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Small Steps for Differentiation: Same Task – Different Entry Points

When thinking of differentiation in the classroom, it is easy to fall into the trap of putting pressure on ourselves to perfectly level activities for every student. My mind goes to having a rotated set of groups and centers all perfectly ready to go. In this scenario you never run out of time, every student is exactly where they need to be, AND they are accountable, focused and staying on task the entire time.

YEAH RIGHT!

Don’t get me wrong, math workshops are a beautiful thing, but it doesn’t always work as smoothly as we’d like. It is okay to differentiate in small ways, taking small steps to be sure that we are meeting the needs of all children without going crazy ourselves.

This past summer I was lucky enough to read work by Timothy Kanold, and then I was able to work with him in a workshop as well. He proposes that instead of coming up with different activities for every student, we have the same task, but with different entry points. So what does this look like exactly?

Here is an example for a second grade classroom where the learning target would be “I can count money up to a specific amount.”(CCSS 2.MD.C.8):

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Task: How many ways can you build 58 cents? Build it and record it.

All of the students in this group are given the same task, but usually all of the students have different levels of knowledge surrounding this task. So instead of coming up with 25 different activities you have only one.  As the activity begins and students begin to work, two things will happen which we all can predict every time. Some students will struggle, and others will fly.  This is when you strategically give certain students more.

For the students who struggle in this case you would lay down another task next to it, where the number is more accessible, and you may also consider telling them the value of all of the coins.

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Instead of 58 cents, the students who struggle are working with a more accessible number, side by side with the other students.

In this case for the students that are excelling there are many options: ask them to find the solution if you eliminate one of the types of coins, ask them to show their thinking algebraically using a table, give a different amount and have them predict the number of solutions they may find before solving, or ask them to write a story in which you may need to come up with 58 cents worth of change.

The main thing is that you have to truly be walking your room, listening to your students and conferring with them as they solve. The BEST part of this method, is students are working together and hearing one another’s thinking, elevating the learning for all in the room.

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What Does Success Look Like?

Pretend with me for a moment, that you have never seen an apple before in your life. Now pretend that someone has asked you to peel it, but you’ve also never peeled anything before in your life.  How do you know what to do to be successful? How will you know when you have been successful?

That in a nutshell is what “success criteria” is.  It’s all about letting students know what success looks like, and how they will know that they have met the learning target.

In my mission to examine learning targets and communicate them, I learned that it wasn’t enough to simply display them for students. It STILL wasn’t enough for students to write them in their math journals.  My students needed to see the learning target, write it, and then have some sort of interaction with it.  This is where I combine this idea of success criteria (Hattie 2012) with Marzano’s Levels of Understanding.

Here is an example of what this can look like.  You begin your content lesson by reading the learning target out loud, allowing students time to write it down in a math journal (or some other place to take notes). Notice the learning target starts with “I can”.  (It would be just like saying, I can peel an apple.)

I can read and write numbers up to 1,000.

Now some students will have prior knowledge about the learning target, so allowing them a moment to interact and think about this learning target is essential.  You can show them (or you can do this orally) what the different levels of understanding look like. Here is what it could be for this particular learning target:

Using success criteria in the classroom can help students understand the learning they are supposed to do.

Using success criteria in the classroom can help students understand the outcome of their learning.

I use Marzano’s Levels of Understanding to anchor my thinking (which I blew up and posted on the wall-this is a free resource by the way!) because the students connect easily to the language.  After I show them what each level looks like, I have the students rate themselves on the current target. Their goal is always the same every day, get to the next level, get higher and get better.

After this mini intro, I teach the lesson. We practice with tiered examples so that everyone is challenged, we talk it through with each other, we help each other come to an understanding.  We break into independent practice work where I can catch the students who still feel like a 1 or 2.  Then we close the lesson with an exit slip or an assignment, rating ourselves once again to see where we fall on the scale.  I take a look at what they wrote for their final rating and catch those students during the review, intervention block or some recess time the next day.

This seems like a lot of work, and I won’t lie that at first it was for me. It was a different way of thinking.  But soon after I started to do this, I noticed that it was easier and easier to think about what a 0-4 looks like.  If I ever skipped the rating part, my students would actually shout at me “What does a 3 look like?!” They wanted to know what it would take to be successful! It was very powerful.  You may not have time to write it out like this for every lesson, but you can do it orally while referring to the levels on the wall.

This tweak to my instruction was a total game changer.  Thank you John Hattie and Robert Marzano for your inspiration!

 

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Real Life Examples of Geometry

The number of terms that students are expected to learn in geometry is a little crazy.  We counted 30 different new vocabulary words at the end of four days of instruction.  So I checked out an iPad cart and decided to have the students find real life examples of geometry in the world around them. After introducing the symbols, and describing each term’s features…they solidified their understanding of each new word with photos. (We pulled out some of the trickier ones from our minds as well.)

We recorded the findings on a giant chart!

Real Life Examples of Geometry Terms

Students captured real life examples of: point, line segment, line, ray, intersecting lines, perpendicular lines, and parallel lines with iPads.

It was both motivating and fun to use technology, as well as promote math talk in the classroom.

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Open Ended Math Problems Promote Reading, Writing AND Math

Last spring I had the opportunity to take a practice version of our new state assessment (the Smarter Balanced Assessment). In some states in the U.S. the PARCC is the new assessment which is similar in nature.

Talk about a jaw dropping, sweat on my forehead, instant anxiety through my whole body moment.

What the students are being asked to do is way more than a few math problems. They are expected to read, write and use appropriate grade level math in VERY complex ways. I realized that I needed to add some deep problem solving to my math instruction.  So I began to make open ended problem solving problems to introduce regularly into the classroom.

I decided to create Doggy Dilemma, a free problem for anyone to try out.  It is a highly motivating, real world problem in which students must read through information to decide what dog they must adopt. They draw a diagram of the dog pen, calculate the cost of the fencing, and write a letter to their parents explaining why they made the choices they did.

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My third graders have gone crazy over it.  They love it!  There are two full pages of reading involved which mimics the new assessments.  I have enjoyed creating it and want to make it available to anyone who teaches elementary math so that you can give your students the experience they need before the real assessments begin. You can get it by clicking on the picture below:

Open Ended Problem: Rigorous Problem Solving for Elementary Students

I’d love to hear how other teachers are encouraging this type of thinking in their classrooms. Please feel free to share in the comments!

I am happy to link up here:

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Spotlight: 4 Really Cool Math Educators

I’ve really always been a learner, everything I ever do I just try to read and read and soak in every bit of information I can.  It is both a blessing and a curse!

If you are like me (you also have the drive and passion for getting better at teaching math), you have this never ending quest to read about math.  I wanted to introduce you to some great teachers I’ve been virtually meeting along the way.  They are just full of great ideas and also have a lot of interesting things to say on their own blogs as well. Check them out!

Evil Math Wizard: She is the first person I met virtually when I got started blogging.  We definitely think alike and have the same goals for our students in math!

The Elementary Math Maniac:  I also have noticed that we have similar beliefs in math. She also connects technology really well to learning, and reviews websites and apps on her blog.

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The Research Based Classroom:  You won’t find just math here at her site, but other subjects as well.  She is focused on those very young learners, and believes in research based teaching methods. Outstanding!

Mr. Elementary Math: Full of great ideas, you can find Greg blogging about all sorts of classroom activities with lots of bright, vivid photos.

     
Enjoy meeting these fine folks!
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Should We Ignore Them? (Tips for When Problem Solving Gets Tough)

Sometimes I feel like a magnet, with a trail of students behind me as I walk around to conference/help during work time.  We are working on Open Ended Word Problem Challenges right now (I have gone through set one in the first quarter, and we are beginning set two.) These problems include a lot of reading, are many steps, and are open ended.  There can be more than one right answer.

So they hit the panic button right away!

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Right now, I am in the middle of training my students to trust themselves, to be okay with feeling a little uncomfortable. I want them to seek the answers to their problem WITHOUT me.  This is very hard for them, especially when we are working on challenging math concepts.

Here is what one of those problems looks like!

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Here are some ways that I try to raise rigor, and to help students persevere:

1. Ignore them! (What? Are you kidding? How horrible!) Of course the kind of ignoring I am talking about, is the kind where they ask for your help without trying the problem first.  There is nothing worse than when you pass out a tough problem, and the hands go up immediately. This leads to my next tip, a very simple tip.

2.  Make sure the students read the problem three times. Read it once to get familiar, read it a second time to zoom in to what you need to do, then read it even closer a third time to circle key details. The answer to their question is almost always in the problem. Most times I’ll read it out loud!

3.  Encourage students to do what they can in the problem while they wait for help. Sitting there with a hand up, or following the teacher around, trains students that they must rely on the teacher to continue on. When I approach students my first question is always: “What parts did you understand?” They realize that they can do much more than they originally thought.

4.  I teach routines when solving problems. For example, my students cannot actually get up and follow me, rather they wait as I circulate so that everyone gets equal time. Sometimes I’ll have a schedule posted where I meet with small groups.  Knowing that they will all get equal time with me makes everyone relax (including me!).

Teach the students that an “I can do it!” attitude is the most powerful problem solving strategy!

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Data Doesn’t Have To Be Overwhelming!

The idea of collecting data has really been getting a bad rap lately. Have you heard these comments (or comments like these) in your building?

  • “We are drowning in data!”
  • “All we do is test our kids.”
  • “I feel like our kids are just numbers, like we are ignoring that they are PEOPLE.”
  • “We collect all this data, then we have no time to analyze it and use it.”
  • “I don’t have time to enter in all this data.”

I think we’ve probably all heard some version of this at some time or another. Some of these comments might actually be true in some districts. I’ve heard horror stories about schools that are doing so much test prep, that they really aren’t finding time to intervene and help their students when they struggle. I feel lucky to work in a district that believes firmly that our data should drive instruction, and if it doesn’t, we shouldn’t collect it.

I had an amazing moment about 5 minutes ago. (Yes, I was working on a Saturday night, not totally uncommon around here!) I was looking at some problem solving we did for report card purposes/parent teacher conferences (THAT explains why I’m working on a Saturday night), and I noticed something amazing.

I use multiplication and division word problems in my classroom about 3 days out of the week. I am a firm believer that students need simple problems to try out before diving into difficult and complex ones. I use Practice Problems for Multiplication and Division because according to the Common Core these students must have multiplication and division mastered by the end of grade 3.  There are also 9 word problem types that are broken down in the common core for students to master in grade 3 so why not teach these things together?

Instead of just diving in and giving everyone all the problems in the entire booklet, I first assess each student on each problem type by giving them the first one. Then, I set up a spreadsheet to look at my results.  I noticed that my class was really struggling with the Type 2 problem, only 8 students got this problem correct. (I score this according to a standards based grading scale, it could also be scored pass/fail.)

My chart:

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So we practiced this problem type. We tried this type of problem five times, each time giving students a chance to come up to the chalkboard to explain their thinking.  Awesome strategies were shared, and students asked many questions to see how they solved it.

The student on the left has pretty good knowledge of multiplication, while the student on the right is just beginning. Both strategies are successful.

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Now we fast forward to tonight.  For parent teacher conferences, I decided I wanted a sample problem solving exemplar to show to parents (it also made sense to have the latest info for report cards!). Naturally I choose this same problem type, since we’ve worked so hard on it. I just finished scoring them, and noticed that 21 out of 25 students got it right this time! I started yelling to my husband (who probably thought I was crazy) that I was so proud and excited for my students.

It really DOES work.  Using data to target instruction is a much more focused way of going about planning instruction.  I haven’t wasted any time on problems that students already knew, and now I know exactly who needs a little intervention work with me! The best part is, this entire process was so simple.  (Instructions are included in the Practice Problems for Multiplication and Division resource. You could also set this up with your own problem types!)

I can’t wait to share this awesome news with my class. I am hoping celebrating our success will motivate them to continue to work hard.