Fishy math in NBC's The More You Know about Graduation Rates

I've always had a soft spot in my heart for NBC's "The More You Know" public service announcements because they give short messages of encouragement which are a great break from typical advertisements.  When I saw this PSA, featuring Al Roker of Today, on Sunday during Meet the Press, I was vacationing with my family.  "What a great math problem to share with my classes this year," I exclaimed to my father.  He couldn't understand what I was talking about.  Watch for yourself and see if you took from it what I did.



Did you catch the math in there? "If we don't double the number of kids graduating from high school in the next 8 years, our country won't be able to compete globally." My knee-jerk reaction was, "Does he realize that's impossible?" We're already well above 50% of our students graduating. Take this article from NEA Today that cites the graduation rate at 74.7% in 2010.*  Doubling that, we'd graduate nearly 150% of the eligible students in a given year.  That's some fishy math. 

So, perhaps the answer here is that we need to look at the actual number of children.  If the birth rate is increasing significantly, the math could work out correctly.  I looked up the number of births in the US in 1992 (when students who graduated in 2010 would have been born), 1995 (2013 graduates), and 2003 (2021 graduates, "8 years from now").

1992 (class of 2010): 4,084,000 births
1995 (class of 2013): 3,892,000 births
2003 (class of 2021): 4,089,950 births

We can see that the birth rates dipped slightly in 1995, but are quite close in 1992 and 2003.  Let's take those children born in 1992.  Since 74.7% graduated:  4,084,000 births  • 74.7% = 3,050,748 graduates.  Unfortunately, I wasn't able to find graduation rates for years after 2010.  If we assume that graduation rates stayed relatively constant over the past three years, 74.7% of 3,892,000 births = approximately 2,907,324 graduates in 2013.  If we double this as Mr. Roker suggests, we'll need to graduate 5,814,648 students in 2021, which amounts to 1,724,698 more children than were born in 2003. 

What about immigrants?  Surely we have children graduate from American schools who weren't born in the USA.  Using some data from this site, I found that there were 40 million immigrants in the US in 2010 of which 6% were ages 5-17.  That equates to 2.4 million school aged immigrants or roughly 200,000 per grade.  If they all graduate, we still need to find 1.5 million additional students to graduate in order for the math to work!  It seems that my initial reaction was correct: there's no way to double the number of students graduating from high school in the next eight years.  Let's strive to increase our graduation rate and continue to reduce the achievement gap that we've been whittling away at for years. 

Going back to the original claim, I'd like to know what the threshold is for the USA to "compete globally."  Are we aiming for inclusion in the top 10?  Top 5?  First place?  I wasn't able to find that information on the NBC website.  You can compare high school graduation rates from around the world at this site.  Currently, Portugal and Slovenia are tied at 96% with the highest graduation rate and the USA ranks 21st.  If we were able to reduce the number of dropouts by half, our graduation rate would be about 87%, good enough for us to be tied with Hungary for 13th place. 

While I'm criticizing the math offered in the first sentence of the spot, I find there's a lot of truth in the rest of the spot and the text on the website below the video.  We do need to provide our nation's children with qualified, capable teachers.  Not only do we need to recruit new teachers to the profession, but we also need to support veteran teachers.  So while this clip touches on some valid points, I'd like to see the first sentence revised.  I suspect the good people at NBC meant, "We must decrease by half the number of students who don't graduate from high school on time."  Granted, that might be too verbose for a 15 second spot, but I'd still love an attainable goal!

Mathematically yours,
Miss B

* This Bloomberg Businessweek article lists the graduation rate as a percent of freshmen who graduate on time and has a nice graph to show graduation rates over time.  I won't be using 78% as I believe it excludes children who drop out prior to high school.

Table Groups!

While seating students in table groups is far from a new idea, it's new in my classroom.  I have been struggling with the best way to seat students given that my classroom furniture consists of only right-handed desk/chair combos.  It's not practical to seat students side-by-side with these desks.  Putting them in groups of 3 is possible in a T shape but this set up ends up taking up more floor space than I am willing to give, even in my large classroom because I need 9 groups to accommodate all of my kids.  

Unfortunately, this style of desk isn't as flexible as single desks with separate chairs and doesn't lend itself to seating students in groups. 

I'm taking a graduate class on Kagan's Cooperative Learning Strategies.  I was already very familiar with the structures but some of the rationale on team building is new to me.  I've been enjoying the class and I came home from it last weekend inspired to change my classroom set up.  I ran through a mental inventory of what is in my classroom and I realized that I had 5 trapezoid tables that could each seat two students.  I decided to use one trapezoid table plus two of the old desks per group.  I managed to get one more table from a coworker who had extras so I had enough to make 6 groups.  Students can get in and out easily and can work together.  The best part is that my classroom now feels huge!  There is a lot of space to move around. 

Here's a table group in my redesigned classroom!

Changing my classroom set-up felt like an impossible dream until I got creative and decided to let go of some things I thought I needed (separate tables for pull out groups).  The first day of the new set up (Tuesday) was rough as my students are just not used to sitting around a table and not talking constantly.  We're working on understanding when we talk to each other and when we work alone.  Wednesday and today were nearly perfect with my lower group of students.  My advanced groups are having a harder time containing themselves but I have confidence we'll model correct behavior and have everyone in line before Christmas break.  A few students have surprised me already at how well they're working together; I listened to some awesome coaching by a few pairs when we worked on volume problems using Rally Coach.  For those of you familiar with structures, we've done Rally Coach, Showdown, Quiz Quiz Trade, Takeoff/Touchdown, Timed Pair Share, Rally Table, and more just this week. 

Have you come up with a creative solution to a near-impossible problem?  Let me know about it.  I'd love to be inspired by your great idea!

Mathematically yours,
Miss B

Problem Master and Mountain Climber

My Facebook status this evening sums it up: "That was the kind of awesome day of teaching that will get me through until Christmas."

Have you ever had a day like mine when the lesson goes seamlessly (or nearly so), the kids enjoy what they're doing, you enjoy what you're doing, behavior problems are non-existent, and the learning conversations are rich.  

The best compliment I got from a kid today, "You know, Miss B, this is the highest class but we do the most fun stuff." ("highest class" = most advanced class offered to 8th grade)

So, what caused this awesome day?  Two new activities.  

The first activity was for my Algebra I class.  We have been studying probability for several weeks and it's been slow going.  Many of my students are struggling readers, so the questions are difficult for them to answer independently.  I decided to use an activity that I adapted from a math blog (I think it was ispeakmath but I cannot find the post now for anything and would love to give credit if anyone knows).  We'll call it Problem Master.

Problem Master Directions

1. Create one problem per student on the topic you're studying. (I used a mix of all the kinds of probability questions we're responsible for in 8th grade: simple, independent, dependent, sample space, permutations, and predictions from experimental probability.)
2. Assign each child a different problem.  Have them work out this problem (I used scrap paper for this step) and check the answer with you.  They need to understand and be able to explain how they arrived at that answer.  
3. Create a packet (or use notebook paper) with a numbered space for each problem.  I have 21 students in Algebra I, so I had 21 problems and a packet with that many spaces.  
4. The "Master" of the problem gets a copy of the question in green.  They glue it into the packet and show the work needed to solve the problem.  They also get a yellow sheet with 20 copies of their problem to give to classmates when they pair up.  You'll need to print one page with all of the questions once on green paper and then make a yellow sheet for each child with their problem duplicated enough times for everyone else in the class.
5. Each child then pairs up with another member of the class, they trade problems to solve, work independently to solve the problem, check their partner's answers, and they coach as needed.  
6. I had students grade each other with smiley faces for how much help they required.  
7. When a pair is finished, they return to a designated area to meet a new partner.  (Rarely was anyone waiting for more than 1 minute.  You could choose to have a secondary assignment for anyone waiting or call out switching times, but my kids were able to handle this bit of freedom because they could work at their own pace.) 
8. I had students carry their glue stick and scissors around with them.  We only cut out one problem each time we paired up instead of cutting them all apart at the beginning because I wanted to avoid them losing a pile of little yellow papers!  Envelopes or baggies would also work, but giving them an entire sheet limited my prep significantly and made it easy when we realized we would like to finish the activity in the next class period.  

We worked on this activity for almost an hour of our 90-minute block.  The kids were engaged the whole time and were taking their responsibility seriously.  They weren't happy that we didn't have enough time to finish and begged to get more time next class.  I'll happily oblige because they were doing an awesome job!  
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With my morning class going so well, I worried some about the potential of my afternoon class.  After all, could I manage two new group activities in one day without pulling out my graying hairs?

This activity probably exists out there in one form or another, but I invented it last night without any direct inspiration.  It's called Mountain Climber. 

My students were very complimentary of my artwork.  Bless them for loving my scribbles!  Coming soon, there will be a picture of the poster we used to track our progress in the "game."  For now, just picture a crude half-mountain drawn on poster paper.  Starting at the bottom and going up the side, there are labels reading "level 1,"  "level 2," all the way to "level 10" and the groups all have a little mountain climber clip art icon colored a different color that they move up the poster.  

Mountain Climber Directions

1. Each group is assigned a different colored marker.  My grouping scheme is discussed here.  I used groups of 3. 
2. Create a variety of problems/tasks related to the topic you're working on and level them from easiest to hardest.  Put each problem on a separate page (half page, etc) and make enough copies for the number of groups you'll have.  I chose to make 10 problems, but this can be adapted to the difficulty level of the topic and the amount of time you have. 
3. Students provide notebook paper.  Pass out one record sheet per group and one copy of the level 1 problem to each team. 
4. Students work in their groups to solve the problem.   Group roles are recorder (writes on record sheet discussed below), messenger (delivers paper for corrections), and scorekeeper (keeps track of group progress).  
5. As the students work on a problem and reach a consensus, the recorder fills in the record sheet, the messenger brings it to the teacher for checking, and the scorekeeper moves the mountain climber up a level when they get a problem correct. Give them the next level of problem when they get a correct answer.
6. I emphasize accuracy over speed in this exercise.  You can see there are three columns on the right of the record sheet.  The first time the group gives me their paper, they get 3 points for a correct answer.  Each subsequent time, they earn less points.  This is a good motivator to help them reach a consensus before bringing me the paper!   The team with the highest point total at the end is declared the winner.  I do not care who finishes the 10 problems first.  

The kids were very excited to play Mountain Climber.  I teach a competitive group in Intermediate Algebra, so they all wanted to be fastest.  Some groups started to realize that they needed to slow down and read the questions carefully so they could get their points.  I had one instance of a team that tried to "divide and conquer" on a problem.  I marked an X in their first box for that problem, and they went back to helping and coaching each other as I'd asked.  Despite that one very minor incident, the activity went well and the kids again begged me to let them finish next class. 

My students want to do math problems.  That's my definition of winning! 

Mathematically yours, 
Miss B

What to do about "I'm done!"

We all have experienced the joys trials of teaching a group of students who work at very different paces.  There are those children who must be encouraged, coaxed, and refocused so that their work gets finished.  There are the kids on the opposite end of the spectrum who, it seems, have finished the worksheet before their classmates have even managed to get started.  What to do with the children who finish early? 

Obviously, you want to ensure that they're producing their best work and not rushing through an assignment simply to be finished.  I had one child who was such a pro at finishing everything quickly that I always saved my classroom chores for him (passing out papers, sorting things, taking a note to a classroom, etc).  It helped him to have something physical to do because he was very prone to getting into trouble and pestering other children within seconds of being finished his work. 

Other than classroom chores and the overused, "read your free reading book," there weren't many options in my classroom for early finishers.  I decided that this was the year I needed to make it happen! 

I'm going a totally different route with my Early Finisher choices.  I'm putting together brain teasers, puzzles, pentominoes, tangrams, 24, and the like with instructions for a short activity.  It's sort of an homage to elementary school math centers.  Each center will be stored in a zippered pencil pouch that the kids will select and take back to their seats.  I think the fabric pencil pouches will hold up and be easy for the kids to use.  I put a binder ring though the zipper on each pouch so it's easy to hang.  My hope is that these stations will build logical and spatial reasoning which are applicable across many subjects.  The start-up cost for me was about $20 for the pouches ($1.50 each at the discount store in my town, probably at Dollar Tree but not worth the drive for me) because I already had the other materials.  Most of them were sitting unused because I either didn't have enough for the whole class to use at once or because they weren't strictly related to my curriculum.  This is a step in the right direction!  I hope to create enough materials so I can swap these out mid-year.  Every term would be awesome, but I don't have enough materials for that just yet. 

These pouches are left over from previous students.  I purchased 12 more (not pictured) for a total of 16.

I also set up my classroom library in a much more inviting way than in years past.  I stacked some file crates sideways and used them as my bookshelves.  I placed some books related to math in a display.  I was so close to selling that pink locker storage piece because the pockets are so deep when it occurred to me that I could stuff the bottom with paper so items would sit up higher and be visible.  Duh!  My library last year, in comparison, had all of my books piled in one crate that was placed under a chair in a corner.  Not exactly inviting!  I could use some better books; most of what I have is so dated I don't even want to pick them up.  I will try to make it to a library sale this year in hopes of adding some attractive books to the collection and I'll go through my books at home to see if I have any that are age appropriate for the kiddos. 

Finally!  A classroom library with a bit of character.

Do you have any great ways to keep kids' brains active when they've finished their assignments?  Please share what works for you.

Miss B

Building Vocabulary with a Word Wall

I think most teachers are familiar with word walls.  I've seen elementary teachers organize them alphabetically.  For my math students in middle school, I organize the walls by unit theme.  Each unit we study is assigned a color so students can look for related words in the group.  We make use of our word walls in countless ways, but here are just a few:

1. I place all of the words for a new unit on the wall.  As we work our way through a unit and learn a new concept, students try to guess which word could have that meaning.  This often guides us through a discussion of prefixes, suffixes, and roots as students break down the words and try to make meaning from them.

2. Students refer to the wall to help them recall words that have slipped their minds and for spelling.

3. Because I am lucky to have two metal walls, my words are most often individual strips with magnets on the back.  We take them down and use them for games.  One favorite game is the fly-swatter game.  Give a representative from each team a fly-swatter (clean, of course), scatter the vocabulary words on the board, and give a definition, example, non-example, drawing, etc that the students have to match to the correct word.  It's fast-paced and they get to smack the board, so they love it!  My rules are that they may only smack the board and they must alternate turns smacking words (otherwise it looks like whack-a-mole gone bad and the kids don't pay attention to the words).

4. Review/Study.  I give a final exam so I encourage my students to use the word wall to identify their weaknesses.  They can read through the words and decide what to study based on what vocabulary is most difficult for them.  This is true for unit tests and quizzes as well.  I also find my students using the word wall when they help each other.  They are frequently overheard asking each other about the words and the responses typically include the related words.  I love hearing my kids use their vocabulary! 

I have experienced a few set-backs with my word walls in the past.  First, the words get a glare once laminated so they can be hard to read.   Sometimes I end up with students who have trouble reading at a distance even with really large font sizes.  So, readability is a big problem in my classroom.  Second, the students can't take the wall home so they don't have that resource when they are completing assignments outside of my room.  In response to those issues, I decided to do a little more with vocabulary this year. 

New to my class this year will be personal word walls.  Hooray!  I designed a template to look like a brick wall complete with a graffiti title.  Kids will be responsible for adding words to their wall when we first learn them in class.  Each unit will be written in a different color and the kids will be able to place the words how they want to on the sheet though I'll encourage them to group like words in some way instead of randomly scattering them.  I'm going to have the kids lightly shade or outline the boxes with colored pencil when they feel they have mastered the term.  To me, that means they can describe/define it clearly, draw it accurately, and spell it correctly.  I think we'll need two or more copies to fit all of our words depending on the course as each size holds about 75 words.  When I taught Geometry in the past, we had nearly 300 words, so we would have needed 4 of these.  I'm going to make this double sided and copy it on cardstock.  They'll keep it in a sheet protector so they can use it to quiz themselves by marking things off with a dry erase marker. 

Here's the file.  You'll need the font "a dripping marker" for the title (or just choose a font that you already have).


  

Now, as we keep the personal word walls, we'll also keep up with the one in the classroom.  I want the students to take more ownership this year, so I'm toying with the idea of letting them write the word strips.  The problem is that they wouldn't all be pretty and uniform and I don't know if I could handle it!   I made a matching title for the word wall in the graffiti font I used on the worksheet.  I'll report back and let you know who is making the word strips, me or the kids. 

If you would like to use this with your class, leave me a comment with your e-mail address and I'll send you the file.  

How do you organize vocabulary with your students?  What makes it meaningful to them?  I'd love to hear more strategies that work with math.

Miss B

Flexible Grouping

This is not a new idea.  It is, however, new to my classroom.  I have gotten so sick of getting kids into groups and then hearing the questions, "Who's in my group?" "Where is my group meeting?" or "What group number am I?" about 25 times in two minutes.  Enough is enough! 

I reclaimed some wall space from other things this year so I could put up pocket charts for flexible grouping in my classroom.  I want to be much more deliberate with my grouping this year.  I am hoping to get at least one or two STEM PBL experiences in for my kids and I know I will need to engineer those groups so the students can be successful. 

This isn't much to see yet because the class lists are far from finalized, so I haven't made name tags.  I got the pocket charts from the target dollar bin and the magnetic hooks are 88 cents for four in Walmart's back to school section.  Total cost is under $9 including a pack of index cards.  Each color will be for one of my block classes.  I haven't decided if I'm going to hang one up for my intervention period or not.  We'll see.

 

I am trying to decide what information I want (if any) on the back of the cards.  I could use state test data, but that doesn't tell me the whole picture.  What sorts of things do you look at as you group students early in the year?   Leave me a comment and let me know what works for you. 

EDIT 9/26/12: After one month of school, I can say this system is truly working well for my classes.  In addition to helping students find their groups more easily, it's eliminated the poor attitudes some students choose to display when presented with an assigned group.  

I also appreciate that I can look back at the end of the day and review which students were grouped together for a particular activity.  

I've also added labels for group jobs.  The jobs are things like timekeeper, materials manager, sharing supervisor, etc.  I'll just place the cards above the chart and say that the first person in the group is timekeeper, the second is materials manager, etc. 

I just found more of these pocket charts at Goodwill for 10 cents so I got the purple ones to replace the red which didn't go with my color code (first period gets everything pink/purple, fifth gets all green, seventh gets all blue, and intervention gets red). 


Miss B

Classroom/Grade Level Economy

Long before I started working at my current school, the 8th grade team had established a grade level currency called "Cat Cash" after our Wildcat mascot.  I'm always amazed at how much harder and longer students will work on an assignment when there's a dollar or two of Cat Cash attached to its completion.  I even have kids who will choose Cat Cash over candy as a prize when we play games.  They know the value of a buck! 

While we give out Cat Cash for good deeds, good work, meeting goals, and other positive things, we also fine children for breaking rules (chewing gum, being unprepared for class, and - the big one - being disrespectful to substitute teachers).  I've never really gotten on board with the fines as much as my co-workers. 

Our rewards are typically one event per marking period.  The students must pay a set amount of Cat Cash to attend the event.  We try to schedule these events for half days so we aren't interrupting instruction as much.  We've had movie days, the chance to each lunch in a teacher's classroom with dessert provided by the teacher, sports, a dance during the school day, and more.  Our last incentive is a raffle and we let kids cash in all of their money for raffle tickets. 

I'm adding a new element to the grade level economy for my students.  They can look at it as a reward or a punishment- it really depends on their level of personal responsibility.  I am completely fed up with freely handing out pencils, cap erasers, and the like to children who are simply not interested in being prepared for class.  If you need a pencil literally every day, you are not being responsible.  I am sure kids could make it through several days on one pencil if they were being careful.  (Just to make it clear, I'm not talking about kids whose families cannot afford to purchase school supplies.  In those instances, I am more than happy to provide a child with packs of pencils, reams of paper, binders, and the like, but I do not want to be handing out supplies on a daily basis.) 

To combat this pet peeve, I'm introducing the class store.  Students will have the opportunity to purchase items from the store at the very beginning of class using their Cat Cash.  After that, they'll need to make do by borrowing from someone or improvising.  I'm stocking the store with the bargain basement basics as well as some decorative items for fun.  I don't care whether they buy the items because they want them or because they need them, but I do hope it cuts down on the pencil parade! 

Do you have any tips for how to hold students personally responsible for coming prepared to class?  What have you tried?  Leave me a comment and let me know! 

Miss B

Keeping paperwork organized

I teach 80 students in an average year, all of whom I see every day for 80 minutes.  Some of these students (and often some I don't have during the blocks) are also in my 45-minute intervention or enrichment period at the end of the day.  It took me a few years to find the paperwork management system that worked best for me and my classes because I am not good at managing papers.  I was always that kid in school with the 2-inch thick folder and nothing clipped in her binder rings dated past September!  Here's what I use in my classroom that I can actually stay on top of.

These hanging file pockets hold four things for each class: missed work from absences, tests/quizzes that need to be made up, no name or not finished papers, and papers to be handed back.  I got these at JoAnn in the dorm section and they've been going strong for two years already with no signs of wear.  It doesn't look like they are carrying them this year because I couldn't find them in my store or online.  In any case, I know you can find similar hanging file organizers in teacher catalogs.  Lakeshore sells some here. 

I teach the kids to check the top pockets any time they're absent and then to ask me about make-up work.   Kids remind me to (let them) hand back papers when some are in the organizer because I am notoriously bad about remembering to pass back what I've graded. 

Not pictured are the bins where students turn in their work to me.  Those aren't as interesting.  They're simply stacked plastic file trays labeled with the class period.  Simple, and they work!

How do you organize paperwork for your students?  

Miss B

Welcome!

Thanks for visiting my new blog.  I currently teach Pre-Algebra and Intermediate Algebra at a middle school and as I was beginning to be inspired for the new school year, I found I had lots to share.  While Pinterest is fun, I needed a place to share my own creations. 

I chose "i is a number" for the title of my blog because it gets at my love of math and sounds like poor grammar- one of my major pet peeves.  Teaching students about i last year for the first time was such an experience!  "Really, kids, it's a number.  I promise!"

I don't know how regularly I'll get to update as the school year progresses, but I'm looking forward to networking with other secondary math teachers, especially any with PBL or STEM experiences to share.  I hope you find something here you can use and that you let me know if you do.  Thanks again for visiting! 

Miss B