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Accountability starts with the students having a clear understanding of what you expect of them. As you plan for implementation, you need to carefully think through your routines and procedures. During the first few weeks of the school year, you will teach your routines and procedures, so you need to plan for what you are teaching.The more you plan, the better your classroom will function. In his book *What Great Teachers Do Differently, *Todd Whitaker says that everything that takes place in your classroom is either *plandom* or *random.* In other words, if you don’t plan for it, your kiddos will randomly decide what to do in any given situation. Even the subtle difference of using the term *math workstations* rather than *centers* sends the message that this is their work. Yes, we want them to enjoy the tasks and games, but at the end of the day, this is their math work. A great activity to do during the first few weeks is to create an anchor chart like the one below that will serve as a visual remind of what Math Workshop should look and sound like and what the student’s and teacher’s jobs are.

When you decide where to put your small group table, remember that if the students know you can see them, that is your first line of accountability. Many teachers like to do their small group instruction on the floor, but that makes it really difficult to see what’s going on in the rest of the room, and the kids know it. My favorite arrangement for small group instruction is a horseshoe-shaped table in a corner where I am facing out into the room. As I’m teaching my small group lesson, I just need to glance up and around the room every few minutes, and the students know that I’m keeping an eye on them.

A math journal in my room is nothing fancy. It’s a composition notebook or a 25 cent spiral notebook. I’ll probably put a cute label on the front or let the kiddos decorate it. Because I don’t like to worry about which workstations students will need their journals, it is the routine that students just carry their journal to every workstation. That way, they’ll have it if they need it. The next step is to build accountability into each task. For example, the picture below shows how students might be held accountable for playing a game of Multiplication War. Each player takes two playing cards and multiplies the factors. The largest product wins the cards. To add a little accountability, the players would just write the results of each hand in their journals, as shown.

The students, however, need to know that you’re going to look at their work. I, for one, don’t want to haul 22 journals home every night or weekend. Here’s an alternative. Each day, at the end of workshop, have students return to their desks and place their journals out and open to the work they did. You might spend 5 minutes having students take turns sitting in the “Mathematician’s Chair”, sharing something they learned during workshop. During that 5 minutes, you can spin around the room glancing briefly at each journal. You are NOT looking at every line item. You are checking for quantity and quality. First, did students get enough accomplished? If not, you can have a private conversation immediately and explain that you expect them to get more done. Next, you are looking for glaring errors. In the Multiplication War example, if I saw a student who reversed his greater than/less than symbol for every single problem, I would pull that student first thing the next day to correct his misconception.

If you are fortunate enough to have technology in your classroom, you really want to check out Seesaw. It is absolutely free and can be used by students to create a digital portfolio. Take a minute to watch this intro video.

Do you see that when you build accountability into your workstations, you are also gathering the data you need for assessment? When it comes to accountability and assessment, they go hand in hand. Think about how to frame your accountability to give you information on the skill students are practicing in the workstation. Take, for example, the place value game Build the Biggest. Having the students glue their recording sheet in their math journal would show that they played the game, but would it really show that they know how to use place value to compare numbers? No, not really. So in addition to gluing the recording sheet into their journal, consider having them explain, in writing, how to use place value to compare the numbers 398 and 412. See how that gives you more insight into the actual skill?

What questions do you still have about accountability and assessment? Please add them in the comments.

See you on Twitter! @MathCoachCorner

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]]>The post Do This, Not That: Aligning to Standards appeared first on Math Coach's Corner.

]]>This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally recommend.

There are so many resources available to teachers these days. It’s so tempting to hit up Pinterest or Teachers Pay Teachers for a cute and engaging activity. But the cardinal rule of workstation tasks is that each one should be aligned to a standard that your students need to work on. Period. Your data should guide your choices. What standards are your students struggling with? What do they need more practice with? Consider creating a correlation chart for your workstations listing the title, skill, and standard. While that might seem a daunting task, it will save you time in the long run.

Teachers often tell me that all workstation tasks should be related to the current skill being taught. For example, if I am teaching place value right now, all the tasks must be related to place value. Let’s look at where that idea came from. In a traditional classroom, the whole group lesson is often followed by independent practice based on the lesson. As teachers move to a guided math format, that becomes part of their new structure. But the last thing I want students to do is to practice a skill incorrectly, so consider breaking that cycle of teach/practice. Place your practice tasks into workstations once you are certain students truly understand the concept. For example, students might practice whatever I’m teaching this week *next* week, after I’ve worked with them in small group enough to know that they are confident with the skill.

If you’re not filling all workstations with tasks related to the current skill, what will you fill them with? Math workstation tasks provide a great vehicle to spiral learning throughout the year. For example, that place value game you use in September could be used several more times throughout the year to make sure that the learning on that important skill becomes permanent. Consider beginning the year with tasks students are already familiar with from the previous grade level to activate their learning and create a smooth transition between grade levels. You can also use workstation tasks to “spiral backward.” If you have concepts at the end of the year, you can sprinkle workstation tasks throughout the year to activate prior knowledge. A good example of this is geometry, which often falls toward the end of the year. By utilizing tasks related to geometry vocabulary throughout the year, you can keep students interacting with those concepts.

As I mentioned in the previous post in this series, the easiest way to make sure you address the math process standards in your workstations is to build them into your structure. Both of the structures shown below have workstations devoted to problem solving and mathematical communications. As you plan your workstations, you are consciously looking for high-quality tasks to populate those workstations.

Your next step is to develop a suite of high-yield tasks that you can rotate through those stations. One of my favorites for the problem-solving station is You Write the Story. Instead of solving pages of word problems, students write their own word problems and solve them. Prep for this task is as easy as writing the expressions for students to use on index cards and putting them in the workstation. Notice how easily differentiated this task is. You see three versions of the same expression below. The top is the on-level version, the middle is the below-level, and the bottom is the challenge version. Since your focus is on the writing process, use friendly numbers for your expressions. Can you see how this could be part of your task rotation all year long?

Another task closely related to this one is The Answer Is. This one is even more open-ended, because students can use any operation they want. Totally self-differentiating.

How about one more to get you started. For this one, use the Snipping Tool to grab a picture of a graph. Released state tests are a great source of graphs. Be sure to leave off any questions related to the graph. Students either write statements about the graph (e.g., Walking was the exercise with the most minutes) or questions that can be answered using the graph (e.g., How many more minutes were spent doing aerobics and rowing than were spent jogging?). Again, you can see that this task is self-differentiating because students will write more or less complex statements and questions.

Hopefully, these three examples give you an idea of the types of tasks you can put in the problem-solving workstation.

It’s no secret that students love games! As you are choosing games for your workstations, look for those that involve strategy. They not only make the game more interesting for students, but they incorporate problem-solving and analytical thinking as well. As students play the game, their strategy often evolves. And it should! In fact, having students reflect on their strategy and how it changed as they continued playing the game in their Math Journal is a great way to build accountability into the workstation. Read more about a couple of quick and engaging games using only a blank hundred chart here.

Often, the only way we use technology in our math workstations is for apps or computer-based learning. While those are both valid uses of technology, we want to look for ways to allow students to use technology to create, rather than just consume. Apps like Seesaw, Chatterpix, and Buncee allow students to communicate mathematically in an engaging and creative way. If you’re looking for innovative ways to use these apps, be sure to follow Renee White on Twitter!

I hope you find these tips for incorporating the math process standards and content standards into your math workstations helpful. If you have other suggestions, I hope you’ll leave a comment below and share! The last post in this series is on accountability.

See you on Twitter! @MathCoachCorner

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Many teachers, frustrated with the limitations of whole-group math instruction, are moving to a guided math or workshop approach to teaching math. In this structure, teachers provide increasingly more instruction in a small group setting, while students work independently in workstations. The chart below shows what the transition might look like as a teacher moves from a traditional structure on the left, to one utilizing a shorter daily mini-lesson, and finally to a situation where most first-line instruction takes place in small group. Note that as you move away from whole-group instruction, students are spending increasingly longer amounts of time working independently. In fact, they might be spending the bulk of their math instructional block working in workstations. Think about the implications of that statement. If we don’t carefully plan our workstation tasks, that time is largely wasted.

Often, the tasks that are used in math workstations focus only on content standards. It’s important that we remember that the process standards, defined by NCTM, “highlight ways of acquiring and using content knowledge.” As depicted in this graphic, they are an umbrella over the content standards. When we designate specific purposes for our workstations, it not only ensures that we include the process standards, but it also actually makes planning easier.

Often, technology is used as a standalone station–one of the rotations is the “technology” station. As a result, digital devices are often used for low-level practice. Now, I’m not saying that apps don’t provide engaging practice or that the practice isn’t needed. I’m just saying that students should be doing more with technology than just using it as glorified flashcards. By integrating technology into workstations, it can be used by students to create, rather than just consume. More on that in the next post in this series.

Many workshop models include the teacher as one of the rotations. This can be limiting in a couple of important ways.

- It determines your group size. You want roughly equal groups rotating through your stations, so the students at your teacher table may not all have the same instructional needs. For example, say that your small group lesson is on place value, You may have two students in the class with significant gaps in place value understanding and three students that are extremely confident with that skill. But your class is 24 students, so you have four groups of six rotating. That means that you will have to group those two low students together with four other students with different needs, just to even out the groups. The same with the high kids. That really undermines the whole purpose for small group instruction.
- It forces you to have homogeneous (similar ability) groups in your workstations. Because you want the students at your teacher table to have the same instructional needs, they also have to be in the same group for independent workstation groups–because you are one of the stations they rotate through. This gives you no flexibility to decide which students work well together and which don’t and compose your groups accordingly. It also means that your students never have the opportunity to work with students of different abilities.
- It dictates the time you spend with each group. Because you are part of the rotation, each group gets exactly the same amount of time, whether they need it or not. By taking yourself out of the equation, you can pull groups for exactly the amount of time they need.

There are many models for structuring math workshop. A very common one circulating right now is based on the acronym MATH. There are variations for what the letters stand for, but a widely-used version is **M**eet with teacher, **A**t my seat, **T**echnology, and **H**ands on. I would like to offer the variation, pictured below. Notice, first, that the teacher is no longer one of the rotations. Now the groups in the workstations can be heterogeneous, allowing more flexibility when creating groups. While the students are in workshop, the teacher pulls students as needed to the teacher table. So if she wants to pull two students, she does. The groups coming to the teacher table can be different sizes and can stay for different amounts of time. Next, the technology rotation is gone. Technology can be integrated into any of the workstations. Apps can be used in the H station to practice facts, but can also be used in the A or T stations for more creative purposes. Finally, do you see that the process standards are embedded in the structure? The A station focuses on problem-solving and thought-provoking problems. The T station is all about communication.

In our book, Guided Math Workshop, Laney Sammons and I included our own version of a workstation structure called GUIDE. It includes five stations, rather than four, but includes all of the principles I outlined above. You can download the cute letters for GUIDE here.

See you on Twitter! @MathCoachCorner

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]]>The first game is the easier of the two. Assuming the number 1 in the upper left corner of the chart, players take turns using their colored pencil to write a single number in one of the squares on the chart. In doing this, students are using the patterns on the hundred chart, which emphasize place value, to determine which number goes in a particular square. A player who gets four numbers in a row on the chart (horizontal, vertical, or diagonal) draws a line through the numbers and earns one point. Play continues. The player who has the most points at the end of the game wins. This game can be differentiated by assuming different numbers in the top left corner. For example, the “starting” number could be a 3-digit number, such as 501, or even a decimal like 0.1.

You can download a blank number chart here. If you use it in your classroom, please drop a comment below or, better yet, take some pictures and tag me in a tweet!

See you on Twitter! @MathCoachCorner

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]]>Personally, I like the idea of giving students different charts and having them discuss the merits of each. Then, let students use the chart that feels right to them. To that end, I’ve prepared a little freebie with four different charts: two bottom up, one top down, and one blank. You’ll also find some flipped hundred chart puzzles.

See you on Twitter! @MathCoachCorner

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]]>Last week I wrote about making math accessible to teachers, and I featured a routine called Would You Rather Math. The website was developed by John Stevens, an instructional coach from California. He is the author of Table Talk Math and co-author of The Classroom Chef. If you are not familiar with the website, then I am happy to be the one to introduce you to it. There are posts appropriate for grades K-12th. Each post presents students with two choices (hence the *would you rather *name). Whichever option a student chooses, he must justify his reasoning with mathematics. It’s a great way to incorporate the mathematical practices into your instructional routine.

Now let me warn you, once you start doing Would You Rather problems with your students, you start down a slippery slope! Trust me, you will begin to see Would You Rather Math everywhere. I stopped at the grocery store on the way home from school today to buy some Easter treats. I got way sidetracked analyzing all the various options for Reese’s eggs! People probably thought I was crazy when I started staging and taking photographs. So tonight I present to you my Easter themed Would You Rather.

And finally, the bank of problems continues to grow because teachers contribute their own problems to John. I’m sending this one his way now.

See you on Twitter! @MathCoachCorner

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]]>I am just back from the NCTM Annual Meeting and Exposition in sunny San Diego, and what a phenomenal experience it was! There was a lot of buzz around equity and making math accessible to all students. I would like to suggest that in order to make that happen, we have to start with making math accessible for teachers.

It is no secret that the way math is taught today is different. It’s different from the way that many of us were taught, and it’s different from the way that many of us are used to teaching. In some cases, it is a shift in thinking comparable to turning the Titanic to avoid the iceberg. Current standards emphasize communication, using and reasoning about multiple strategies, justification, and authentic math modeling. Memorization of procedures and speed, once the hallmark of strong mathematicians, are no longer the gold standard. In fact, thanks to research, we now know how detrimental an emphasis on speed in math can be.

We are asking math educators to fundamentally change the way in which they teach. You know what? That’s pretty dang scary. I believe that how we handle that change has a lot to do with growth vs. fixed mindset. Teachers with a growth mindset, regardless of their years in the classroom, see themselves as a work in progress, and that helps them to overcome the fear of trying a new approach. So how do we help **all** teachers shift their teaching practices in a way that we know benefits students? We make math feel friendly. We let them play. For my last session at NCTM, I had the opportunity to hear John Stevens speak on a curiously titled topic: Creating the Staff Lounge You’ve Always Wanted. John wrote a wonderful book called Table Talk Math, and I knew I’d leave with some good ideas. The thrust of the discussion was that teachers rarely get a chance to play with math, so he talked about ways to spark curiosity in the staff lounge. He presented us with the Would You Rather math problem shown below:

At first glance, it might seem obvious that 5 pencils that are 6 cm each is the better choice. I mean 30 is greater than 27, right? But the discussions we had were amazing and wide-ranging. What if you put a premium on erasers? What if you prefer to use longer pencils than shorter ones. What if you measure the eraser portion of the pencil and factor that into your reasoning? John’s suggestion was to post problems such as this in the staff lounge and let teachers engage in the types of mathematical discussions we hope for our students to engage in.

See you on Twitter! @MathCoachCorner

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]]>You may think it’s easier to run off a stack of worksheets than it is to prepare the materials for workstations. In the short term, you might be right. But in the long run, you actually save time with math workstations. Throughout this post, I’m going to use as an example telling time to the hour and half-hour using the cards pictured below, which you can download for free. Skills that students need to practice include reading time on both analog and digital clocks and elapsed time. To provide students with adequate practice for these skills, how many worksheets do you think you’d need? Maybe 5-10 worksheets for each skill? That’s a lot of copying. Once I make and laminate these cards, I can use them in a variety of ways for several years to come. That means next year when I plan my time unit, I literally have zero prep time.

- Choose a subset of the cards and have students play a memory game. They lay the cards face down in an array. Taking turns, they turn over two cards. If the times on the clocks match, they keep the cards. If they don’t match, they turn them face down in their original positions.
- Use the cards to assign partners. Give a card to each student. They move around and find another student with a matching time and that is their partner.
- Put the times in order with the analog times on top of the digital times.
- Select two cards and use an open number line to find the elapsed time between the two times.
- Choose one clock card and an elapsed time card and find the starting or ending time. Geared student clocks are great to support students with this activity.

Because each time the students do an activity they will be using different cards, students are provided many opportunities for practice without making copies of lots of worksheets.

Next, let’s talk about accountability and communications with parents. Worksheets make it easy to document student work, and it’s easy to send worksheets home to parents. I would suggest, however, that there are other ways to hold students accountable and communicate with parents that are far more effective. Seesaw is a free digital portfolio that students can use to record their work through pictures, video, audio recordings, or some combination of those options. When the teacher approves a portfolio entry from a student, there is an option to immediately notify the parent via text message. What a great way to bridge the divide between home and school. So, for example, if students are playing the memory game with analog and digital clock cards, they could record a short video when they finish playing showing a pair of matching digital and analog clock cards and explain how they know the times on the two clocks match. You’re just not going to get that from a worksheet.

So here’s my call to action. Choose one worksheet you plan to use this week and think about how you could accomplish that same learning objective with a workstation activity rather than the worksheet. If you can, post a picture of the worksheet and how you plan to transform it in the comments. I’m excited to see all the ways we can transform worksheets into more active learning for students!

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]]>For as long as I can remember, math was about finding the right answer. Some people even say that they like math because there is a right answer and a wrong answer. That is changing. With standards that emphasize understanding over rote memorization of procedures and increasing calls for balancing content with process, math instruction is beginning to look different. Students need opportunities to see that while, yes, there might be only one right answer, there are many approaches to solving the problem. Even if the problem is as simple as finding the sum of 6 + 7.

*I know that 6 + 6 equals 12, so 6 + 7 is just one more, or 13.**I decomposed the 6 into 3 and 3. I used one of the 3s with the 7 to make 10, and then added the other 3 for 13.**Seven and seven is 14 and one less is 13.**I put 7 in my head and counted on 6 more using my fingers.*

I recently taught a lesson in a 1st grade classroom, and I knew some kiddos would know the solution as soon as we finished reading the problem. So before I began I made them promise to keep their solutions in their heads because the really “fun” part of the lesson was discussing all the different ways we could solve the problem and how we could communicate our mathematical thinking. Just look at all the wonderful thinking we captured from our discussions!

Face it, we don’t all process at the same speed. It’s time to think about the routines in our classrooms and reflect on what we are rewarding, speed or depth. Often, we ask students questions, hands fly up, and we call on the same five hands every time. Build think time into your routines. I’m a big fan of Sherry’s Parrish’s number talks. When I began using them in my classroom, I adopted the thumb-to-chest signal from the videos in the book for children to indicate they were ready with their answer. No hands shooting up in the air and waving around, because how distracting is *that* if you’re trying to think? I soon realized that I liked the signal so much that I began using it all the time in place of raised hands. It is a subtle shift that makes a big difference to students who need a little more time. It is also an expectation that I’m going to wait until I see “thumbs” from most all students before I call on anyone, and that I’m more interested in how you got your answer than the actual answer itself.

There is just so much research to indicate that timed tests are the beginning of math anxiety for large numbers of students and that the effects are long-term. This is a harmful practice that needs to be stopped. We would never put a reading passage in front of students, time them for a minute, and put big red x’s on any words they didn’t have time to read, so why in the world do we still do it in math? Do we want students to have automaticity with their basic facts? Of course we do! The difference is how we achieve automaticity, and it’s not from rote memorization and timed tests. Students learn their facts through reasoning strategies and they develop automaticity through practice with games. Be mindful of games like Around the World that not only emphasize speed, but do it in a very public way. Be sure to check out the links in this post, because several of them contain freebies that you can download and use in your classroom. But here’s one more little idea that requires nothing more than a deck of playing cards. Remove the Jacks, Queens, and Kings and use the Aces as 1s. Students turn over two cards, add the numbers, tell the sum, and explain their solutions. The player with the greater sum takes the cards. If both sums are the same, the cards remain on the table and are taken by the winner of the next hand. This game works for multiplication as well, of course.

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]]>What a great summer of learning as our book study of The Formative 5: Everyday Assessment Techniques for Every Math Classroom by Skip Fennell, Beth Kobett, and Jonathan Wray comes to a close. Have you had a chance to check out the hashtag #Formative5BookStudy? So much good conversation! If you have not tried Twitter for professional development, this might be a great time to jump in. If you can do Facebook, you can do Twitter.

- Book Study Monday announcement
- June 11: Why Formative Assessment? Issues and Opportunities
- June 18: Chapter 1, Observations
- June 25: Chapter 2, Interviews
- July 9: Chapter 3, Show Me
- July 23: Chapter 4, Hinge Questions
- July 30: Chapter 5, Exit Tasks

- Follow the reading guide posted above. Each Monday listed on the schedule, I will publish a post with my thoughts. I’m planning to use the format suggested in the book study guide included at the back of the book (Sharing, Aha!, and Let’s Try!).
- Participate by adding a comment to this post or by replying to the comments of others. Your comment will be displayed once approved.
- Use the hashtag #Formative5BookStudy to participate in a slow Twitter chat. Search on the hashtag anytime during the week to follow the conversation. I will be posting questions throughout the week, and you can add your thoughts using the same hashtag, as well as the hashtag #Formative5, or just read what others are saying. If you haven’t used Twitter for professional development, this is a great way to start.

The authors started by answering a question that many of us were probably wondering–what is the difference between an exit slip or ticket and an exit task? The short answer is that it’s a difference in the cognitive demand of the task. Exit slips and tickets tend to be low-level, computation-based questions, while exit tasks require a higher level of thinking from students. The Mathematics Task Analysis Guide (page 110), examples of task types (page 111-112) , and discussion of DOK levels (page 112) are good reading for experienced and novice teachers alike. I’m planning to put a copy of the Mathematics Task Analysis Guide in my planning notebook, so I can easily put my hands on it during planning.

I found the comments from Claudia and Darshan (pages 114-116) to be very insightful. Claudia shared some of my favorite websites for tasks, and the example of how she revised a district task for her exit task was extremely helpful. On page 116, Darshan recounted how his planning team moved toward more meaningful tasks after the team helped a colleague realize that the tasks she was purchasing from an online website were just “fancy worksheets” and not necessarily aligned to standards or cognitively demanding. With resources so readily available, that’s an important conversation. Thankfully, the chapter provides several resources for evaluating tasks.

This book is a book about good mathematical teaching practices disguised as a book about formative assessments. Don’t get me wrong, that is not a criticism. I went all the way back to the Issues and Opportunities chapter to grab this quote:

*An important prerequisite to such planning is your own understanding of the mathematical content and pedagogical knowledge related to your grade and beyond. *The Formative 5, page 11

In other words, in order for the formative assessment strategies to be most effective, teachers need to deeply understand their standards and the best practices for mathematics instruction. They must also consider the best instructional approach, teacher-centered or student-centered, for creating the type of environment where authentic math tasks and discourse are the norm. If you think of each of the assessment strategies, the process standards/mathematical practices are interwoven all through them. Observations and interviews require students to communicate their mathematical understandings, while Show Me, hinge questions, and exit tasks typically call on students to use representations to justify their solutions. The mathematical practices are specifically listed on the Exit Task Organizer Tool on page 122. That will be the big shift for some teachers–moving from a teacher-centered, procedure-based type of instruction to one that emphasizes deep conceptual understanding through student-centered instruction.

I love the emphasis on team planning and collaboration in developing a bank of exit tasks, because finding and/or creating high quality tasks is a tall order. With everyone working together, it definitely seems more doable. Imagine a well-organized binder filled with completed Organizer Tool sheets (page 122). What a valuable resource!

Share your thoughts and/or observations either below or on Twitter using the hashtags #Formative5BookStudy and #Formative5. Thank you so much to everyone who participated this summer! Remember to use the Twitter hashtag throughout the year to keep in touch and share your Formative 5 journey.

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