All in with OUR/IM – Digging in to Planning – Part 1

Spinning my wheels

Is anyone else is finding themselves filling their time with things besides actually planning lessons? I have definitely been falling into that. In the last couple weeks I have made carefully color coded pacing calendars for 8th grade. Here was my first version:

Notice how awesomely the unit colors match the book colors. Made me so happy.
This one looks great on my computer screen, but when I printed it, my printer did not translate colors well. So I spent about 3 more hours and what seemed like a full ream of paper until I got it to print in colors I was happy with. Here is that version.

Then I made a binder with color coded tabs by unit for my teaching notes. Then I added lesson tabs to my copy of the Unit 1 teacher’s edition. Then I decided I wanted to do the same for my student edition. Now I have decided that tabs on the side were maybe a bad idea, because they get bent on the shelf. So I begin contemplating moving all my tabs to the top.

If I was a classroom teacher I am sure I would also be spending time on labeling my storage bins, creating file folders, deciding on how to arrange desks, handle geometry toolkits, etc, etc. And all those things would be awesome and make it easier to stay organized as the year progressed. But none of those things alone help me know what I am going to say when the students are sitting in front of me.

So wherever you are in your prep, at some point you need to evaluate the time you have left and say, “Enough of the side dishes. Time to dig in to the lessons themselves.”

How to begin

The experience of planning feels a little different to me now that I have a print teacher’s edition. This January I planned a bit of Grade 8 Unit 1 using materials I was looking at online. This summer I am planning with a hard copy of my teacher’s edition in hand. To be fair, 100% of the teacher edition material is on line. But the way the teachers editions are put together helped me personally not skip important steps, and allowed me to make notes and highlight questions and ideas I wanted to make sure to include when I ran the lesson. Here is a picture of the table of contents for my Grade 8 Unit 1 teacher’s edition:

table of contents

Step 1: Unit Overview

So I started at the beginning and read the Unit Overview. I underlined, circled and highlighted the things that I wanted to remember and come back to just before we start the unit. I made a list of terms that students would be learning in the unit, and I added post-its to things I did not understand or wanted to read more about.

8.1 overview

In the picture above, the post-it quotes “Experimentally verify the properties of transformations, reflections and rotations.” I wondered which properties in specific. To resolve this I looked at the 8th grade common core standards for Geometry. Because I am obsessively thorough, I also talked to some knowledgeable friends who suggested I read the 6-8 Geometry progression documents from Achieve the Core. Any of these are good options for your questions as you plan. The facebook community, Open Up Resources 6–8, by Illustrative Mathematics is a great place to look for knowledgable friends.

Here is what I found:

Screenshot (7)

“Which properties?” was answered right there, under the main standard. Yeah!

Being an old high school teacher, I wanted to also include that reflections carried a point perpendicularly and an equal distance across the line of reflection. When experimenting, students might notice that, but it is not an 8th grade standard and I do not need to add that detailed definition at this point. I share this because no matter which grade or which unit you are teaching, it is easy to overteach. So as you begin to go through the unit, it is important to decide what you are actually responsible for. This is the number one thing you can do to make sure you are able to make it through the whole year of curriculum. Good news – The reason there is only one post-it on that page is because all my other questions were answered as I read the materials included with the curriculum and worked through the rest of my planning.

Step 2: Assessments

Next, with the overview fresh in my mind, I worked through the assessments – pre, mid- unit, and end-of-unit. Most units do not have a Mid Unit Assessment, but if they do, realize that most of that material will not again be tested on the End of Unit assessment. You and your PLC need to come to some decision about whether those will be counted as two separate unit exams, two half exams, or a quiz and a full assessment. In 8th grade, because the first unit is so long and we need to send report cards at the end of 6 weeks, I am leaning toward weighting them equally just to get more grades in the grade book.

When you are looking at the assessments in the teacher’s edition or teacher materials online, you are looking at the full answer key. In the Pre-assessment that includes why each question topic was chosen and when they are going to need that information in the unit. In the later assessments, solutions include discussion about what misunderstandings would cause students to pick each multiple choice answer, and rubrics that helped me fine tune my understanding of what was expected from students.

As I worked through these I removed many of my question post-its and added details to my notes on the overview page.

Step 3: Sections

Next I opened the teacher materials on the computer and marked out section grouping on the table of contents ( see pencil brackets in picture above). The lessons in the same sections are developing the same set of ideas. I found it helped to think of them as one giant lesson, because one day does not complete one idea like it did in my previous textbooks.

In one sitting, I:

  • Read through each lessons learning goals and learning targets,
  • Looked at the Alignments in the print version (called CCSS Standards online), and
  • Read through the cool down and possible answers.

Then I moved to the next day. In the Alignment section, I noted whether the standards were listed as Building on, Addressing, or Building Toward. This really helped me get a better feeling what I needed to talk about in each day, and what could wait for a day or two.

2018_07_20 3_40 PM Office Lens

2018_07_20 3_41 PM Office Lens

2018_07_20 3_47 PM Office Lens

I especially liked this one from 8.1.3, which should me they were addressing standard 8.G.A.1 in that lesson, but there would be more work in subsequent days on that same standard.

2018_07_20 4_47 PM Office Lens

Why so many days on a single standard?

According to course guide, each sequence of lessons includes the following:

  • Activate prior knowledge – invites all students in
  • Introduce representations and contexts – essential for developing an understanding of the mathematics
  • Concepts – where I used to start if I did a great lesson
  • Language and notation – where I started if I was pressed for time
  • Connections and consolidation – the place where students can move to the most efficient method of solving problems
  • Procedural fluency – the goal

As you look through the section, think about which of parts of this progression are happening during each lesson. Having a clear grasp of what exactly you are trying to accomplish in the day will make sense of everything you are doing. It will also help your activity and lesson synthesis be clearer and to the point.

Under Pressure

In a perfect world, you would do this for all of the sections of the unit before you begin you lesson planning and teaching for the unit. Having the assessments fresh in your mind will be a huge help in figuring out where you are headed. If it’s summer and school is still two weeks away, invest that time. If you need to know what you are teaching tomorrow, that is probably not realistic. Finish your one section and then begin digging into the lessons. Not optimal but it will probably happen sometime this year.

So Much Time

Yes, planning for new curriculum is going to take time. But until now, you have probably been in the curriculum writing business. Writing warm ups, searching out and adapting activities to support your lessons, finding or writing performance tasks or other problem solving opportunities – all that took time that you no longer have to spend. And the thing that is making you nervous now is the nagging feeling that you have no idea what you’re getting into. So let’s fix that. Sit down and put in the time. The confidence you gain in knowing where you are headed and what you are talking about from day one of the unit will definitely be worth it.

Up next- Planning a lesson

How I Became a Stand and Talk Believer

stand and talk
I wanted to share a story of how I ended up using Stand and Talk during a high school model lesson, because that day I became a huge believer.

I was teaching the same lesson 4 period in a row with a colleague in her classroom. The point was supposed to be to demonstrate how to run a lesson on desmos, and I had wrongly assumed that because the students had been taught something 2 days prior, they actually fully understood and could use those skills. Immediately I could tell that was not the case, and they were going to get stuck right away if they didn’t know that previous learning.

In the first period i decided to direct instruct the material, because that seemed fastest and I wanted to get to the fun stuff. After 20 minutes I had said all the stuff i needed to say, but the glazed eyes i was looking at made me wonder if I had accomplished anything.

The next period, I decided to handle the pre-teach with a Stand and Talk. Since we were on the fly, we did not orchestrate who they paired with. (Topic doesn’t matter. For this class it was high school trig and using the unit circle. Look past that and think how it could apply in your room.) We quickly wrote 3 pairs of short questions.

“Everyone grab your unit circle and stand up. Find a partner not from your group.Person with bday closer to start of year is partner A, other partner B.”(1 minute)

“Partner A, show your partner how the unit circle helps you find the sine of pi/3.”

One student told me he had been absent. I told them to switch so he could go second. He didn’t have a unit circle. I gave him my copy that was filled out.

In this first round, we told them the correct answer and then had them talk again about how to adjust their thinking if they had missed it. (2-3 min this first round for partner A).

“Partner B, tell your partner how to use the unit circle to find the cosine of pi/4.” Students had never been trained in this routine and were pretty cool/apathetic juniors and seniors. But by this time the class was acting pretty collaborative. Groups where neither student understood were being helped by other groups. We also had the luxury of two teachers circulating and listening to conversations. When we told them this second answer there was a small cheer.(1.5 minutes)

We did two more rounds of partners, upping the difficulty or bringing up something slightly different with each round.

“Person with longest hair is partner A”

“Person whose first name is first alphabetically is Partner A”

Round 2 and 3 took about 2 minutes each in total. By round 3 the student who had been absent was explaining to one of the RSP students how to do it, and by the end they both understood.

I looked at the clock. Just under 10 minutes. Everyone was alert and back to their seats. Everyone was awake. There was energy in the room. And EVERY SINGLE STUDENT was ready to apply the prerequisite skill.

Sometimes I just need to be quiet and let the kids talk.

Here is a link to Sara Vanderwerf’s original post on Stand and Talks. Enjoy the read!

And here is one of my favorite ignites by Graham Fletcher, The Less I Talk, The More I’m Listened To. 

All in with IM/OUR – Planning your year

In the last few posts in the series I encouraged you to:
✓ download your blackline masters and cool-downs and start your materials prep
✓ Dig in to IM resources to get the big picture of how this curriculum is built to be taught
If you haven’t read The Big Picture post, I encourage you to stop and do that first. Without a grasp of how differently this curriculum is put together, the specific planning you do will be less effective.

Pacing out the course

Finally it is time to answer everyone’s burning question – can I fit it all in? The best way to know is to sit down with a calendar of the year and start filling in squares. Everyone’s district calendar is a little different so this is something each site really needs to do for themselves. Before you begin, here are a few things to keep in mind:

Minutes Minutes Minutes

Not every lesson is written to take the same number of minutes. If you are in a self-contained classroom, this may not be a big deal. But for those who will teach 5 different sets of students per day, how things fit into a period is really important – even more so if your site runs a block schedule,where you see students in 110 minute chunks of time every other day. For you thinking about minutes per lesson is crucial.
In our district, 6th grade is self contained, but 7th and 8th grade students move classrooms period by period. To help get a grasp on the difference in lesson length, I made a spreadsheet for 7th and 8th grade. You can access this spreadsheet here.
Below find a picture of unit 1 from the 7th grade sheet.

7th minutes

A few important things to recognize –

  • Not all lessons are planned to take the same number of minutes. Notice as you look at the second column in the table above, the number of minutes per lesson varies. Especially if you are planning for a block schedule, some lessons are easier to put together on a block day than others.
  • The lesson synthesis is not included in the number of minutes. That lesson synthesis is where you lead discussion, drive home the important learning of the day, have students write down new vocabulary, orchestrate discussions, and tie ideas together. As you make decisions on whether you will include optional activities or discuss a previous cool down that students struggled with, you need to make sure you think about how long that Lesson Synthesis will take you. Most teachers say that for the first unit or so it took them longer than it did later in the year, when the they and their students were used to the structure and routines built into the curriculum.
  • Some lessons are optional. For myself, I begin by calendaring them all, but marked optional lessons in case I got behind or really wanted to add a day of error analysis and practice. Fyi 8th grade has less optional lessons than the other two.
  • Some activities are optional. We will worry more about choosing which activities you want to include as we plan individual lessons. For now, knowing you have some flexibility on those days will help you plan when you might have time to include any extras you are wanting to add (setting up classroom norms, error analysis, homework discussions, fluency games and review activities are all things that might be on my list.)
  • Units are divided into sections. Notice in Grade 8 Unit 1 pictured below, there are 4 separate sections plus a culminating lesson that is not pictured. Lesson from the same section will fit together more seamlessly on a block period.
  • Your previous experience If you have experience with the instructional routines embedded in the curriculum and with orchestrating class discussions that build on student thinking, the transitions to this curriculum will be easier for you that the rest of us. But for many, the transition will take some getting used to for both us and our students. Lesson synthesis time may just take longer at first. If that’s you, plan to move a little slower through the first unit.

Getting started

Chose a planning calendar you are comfortable with. Here are a few options you can download:
Year at a Glance – one page, back to back

year at a glance

I love that I can see the whole semester on one page with this calendar. There is room for 3 separate rows of text on each date, but two of them are pretty microscopic. Good for noting special schedules and lesson minutes.
2018-2019 traditional school calendar template

traditional school calendar

Handy for someone who likes to a little more space to write or who prefers to see only a month at a time.
Look up your own district calendar and put any holidays, staff development days or other special events on your document.

Some planning information and pacing guidelines to help you:

In our district, there is one teacher on special assignment supporting each grade level as they roll out the Illustrative Mathematics curriculum. These are some rough calendars we made to assist our school site PLCs in pacing out their year.
planning and pacing info 6th, 7th, 8th
The grade level I support is 8th grade, and I have reworked and revised this several times. I think it would be ideal if we could finish unit 4 before winter break, but that leaves little time to go slower at the beginning or establish class norms. You will see both versions reflected on this document.
Here is an example of how I paced 8th grade using our district calendar. As you can see, it really does all fit. Yeah!
8th grade calender draft This map is color coded to match the workbook covers. That makes me unreasonably happy, so if you are into details like that, you might enjoy this one.
Did you sit down and try it yet? No time like the present . . . everything is right here.

A Good Start

Take a moment to enjoy the sense of accomplishment as you look at your completed calendar. You know there will be little adjustments as things come up during the year, but with the number of minutes and the optional lessons noted on the document, it will be easy to make those adjustments when the need arises.

Sharing the work

Professional Learning Communities (PLCs) can be wonderfuls ways to share the workload and advance your practice. But it is easy to let them become bogged down in the details of calendars and the tasks that need to be done. This year, with this new curriculum, you are going to need to spend that precious meeting time on the math and the teaching. In fact, when discussing with school districts who used IM this last year what teachers needed most in the way of administrative and district support, they universally said time to talk and plan together. We encouraged out site leadership to be ready to provide substitutes so teachers could have this time to prepare. And as teachers, I encourage you to do whatever you can to take care of those routine tasks in advance or via email. Save meeting time for digging in and uncovering the mathematical purpose for each activity and warm up, so you can make sure your students get out of them what they should.
In support of that, there are some recurring jobs that will need to be done. Below I have listed a few tasks that your team might find helpful to delegate.You may able to be able to lighten your load even further by cooperating with the person that has a similar role at other sites. Check if there is someone in your district who can help facilitate this inter-site collaboration.

possible plc jobs

An aside about final exams

An aside about final exams. We are considering using this as the final retake opportunity. Since the curriculum is coherent and the practice problems are spiraled, student continue to have opportunities to improve their understanding of content from previous units. We want to honor their continued hard work at growing their understanding and computational fluency. If the final is loaded into our assessment program with questions grouped by unit, teachers can chose to replace a unit score with a higher score on that unit at final exam time.

But what about me?

If you are the only teacher on your site that is using IM, consider linking up with other users via the Facebook User Community Open Up Resources 6-8, by Illustrative Mathematics. It is a closed group, but if you ask to join you should receive acceptance pretty quickly.
Speaking of the user’s community, one of the hot topics there has been organization and storage. That would be another great thing to get set up before school begins. See a small piece of this conversation blelow:

facebook community 1
And here are some other recent posts:

facebook community 2
If you are on facebook, I encourage you to make this group a part of your year.

Next up – planning a unit, a lesson.

All in with OUR/IM – The Big Picture

The Big Picture

You can’t really get a picture of where you are going in a new city looking only at the zoomed in 30 feet of street that is shown on your phone’s navigation app. That’s handy and helpful, but almost everyone I know starts by zooming out and looking at the big picture. Where am I now and how does that relate to where I am going?

So time to zoom out a bit. Let understand a little about how the course is put together. I promise I’ll try to keep it brief, but I’ll give you places to look for more detail.

From Lecture to Problem Based Learning

For 20+ years a typical day in my classroom begin with going over homework questions, me “giving notes”, and then students working together in pairs or groups to practice the concepts and procedures I had just attempted to deposit in their heads. In my “giving notes” I made it a priority to make connections and help students really understand the mathematics. I tried hard to keep students engaged, asked them to discuss their thinking with their partners, and invited them to ask clarifying questions for the good of all.  “No such thing as a stupid question” and “If you are wondering, so is someone else” were repeated again and again.

This was how school had looked when I was a student, and I did my best to replicate and improve on the experiences I had as a learner.

Attempts to venture into changing the way class was organized were difficult.  Books were written to break things down into tiny separate procedures, and if I was going to make it through the curriculum, I needed to get through one of those procedures pretty much every day. My classroom structure was the most efficient way to get that done.

If you have been teaching very long, you know that not every student can gain complete understanding and fluency in a day.  And so, every year, some kids would get left behind. Not because I didn’t believe “All Means All”.  Not because I didn’t give every lunch and after school to support them. Just because the ideas were flying by so fast that it was hard to keep up.

Add to that those students that at 13 just can’t stay focused consistently on a math lecture for 20 to 30 minutes.  The in and out of the natural attention span of an adolescent created gaps in understanding, missing connections, and fuzziness regarding procedures even if my explanations were flawless.

It felt like a trap.  The only way we could “get through” the material was inadequate to actually have all students learn the material.

Until now.

This new curriculum from IM gives me hope that we can keep all of our students engaged. We can let our students’ understanding of the content deepen over time. We don’t have to leave any students behind. This curriculum is built differently, to allow it to be taught differently.  

From this point on, I will be referencing the curriculum course guide. I strongly recommend you take the time to read it. I have only pulled out a small portion of the many parts that I think will really help you get a better view of the big picture

How IM is Built

Unlike the many text book series that I taught from, which were designed for lecture based classrooms, Illustrative Mathematics 6-8 curriculum is designed to support Problem Based Learning (PBL). The overarching idea of PBL is that students learn math by doing math. This curriculum was written to set teachers up to make that happen.

“In a problem-based curriculum, students work on carefully crafted and sequenced mathematics problems during most of the instructional time. Teachers help students understand the problems and guide discussions to be sure that the mathematical takeaways are clear to all.

From the course guide

 

One of the pieces of the IM 6-8 curriculum that I am continually impressed with is how carefully crafted it actually is. Here are a few posts from the Illustrative Mathematics Blog that brought this idea home for me:

Warm Up Routines with a Purpose

Vocabulary Decisions

Respecting the Intellectual Work of the Grade

All together, the pieces of each unit tell a story, with each individual lesson bringing new dimensions of that story to the table. “The goal is to give students just enough background and tools to solve initial problems successfully, and then set them to increasingly sophisticated problems as their expertise increases.”**

From the course guide again

How IM is Taught

As a teacher new to problem based learning, the most common error is to focus on what students are doing (fold, cut, pass to the left) instead of what math students are learning.  Each activity and lesson has a purpose, and students are supposed to land somewhere. As a teacher your job as you prepare is to understand the mathematical idea behind each part of the lesson, and make sure at the close that you bring those thoughts to the forefront.

“Not all mathematical knowledge can be discovered, so direct instruction is sometimes appropriate. On the other hand, some concepts and procedures follow from definitions and prior knowledge and students can, with appropriately constructed problems, see this for themselves.”

Once more from the course guide (might be worth a peek)

You are the essential piece to the puzzle, the one that makes sure the intended math is clear to all. If you are running out of time, it can never be this lesson close that you skip. However in that close, you don’t have to do all the talking.* Since the kids are working for much of the lesson, you have time to be listening. Be listening for those key learnings that you might draw out from students.**  

If you are now hankering to get a peak at what a lesson might look like, guess what? The course guide is a good place to find that information. Time for you to break down and follow a link to the section of the course guide  titled How To Use These Materials.

Patience

Because ideas deepen over time, one lesson does not start and end the teaching on a subject.

The initial lesson in a unit is designed to activate prior knowledge and provide an easy entry to point to new concepts, so that students at different levels of both mathematical and English language proficiency can engage productively in the work. As the unit progresses, students are systematically introduced to representations, contexts, concepts, language and notation. As their learning progresses, they make connections between different representations and strategies, consolidating their conceptual understanding, and see and understand more efficient methods of solving problems, supporting the shift towards procedural fluency. The distributed practice problems give students ongoing practice, which also supports developing procedural proficiency.”

-From guess where? ( spoiler: the course guide!)

 

I am going to make a prediction here. You are going to worry at the end of a lesson that your students don’t seem as fluent in procedure as they did with your previous curriculum.  Be patient. Remember how carefully crafted this work is and trust a little bit. Notice in the quote above the learning progression:

Activate prior knowledge – invites all students in

Introduce representations and contexts – essential for developing an understanding of the mathematics

Concepts – where I used to start if I did a great lesson

Language and notation – where I started if I was pressed for time

Connections and consolidation – the place where students can move to the most efficient method of solving problems

Procedural fluency – what we tend to focus on as the goal.

Being patient enough to let your students have all those stops along the way is the best way to help them learn in a way that lasts past a unit test.

This video by Dr Jo Boaler from Stanford University explains that further:

Concerns

According to one IM trainer, the two biggest concerns that teachers seem to have with the IM curriculum are

  1. The pacing seems really tight

  2. There is not enough skill practice built in

I am not going to say to you that pacing will be a breeze or that you won’t want to add extra practice activities from time to time. But I am going to say that both these problems are exacerbated by a lack of patience.

The pacing will definitely be tight if we over-teach. If we think the first time something is mentioned you have to teach everything there is about that subject, you will consistently run out of time. One way to help yourself trust the curriculum is to stay ahead in your planning. First look at the big ideas of each week in a unit, so you can see when things will come up again.***

The pacing will definitely be tight if we try to keep everything else we always have done and add Illustrative Math. This is a complete curriculum. You do not need to be scrambling to make warm-ups and find performance tasks. It’s all in there. Each and every lesson starts with a thoughtfully chosen warm up ready to use. Each and every unit ends with a culminating task that applies the mathematics. And because topics continue on throughout the chapter, going over homework time isn’t the only chance you have to revisit the previous lesson’s ideas. As an example, look at the development of major work of 6th grade:

And what about that “not enough skill practice” worry? Students do need to practice and apply skills. But if you look at the lesson progression above, where do you think it is appropriate to have the bulk of the skill practice? It won’t be on that first day. By spiraling the homework we allow students to get practice over time, as they move through consolidation and toward procedural fluency.**** 

 

Trust

We all have a lot of learning to do, but based on the experiences of the teachers who used the curriculum this year, we have a lot to be excited about. We are part of an amazing shift in math education. Finally all really can mean ALL.

 

Extra Resources:

  • *One of my favorite ignite talks about learning to cede the role of sage on the stage:

The less I talk, the more they listen by Graham Fletcher

  • ** A fabulous book for helping us learn to lead discussions for math learning is The Five Practices for Orchestrating Mathematical Discussions. Much of the learning from that book is baked into the IM 6-8 curriculum. A couple Illustrative Math blog posts on the topic are linked here:

How the 5 practices changed my teaching

The 5 practices framework- explicit planning vs explicit teaching

  • *** Speaking of over-teaching, see this IM blog post on why teaching students to cross multiply is delayed in grades 6 and 7:

Why We Don’t Cross Multiply

  • ****A non-IM aside – if you do decide on a certain section that your students need more practice, there are a million wonderful resources for creative skill practice out there that can be just as effective as a 1-31 odd worksheet. Truth -sometimes they are just an old worksheet, just delivered in a more interactive way.  Here is a post by Sarah Carter at Math = Love that lists a few practice structures. She explains some of them, with more promised on the “practice structures” tab at the top.

 

  • Much of what I am going to share in this post can be found in the Course Guide  provided by IM for each grade level. If you are looking online, you can find it here:

If you purchased the print Teacher’s Edition that same Course Guide is the small darker green book that came in the package.

Pro Tip:  if you did not purchase print versions of the material for your students, you may still enjoy getting the print Teacher’s Edition for yourself.  Everything it says is also online, but I find it easier to highlight suggested questions and add post-its to remind myself of something for next year if I have a hard copy.  It comes with a separate booklet for each unit, which makes it really nice for carrying back and forth to school.  Here is where to contact about any print option needs. 

 

All in with OUR/IM – Materials Prep

So I know, we should start with the math, with understanding what focus, coherence and rigor actually mean, with the philosophy of Illustrative Mathematics and of Open up Resources.  But I am going to assume you have done your research and have already decided that the is the curriculum you will be using in the fall.

If I am wrong, I suggest a deeper dive at the sites above, and perhaps a look at Brooke Power’s Blog posts about her experiences with the 7th grade IM curriculum last year:

Sept – Seeing the Light of Conceptual Understanding

January – Letting Go of What I Thought I Knew

April- Closing the Gap

But if you are all in, I am going to start at an unusual spot – materials preparation.  Not because it will give you the happy feeling that you are getting something done. It will, but it will not fool you long. The dull realization that you have no idea how to teach like this, the worry that it seems like an awful lot to manage, and the question ‘will it really be best for my kids if their teacher has a nervous breakdown in the process?’ will keep you unsettled until we address those things in future posts. Don’t worry . . . we’re gonna get there. You’ll be ready and it will be awesome.

The reason we are starting with materials prep is money. The fiscal year ends in June, and that means budgets are wiped clean and start over. In our school district, teachers have a Teacher Center account that will be reset on July 1st. Money you didn’t use by June 30th is not yours anymore, and you account balance is reset to $100 for the upcoming year. So to get the most out of that budget, you want to print as much as you can afford before the end of June (especially if color cardstock and laminate is your thing).

Before you rush to your copy machine, a tiny bit of of preparation will make life easier. Start with your computer.  Whatever disorganized collection of individual pieces you have downloaded in the past is not going to do if this is your core curriculum for the entire year. So start clean.  Make a folder for IM, fill it full of empty unit folders, and rename with a quick copy and paste.

making im folders

You may be tempted to make folders inside each for cooldowns, student practice, assessments. Hold on . . .those will happen automatically as you download and unzip files.

Now head to your grade level curriculum site. Here I am at grade 8.

curric home page

Choose unit 1, and then click on unit

downloads near the top. Unit downloads

Unit 1 downloads

For now, focus on Student Handouts.  We’ll get to teacher preparation in a later post.

Student handouts

If your district has purchased the print workbooks for your students or if you are working 1 to 1, the only things you need to download are the Blackline Masters and the Cool-Downs. If you are without workbooks and computers, I would go ahead and download them all.

For now, we are going to focus on the black line masters.  If you can take care of these things in advance you will never have a night during the school year when you have to decide between knowing what you are doing and preparing handouts.

Here is what that Unit 1 blackline master download looks like.  Make sure you have downloaded in into your Unit 1 folder before you extract.

Blackline masters compressed

Then, go ahead and click Extract now.extract compressed folders

extract

PDF versus Word Downloads

A pause here for those of you who are noticing these are pdfs and the site also has word documents available.  I mean, why not get something I can easily edit and personalize, right?

A couple reasons actually.  I did that last January when we decided to try a unit, and editing and resizing takes TIME. It took two of us working full time on the process several days to finish all of unit 1. And it really wasn’t worth it.  The cool-downs, for instance, we wanted 2 on a page because copy money and paper were scarce at some of our sites. This meant rearranging graphics and respacing. But guess what, my printer prints multiple copies per page if I chose. Why did I make it so hard??

In addition, there is a formatting issue in the word copies. (At least there was this spring. Maybe it is fixed by now? Someone comment and let us know). The numbering does not download correctly and renames problems in ways that do not match the on line images you might chose to project.  Fixing all those issues was one of the big time wasters when we used the word versions.

And honestly, you really need to learn the curriculum as is.  The tiny decisions of why this particular warm up are not obvious at first glance. For instance their might be a number talk warm up that brings up multiplying by fractions in a lesson on scaling, because later in that lesson, mid problem, students will need to access that skill.  Although we’ll do our best to prepare, some   things you won’t notice until you are mid second period next year. My strong advice is this year trust the process AND save yourself some work.

The Blackline Master Report

This little document is a lifesaver – don’t miss it! This is the list of blackline masters for Grade 8 Unit 1. A lot, but don’t worry.  It had more than any other unit from grade 8.

blackline master report 1

See? Here is Unit 5:

blackline master report 5

Let’s decode for a minute looking at unit 5.  The first Classroom activity you are going to use in lesson 1. It will be the second activity of that day. Hence 1.2. (The long name is 8.5.1.2, which means Grade 8, Unit 5, lesson 1, Activity 2)

For that activity you are going to need 1 copy for every 4 students. It is not a one time use, so one class set will do you for the whole day. If you look up and down  the list from unit 1 and unit 5, notice there is only one time where you need a new set for each class. Classroom ACtivity 1.2 does require cutting, but that doesn’t have to happen right now. If worse comes to worse, period 1 can do that for you. It does not need to be run on card stock. Although some will chose to do that, or to laminate, to make the activity more durable, you don’t have to.  I only found one or two in all of 8th grade that required cardstock, so this doesn’t have to cost you a fortune. And it doesn’t need colored paper. I know, colored paper is pretty, and if you have free access to colored paper, cardstock, a laminator, and unlimited cutting help, go wild.

So here’s how we did it with our teachers. We printed all these black line masters and master reports and loaded them into folders for our teachers so they were ready to go. First semester on side 1, second semester on side 2.

20180518_154915.jpg20180518_154844.jpg

You probably have to do this yourself. If you run things off this summer, you can pass that folder around your PLC to help everyone get off to a good start.

To see what kind of time we were talking about, I went and made myself the whole year of blackline masters.  It took me under two hours.  I had a big stack of 9 by 12 envelopes and for each activity I dropped it in an envelope and wrote on the envelope to label what it was. I didn’t take the time to cut up and I didn’t laminate, but I did run each unit in a different color to help me keep organized as the year went on.  At then end I walked out with a paper box about half filled with standing envelopes. If I was in the classroom that would just slide in the back cupboard, and as the new unit approached I would hand over cutting and bagging jobs to the students that are inevitably hanging around my classroom at lunch or before school.

A warning – one of our schools, so excited after the IM training we had, went to the teacher center together to knock materials prep out.  They used colored card stock and laminated everything with the high quality lamination machine. Several hours later they were only finished with a little more than two units and had blown their whole collective budget at the teacher center. And that much uncut laminating takes up way more space than my one little paper box, so the cutting has to happen now. Once they are all cut and rubber banded they will be awesome, but right now, it has turned into a big, expensive job.

I love the pretty laminate, but don’t trap yourself into thinking it is a must have.  If this year you run them all just on paper without laminating, that can work. Spend your evenings this year learning the curriculum – what math am I supposed to get out of this activity? Being able to connect and synthesize the lesson is about one million times more important to your students learning.

Stop.

I hear your self -talk.

“But the laminated cardstock is so pretty! And it will last forever if I just put in the work this one time.”

Don’t kid yourself. Unless this is your first year, you know it won’t.  Their will be the pieces that get lost, the pieces that get used to hold someone’s piece of chewing gum, the pieces that get thrown away as a group cleans up, or swept into someone’s backpack. And when you go back to make one more set, the color of the paper will be slightly off. And it will drive you crazy.  You know it’s all true.

You know what prep will last forever? The knowledge you develop, the connections you make, the understanding you grow within yourself as a teacher and a mathematician. Put your time in there.

So yes, go use the rest of your 17/18 school budget and get some materials made. Go back in July and knock the rest out. If you keep it simple, you can be done this summer, and spend your limited time during the year focused on prepping the instruction. You won’t regret it.

A few quotes from teachers who taught out of IM 6-8 this year:

 

I became a better teacher in year 13 thanks to @openupresources and the #LearnWithIM curriculum. I’m not sure I ever thought a curriculum would make me better but @IllustrateMath did. Then @Milken helped give me a stronger voice and now the sky seems to be the limit. So thankful. pic.twitter.com/0DoIr684O6

— Brooke Powers (@LBrookePowers) May 30, 2018

 

Up next – All in with OUR/IM – The Big Picture.

Open Up Resources 6-8 Math by Illustrative Mathematics: All together, All In

If you are part of the online math community or a reader of Ed Reports, the fact that Illustrative Mathematics’ new middle school math curriculum is taking the math teaching community by storm is no surprise. We heard whisperings as it was being written and heard glowing reviews from the piloting districts. We recognized many of the research based instructional practices and structures. They were things we had worked hard to embed in our classroom – desperately trying to teach in ways true to our standards using materials that were criminally misaligned.

 

Since this curriculum is published by Open Up Resources, a non-profit publisher dedicated to “increasing equity in education by making excellent, top-rated curricula freely available to districts”, we didn’t have to wait.  We logged on, dug in, and tried out a few lessons. But as anyone can tell you who has looked deeper, the materials are artfully crafted, with the key ideas of the grade woven and deepening throughout the course. Teaching anything less than the full curriculum is a disservice to the work.

And so next year – we’re all in.

Lots and lots of us.

For some of us, it is with full district support, with training and coaches and enthusiastic teammates in our PLC to learn with.  Open Up’s commitment to providing the curriculum freely to all means that lots of districts have money for training, and some of us have had the pleasure to attend and begin our work toward an awesome school year.

 

 

 

But for others, they are venturing forth with very little back up. . . because they believe (hope) it will be what is best for their students.

If that is you, this series of posts is written with you in mind. 

You don’t have to go it alone.

***

Some spots to learn:

Follow to receive emails when there is a new post, so you don’t have use your limited time to lurk expectantly.

  • The Twitter hashtag #learnwithIM :

A place where the community of educators using or learning about the curriculum can ask questions, share successes, and collaborate to improve our practice. Not on twitter? Start by just googling the hashtag and seeing what types of things you find. You don’t have to make an account or sign in to read what is there. If there is a comment that interests you, click on the side to pop it out and read the full conversation. Twitter is a place that educational professionals go to share and learn. Since so much of our days are spent shut in a room with no other adult, we need this forum as a spot to grow our practice. When you are ready to ask a question or join a conversation, make a twitter account and join in.  There is not an “in crowd” here. The authors of the curriculum are as likely to join the conversation as a first year teacher. All are welcome.**

  • And for the summer at least, add this blog to that list.

I am a teacher on special assignment in a central California district, and my job for the next year is to support the teachers of my district as they spend a year piloting Illustrative Mathematics 6-8 curriculum. So while I am at it, thought I might as well add you to the list. I am a professional, but not an expert.*  I’ll be sharing the things I am figuring out along the way and passing on to the teachers of our district. And to you too – welcome!

Next post – All in with OUR/IM – Materials Prep

 

Notes:
*For experts I encourage you to find a IM sponsored training, even if you have to pay your own way. They are fabulous quality, and really gave those of us lucky enough to attend a clearer view of how it all works together.
 
**Other hashtags that will connect you to math teachers are #iteachmath and #mtbos . (Yes,that’s a weird hashtag. Follow the link if you are curious).

 

***If you need to play the whole song now:

A Day of Desmos – Parabola Slalom

On the Thursday before Thanksgiving break I had the opportunity to try out the Desmos activity builder Parabola Slalom in Scott Davidson’s Math 2 class. This is how that happened:

Tuesday: Spent the day at a Desmos training and played Parabola Slalom for the first time. So much fun and potential for learning! If only I could do this with students. . .

Wednesday morning: I reached out to the teachers in my district who I knew where teaching quadratics. “Can I come do a lesson on Thursday or Friday with your kids?”

Wednesday afternoon: I heard from Scott Davidson, the Math 2 lead at a high school in my district.  “Sure, but time is a little tight.  Thursday Block we are reviewing and Friday students are taking a midterm on all things quadratic.”

From there the whirl-wind began. 15 hours until I’d be teaching a lesson with students I had never met.  And some of that time needed to be spent on eating and sleeping.

This first steps I took were getting to know exactly where the students were at and what was expected of them.  I looked through the list of topics they had been studying and at the midterm assessment they would be taking on Friday. About 7 of the 20 problems were things I thought I could address with Parabola Slalom. Their learning had focused on vertex form, and this was  reflected on the exam. Students, however, were expected to consider which forms of quadratic functions would be helpful in various situations. Completing the square, quadratic formula, and imaginary solutions did not easily come up in this activity. Factoring as a skill did not come up, but I could discuss why factored form of a function was helpful. I asked Scott if I could have the first half of his block period.  The second half he could do last minute review on topics I did not address. Scott is wonderful, trusting, and adventurous. “Sure,” he said. “Can we invite my PLC in to watch?” My dream question. “Yes, Yes, YES!”  A couple teachers had prep.  For the others we got 15 minutes of coverage one after the other. Fortunately Scott has a big room. The stage was set.

The next step is where you’ll begin if you are a teacher using a Desmos activity with your class. I went to the activity builder and played it again. You can try it here. On Tuesday at the training I had the opportunity to talk with other teachers about which slides would be good to stop and talk at, but now I had specific students at a specific spot in their learning, and I needed to rethink where the valuable conversations would be for this group. After playing it again, I printed the attached Teacher Guide. (see button in top right corner)

parabola slalom

Teacher guides are a great place to start with any Desmos activity.  They allow you to think through what you want to get out of the activity, the teaching moves you will make, which things you can skip and which things all students will engage with. This checklist is at the beginning of each teacher guide:

activity builder checklist

I had already done step one. Check! That felt good. On to step 2 – learning targets.  Desmos activities are very flexible, and you might chose to use them at a wide variety of spots in a learning progression. I’d love to try Parabola Slalom as an introduction to vertex form sometime and let students explore what the happens as you change different numbers. If I did that, my goals and planning would be very different. For this day I settled on these as my goals:

learning targets for parabola slalom

Next, according to my checklist, it was time to think about how I wanted to lead discussion with these kids I did not know.  When would I bring the class together using “Teacher Pacing” and “Pause Class”? What would I discuss on those screens? I felt a lot of pressure to make sure the lesson prepared the students for the next day’s exam, because Scott was trusting me with this time. I wanted to make sure I picked up the students that were really struggling and gave them one more opportunity to make sense of this equations of parabolas thing.  I decided that screen 3 was the first place where equation of parabola came up, so I would stop and question to see where kids were at. For students that were confused, I planned to make a connection to the y=mx+b as an equation of a line.I decided to look for these examples to discuss:

  1. I wanted to look for a sample of student work that used an upside down graph and asked what in the equation made that happen.  
  2. I wanted to find a student that had made a parabola with vertex other than (0,0) and discuss what about that equation caused the shift.
  3. I also knew I wanted them to realize that the square was important, so decided to watch for someone who entered an equation without the square and then pause to discuss the resulting graph.

After this discussion, I would pace them to work on slides 3 to 5. The Tip for Teachers provided by Desmos gave me some suggestions to help lead conversation on slide 5.

teacher tip parabola slalom

Having looked at their previous work, I anticipated that most students would give an answer in vertex form. I decided I would focus on those answers here with the whole group, and help those lowest students focus on what vertex form looked like. I decided I would NOT give away yet what effect changing the a, h, and k would have, even though technically this should have been review.  Instead  I would encourage them to play with the form, trying in different numbers and seeing if they could figure out what changing each of them did to the graph.

I decided slide 6 and 9 were other places I wanted to have discussions. Slide 6 would give me a chance to talk about the usefulness of factored form. I considered taking time to explain why x-intercepts are easy to solve for from this form, depending on student response. This was a secondary goal for me and I didn’t want to overwhelm with too much information.  Slide 9 would give me a chance to consolidate the learning, and I would chose to push kids all to 9 at some point to catch the struggling students up and clear misconceptions.  In the discussion about slide 9 I would listen to what they had discovered about a, h, and k in vertex form, and make sure all students were hitting the learning targets.  To support their arguments about why each answer was incorrect I might open a desmos calculator page, graph the given points, and put in the equations. With their groups, I would ask them to propose an equation that would work. From there I would open slides 3 – 11 let them work at their own pace, giving extra time to students who had misunderstanding I had uncovered.

The teacher guide encouraged me to plan something for students who finished quickly, but I felt like slide 10 and 11 would cover that.  I only had an hour and the note at the beginning said the activity could take more than one regular class period.  I decided I would have students log in so they could go back to the activity at home.  

Last steps – I printed a copy of my teacher guide with notes for the teachers that would be coming in and out to observe.  That way they could quickly see where we were in the lesson and what had happened so far.  Excited to work with actual students tomorrow, I set my alarm and dropped into bed.

Thursday morning at 7:15 I arrived at Scott’s classroom.  I connected my computer to the projector, logged in, and made a class code for the activity.  I jotted the code down on my teacher guide and copied it to the whiteboard. I paused the activity so early students couldn’t begin before I was ready. Then I helped Scott set out laptops and soon students begin to come in.

The activity was even more fun than I imagined. Being with kids was such a rush, and watching the ah-ha moments gave me all the warm fuzzies. Man, I love teaching.

A few things that came up during the activity/lesson:

  • Making the connection between forms of equationsended up being a big thing for a few students. There was more good discussion to be had there about how an equation in two variables defines/creates as set of points that are arranged in a certain shape. Something to come back to.

 

  • As we consolidated their understanding of vertex form, I wrote the equationvertex form exampleon the board and asked students to predict where the graph would be and what it would look like.  Students readily volunteered a correct description of the graph, which I sketched on the board. I wanted to emphasize the horizontal shift being opposite the sign, so I asked the class “Is there anything surprising to you about the graph that you wouldn’t have expected just looking at the equation?” A girl raised her hand. “The negative three.”  Excited she was bringing up what I was looking for, I said “ And what was surprising about the negative three?” Her reply was a shock.  “ Well usually when there is a negative the parabola is upside down.” Man, I had almost missed this misunderstanding and assumed we were on the same page! But with a poker face I said, “That’s true. Lots of times a negative means the parabola will be upside down.  Does anyone have an idea how you can tell when the negative makes it upside down?” Students were ready and able to clarify that, and I let them be the voice that shared that it was only a being negative that made the parabola upside down.  “So what happens if the negative is in a different place?” And I unlocked the screen and let them experiment. How many opportunities like this have I missed because I fail to ask a follow up question and really listen?

 

  • Several students brought up the fact that the squared term is what made the graph a parabola.  This was overgeneralized by students, so that if they didn’t see a superscripted 2 written in the problem, they thought that it could not be a parabola.  They did not expect factored formto have a graph that was parabolic. I had not anticipated that misconception. And actually, I was lucky to have discovered it, because the students had not shared that confusion out loud. One of the visiting teachers brought it to my attention near the end of the hour, after she spent some time talking to a student. Scott then addressed this misunderstand with the class after I left. 

One of the many great things about an activity builder is that it gives the teacher:

  1. an easy way to spot struggling students (the dashboard), and
  2. the time to actually have a conversation with that student about what they are thinking.

If we want students to think in our classrooms, we need to give them opportunity to be more than a consumer of information. We need to let them figure things out, propose hypotheses and hash out what is true. Desmos graphing calculator and well crafted Desmos Activity Builders are a wonderful way to open the door to that opportunity. Listen to what the students said about the lesson:

What thing do you know understand better after the activity?
how to find the parabola and the equation
how to graph and where the numbers go
the vertex form
how to make parabolas
parabolas
how to graph better
Which letters in the function of the vertex and stuff.
How to make parabolas.
I understand the form used to graph parabolas
I understood the vertex form much better.
graphing and how to make an equation for the graph
How to look at points on a graph and make an equation for the parabola.
how to graph and move around parabolas
vertex’s
all of it
vertex form
how to plot
I understand how to graph the parabola with the equation.
how to make parabolas out of equations
I now know how to solve for parabolas.
parabolas
HOW TO GRAPH PARABOLAS
how to make the parabola wider or narrower.
which numbers you put onto the graph
I understand how to graph the parabolas and how to put the values into an equation.
the way graphing equations work
I already understood everything. I just got to put what I knew into practice.
More about how squares and how each letter in the needed equation works
The thing that I understand better is how to find what equations would go into the parabola.
the vertex form and how to correctly make a parabola/solution

 

Any other things you would like to share about the activity?
it was fun
i liked the activity
it wasn’t confusing as much as regular teaching
It was a fun way to learn how to make parabolas.
It helped me a good amount with solving parabolas, vertex, zero property and such.
it really helped me a lot
It was hard, but beneficial.
It was very fun to work in groups and solve together
It was fun.
It was better to do something a little different instead of sitting around and doing the review
This activity really helped me get a better understand parabolas and I now feel like I have a better chance of passing the mid-term then before.
IT’S FUN AND EASY TO USE
It was actually pretty fun
This activity helped
It was fun although it was math.
Not really, other than it was informative and helpful to my test
The activities really help you get practice and help you get better at finding the equations for the graphs.
We should do this more often.The learning experience we were able to have as a class was very helpful. We are very into technology these days so it is easy to connect and study using a resource that we have access to.

 

Holiday Giveaway – the gift of professional growth

Here’s an idea that has been really fun this year. It begin with recruiting support from administrators who work with math teachers at each of our secondary sites. They helped finance buying the book prizes. The remainder were provided by my office in Curriculum and Instruction. I chose to focus on Tracy Zager’s book, Becoming the Math Teacher You Wish You’d Had, because that was a learning I was interested in spreading around the district. It is more suited to my intermediate teachers than high school teachers, but there is so much good discussion about what it means to teach mathematics that I feel it is worthwhile for all of us. Perhaps in your district you would pick something different. Whatever awesome book you choose, you are getting great professional learning materials into the hands of interested teachers, so it is all a win. In addition to the book, I decided to give away a “Day of Desmos”. This is producing a list of wonderful and willing teachers for me to work with in the next semester.

 

Once the prizes were established and gathered, I sent the following email to the math teachers at each site, signing my name and the name of their supporting administrator. I included a link to a google form, where they put their name in for each prize they were interested in.  Winners of prizes contributed by site administration will be chosen just from teachers on their site. Winners of district office prizes will be chosen from everyone in the district that signed up for them.  I have a near infinite supply of days of desmos, so woo hoo – everyone there is a winner!

Here is the email I sent out:

The gift of professional growth

Why: Because we are grateful for you and the work you do every day with the students in your classroom.

What: We want to give you something to enrich your teaching and demonstrate the respect and friendships we have developed working together.

When: During the last two weeks of December, we will be giving gifts to teachers, based on their interest. Below find a chance to check out the gifts and put your name in a drawing for those you are interested in.

Start making your wish list here:

Book: Becoming the Math Teacher You Wish You’d Had by Tracy Zager   https://www.stenhouse.com/content/becoming-math-teacher-you-wish-youd-had         Video description here          Companion website and discussion forum here  

Set of posters:  10 posters that call out habits of mind exhibited by mathematicians (based on the 10 chapters in Becoming the Math Teacher You Wish You’d Had by Tracy Zager)

zager posters

Day of Desmos: Leeanne will come in a teach/co-teach your classes with a desmos lesson that supports whatever topic your students are currently studying. It can introduce a topic, replace a lecture style lesson, or practice applying something you already taught – Your choice!

Surprise: smaller gifts for your classroom

Sign up to participate in this holiday giveaway here (here is where the link went)

Looking forward: New Year, new resolutions. The learning you receive can be your present to yourself, your students, your PLC, and your team in the coming year.

 

The teachers are excited and emailing how much fun this is.  The administrators are excited because that was pretty easy and painless. I am excited because I get to show my appreciation for them AND give them awesome resources to improve their craft.  Win, win, win!

Practical Thoughts on Differentiation in the Secondary Math Classroom

“There might be a student that doesn’t need modeling, but there is always one who does. So why wouldn’t I provide that first?”

I heard this recently on a favorite site. It sounded reasonable, and was spoken by a teacher acutely interested in her students’ success. She was talking about the “I do, we do, you do” strategy of gradual release, making sure that her students fully understood the expectations of the task she set before them. At times it may seem like the perfect fit, but far too often in secondary math classrooms we overuse this well intentioned, time tested lesson plan.

One powerful reason NOT to provide that first is that the modeling robs students that don’t need it of a chance to be creative, problem solve, and use strategic thinking – all higher depth of knowledge ways of processing their learning.  When we provide scaffolds for all it is easy to reduce everything to a dok level 1 – “Watch and do exactly as I do.” For more on depth of knowledge, see Robert Kaplinsky’s work here.

Differentiation is an important topic in education. At the high school level many people find it challenging to truly differentiate in a 55 minute period.  But here is a simple opportunity that actually creates time in your period – time that students can engage in those higher depth of knowledge types of thinking.

How can that work? Several models are possible, but all revolve around reducing or eliminating the whole class modeling and instead planning timely hints appropriate to various sticking points in the process.  Start with thinking about hints for your highest kids. What is the least you can say? What question could you ask to spark their thinking? The next set of hints could be more directed, potentially less open, and may encourage them toward a specific method. For the most helpful hints, basically just do your “I do” – either in writing or by giving then a link to a short video they watch on their phone. Label the hints 1A, 1B, 1C, 2A, 2B, 2C . ..etc. 1 represents the earliest sticking point – how to start.  A, B, and C represent the level of the hint. Students should be encouraged to take the least help possible. It is amazing how quickly your highest kids will adapt to that suggestion . . they are inspired by the challenge. But kids who need more help have it readily available.  

Double the effectiveness of this strategy by putting the students on vertical non-permanent surfaces. Definitely worthy of a blog post all it’s own, but simple enough to implement tomorrow. For a look at this strategy and the research behind it, check out Laura Wheeler’s blog here. A quick summary of the fuller body of work, “Building Thinking Classrooms” by Peter Liljedahl, can be found here.

Struggling with the mismatch between some hypothetical classroom ideal where every student is motivated just because they want to learn and grow, and the reality of grade-chasing, point-grubbing, homework-copying in your classroom?*  Long term, the research above can really make a difference, but to help in the meantime, some teachers use a pointing system for their hints.  All groups start with 10 points (or more if it is a pretty hard task with lots of sticking points).  C hints cost 1 point, B hints 2 points, A hints 3 points.  Points that aren’t used are extra credit on the assignment, and students can spend into debt – making their highest possible score 95/100 for example. Remind struggling students that 95, or 86, or whatever they work their way down to is so much better than the 50% for an incomplete assignment, or a 0 for not turning it in. And to begin to change that culture, be sure you celebrate successful completions equally – let students have joy in completing the challenge no matter how many scaffolds were used along the way.

Every day and lesson is different, and occasionally a bit of “I do, we do, you do” may be just the perfect amount of scaffolding/guided release for the specific task your students are working on.  Optimize those moments by listening to your students thinking along the way. But too often in a diverse regular classroom, we mis-serve both the top and bottom segments of our classes by doing all the higher level thinking for them. This model of differentiation is one way to support ALL learners in those classes.

 
*Ready to try something different with grading? Matt Vaudrey has a nice post about his experiments with a variation of Standards Based Grading  here.  And there are a thousand other great ideas out there. Look here for what came up when I googled: MTBOS on homework.

It truly is a wonderful time to be a math teacher.

 

Over-scaffolding: the loving art of loosening our grip

Parenting is an ever-changing job.

In the youngest years we are required to give our children instruction and advice on how to do every minute life task: how to angle their foot to put on a shoe, how to walk safely in a parking lot, how to put their pee in the potty, how to pick up the edge of their long t-shirt before putting pee in the potty. Those things are eventually mastered and we smile as we watch our little ones handle them all by themselves. Then we move on to new tasks: how to pick out a matching outfit, how to make a bed, how to clear dishes, how to put those dishes in the dishwasher,  how to put the laundry in the hamper, how to take the laundry out to the washer and run it through. For most of my kids-at-home parenting years, these tasks did not seem to stick as well. They were learned, but never seemed to be owned. But when my children moved out, and had to do it themselves, that training finally came to fruition, and now they manage all of those things with ease and grace. I never have to call my 26 year old and ask him, “Did you wash your work clothes? Are you wearing clean underwear?” But they’ve been through the stage where they had to decide it was important to them to have clean dishes to eat from and clean clothes to wear to work. Clean clothes for a college chem lecture did not seem to be equally motivating at first, but happily they eventually began to see the advantages of not stinking to high heaven when sitting by an attractive co-ed, and they reassessed their prioritizations.

 

Maybe those early tasks are mastered with independence earlier because we let them go. When a problem arises – like pee along the front hem of a t-shirt – we can step in and provide some additional instructions and advice. We do not stand and watch our nine year olds put pee in the potty and critique their technique.  We provide scaffolds as needed when problems arise. And then we step back.

 

Stepping back has been the hard part of parenting. All of my early on the job training was at the level of minutiae, and detailed instruction with constant reminders were essential. But gradually, if we let them, they grow to be able to figure a few things out for themselves.  Maybe if I had let it happen my kids would have learned earlier that underwear with skid marks were not a good idea to wear to gym class and they better get a load through. Maybe if they had to scrape yesterday morning’s oatmeal off their bowl on a semi-regular basis, or their ice cream got served up in their dirty spaghetti bowl, timely cleaning of dishes would have seemed more important.

 

Thank goodness, in spite of me, they are making their way to being amazing and wonderful young men who can problem solve as things arise and handle life. I wish I could say I was as good at learning the parameters of my new role. “Did you call your landlord about that broken garbage disposal?” “Did you check reviews on that car repair shop?” “If you hang your clothes right when they come out, you won’t have to iron those dress shirts so much.” “Is that sweater dry clean only??? You really should check washing instructions before you buy. You can’t afford dry cleaning every week.”

 

When they are young, we tell our children what to do because we are applying our priorities to our life. It was a priority for me to get them out of diapers for my life, not just because eventually at 5 they’d be glad to not wear diapers to kindergarten.  But when they are adults, their actions and decisions have to come from their priorities. Fortunately life has a wonderful way of providing timely feedback to help us all make decisions around adjusting priorities. As parents, it’s important for us to learn how to get out of the way and let that feedback get to them.

 

Adulting is hard. . . and then it’s not. It’s up to us to give them the chance to get there.

 

So lately, I have been thinking about how this plays out in the classroom.

 

The current buzz word is “over-scaffolding”, which translates to helping more than students  really need. If we insist on owning the responsibility for all the thinking, they will eventually stop trying to think.  Instead we need to carefully structure activities that help only as much as they need.

This is extra tricky because students grow at differing rates. I used to think that was about ability, but now I think it is mostly because of the access or lack thereof to appropriate feedback. The student who waits in his group for others to decide on a solution path is never trying out his own ideas and learning what works and what doesn’t, or why it’s important to, for example, isolate the radical before squaring both sides of the equation.

 

Imagine if class begin with two or three simple equations on the board
equation 1

and you ask your students to work individually to play around with and figure out the answer. Many would use their natural number sense to guess and check, but a few would use their equation skills they are comfortable with and reason about what they might add to the new situation. It’s likely at least a few will come up with “ Well, if that equals five, then before the square root it must have been twenty-five.”

However they approached it, encourage them, still all by themselves, to check their answer and see how they did. Guess-and-checkers started with this, because they are still trying to make sense of the numbers.  But for many whose heads are full of procedures, they have let go of this sensemaking move, and only do it as the last step in a procedure if that is what their teacher requires.  So here we see the first of the difficulties we often cause for our students – we teach compliance over thoughtfulness. I am beginning to think the most important thing we can teach them is to seek and use feedback -especially feedback they seek out and create from their own efforts.

 

Next, gather answers. Listen to methods and value all of them. Form hypotheses together about how this might work.

Some guess-and-checkers will be be persuaded to the “square both sides” method, but others will continue to trust their better skill – number sense. That’s okay. Children learn at different rates. We need to give them the opportunities to learn. So up the ante with the next question. Give the higher students a chance to explore the edges of their thinking, and the slower ones a chance to clearly see the limitations of their method. Again, gather answers, listen to methods and what has been learned. Adjust hypotheses.

 

You might have to keep raising the level of difficulty several times before the strong-number-sense/poor-equation-sense students decide that maybe there is something to their classmates methods.  Here are a few ideas:

equation 2

Finally, when they are mostly won over, together compile the methods they have figured out with your careful guidance, using their own developing number sense and feedback-seeking skills.

 

Scaling parenting to 35 kids in one classroom is hard. But continuing to tell 100% of them exactly what to do is preventing them from growing up and owning their own learning. I challenge you to build a thinking classroom, one that respects the strengths of all your students and gently prods them to the next step in their development. Encourage them to try something and see if their answer makes sense, and to think for themselves about how to approach a problem.

When problems arise, as needed, give just enough help and then get out of the way.

Be watchful, be positive, and even prepare in advance some scaffolds they might need, but give them as needed.

 

And I encourage you to be patient with yourself in the process. Learning, real learning, takes feedback and adjustments. It’s messy. So you won’t be perfect the first time, but you’ll learn. And guess what – learning can be exciting and fun! And helping the children in your class, the children I am sure you love,  grow to an adulthood that doesn’t require the scaffolds of childhood, can be the most rewarding part of your job. It is why teaching is such a rich and rewarding profession. Let it be that for you.