## Saturday, September 29, 2012

Do you have a lesson that was just awful?  Well, we want to hear about it.  It's one thing to learn from your mistakes, it's another to learn from someone else's.

Write a post about this horrible lesson and what you learned from it.  Maybe it could even be salvaged with a few suggestion from another helpful blogger.

## Friday, September 28, 2012

### Bucket O Lies

I have a problem with throwing away plastic.  I just can't bring myself to do it.  In the borough where I live, there is a recycling program but it will only recycle #1 and #2.  This cute little bucket below is #5.

Have you seen these?  They put your fries in them at the fair.  Every year we order one of these, not only because we love to eat fresh cut fries, but because it makes carrying the goldfish we win easier.

I've been looking at these buckets for quite some time now and I starting to think about the Made4Math Challenge.  What could I do with a Bucket O Fries?

And then it hit me, they would be transformed into Bucket O Lies!!

At one point, I had only collected 3 buckets, so I turned to my Facebook friends who came through for me with 3 more buckets.  Thanks guys!!

For formative assessment, I created 12 quadratics that were solved (factoring, completing the square, and quadratic formula).  Some were solved correctly, others were solved incorrectly.  In groups of 4 the students had to sort through the papers and decided which ones were correct and for those that were incorrect, they were to indicate where the person went wrong.

After all groups were finished we looked at each problem one-by-one.  I called on students randomly with the name cards (popsicle sticks).  I was surprised by how many misconceptions that were uncovered by doing this.

One student asked, "Can we make our own bucket o lies?''
My response, "You bet!  It would count towards High Performance."

I'm getting it now.  You know, the whole being-a-better-teacher thing.
Standing up front lecturing everyday stinks.  But this lesson had the students working together, analyzing problems, justifying their reasoning, responding to other students' ideas, and of course learning the lesson objectives.

## Thursday, September 20, 2012

### Preparing For The Complaints That Didn't Show Up

Here's a short list of my most-hated student questions:

1) Is this going to be graded?

2) How much will this bring up/down my grade?

3) What can I do to bring up my grade?

4) Do I get points for trying?

5) Will I get extra credit for doing this?

Do you notice a theme?  In all fairness to these students, they have been conditioned their entire lives that the grade is what is most important, not the knowledge they have.

When I made the decision to try to make this shift with my students from an emphasis on grades to one on knowledge, I have to admit, I was ready for the worst.  And then it hit.  It was the second day of school, I asked the students to work with a partner to complete some questions when a student's hand flew up in the air, "Is this going to be graded?"  My response was, "I look at and evaluate everything you do in this class." and left it at that.

I decided to no longer show students their grades on minor assignments like classwork, entrance tickets, exit tickets, etc.  I keep record of those things on paper and keep that information to myself.  And by grades, I mean colors (red, yellow, and green).  Once I see a lot of green on the score sheet, I know it's time for a test.  Note: I do put a grade on the test.

When I handed back their first assignment without a grade I was ready.  I spent the entire night before mentally preparing for the backlash:  What's my grade?  Why should I do it if you're not going to grade it?  What's the point of doing all this work if it's not going to bring our grade up?
I rehearsed my responses and knew that I was going to stay cool and stick to my guns.

But then this strange thing happened...
I gave back the assignment that had no grade on it, only comments, and asked the students to make corrections and hand it back in.  Not one word about a grade and the students readily got to work on corrections.

The good things that I have noticed from this:

1) In the past 17 days, I only caught one student cheating/copying.  In the past, where assignments were scored, I saw at least 10 students copying by this time of the year.

2) If my memory serves me, the students complained about the work I asked them to do in the past.  This year, when I ask the students to get started, they get started.

3) Students readily help their neighbors when they are confused.  I wonder if this is because the competition of grades is eliminated.  I'm not sure why this is happening on it's own this year, when it didn't in previous years.

I'm hoping this trend continues.  I'll keep you posted.

## Wednesday, September 19, 2012

### Absent Students

Don't want to read the entire post?  Scroll to the bottom and read "In a nutshell".

I've been seeing so many posts and ideas about how to handle work when students are absent that I thought I would share my method.

A few year ago I invested in two file containers.  That seems to be enough to handle all of my classes.    I label each hanging folder with a student's name on it.  I call these my "hand back folders", because this is how I hand back work to the students.  The idea came to me one day when I was yet again handing back papers to students in the beginning of class, and it felt like such a waste of precious class time.  Now as the students come in the room they first take their assigned pencil case (read about those here), next they proceed to their hand back folder to get any papers I returned, and finally they find their seat by completing the warm up activity (read about that here).

Okay great Nora, but what does this have to do with absent students?
Well for one, if a student is absent when I hand back work, I don't have to hold on to it and remember to give it to the student when they come back to school, it's already waiting for them in their hand back folder.  For two, if I hand out any papers in class, I also place those papers in the folders of absent students.

Okay, so now absent students have any material they needed while they were absent.  What about notes and lectures?

This is where my smart pens come in.  I wrote about how much I love my smart pen awhile ago (you can read about that here).  For the last few years I have been running myself ragged making pencasts so that students can study to reassess and also for absent students to learn what they missed in class.
I was pleased with the outcome of the pencasts, but I knew they could be better.  For instance, the pencasts that I was created were a review of an entire outcome in one pencast.  If a student is struggling with one skill of that outcome, the pencast wasn't too helpful because it wasn't focused enough.
For my pencasts to do what I would love them to do, I would have to create a pencast everyday based on what was done in class that day.  No thank you!  That would have been another 1-2 hours of additional work every night.

Then this quote I heard a few months ago popped into my head, "The person doing all the work is doing all the learning."  Bingo. The students will be making the pencasts.

I asked my IT guy for two more smart pens.  (Note - if possible, your IT person will buy you technology if you use it.  So use it.)  Three days later, there were two brand-spanking new smart pens sitting in my school mailbox.

I've only starting doing this with my Pre-Calculus classes.  Each day a student takes the notebook and pen home and creates a pencast based on what we did in class.

The results?  I'm tickled pink.  This is the best decision I have ever made.  I got my life back!!  Now when a student is absent and comes back and asked, "What did I miss?"  I reply, "Check your folder and the class website."  And that's it.  No more rummaging through my files to give them the papers they need.  No more giving up my lunch or prep to teach them what they have missed.  No more losing the start of class time because I'm getting absent students squared away.  Just those 7 little words and I'm done.

Want to see my class website?  Here, I'll link you to the pre-calc page, but feel free to take a look around.

#### In a nutshell:

For missed papers:  Have one hanging folder for each student.  Instead of handing back papers to student individually, put them in their folder before class begins.  As students enter the room, they check their folders.  When handing out papers or worksheets in class, place those papers in the folders of any absent students.

For missed notes and lectures:  Have students who are in class create a pencast based on what was done in class and post to the class website.

When absent students return:  They check their folder for returned/missed papers and listen to the pencast on the class website.

## Friday, September 14, 2012

### The Tile FACTORy Results - Factoring Trinomials

A few weeks ago, I wrote about a game that I created called the Tile FACTORy.  You can read about that here.

#### Monday:

On Monday I reviewed factoring trinomials where the lead coefficient is 1.  My initial thought was to skip the game, because so many of the students seemed to know what they were doing.

#### Tuesday:

On Tuesday I started class with a pre-test.  You can see that here.
The students were very confused about the first question, so I did an example with them.  I also explained that each of the those numbers are written on a card, therefore if you use the number 4 in one place, it can't be used in another.
The example I gave them was    x^2 + -4x + 4 because that can be factored to (x - 2)(x - 2).

The pre-test is broken down like this:
part 1 - create a factorable trinomial
part 2 - multiple choice factoring problems
part 3 - open-ended factoring problems

Next, we started to play the game.  The rules are confusing.  I don't know how to write them better, so if you have a clue, please pass that along to me.

By the end of class, the students were starting the get the hang of the game.

#### Wednesday:

I allowed students to play the game almost the whole period.  We played in groups for 20 minutes, then the winners of each group played together to have a class champion.

Last 10 minutes of class I asked students what they thought about the game.

#### Thursday:

The students took the post-test.  You can see that here.
I had to stop some students because they would have spent the entire period trying to come up with factorable trinomials.

I continued with the curriculum for the rest of the period.

#### The Quantitative Results:

Here is the google doc if you want to poke around.

For part 1 of the pre- and post- tests.  On average my students could create 3.3 factorable trinomials with the given numbers.  But by the time they took the post-test on average, they could create 6.4.  I think this is huge.  That's almost double of what they could do to start with.

For parts 2 and 3 of the tests they increased by a little more than half a question (0.65).  The biggest reason is that most students got them all right on the pre-test and had no room for improvement (hence my thought at the beginning of the week to not play the game at all).

However, not everyone increased their scores on both parts, although the majority did.
For the first part where they created the trinomial, out of 40 students, 35 were able to increase how many they created and 5 of them actually created less.

For the second and third parts of the test:  15 increased, 6 decreased, and 19 stayed the same.  One student went from only getting 1 correct to getting all 8 correct (student #29. success right there!).

#### My Thoughts:

Like I said, on Monday I wasn't even sure I wanted them to play the game.  However, now that I see these results, I'm glad I did.  The average percent correct when they answered parts 2 and 3 went from 88% (not bad) up to 96% (awesome).  Plus, as I walked around the room, I heard really great conversations about the trinomials they were creating.  I saw students helping each other create and factor.

#### The Students' Thoughts or Qualitative Results:

"I thought the game was fun and helped me understand factoring better."
"I didn't like it at first, but by the end of today I realized I started to factor faster and more easily.  I'd like to play it again."
"Helped me a lot. Got me thinking. Was not a bad game to play."
"Truthfully, I didn't really like this game.  I don't think it helped me with factoring.  I think it was actually harder than factoring."
"I liked the game once I understood it.  After I got it, it was fun and I wanna do it again."
"BEST GAME I'VE EVER PLAYED!  AND IT HELPED AND I LOOK FORWARD TO PLAYING AGAIN."
"The game was kind of slow moving.  The factoring part of the game is what killed it, but it helped me understand factoring even though I got a headache from thinking."
"The game was fine, but the rules were complicated."
"The game itself was not personally helpful.  It seemed as though other students benefited though.  It is a fun and enjoyable game as far as math games go."
"I feel that the game helped a little bit, and it was fun.  I could tell it helped the people I was playing with.  I need to play a bit more to understand it fully."
"I didn't like the game because I just didn't get the concept.  The rules were a little confusing so it took me a couple of rounds to get the idea."
"I like the game.  I thought it was fun and it really helped me understand how to do it.  And now I get it because before I didn't get it.  And I also think that we should play it again."

#### Next Time:

I am going to rewrite those rules before I play again with students.  Maybe I'll even create a video of the game in action that they need to watch before we play in class.

#### Update:

Since a few of my students told me how confusing the rules were, I tried to rewrite them.  Here is the new rules set.

## Thursday, September 13, 2012

### #MyFavFriday Problem Experts

I have created an activity that I love, the students like, and it incorporates so many of the things I want the students to do this year.

By completing this activity with my students...

...the student are teaching each other.
...the students are working together.
...the students know a problem well enough to teach it to someone else.
...the students are constantly self-assessing their knowledge.
...the students are completing many problems in a short amount of time.
...the students had a personalized study-guide.

#### Background:

I've been trying to teach my students how to solve compound probability problems that involve "OR".  The process was going so slow.  So many of my students needed one-on-one attention for these problems and I couldn't afford the time to give it to them.  From this situation, the Problem Experts activity was born...

The largest class I have for Algebra 1B is 16 students.  So I created 16 Probability "OR" problems.  I decided that each students would get exactly one problem and become an expert on it.  After I was sure each student knew their problem, they were going to pair off and teach/coach the other student on their problem.

On one paper I had each problem typed multiple times (as many times as would fit on the paper).
For instance:  On one paper problem #1 was typed multiple times, on another paper problem #2 was typed multiple times, etc.
The problems were typed in a text box with the outline feature.
These papers were copied on colored paper!

I also created a packet for the students so, when they were finished they would have all their problems in one place.  I created this document so that the problems would fit perfectly in the rectangles with the number.  Their solution would be done to the right of the problem.

Then I took 16 envelope and wrote the numbers 1-16 on each envelope.

#### Discussions to have before you begin the activity:

What makes a good coach.  Here is yet another idea stolen from Square Root of Negative one.  I will just direct you to her sight and have a look for yourself.

The goal of this activity is to become more confident in solving Probability "OR" problems.  The goal is not to finish a certain amount of problems in a certain amount of time.
*I found one student copying from his partner and needed to remind him of our goals.

#### The first day of the activity:

As the students walked into the room, I handed them a random envelope with a number on it.  Keeping with my warm-up activity (read about that here) they were instructed to sit so that the sum of them and the person sitting next to them was 17.

I handed each student enough copies of the problem that corresponded with their envelope number and instructed them to cut out each problem and place it in their envelope.

Next, take one problem out of your envelope and adhere it to the correct place in the packet.

Solve your problem.  This is the step that took the most time, but was well worth it.  I went to each student individually to make sure their problem was correct and that they could teach it to another student.

That was the end of day 1.

#### The second day of the activity:

As students came into the room they were instructed to sit with a partner.  The students exchanged problems with their partner and adhered it to their packet.

As the students were completing their problems, I instructed them to coach each other and offer help without taking over.

Students would try to ask me a question, but I would turn the question back to their partner.  After a while they figured out what I was doing and began asking their partner right away rather than me.

After each problem, the students has to place a dot next to that problem with colored pencils.  If they needed no help to complete the problem, they drew a green dot, if they needed some help they placed a yellow dot, and if they needed a lot of help they put a red dot.

Once they were finished, they found a new partner and did the process all over again.

#### The end of the activity:

By the end of class the 2nd day, the students had completed about 7-8 problems.  I noticed that as the period went on, they were getting fast and more accurate.

I did make a homework suggestion (strongly suggested):  any problems that were marked as yellow or red should be completed again that night.  This created personalized study guides.

#### What the students said:

"I was surprised by how I did all the problems by myself."
"After this session, I feel smarter."
"After this session, I feel that I can do these problems better now."
"Today I learned how to do the probability with the charts better."
"What I liked most about this lesson was that it was not just sitting copying notes, but we got to interact with others."
"After this session I feel a bit confused about the way probability works."
"One thing I am not sure about is the problems with the 2 dice being added."
"Today I learned how many times I could get something wrong and liked getting help."
"After this session I feel very confident about doing probability problems."
"Today I learned that a die has 36 dots on it."  Hmmmm....
"I was surprised by how fast I learned how to do this.  It surprised me how well I did also."
"Today I learned that I do need to write the formula when writing a problem."

#### Next time:

I copied the packet in white and the problems in pink.  Next time, I think I will copy one of each problem in a different color, say green, so that the problem they are an expert on will be green and they can find it faster in their packet.  I noticed a lot of students flipping their packets around, looking for their problem.

I mostly left it up to the students to find their own partner and it worked pretty well.  However, next time I think I set up areas in my room.  One area for working and one for finding a new partner.  As the students come into the room, the seats will already be set up for pairing.  When a pair of students are finished they will go to the waiting area to wait for another pair to arrive.  With their new partner they can go back to the paired desks.

For my own sake, maybe next time I'll put a chart up on the board (tape a piece of paper to the board with colored pencils nearby) to see what students have done what problems.  As they finish problems they can put their color on the chart.  I'm thinking something like this:

This way I can see if there is a particular problem that the students are struggling with and also if any student is having a hard time, like student 2 above.

## Monday, September 10, 2012

My second outcome in CP Pre-Calc is Solving Quadratics by Factoring.  I decided that I wanted to students to know 5 skills in order to pass this outcome:

--> GCF
--> ax^2 + bx + c = 0      a = 1
--> ax^2 + bx + c = 0      a =/ 1
--> Special Trinomials (Difference of Two Squares AND Perfect Square Trinomials)
--> Combination of the Above

Then I went to the internet in search of a foldable that would allow for 5 topics and came across one like mine in the picture.  Perfect!

I also created a PowerPoint to go along with the foldable.  It's nothing fabulous, it's just a slide show of the example I will be doing in class, but you are welcome to it.

I was curious how the students would react to something like this.  I find that students in this class are typically serious and not interested in stuff like this.  I found that the students liked it.  Not only could I tell by their reaction, but I came right out and asked them.

## Sunday, September 9, 2012

### Vertex Form of Linear Equation

Just read this post.  I'm sold...

Writing Linear Equations

## Friday, September 7, 2012

### #MyFavFriday Sept 7, 2012 Try, Try Again

My Favorite Friday this week is the format of a practice sheet that I created.

My first though with this is that it was going to take me for-ev-er to write all these comments.  In order to manage that, I cut back on the amount of problems that I assigned.  I went from about 10 down to 3.

Here's how the lesson went:

The class and I discussed how to find probability of simple events.  We did a few examples together.  As their exit ticket, I asked them to complete three problems and turn them in.

This photo isn't the greatest.  But, in the first column I typed the problem.  In the second column, the students did their work individually.

Since there were about 10 minutes of class left (I did plan it that way, honestly), I randomly picked a student's paper, placed a sticky note over their name and put the paper under the document camera.  As a class we discussed if the problems were correct or not.  If the problem was correct, I wrote "Super!" or "You rock!" in the third column under the heading "Teacher Comments" and in the fourth column under "2nd Try" I put a big X, so they knew they had nothing more to do for that problem.  However, if the work was incorrect we discussed what I should write that would be a helpful comment.

That night I finished writing all the comments and handed the papers back the next day.  The students read the comments I made, wrote their corrections in the 4th column and turned the paper in again.

I have to say, the corrections were pretty good.  It was their first attempt at making corrections this year, let's see how it goes.

This post got a little wordy on me.  So here is the format in a nutshell:

Column 1:  Type the problem
Column 2:  Student makes their first attempt at the problem
Column 4:  Student makes corrections based on teacher's comments.

Suggestions:
Don't give more problems than you are willing to comment on.
Give the students time to fix their work.
Show students the difference between a helpful comment (Remember that the denominator is the amount of total outcomes) and a not-so helpful comment (Read the problem again).

## Monday, September 3, 2012

### #Made4Math September 3, 2012 Learning Prompt Poster

If you read my last post, you saw how much I enjoyed reading Dylan Wiliam's book, Embedded Formative Assessment.  Here is one of the many ideas I adapted from the book:

I like to give exit tickets and typically, they are of the form, "solve this problem".  I figured that this was the best way to know what was going on in their head.  I instructed my students to show all of their work in order for me to know exactly what they know.

Dylan Wiliam has the following prompts listed in his book (He had 9, I picked my favorite 8).  My first thought was that this is a bit of a waste of time, because if I ask these questions, I won't know if they know how to solve the problem I just taught.  WRONG!

My #Made4Math this week is my Learning Log Prompts Poster.  We have a poster-maker in our school and I have this hanging in the front of my room if ever I want to have the students write about a particular lesson.  This poster is 2 feet x 3 feet.  It's difficult to tell it's size in this photo.

I found that my students were very honest with me.  I didn't need to see them solve a problem to know if they knew what they were doing, they came right out and told me in black and white.

The first outcome that I teach in pre-calc is Complex Numbers.  On that particular day we were reviewing (at least I assumed it was a review) how to add, subtract, and multiply Complex Numbers.  At the end of the lesson, I asked the student to pick one of the eight prompts and respond.  Here are a few of the comments that I received:

"After this lesson, I feel confused because I didn't really understand it."

"Today I learned the standard form of complex numbers."

"Today I learned that i^2 = -1.  I didn't know that."

"Today I learned the box method from (little Suzy)."

"After this lesson, I feel confident in knowing how to add, subtract, and multiply complex numbers."

"After this lesson, I feel...kind of bored."

"I was surprised by the fact that I remembered this lesson."

"I might have gotten more from this lesson...if we covered more material."

"After this lesson, I feel even more confident about my math skills and it's feeding my ego."

"I was surprised by how much I forgot over the summer."

Without doing this, I never would have known that about 5 of my students didn't know (remember) that i^2 = -1.  The next day we had a discussion as to why i^2 = -1.  This way, not only do I know if the students can solve the problem, but I know who is bored with it, and who is slightly challenged by it.  Getting the right answer, never would have given me that information.  I also like that students were learning new things from each other.  Little Suzy uses a 2x2 table to multiply binomials.  This way she doesn't miss any of the 4 terms, nor does she repeat a product by accident.

One thing that the book recommends is to give the students choices.  With this poster, the students are allowed to choose which writing prompt they wish to respond to.

## Sunday, September 2, 2012

### Best. Warm-up. Idea. Ever.

Previous Warm-Up Questions:  (Yawn)

Last school year, I observed another teacher and picked up this idea from him, to have questions on the board for students to complete as they walked in the room.  OK, this is not a new idea.  Call them warm-up questions, bell-ringers, whatever.  I've heard of them before, and this was just a good reminder that I should be doing them too.  At one point, he did need to poke his head in the room (he was monitoring the hallway) and remind students to get to work on the questions.

I took this idea back to my room and seemed to have the same problem.  Most students came into the room and started on the questions as they should, be there were always the same few who sat in their seats and ignored the problems on the board.  I felt like a broken record, "Sit down, get your journals out, write the questions, answer the questions, discuss your answer with your neighbors, blah, blah, blah."  I was sick and tired of listening to my own voice.

I'm going to change the subject now to first day activities:

I decided to try something different for the first few day of school this year.  And you can find this "something" here.  You will see activities to have your students get to know each other and find their seats.  I thought that was a nice little blend of first day activities.  The website offers a few different ideas to try a few days in a row.  I made up my mind to do this for about 3 days before I gave the students their permanent seats.  I feel that I learned the students' names faster this year because I linked their names with their faces rather than their seats.

On the third day of this, the light bulb went off when this one girl walked in the room.  I had this student in class before, and she was one of those that sat in her seat and ignored the warm-up problems.  When she walked into class that day, she immediately looked at the board and asked, "So, what are we doing today?" and then she READ the board.  Light-bulb!!!

Put the two ideas together:

I'm not going to give my students assigned seats this year.  In order to find their seats, they must do the warm-up problem.  This way they can't sit down and ignore the board because they don't know where to sit down.  Genius!

On Thursday, I told the students to get into groups of 3-4 based on their shirt colors (we have uniforms red, white, and blue).   OK, this is not a math problem, but who said it had to be?

Friday was awesome.  I gave each student an index card with a fraction on it.  They needed to sit so that the fractions were in order from least to greatest.  I thought the students would hate that one, but they said it was the best so far.

Here's what I have planned so far for next week:

On Tuesday, I have multiple choice questions on index cards that are geared toward our state tests.  Those students who have an answer of A, will sit in row 1; B row 2; C row 3; D row 4; and I have 4 questions where the correct answer isn't list, those students will sit in row 5.

On Wednesday, I have clues written on index cards.  There are 4 different clues to answer the question, "What number am I?"  The students need to sit in groups of 4 making sure that there are no repeat clues within the group.  Once they find their group members, they need to figure out the riddle.  Here are the clues:

What number am I?
I am not divisible by 2.
If you reverse my two digits, I would be 18 less than I am now.
If you add my two digits together, you would get a perfect square.
If you add 3 to me, you would get a perfect square.

Answer:  97 (double check me on that)

We've only been back in school 5 days, but I can tell you who my class leaders are already.  It's nice to sit back and watch them work together.  Once in a while I will intervene, and offer a suggestion, or point out that Little Suzy has a good idea.  But for the most part, I let them work it out.

Most of these I can reuse, like the fraction and multiple choice warm-ups.

Now, I need to keep this going for another 175 days.  Any ideas?