Reflections of a Techie

Wiggins got it right...we need more assessment, not less

One of my all time favorite online articles is by Grant Wiggins where the first sentence says,

 "Here's a radical idea: We need more assessment, not less."

That always gets the conversation rolling.  Teachers jump up and start the long and loud protest about how we're overtested and the kids are burned out.  And then they read a bit further and he says,

"Seem crazy.  Substitute feedback for assessment, and you'll better understand what I mean."

These two simple sentences are enough to launch hours and hours of productive conversation about how we amp up student learning.  Learning in ways that honor and respect the intellectual nature of our student because using formative assessments to pace your instruction, help you know what you need to skip or reteach and empowering students is where it is at.  Doing formative assessments well forces you to figure out what you really value in the curriculum standards and gives students AND teachers valueable information for every step of the way.

The Blueprint says this...

Districts and schools that are improving generally show a commitment to the use of student assessment data to diagnose weaknesses and guide improvement efforts. They provide data to teachers and principals in a timely manner, train teachers in how to use these data effectively and give the teachers time to analyze the data.

I'd like to see us blend the ideas from Wiggins article with the notion that teachers need more formative testing (or substitute feedback).  The best part of this idea is that it doesn't require huge data warehouses...just teachers who know how to develop measures that can be taken along the way so that they can make sure everyone learns as much as they can as they go along.

Let me give you a concrete example from this past month.  I assigned a project where students had to apply what they had learned about similar shapes....they had to write algebraic "rules" to define how they were going to manipulate their shapes, mathematically compare different dimensions of those shapes (ie side lengths, perimeter and area) and then write a report.  The due date was about 2 weeks from the assign date.  On the first day, I hand out a rubric that has the dimensions that I expect in every project, I define what those dimensions look like at various levels of performance AND I show them past student projects so they can see what those levels look like. 

Formative assessments allowed me to walk by and check with my students everyday on how they were doing...and when I could see they were all struggling with something similar, I could immediately do a mini-lesson the next day to remedy those problem areas.  If I saw that one or two students were struggling with something that no one else was, I could adjust and make sure I spent more time with them.

You see....high stakes bubble bound tests don't do this.  They see what you've learned at the end and the chips fall where they may.  In my project, I make sure they all arrive at the end point....yes, students take many paths, but they are all pretty much successful to the minimum I set.

You might be wondering what I do with those students that always finish things like this quickly.  Well, I have two additional challenges.  They can supersize their enlargements...ala the Oprah Winfrey slogan of "Go Big or Go Home".  This delights all of them and their enlargements get bigger and bigger and bigger.  For those that are not so art inclined, I designed a creative story element.  Each of the similar shapes they create looks different from the original...but they are still in the "family".  Students must write a creative story that tells the tale of how each shape came to look the way it did.  I'm telling you these stories are funny, sad and completely true to who these middle schoolers are.  The only thing that was more fun that the stories were the "Family Portraits" we took...each student posed with their family members...and I created an album of all our families.  Korny, but part of what it takes to engage students and make taking a long term assessment like this fun.

All of this is to say......that when I look at how the reauthorization of ESEA will help me do more formative assessments, I just don't see it.  I see lots of commitment to bigger testing systems and if you look at the recent testimony in front of he Committee on Education and Labor, I hear lots of support for bigger and better data warehouse kinds of things. 

But you see....I don't need a data warehouse to know what each of the kids sitting in my room needs me to do.  I just can figure that out by watching them work on the project or talking to them....or even by listening to them.  I can also prove, using student work samples as my evidence, that they've learned every objective in my curriculum.  And I know it all hinges on that all important formative assessments that I've created for along the way.

I wish the folks would realize that teachers are smart; we know our kids, we know our curriculum and we can build systems of MORE assessment...if you just let us build the right kind.

 

The Wumps Add New Family Members...did you ever think similarity was this much fun in math class????

I have taught the Stretching & Shrinking book on similiarity for several years.  There is a storyline that goes along with the book...it's about a set of similar shapes that are represented by the Wump family.  This year, I decided to challenge my upper level students, with creating a new Wump family member and fashioning a story that explains how they came to be.

Cracks me up.  They are so wonderful.  And it gives me a chance to see them use a different intelligence than I normally see as their math teacher.  I will post pictures of the new Wumps as soon as I can scan them in.

Here's are some of my favorites...

Sug Wump is a new member of the Wump family. He's as tall as Lug, but as short of Zug.  Though he was not as flat and fat as poor Lug,  Sug still felt left out.  Sug used to look exactly like Bug.  (They were actually twins.) 

One day at school, the bleachers in the gym fell flat on Sug's head.   He escaped being as flat as Lug by running out from underneath.  Luckily, the bleachers only bounced on his head once, so Sug was able to survive.  He was sad he was no longer an identical twin, but happy that he was different.

If you want to find a picture of Sug, you'll need to follow this rule.  Transform Mug's coordinates using this rule...(3x, 2y).

And another story of tragedy......

When Nug was a baby his mother was Bug and his father was Glug.  He was very tall and a bit fatter than than Glug because of Bug (a fatter one yet). 

He was squashed by a garbage compactor but Bug shut it off before he could become as skinny as Glug.  A year or two later,  he was abandonded by his parents because they found out he was too hard to handle.  He found a family of Goombas who took him in because he looked like them.  They taught him how to survive being squished by a boot.  Then they set him on his way because they thought he could survive on his own.  He was met up with long-lost brother Lug, who unfortunately, was squashed by a boot.  Lug took Nug to Bug and Glug who greeted him.  They were crying and apologizing for letting him go. 

 He told them the story of his life and the family (Mug, Lug, Zug, Bug, Hug and Nug) lived happily ever after.

This is a sad tale, but has a great ending.

Mug and his mom, Zug, and his data, Bug, are cleaning the house up so that Aunt Hug can come.  The Wumps went to pick up Aunt Hug at the train station.  Aunt Hug hopped in the car and they headed home.  When they got home, there was a fire.  Mug ran inside the firey house because he didn't want his stuffed animal to burn.

Of course, Aunt Hug ran after him.  She saved him (sadly not the stuffed animal) but in the process her ears burned and shrunk.  So that's why Aunt Hug has very small ears.

To make your own Aunt Hug...use this rule of (2x, 3y)

Writing & talking to learn in math

These past two weeks have been the best in my math class.  We are done with test prep and I'm finally able to return to open-ended problems.  We're heavy into figuring out whether a table, a graph or an equation is a better way to represent the relationship between two variables.  We've considered all sorts of real world situations...from projecting costs to determining profits. 

When we are done with these, we work with the Problem of the Week from Math Forum.  This week we are considering the problem of planting a spring flower garden.  The issue arises from the fact that students know how much of the garden is planted EXCEPT for one small corner.  They don't know what fractional piece that corner represents but they do know the square yards that the corner represents.

This puts the kids in a wonderful position to solve the problem in a variety of ways.  Some started out creating pictures of how the problem is presented...some used fractions and Least Common Mulitples...and some used a blend of both.  Regardless they ended up discovering the proper fraction that was missing and then what the overall dimensions of the garden had to be.  The extension to the problem comes in the work the past two days...they must now figure out how to represent these ideas using algebra.  That's a much harder problem for them. 

The writing is brilliant..."listen" in how part of the problem was described by one of my partner groups.

After making sure we understood all of this, we first found the common multiple of the denominators used in the problem. We found the common multiple of 3, 4, 5, and 6 to be 60. Then, we made a table with 60 boxes, and filled them up with the appropriate amount per flower. For example, we knew 1/6 of the boxes were Trillium flowers, so we took 60 divided by 6 to get a total of 10. So, we would then know to fill in 10 of the boxes with trillium. We went on doing this with all the flowers. However, once we filled the boxes appropriately, we found that there was not a way to make the length 3 feet longer than the width if we used an area of 60 square feet.

After this, we searched for a higher area that might meet our needs. We found 180 square by finding more common multiples. We were pleased to find that it could have a length 3 feet longer than width, at 12 by 15 feet. We used the same strategy of taking the area divided by the denominators of each flower's fraction to find what portion of the garden will be filled with each flower. The sunflowers would fill 60/180 of the boxes, the brown eyed susans would take up 45/180 of the boxes, the columbines would take up 36/180 of the boxes, the trilliums would take up 30/180 of the boxes, and the foxglove would take up exactly 9/180, which is the perfect area for foxglove because 9 square feet equals 1 square yard. We then decided to try and convert this answer to yards.

So we talk and talk...try different things.  I give little hints along the way.  We share on the SmartBoard different strategies and slowly some of them are figuring out a way to do this problem using algebra.  We spent one whole class period projecting everyone's answer and using the rubric provided by Math Forum to eevaluate/rank their answers.  This helps people see what others are thinking and almost immediately some the kids know they need to revise their answers.

Between now and Wednesday of next week, they are working to reflect on their answers.  The rubric gives concrete ways to reflect.  That's important if you're a 6th grader because you have no idea how to reflect.  But the rubric leads them with multiple ways to go back and look at the comments I've left them and morph those into an improved answer.

Best of all....by next week everyone will get the problem, all it's parts, the different strategies that could be used to solve the problem, how to write about it and some will get how to express it algebraically.  It will then be time for us to start the next problem.  I know it's seems slow to take 2 weeks to completely finish a problem, but I think the marinating time is what builds the math sense for problem solving.

And this is so much better than test prep.  Heck....if anyone wants to know how to make our country's math skills stronger.  They need to spend 2 weeks studying a rich open-ended problem like this with a bunch of kids.  You can see the skills buildings that we'll need to have engineers, architects, scientists and the like develop from kids like mine.  Why?  Because they've learned perserverance, revision of thinking, creativity, and MATH.

Proud of My High Stakes Testers

My math kids rock!!!!   Our state assessment is an endless stream of low level questions that are very narrowly defined by the state's tested indicators.  This year it's been very difficult for them to prep...they came in behind where other classes have been.  They worked and worked to get ready for this test.

You'll crack up, but our biggest problem in all the formative tests....guess what it is????  They click the wrong answer.  They come up and show me how they really have the correct answer but they just entered it wrong or they pushed the wrong button.  It has only slowly come to them that it's still WRONG.

I teach fractions, decimals, percents and long division mostly.  And it isn't the most interesting part of mathmetmatics...so it's been dry and we've practiced and practiced.  They've been involved in developing strategies to help them remember the procedures...little memory devices, pictures or "tricks" for making sure they do all the multi-step processes.  Somehow they've hung in there...kept a great attitude and found ways to remember.

Just last week one of them discovered if you write TAMPA in all capital letters, cross off the T, you'll be left with AMPA.  OK, so how does that help you ask?  Well, it helps you remember if you mulitiply for area and add for perimter.  A= area; M=multiply; P=perimeter; and A=add.  I was thrown off by the presence of two A's but they assured me that it makes total sense.  Believe me....I would not have thought of this.  Who thinks of taking the T off of TAMPA...we live in Kansas.  I think it was probably that they were dreaming of spring break in Florida.

You know the hardest part for me?  There's a new rule put out by our state this year.  No sitting down while I proctor the tests.  I have to "actively" monitor by walking up and down the room.  Mind you, I've always made sure I couldn't see the test questions by keeping myself busy with grading papers and checking emails.  I made sure kids had different forms and were separated by empty computers.  I was watched what they were doing from my seat and made sure no one passed notes or talked.  But apparently, that wasn't good enough.  Nope.  Now I must active monitor (which I interpret as patrol) up and down the isles.  It is NOT how I proctor tests ever so I think my kids think I've flipped my lid.  I told them it was part of the rules, just as the script is that I must read aloud to them.  I get why, in theory, all these things are important.  But it's just so dumb in practice.  Believe me....I do everything I promised to do...down to the letter. 

I've learned to look at the kids as I actively monitor without looking at the screens. I practice my wall sits so I don't sit and I can continue to monitor while I try not to walk back and forth next to them every second of the 90 minutes.   I try to not wear my glasses so that I'm too blind to see what the screen says, but I still am sighted enough to tell if they are working on the test.  I've learned to make sure ever scrap of scratch paper is in the shred box.  One kid asked me how much I thought his scratch paper would be worth on eBay.  I told him we'd never find out because it wasn't leaving the room!!!!  We both had a good laugh at that.  I am NOT going to be someone who inadvertently does something wrong and find out all the pledges I've signed causes me to lose my job.  I've never signed so many forms that certify that I'm honorable and won't let my kids cheat...it's insulting.  I've been using icepacks on my knees at night (and actually it's been a good excuse not to workout) and taking ibuprofen for the swelling.  But if they can endure the testing, I'll endure all the mistrust of me and all the weary knees that it takes.

Bless their hearts.  They are still working at it...we've just finished Part 2.  An hour and a half to take each part, so they work their fingers to the nubs for 4.5 hours.  I know they feel confident everytime they finish and we celebrate.  Even though I don't let them know, I'm worried about all the wrong clicks!!!!  It is what it is and I they can do no more...they have done everything.  That's good enough for me.  I'll be glad to be back to teach real math and the joy/fun of figuring out about patterns, algebra and all the things that make math the best after these tests are over.

SmartBoard Recorder--First Attempts at Math Tutorials

We are working on making tutorials for different kinds of math procedures.  This was one of our first attempts to use the SmartBoard video recorder to make the movie.

Mulitplying Decimals from Marsha Ratzel on Vimeo.

What I learned is....

• You can't show them too many examples before your start.  This way the product they create has a better chance of quality than if they don't know what you expect.
• It is going to take several tries.
• Encourage them, require them to make a script or storyboard...but the best lesson is letting them try it without that and they will immediately see how they fumble around.  Then they ASK to go and write the script.
• Do in-class consultations...ask the other students to offer suggestions for ways it could be improved next time.  Calling it a consultation makes the critiquers feel important and makes the creator feel less threatened with their suggestions.
• Movies will get better and better...the more we do, the better they get.  This first attempt is pretty lame, but it's a great start.

The techie stuff I found out...

• The file type that the SmartBoard recorder uses is not friendly for blog posting.  I had to use Zamzar to convert the file to an mp4.  Maybe I don't know what I'm doing (that happens quite a bit) so it's something I will work on finding out for sure.

Trust Builds Math Knowledge

I want to write about trust.  I know that's a weird thing for a math and science teacher to reflect upon, but it was my focus last night as I thought about my teaching day. Yesterday I had an uprising (figurately speaking) where students refused to comply with my directions.  I was teaching how to find percents using a different method from their teacher.  Honestly they were intellectually and temperamentally unable to think about my method.

At first I was offended because I'm too tenderhearted.  The more I thought about it, though, the more I came to realize it was a trust thing.  OK...there's also a big measure of student laziness mixed in...but I think the trust is the bigger issue.  The students in this recitation section that I have for math just plodded along, complying with my instruction.  I think they did this because they knew, while it might be different from what we were doing in class that it was OK.  I tried to reassure everyone that, while it might be longer, it taught them the math concepts more than doing just the "trick".  Knowing that math would be important when we get to algebra units later this year...you know learn it now but reap the rewards later.

The students that couldn't get that idea were the ones that I think don't trust me.  They don't know I really have their best interests at heart.  They believed I was just being a "dumb old math teacher who wants to make more work for us".

It was an interesting insight for me.  I lareayd knew that this was true, but I hadn't had such a vivid reminder experience in quite a while.

Image was taken from http://lifeinthenhs.wordpress.com/2009/05/17/trust-and-personal-values/

Mini movies with SmartBoard recorder

I've been experimenting this week with using the SmartBoard recorder.  I watched the Alan November ISTE address about Students as Contributors.  He spoke passionately about how students can prepare explanations to other students using screencasting software.  I tried to get Jing to work and it just wouldn't go.  So I tried the SmartBoard recorder.

It was a great experience.  My students thought it would be a piece of cake because I didn't ask them to do complicated processes.  But once they started recording and watching their products, they realized they needed to do a better job of planning out who would be the scribe and who would be the color commentator.  Their screencasts got better and better.

The unexpected byproduct that I witnessed was how much they improved their process proficiency.  They figured out more about what they were doing and why they were doing it.  It sort of cracks me up because I used the questions from my math series...the Connected Math Programs.  The questions the kids hate to answer but LOVE to screencast.  Ironic isn't it?  I can't shut them up on the screencast providing example after example...but I'd have to threaten and bribe them to even one example if they were writing.  Love that technology motivation.

Building number sense interactively

Building an internal sense of where numbers are on the number line is such a huge skill.  When students finally acquire that sense of numbers, they have a decided advantage over students that don't.  I've been working with my students on learning fractions and now I've found something that will be invaluable in helping me develop that sense with decimals.   Free Mathsframe Interactive Whiteboard Teacher Resources. is such a site.

It offers free resources that I can project onto my SmartBoard and we can watch and learn where the decimals should go.  I love the fact that the scale on the number line keeps shifting...that way students have to learn to pay attention to the hash marks.

New students; same old weaknesses---the data reveals the trend's still there

Well it's about that time....only another week of summer schedule before I head back to school.  I got up early this morning, dragged out my purple file folder that has all the incoming 5th grader math standardized tests scores.  I need to plan my first weeks of school and there's nothing like starting with some data to get the old brain in gear.

Reviewing these data make me smile in that, while I have two completely different sets of schools, the highs and lows in math skills are remarkably the same.  I don't trust these standardized tests for up-close analysis on a kid by kid basis....but I think it gives a pretty accurate picture of the group's strengths and weaknesses.  They are 30 percentile points lower on these skills that their best skills.

So what's up with estimation????  Once again, estimation seems to be a sticking point for them.  I know it seems to me that it's just the lack of experience and repeated practice.  But year after year, this is a collective weakness. 

And Greatest Common Factor and Least Common Multiple are on the bottom three skills again!!!!  Sometimes I think this springs from how poorly some students know their "facts".  I'm not sure when it is that they learn these facts, but I have many students who struggle with them.  If you don't know your facts, then it's a good bet you won't be able to LCM or GCF very well,  I guess it's back to factors....getting out the millions of games that I have developed over the years to practice finding factors.

Sometimes I wonder if just their age and they are cognitively ready to hang onto the idea.  That's the way I see fractions for many students....I know they learn it with me but it's vaporizes as soon as they walk through the doorway.  Then somehow they get it in 7th or 8th or 9th grade.

The good news is that I know how to address these issues and that the trend in their weakness is still the same.

Picture from Flickr under CC license  http://www.flickr.com/photos/pinksherbet/

Can a class be fun and challenging? at the same time????

I've been reflecting on my meeting with math colleagues last week.  We met to discuss what types of enrichment activities we'd offer to our students.  These are wonderful math teachers who are very dedicated to their students, who want to see them excel and you care deeply about the discipline of mathematics.

We hit roadblocks, I'll have to be honest.  Our first hurdle, and I definitely sure we did not solve this problem, was how to keep the pace up of learning while some students lag behind.  The class we were focused on is one that is designated for above average students....the course description is written so that parents and students know that the pace will be faster and the homework will be a higher level.  Our dilemma is that the course is opt-in by parent/student decision. 

I have no problem with that UNTIL the student can no longer keep up.  When the student requires so much remediation that they are holding back the majority of other students and when the parents are frantic that their child is no longer getting "good enough" grades.  As a teacher of this class, I can recommend that they move their child to the regular class, but it is utlimately the parent's decision.  Often the parents decide based on things far, far removed from what's academically best for their child (ie. popularity concerns, community status concerns, etc).

To my mind there is no solution because you can't leave anyone behind even in the advanced class and you can't keep the pace up because you can't leave anyone behind.  Extra tutoring, modified assignments, more tutoring, extra parent help....sometimes it isn't enough.  I don't know how to make everyone into an exceptional student.

Luckily for me, I must be a persuasive voice.  When I've had students that aren't succeeding, I've had pretty good success at helping parents arrive at the place where they move their student to a different class.  The ironic part of all this is that no matter which class you are in during our middle school years, you'll arrive in 9th grade taking the same honors geometry class.  Usually when you point this out to parents, they relax and move the student. 

Second hurdle.  Many teachers don't want to up the complexity of the instruction they are offering because they fear the lack of the "fun" factor.  By that I mean they want to hang onto projects that are fun so kids will like math.  Sometimes taking these advanced students into more open-ended problem solving won't win you points for being fun, but they learn to derive a different experience.  I guess I'd probably define that as satisfaction...satisfaction from being challenged, failing, learning how not to fail the next time, and then being successful.  In the end, I think they'll remember this kind of learning experience as favorably as those deemed "fun".

It takes courage to go with this kind of learning instead of fun.  Dare I say that I find myself lonely at taking this view? 

My solution to this roadblock is to keep on doing what I believe is best for students in the long run.  I guess I'm sort of freed up because I don't care too much if my projects are fun.  I mostly care if they earn themselves more self respect, if they grow in confidence and build their self esteem for legitmate reasons.  We all have different students who we must "read" and respond to...so I will continue working on those open-ended problems with multiple solutions and teaching six or seven of the best problem solving strategies from MOEMs or Math Counts.  It may sound too hard to others, but I have seen my students transform.

These are two pretty big roadblocks to finding a thriving, enriched math curriculum.  You see the point of this class is to provide an extra punch of math if they are already conquering the curriculum without accelerating them onto the idea/concepts they'll have in future years.  It isn't easy.  Sometimes I wonder if it's even possible.

I also have a bead on some super fun projects that I will try to incorporate, too.  Fun never hurt anyone and I'm up for that right along with the next guy.