sheet that I created for an outcome on Slope and Graphing with Slope-Intercept:

I'm trying to make a list of all the problems this will solve for me.
  • Test security will no longer be an issue.  Since I only teach Algebra 1, creating problems on the spot isn't that difficult.
  • Those who just need a little push to be successful will have this.
  • I'm wondering if this will help with some students who are falling behind.  Will it create some pressure for them to be ready?  
  • Feedback will be immediate.  

A list a new problems.
  • I'm not sure I have enough time to interview every student on every outcome.  I suppose that's where the paper and pencil versions will come in.  
  • I think educreations has limited space.  I can't save recordings forever.  

Tuesday, January 20, 2015

There's Something Here I Just Know It - Take Away Game

I don't know the name of this game, but I have always enjoyed it.  The game play is where two players have a bunch of objects in front of them (I used pennies) and they take turns taking away pennies.  They can take away up to a certain amount on their turn and the person who takes the last penny loses.

Here is the version I played:
We started with 43 pennies and the players could take away up to 5 pennies on their turn.  I won every single time.  The reactions I got from the students is something I want to bottle.  They were fighting over who got to play next.  They got their calculators and were doing crazy things there.  They were watching me closely.  They wanted to watch what I did over and over again.  They were playing against each other to try out their strategies (without being asked!).  And the same question again and again, "How are you winning?"  (answer at the bottom of the post)

There were other questions formulating in their heads that they weren't asking aloud.  Questions such as how many pennies should be remaining on the 2nd to last turn? and Does the number of pennies a player take depend on how many were taken on the last turn? 

They were shouting out ideas to each other during game play.  "She always takes 1 more than you do!", "She's doing math in her head!", "Just take the same amount she takes.",  "If she takes 5 you take 1!"

Once a student determined what I was doing and was able to beat me (okay so I didn't win every single time), I changed the rules.  Now it was 41 pennies and each player could take away up to 4 pennies.  If that student won again I knew they understood the how-to-win rules.  

Here's the thing.  This felt like a 1st act.  But I'm not exactly sure what the 2nd and 3rd acts are.  I'm not even sure of the math topic this is covering.  Patterns??  Linear Equations?  Developing formulas?? All of the above??  Please help me here.  What do I do next with my students?

Here is how I develop a version of the game.  I decide the maximum number of pennies a person could take on their turn.  Let's call this p.  Then I need to determine the total number of pennies needed to play this game.  There are many answers to this, but here is the formula g = t(p+1) + 1 where g is the total pennies in the game, and t is the number of turns each player would have before the end of the game.  

*Spoiler Alert*  Below is how to win.  

Remember that number p?  Add 1 to that.  That is the sum of the pennies that need to be taken during 2 turns.  For example, if you are playing a game where you can take up to 4 pennies, then 5 pennies need to be taken between you and the other player.  Allow the other player to go first.  If they take 1 penny, you take 4.  If they take 2 pennies, you take 3.  If they take 3 pennies, you take 2. And if they take 4 pennies you take 1.  
Sometimes the other player will insist that you go first.  If so just make sure you get back to being the one that takes the 5th penny.  

Thursday, January 15, 2015

Rolling Throne: An Exponent Game - The Results

For the past three days I have been doing some informal research on my game Rolling Thrones.  I often wonder if playing games is worth my time, or any activity for that matter, and created a pre/post test to help me determine.

Link to the Game

Pre/Post-Test on  #soc14351941

Period 1:  Playing Rolling Thrones

The Pre-Test:

19 Students took the pre-test
The class average was 46.7%
6 students scored above 70%
1 student scored 100%

The Post-Test:

21 Students took the post-test
The class average was 75.9% (a change of +29.2%)
15 students scored above 70% (a change of +9 students)
4 students scored 100%

3 students' scores stayed the same (1 of them was the 100%)
2 students' scores dropped

Period 4:  Lecture and a Worksheet

The above information doesn't tell me too much if I don't have a control group.  So, for the other class, instead of playing a game, I gave a lecture and a worksheet.  The results were very similar.

The Pre-Test:

19 students took the pre-test
The class average was 45.6%
4 students scored above 70%
0 students scored 100%

The Post-Test:

19 students took the post-test
The class average was 77.2% (a change of +31.6%)
13 students scored above 70% (a change of +9 students)
0 students scored 100%

2 students' scores stayed the same
2 students' scores dropped

My Conclusion:

Since there wasn't too much difference in the amount of learning that takes place, I would personally play the game because it was more fun.


Students who played the game were involved, out of their seats, yelling (if you like that sort of thing), asking questions and advice (more than I can count), and awake.  Compare that to the student who had the lecture; I noticed at one point that 3 students put their heads down and weren't taking notes, students complained that they had to do the problems on the worksheet, and only 2 students asked me for help/advice with their problems.

Amount of problems:

During the game we perhaps did a total of 6 or 7 problems (I should have kept track), while the students with the worksheet were required to complete 40 problems.

Amount of time:

The students playing the game reluctantly stopped playing when there were 4 minutes left in class, while the lecture/worksheet students finished as quickly as they could and went to work on something  else.  Depending on how you look at it, the lecture/worksheet students were able to accomplish more in a class period than the game students.

The Next Day:

The day after we played the game in class, the students asked if we could do that more often.  The students in the lecture/worksheet class did not ask for more lectures/worksheets.

Game Tweaks:

There are a few things that I would change about the game next time.

Hardly any groups purchased dice with their points.  The teams that did, lost too many points to be able to come back from that and possibly win.  Next time, I will make the price of new dice 2 points each.

Groups of 2 or 3 worked just fine.  It seemed as though all students were engaged especially with the smaller groups.  I was not frustrated with the number of teams.

I did keep track of team rank on the board.  That went over well with the students and they kept me honest as to what team was at what rank.

There wasn't a team that reached the royalty status, so the team with the highest amount of points was crowned.  The students loved the story line with the game.  I was tempted to leave it out because high school students are too old for that stuff.  <--sarcasm.  
If you play this game DO NOT forget to award the winners their crown!

The winners:

Monday, January 5, 2015

Solving Real-Life Problems: Baseball Jerseys

I recently did the lesson Solving Real-Life Problems:  Baseball Jerseys with my CP Algebra 1 9th grade students.  Click on the link to take a look at that lesson.

My Timeline:

Monday:  For the last 15 minutes of class I gave the students a copy of the Baseball Jersey problem and a blank piece of computer paper to do their work then emphasized the importance of doing their own work.  The students handed in the paper before the end of class.
That evening I looked at each students work, attached a copy of the Suggested Questions and Prompts (I cut off the common issues) and highlighted the questions that I wanted each individual student to focus on.  I created heterogeneous groups of 2 or 3 students based on their work.

Tuesday:  At the beginning of class I gave each student their work back from the previous class with the attached questions and another piece of blank computer paper.  I instructed students to write all of their work on the new piece of paper.  The students were given about 10 minutes of quiet time to work on this.
Next, I asked students to get into the groups I created and come up with a solution to the problem.  Students needed to create one poster per group that showed the groups common work and answer.
That evening I looked over each poster and decided which ones would be presented in the class the next day and what order based on the work.

Wednesday:  Class started with the students presented the posters that I picked with me asking probing question to help move them along.
I gave the students time in their groups to look over the sample student work that was given in the lesson and we discussed as a class what we noticed for each sample solution.

Thursday:  I created another problem similar to the baseball jersey problem and asked students to solve this.  I used it as an assessment and a way to see their growth with this topic because of the lesson.

The Results:

For the pretest:  34 students Not Yet Proficient, 3 students Proficient, 0 students Advanced

For the post-test:  8 students Not Yet Proficient, 13 students Proficient, 16 students Advanced

My Thoughts and Other Ramblings:

Quite a few of the students were very vocal about not liking this activity.  They wanted me to just give them the answer or at least tell them how to do the problem.  I always doubt myself when they do this.  I suppose this is because I'm out-numbered.  But as you can see from the results, this works.  A little productive struggle is a good thing.  

I've been made aware of this site before but didn't think too much about it.  But then I was invited to attend a three-day conference at our IU about that website.  Okay, I'll bite.

We met back in October for two days and the instructors took us through the two types of lessons available on the website: Problem-Solving and Concept Development.  Then our homework assignment was to complete one of the lessons with at least one of our classes and report back in December.  Finally, we are to go through another lesson with at least one of classes again and report back.

Here is a screenshot of the pre-test:

I found it interesting that quite a few students didn't bother writing about the price of the jerseys but focused only on the quality of the jerseys.  

This is the post-test that I created:

Nadia wants to rent a bike so she can ride of the D&L trail with her friends.  Bikes for All has an insurance fee of $28 and charges $12 per hour to rent one of their bikes.  Ride with Us charges $16 per hour to rend one of their bikes.  Under what circumstances should Nadia rent from with bike rental company?

Answer:  7 hours

There were about 4 or 5 students who started by creating a table, but didn't go far enough to see when the costs would be the same.  When I spoke to them about this, they said that they only went as far as made sense.  They didn't believe that someone would ride a bike for more than a few hours.

Other students said that there were too many variables to assume.  What if she was paying for 2 people, 3 people, or even 4 people?  They were overwhelmed with too much information so they didn't even start the problem.  As a class we discussed the difference if she paid for only herself or if she paid for herself and a friend.  We discovered that the amount of time for the prices to be equal were the same under both circumstances, the difference was that the price for two people was twice as expensive.

Friday, January 2, 2015

Rolling Thrones: An Exponent Dice Game

How about a game to get the new year started right?  It seems that every time I ask my colleagues what topics their students struggle with and would like a game for, they mention the laws of exponents.  I've been rolling the idea of a game around in my head for a long time and decided to finally sit down and get serious about it.

Please note that this game has not been play tested yet.  If you play this game at all I would love your feedback.

Game Objective:

To reinforce the laws of exponents.


  • 3 6-sided dice for each team. 

  • 1 20-sided die for you.
You will need to print the net and select the D20.  Hold the paper up to a window so you can write in the spaces on the back.  Write the integers -9 to 9, and "re-roll".  Cut out, fold, and tape together so that your numbers are facing out.

  • Lots of Blank dice 
I'm not sure of how many because of the whole play-testing thing.  If I had to guess I would say 3 for each team.  I would use my blank dice, cover them with clear tape so the students can write on them, and then I can take the tape off at the end of class.

Set Up:

Divide your class into smallish teams of 3-4.  You need to find a balance here.  If the teams are too big, some students will do nothing.  But if there are too many teams, the game may be frustrating to play.

Give each team 3 6-sided regular dice.

Write the team names on the board and keep score underneath.

Game Play:

Roll your 20-sided die and write x to that power on the board.  For instance, if you roll a -5, write x^-5 on the board.  This is the target for this round.

Each team rolls the dice they have and try to create an expression that will equal the target.  The numbers that they rolled are used as exponents for the base x.

Suppose Team A rolls 4, 4, and 5.  They could create the expression (x^4) / (x^4 * x^5) and this would be equivalent to x^-5.  Since that team used 3 dice to create their expression they receive 3 points.

Suppose Team B rolls 1, 2, and 6.  They could create the expression (x^1)/(x^6) and receive 2 points.

Suppose Team C rolls 2, 3, and 5.  They could create the expression (x^5) ^ (2-3) and receive 2 points.

Suppose Team D rolls 1, 1, and 2.  They are unable to think of a way to create the expression x^-5 and receive 0 points.

Buying Stuff:

With the points they are accumulating the students are able to buy things.

For 1 point (and this needs to be play-tested) a team can purchase a re-roll of their own dice.

For the number of dice they currently have, they can buy a blank die for that many points.  In other words, if a team has 3 dice they can purchase a blank die for 3 points.  If a team has 4 dice, they can purchase a blank die for 4 points, etc.  I hope this is making sense.
Once they have their blank die, they can write any positive or negative numbers they wish.  They must do this before the next round begins.

Helping Other Teams:

I love when my students help each other.  So to add some cooperation in with the competition, teams are able to help other teams.  If a team is struggling to find an expression that is equivalent, another team may help.  If they are successful in finding an expression, the two teams split the points.  Yes, split the points even if it's an odd amount.  The decimals will be good for them.

Winning the Game:

I imaging this game ending when a team reaches a certain amount of points.  If I had to guess I would say 20-30 points.


You could play for a certain amount of time and the team with the most points wins.


To have multiple winners, you could set a goal for the class.  Every team that reaches ____ points is a winner.

What Could Go Wrong and Possible Solutions:

Possible Problem 1:  What if students cheat?  What if they change what was rolled?

Possible Solution 1:  Have one student from each group come to the front of the room, roll their dice, write the numbers on the board, you roll the D20 and write the target on the board, and the students work at their seats on their expression.

Possible Problem 2:  What if students are unable to create an expression with the three initial dice?

Possible Solution 2:  Start each team with 2 points, so they can purchase re-rolls.  If this doesn't work, each team could start with 4 dice instead of 3.

Possible Problem 3:  What if a group takes too long to create an expression?

Possible Solution 3:  Set a time limit of say, 60 seconds, to create and write the expression on the board.  This time includes any re-rolls.  If a team needs more time, they can purchase 30 seconds for a point.  Each teacher will need to adjust time limits according to their students' abilities.
For creating expression for other teams:  If a team does not have an expression after the time limit, the other teams have 30 seconds to create one and write it on their spot on the board.

Possible Problem 4:  What if one student is doing all of the work?

Possible Solution 4:  Have students in the groups take turns rolling the dice.  The student who rolls  is the student who writes the group's expression on the board before time is up.  This way, if one student is doing all of the work, at least the others seeing and writing it too.

Possible Problem 5:  What if students write 0 on their purchased dice?

Possible Solution 5:  My initial thought was that students shouldn't be allowed to write a 0 on a die because it would be too easy for them to earn a lot of points.  Let's say that a team buys a die and writes 0 on all 6 sides.  Then let's say the target is x^4.  That team rolls 0, 3, 4, and 6.  They could create the expression x^4 * (x^3 *x^6)^0.  And there is an easy 4 points.  I like that the students could have the option to discover this, but not have it available every single round.  So, here's the new rule. When students are writing the 6 numbers of a new die they must be 6 unique integers.

Possible Problem 6: What if a group is able to create more than one equivalent expression?

Possible Solution 6:  Yay!  Isn't this what we want?  This isn't a problem, this is something to celebrate and reward.  If a group is able to create more than one expression that is equivalent to the target they can and should do so.  However, a die cannot be used more than once.
For example:  Target is x^6 and a team rolls 2, 2, 3, and 4.  They could create (x^2)^3 and x^2 * x^4. That's 4 points.

Possible Problem 7:  What if a group comes up with an expression that is not equivalent to the target?

Possible Solution 7: My initial thought is that there should be a penalty, perhaps a deduction of points.  But the more I think about it, I would rather the groups just get no points.  I want this to be a learning experience, I don't want the students to be afraid to try something for fear of losing points.

Possible Problem 8:  What if the students aren't learning the laws of exponents through this game?

Possible Solution 8:  Create and pre- and post-test to determine if this game is getting the job done.  I created one that you could use on  #soc14351941

What About a Story?

I believe this game would work well enough without a story, but stories are always fun and more memorable.  

When I started to think about a title for this game, "Rolling Stones" popped into my head.  A simple rhyme with stones gave me "Rolling Thrones" and I have a story.  Each group is controlling a character that desperately wants to become King while he is currently a peasant.  He must work his way through the ranks to become royalty.  

As the teams earn points, their characters becomes more powerful within the kingdom according to the following chart: 

1-5 points --> peasant

6 - 10 points --> Knight

11 - 15 points --> Count

16 - 20 points --> Duke

21+ points --> King

You may have to adjust point values based on the length of your class and the skills of your students. 

Because teams are able to purchase things with their points, their character may go down a rank.  

When a team's character becomes king, that team wins.  I'm picturing Burger King crowns in my future.  

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