Beyond the Test

As Georgia's standardized test scores have been released, the recurring question that flows through the air is, "How did your school do?"  I think there are two ways to respond to that question. 

The first way is from the perspective of stakeholders, administrators, policy makers and many teachers. They look solely at the snapshot of the test scores to say this school is a high performing school or this system is a high performing system. 

For those tests, on those days they make a superficial determination about the work of the teacher, the knowledge of the students and the effectiveness of the school's instructional practices. 

So this means, a school with disengaging practices, procedural mathematics teaching and learning, and textbooks with superficial understanding for the teachers and students can be praised for the work they've done based on their test scores. Conversely, a school with highly engaging problem based tasks, conceptual mathematics teaching and learning, and standards-based practices may be frowned upon for low test scores. 

This brings me to the second perspective. This perspective sees the whole picture which includes student growth and "out of our control" factors. For example, a 3rd grader can enter the year reading on a kindergarten level and with intensive work end the year on a 2nd grade reading level. That same student struggles with counting one to one coming in but by the end of the year they can use simple part whole strategies to solve addition/subtraction and multiplication/division problems. This student made tremendous gains throughout the year, but will not meet grade level expectations on the state test. That teacher's and student's hard work is now overshadowed by a "does not meet" on the state test. 

The second perspective also tells the tale of two worlds. On one end you have the population that has high parental involvement, funding for tutoring and a healthy overall home life. On the other side there's very little parental involvement, which leads to no additional tutoring outside of what the school offers, a high population of homeless and/or foster children, not to mention a spike in child abuse cases. The students on both side can receive the exact same highly effective instruction in school, but due to the factors outside of our control, the students begin in two different starting places. 

This is why I believe it's so important to look closely at the student growth versus the snapshot test score. I found myself making comparisons based on that snapshot score and I'm sure others of you have as well. It wasn't until @Math_HCS pointed out the perspectives mentioned above. It helped me widen my view again to see the student growth pieces that were being overshadowed. So I encourage you to do the same. Widen your view, analyze your student growth data and create your own celebrations and goals based on those. Don't write a biography on a student based on one moment of his/her life. 

A Troubling Problem

   Solving word problems has been a thorn in teachers' sides as long as I can remember. We've all attempted to remedy this issue by pointing out key words, saying key information with heavy emphasis and even making students redo the problems until they get it right. With all of these efforts, we still end up with students who cannot independently solve a word problem. Ugh!!

   SMP 1 tells us students should always be making sense of the mathematics. As I compare that standard to the practices even I have implemented in my classroom, I realize if this is happening students are not making sense of the mathematics. No wonder when students are working with word problems they just spend the wheel of computation and does what "feels" right. So how can you get students to the place were they are exhibiting SMP 1 when solving word problems?

(Sorry for the sideway images.)

    This problem was solved by a 4th grader. When I asked how confident he was with his answer, he felt pretty confident. 

   I rewrote the problem on another sheet of paper minus the question stem and we started anew. I first asked him to read the problem. 

Me: What's the context of the problem?  What's happening?

Student: They're ordering pizza and there's pizza left over. 

   We read the problem again. 

Me: What mathematical information is there?

   We read the problem a third time. 

Me: What mathematical questions could we ask about this problem? 

Student: Do you need to add or subtract?

Me: Think again about the context. 

  I asked the student to compare his answers. He pointed to the 3 wholes and said, "This one is correct.  The questions are different."

Me: What's different about them?

Student: This one says 'How much pizza was left over'. 

Me: Well what made this problem easier (referring to the problem without the question stem)?

Student: I was able to answer my own question. 

  This 3-Read strategy changed my perspective on solving word problems. This idea was flushed out in the document Instructional Toolkit for Mathematics shared on Dan Meyer's blog http://blog.mrmeyer.com/wp-content/uploads/OUSDMathInstructionalToolkit2013-14.pdf. When asked was this strategy just for the kids who can comprehend well, I swiftly replied, "No!"  Don't limit this strategy to just some kids, expose all students to this strategy, especially those we have trouble with solving problems. 

So Who's Failing

It's that time again, the end of the unit. You pass out your multiple choice assessment, confident in knowing you've taught your students everything they needed to know. You've shown them everything you could to make them understand the unit's concepts. You even supplied students with a study guide mirroring the unit assessment and went through every question on the study guide prior to the test. 

After taking the time to analyze the data from your assessment you're stunned by the results. 

How could this be?! More than half of your students are not proficient on the unit assessment. You think to yourself, "They failed.  These kids just don't get it.  I need to assign more homework.  They just don't listen to me!" All while you are denying any wrong doing on your part. 

As an effective teacher, you watch for pitfalls, wrong way turns and plain out misunderstanding along the way. This is hard to do when you are cruising through the pages of a textbook, covering the content superficially. It's hard to do when the only assessments you administer come at the beginning and end of the unit. It's also hard to do when you implement 20 question tests which take several days for you to grade. 

What's a better alternative to ensure at the end of the unit journey you haven't left half your class behind?  Observation rubrics.  As students are working through a task, the teacher circulates listening to math discussions, looking at student work and asking guiding questions.  The rubric has predetermined expectations based on the standards and related to the task. Once the teacher has checked on a student's thinking, the student's name is recorded next to the appropriate level of understanding. 

In this example you can clearly see which students are on target to master the standard and which are not quite ready. You can vary the task students will complete the next day or pull small groups to remediate and accelerate students. This process is continuous through the unit and provides a better idea of how you adjust your instructional strategies to meet students' needs. 

If you come to the end of a unit and half of your students still lack understanding, you haven't met their needs. The use of informal assessments such as an observation rubric is an extremely effective way to gauge where students are and what you need to change about your instructional practices.  Because my friends, if half of your students lack understanding at the end of the unit, they haven't failed, you have.

It's Like Standing in Line For Your Favorite Coffee

As a coach, majority of my work is directed towards teachers, so my interaction with students is secondary.  When I get the opportunity to work with students, I realize how much I miss it. 

I had the pleasure of working with students on dividing with fractions.  Their teacher jumped into the action to build her conceptual understanding. From that experience I realized, "I miss this!"  I miss the excitement students have when they make connections for themselves.  I miss asking those guiding questions to help students get to their understanding. 

So I've made the decision to pursue a classroom position.  I personally know teachers who would scoff at that statement. But have you ever wanted your favorite coffee so bad that you waited in the Starbucks line for "I don't care how long it takes" amount of time?  Well for me, working in the classroom is like waiting for that coffee.  All of the paper pushing and evaluations will not keep me from enjoying the sweet brew of students thinking critically and making sense of mathematics.  

To start from the beginning of understanding and watch them as they grow is my goal for the next school year.  It's like waiting in line for your favorite coffee. 

I Believe the Children Are Our Future

Wednesday morning I awoke to a retweet by @Natasha_Neffy which read, "Georgia Senate has passed a bill to withdraw Georgia from Common Core". WHAT! 

 I spiraled into a tizzy thinking about all of the work we have put into getting students to a place of understanding in mathematics. I thought about all of the ineffective teaching practices that were on their way out of the door due to Common Core.  I thought about all the teachers who set aside their fear of change to do what's best for students. 

Common Core has developed a bad reputation. From people believing it is the government "enforcing its rule" upon us, to others believing it confuses students with the mathematics. Common Core has sifted fears and insecurities of many teachers to the surface, exposing them. Instead of admitting these things and having a sense of vulnerability, they have found excuses and remain misinformed. They passed on these fears to parents, who in turn are misinformed. With all of this, Georgia now finds itself in a compromising position. 

Do we compromise the understanding of our students to appease those who are afraid of change?  Do we subject our kids to a life of, "I was never good at math"?  Do we bow to the pressure of the misinform?  Withdrawing from Common Core does just that!  These standards were written to build understanding of math concepts gradually. You would not want to live in a house built in a day, because chances are it would not withstand any storm. So why would we subject our kids to such construction?

Bottomline Georgia Senate, if you believe the children are our future, which they are, what future are you creating for us all?  Have you considered the ramifications of removing critical thinking and understanding by changing from rigorous standards to those which do not allow the building of understanding?

"I believe the children are our future.  Teach them well and let them lead the way, show them all the beauty the possess inside. Give them a sense of pride, to make it easier..." - Whitney Houston

Lessons From Homeschooling

Like other areas of mathematics, teachers too often rely on memory to ensure students, dare I say, understand measurement concepts. We go to various lengths to find the cutest activities for students to complete and encourage them to "Remember the one time we...?"  Only unfortunately they don't remember, some yes, but we weren't aiming for just some.  The connections are not made for all. Why is that?

I have a friend who home schools her four girls.  Before you begin making your judgments about what homeschool is or is not, please hear me out.  One thing I've learned from discussing homeschooling with Dawn is, her girls have authentic experiences with math concepts on a regular basis. Her oldest daughter has a solid understanding of measurement concepts, this I know based on your demonstration of her understanding.  

The pictured tasty treat was made from scratch, by for 11 years old daughter!  From scratch meaning, she didn't drop the contents of a box into a bowl and mix.  She measured the ingredients using tools accurately.  She has adjusted the recipe for make more or less cupcakes, no seriously guys, she made 1 just one cupcake from a recipe meant to make many more.  

So what's my point?  It is the experiences with measurement that help to shape and deepen our understanding of its concepts. What does this look like in a classroom setting?

It looks like activities where students engage with the tools and connect the use of the tools to understanding the concepts. An experience measuring how tall you are compared to your friends or teacher and what you used to determine the heights are retained more than completing a worksheet on "Which item is taller" or "What tool would you use to measure..."  

An activity using student feet to help determine why we have standard units of measure and what they are will aid in students using rulers correctly more than completing pages in a textbook.

Many of these types of activities can be found within resources like Math Solutions' Investigations, Tasks, and Rubrics to Teach and Assess Math; John Van de Walle's Student Centered Mathematics or Math Solutions' Sizing Up Measurement.  If these resources are unavailable to you, take a lesson from homeschooling and create authentic everyday measurement activities to implement in the classroom. 

For more ideas, you can visit my webpage Sensible Mathematics https://sites.google.com/site/sensiblemathematics/.  

Friends with Benefits

Personally and professionally I like to surround myself with people who challenge me, who make me better.  I tend to shy away from the "yes" men and women whose constant approval will create a fixed mindset and leave me with a big head and overgrown ego. Thankfully, I haven't had too many of those relationships. No, I have friends who quite often call me on my nonsense and challenge me to try new things. 

The new thing I'm trying, courtesy of my friends Graham Fletcher, Michael Wiernicki and Turtle Gunn are 3 Act Tasks. I started with the Apple's Solar Farm task, shared in a previous post and since then I've been on a bit of a snowball effect. I've created five more tasks which can be found on  https://docs.google.com/spreadsheet/ccc?key=0Are6h0vMbntddGVlQkE2VzgyZkdJb3NBWWwtamhJQXc&usp=docslist_api. These tasks will soon be found on www.101qs.com. Not many coaches in my district have made the shift to this innovative teaching practice that I have. That's one of the many benefits of having friends that challenge you.