Wrapping Up a Year of Math Intervention PD

Earlier this school year, I blogged about an exciting opportunity I had to offer PD to all 107 of our district’s interventionists spread across the entire school year. I anticipated blogging about the experience during the year, but life got in the way. Here we are at the end of the school year and I am about to offer my final PD of the year tomorrow morning.

At first I wasn’t sure what I would do with them tomorrow. The way the schedule worked, I haven’t had a session with them since February. And with it being the end of the school year, I wasn’t sure what theyd be interested in hearing about. More than anything, they’re probably counting down the days to summer like their students are!

I thought a lot about it yesterday and today, and I came up with a plan that I think does a great job of honoring the work we’ve done together this year, brings us full circle to where we began, and even hints at directions for next year. As with anything I plan, it won’t go perfectly tomorrow, so I want to capture my ideas tonight of how I’m imagining and hoping it will go.

I’m basically going to give the same session 3 times in a row for an hour and a half each. That’s the only way we can cycle through all of the interventionists and provide PD on math, ELA, and a third rotating topic. The trouble is that the first group in the morning is invariably late. The starting time is 8am, but I doubt I’ll have everyone until 8:15. The session post-lunch is just as bad. The only group that will maximize the hour and a half is my middle group from 10:10 to 11:40.

I have too much to cover, so I am planning to start with an activity that I can do with whomever is in the room when the session starts. I’m going to ask the folks in the room to brainstorm at their table all the different ways they can make 120 using base ten blocks. If you miss the activity, it’s okay because you might catch the sharing portion. Even if you miss that, you’ll actually see various representations in the reading we’ll move into after this activity.

All year long, the interventionists have been doing a book study of Kathy Richardson’s How Children Learn Number Concepts. It’s been a great book study because I didn’t require any reading outside of the sessions. Knowing how busy the interventionists are, I know many of them wouldn’t do the reading. Instead, I let them do all the reading during our sessions. Did it take a lot of time? Yes. However, it meant every single one of them got the chance to read and discuss the book. And this is a book you don’t want to miss!

Unfortunately because some of the planned sessions were axed from the calendar, we only got to fully read 4 of the 6 chapters. We don’t have time to read chapters 5 and 6, but I am having them read the introductions to each chapter which is 9 or so pages each. Chapter 5 is about understanding place value (hundreds, tens, and ones) as well as addition and subtraction. A key idea from this chapter is that students must understand how to decompose and compose numbers flexibly, which will serve the students when they add and subtract multi-digit numbers. The example from the chapter is composing 120 in a variety of ways using base ten blocks, just like in our opening activity.

 

  As people finish reading, I want them to solve 397 + 205 in two different ways. We’ll chat about the reading for a few minutes to reinforce the importance of unitizing, and then we’ll do a brief number talk of the addition problem. I specifically want them to connect their strategies to the concepts in the reading.

Then we’re going to jump over to watching some videos of students solving 1,000 – 998 from the Math Reasoning Inventory website. The first two videos show students who quickly recognize that the difference is 2. The third video shows Ana, a student who uses her finger to draw and solve the problem on the desk using the standard algorithm. After comparing and constrating the students, I want to show them two more videos of Ana solving 99 + 17 and estimating 18 x 21. In every video, Ana gets the question correct, but she relies completely on writing the standard algorithm with her finger. She does not evaluate the problems or demonstrate any number sense.

I specifically want to focus on Ana because I want to talk about how an emphasis on skill-building over sense-making with intervention students can result in students like her who can get correct answers, but they only have a strong grasp of procedures, not necessarily mathematics. I want to ask them how they think Ana is going to perform when she moves up into middle and high school math. Is there a point at which her procedural skills aren’t going to be enough?

After this we’ll move into the pre-activity for the next chapter in Kathy RIchardson’s book. I’m giving the teacher’s this problem along with three sample solutions.

“There are three fish in an aquarium. The middle-sized fish eats 2 times what the first fish eats, and the big fish eats 3 times what the first or little fish eats. If the first fish eats 3 pieces of food, how many pieces of food would the other two fish eat?”

One of the solutions correctly shows how much food the other two fish will get, while two of the solutions show misunderstandings about the multiplicative relationships in the problem. I’m not going to call anybody out here, but I do want the teachers to sort of self-check before they read whether they are able to recognize the multiplicative relationships in the problem.

This problem is talked about in chapter 6 of Kathy RIchardson’s book, which is about understanding multiplication and division. I liked this problem a lot because she shared how questions like this were given to students, and the results showed that 45% of the second graders in the study were able to think multiplicatively, but only 49% of the 5th graders were able to do so with ease. This implies that despite three years of learning about multiplication in grades 3-5, the students in 5th grade did not demonstrate any greater understanding of multiplicative thinking than students in 2nd grade who have had little to no formal study of multiplication or division.

I love this chapter because it demonstrates how all of the work students should have done learning how to unitize tens and hundreds lays the foundation for unitizing in multiplication and division. Students must be able to think of counting groups of things and thinking of each group as a unit. She gives the following example to demonstrate the subtle shift in thinking students need to make to move from additive to multiplicative thinking:

Rick: I figured out 8 + 8, and that was 16. Then I added 8 + 8 again.
Emily: I had two 8s and that was 16, and two more 8s make another 16. That means four 8s makes 32.

From here we’ll briefly talk about the results from a survey given to over 1,000 teachers who were asked the following two questions:

  1. What reading skills do you most often teach to skilled readers?
  2. What reading skills do you most often teach to less skilled readers?

The results are, sadly, not surprising to me, but having the data helps drive home the point that we have to be mindful of what we’re teaching to differnent populations of students. You can read more about this survey and see graphs of the results here.

At this point, I want to share our district math goals, which I shared during our first PD session back in September:

The K-12 RRISD mathematics standards articulate five general goals for all students:

  • That they learn to value mathematics,
  • That they become confident in their ability to do mathematics,
  • They they become mathematical problem solvers,
  • They they learn to communicate mathematically, and
  • That they learn to reason mathematically.

Just because a student is struggling in math and put in an intervention program does not mean that we should ignore these goals. If anything , we should strive that much harder to reach them with these students! Based on their struggles, these students are already at risk of not valuing mathematics and not being confident in their abilities. We should build up their skills, yes, but we should also help them find ways to value math, to learn how to use it for work and play.

To this end, I’m using a few imbalance puzzles I got from Sue VanHattums’ wonderful book Playing With Math, (they are originally from this blog post).

  
I’m giving the interventionists two to solve, though if they can figure out one, that might be all we have time for. I’m not advocating they give these to their kids, but I want them to experience something that requires some problem solving, but it’s also fun and gets you communicating with your peers. I want them to experience something that might inspire them to create some new interactions with their students that work toward our district goals.

I want them to feel like they are walking away with something they can actually use with their students, so I’m introducing them to open middle problems. I was already a fan of the website, but it was Michael Fenton’s recent Global Math Department session that put them back on my radar in a big way. If you’re unfamiliar with the open middle problem type, basically it’s a problem that has a lot of solution paths, though not necessarily multiple solutions. Here’s an example of one from the website:

  
This problem has one correct answer, but students can attempt to find it in a variety of ways. I’ll share a few more examples with them so they get a feel for why these can be powerful problem types to include at times in their work with their intervention students.

I’m going to wrap up the session by showing Megan Taylors Ignite Talk about replacing “teacher-proof” curricula with “curriculum-proof” teachers. I just saw this for the first time recently, and it resonated with me with regards to intervention. So often I hear the cry for “teacher-proof” curriculum materials for RtI that can be used with fidelity and “get results.” While I see why this appeals to some people, I don’t think it’s the right way to go. 

When it comes to response to intervention, the key idea to me is that the interventionists should be constantly responding to their students’ needs. This means having a skillset that allows you to adapt and customize as needed to help the children grow mathematically, not to follow some prescription as though we’re trying to cure a cold. My goal this year has been to help build that skillset in the interventionists so they feel empowered to do that with their students, and I want to end our yearlong PD journey on that note so they can venture into their summer feeling like they are confident and ready to take on the challenges of next school year.

The Fast and Furious First Grade

Despite being the elementary math curriculum coordinator for my district, I have rarely gotten the opportunity to visit classrooms this year. Today was one of those rare days, and I was so blown away by the two classrooms I observed. Hopefully I’ll have a chance to write about both of them, but tonight I’m going to focus on the first grade classroom.

All year long I’ve heard great things about this first grade teacher, so I was excited to finally have a chance to visit her classroom. When I came in, she had the students on the floor in front of her. She was sitting in a chair holding up seven fingers.

  

The students each had a small whiteboard on which they wrote all of the “facts” they could about the number the teacher was showing. After the students had a minute or two, she called one of the students up to the front to share her facts. One of the things she did that I really liked was tell the student, “Please check your audience to make sure they are ready before you begin.” The student actually stopped, looked, and waited for her peers to be quiet before starting!

Here are the facts the student had written on her board:

  • 5 + 2 = 7
  • 2 + 5 = 7 (When they got to this one, the teacher asked, “What kind of fact is this?” and the students responded that it was a turnaround fact of the previous fact.)
  • 7 – 5 = 2
  • 7 – 2 =5 (Again, the teacher stopped and asked, “What kind of fact is this?” and the students responded that it was a related subtraction fact to the previous fact.)
  • 5 + 2 + 3 = 10
  • 10 = 5 + 2 + 3 (This time the teacher stopped and asked, “This one’s interesting. The 10 is on this side of the equal sign. Why does that work?” She called on a student who gave an unsure response, but he kept at it, and the beautiful thing is that she gave him plenty of think time rather than quickly passing to another student. She knew equality was a tough concept for her students so she wanted to slow down at this point. After the student finally articulated that the values on both sides of the equal sign were equal to 10, she called on another student, “What does the equal sign mean?” and another student, “What does the equal sign mean?” and a third student, “What does the equal sign mean?” I saw that she does this repeated questioning anytime there is an important point that she wants to make sure the class hears multiple times.)

She did the same routine holding up 9 fingers and had another volunteer share his answer. Then she told the students that they were going to count and needed to get in their counting circle. What surprised me is that her students all quickly put away their white boards and ran over to another area of the room to sit in a circle. I’m envious of her fast transitions. Her students wasted no time. She was able to start her counting circle in less than a minute.

She sat down on the floor with them and told them they were going to start by counting to 120 by ones. She said, “One,” passed the ball she had in her hands to the next student, and off they went. The class quickly counted, although a couple of students got hung up here and there. Again, she did a great job of giving the students think time, and it’s clear she taught the other students to be respectful of one another because the other students were very patient about waiting.

After counting to 120 by ones, she had the students count backward by ones starting at 90. She said, “90,” passed off the ball, and then they came to a screeching halt. The first student had no idea what to say! She thought for a minute and finally said, “91?” The teacher replied, “Remember, we’re counting backward, not forward.” She gave the student a little more time and then said, “Do you want to get some help?” The student nodded and then ran over to their class hundred chart. After consulting it, she came back and said, “89,” with confidence. From there the count continued a bit more slowly than counting forward, but still very smoothly. When the count got back to that first girl, she had no trouble at all.

Next the teacher challenged the students by saying they were going to start at 33 and count to 52. They must have been familiar with this routine because the students immediately started trying to figure out who was going to say 52. Once all the students held their thumbs up to indicate they they were ready, she asked for their predictions. It was interesting to see that four different students were guessed, but they were four students all sitting next to each other, so clearly the students were all within a reasonable range, but not perfectly accurate. They tested out the count to see who it would actually land on and then jumped into yet another count! For their final count, they counted forward by tens to 120. Because the count went through so few students, she actually had the count go clockwise and counterclockwise to ensure every student got to take part at least once. Nicely done!

Then the students were up yet again. This time they moved back to the area they were sitting in when class started. They continued counting by tens, but this time they used a Math Rack.

  
 

The students clearly have used this tool countless times throughout the year. They were able to count by tens from 0, from non-zero starting numbers, and they even counted backward by tens from 100, 98, and 91. I liked how she even had them make connections to their work this year making tens.  When the students counted by tens and got to 93, she covered the remaining counters and said, “We’re at 93. How many more to 100?” When a student said, “7,” she replied, “How did you know?” and the student said it was like a tens fact, he knew 3 + 7 is 10.

And that’s not all! She had the students hop up and meet her back on the carpet where they had done the counting circle so she could show them how to play a new game. It was a matching game. Students drew a green  card that would say, “What is 10 more than ___?” The blank was filled in with a number. The students then drew a white card looking for the matching answer. After teaching students the game, they got to play it in pairs for 5-10 minutes.

And that’s not all! When the game was over, the students quickly put away their cards and met the teacher back on the carpet where class began. She started showing them an activity they were going to continue the next day. This time they would play a game by themselves where they would roll a dice that would give them a starting number from 1-6. Then in their journals, they needed to count by tens starting at that number and record their counting pattern in their journal. She modeled one turn and then had other students model a few more turns before the class ended.

Whew!

Recounting it all, I can’t believe how much math these kids did in 60 minutes. It was incredible! And while it seems like they bounced around a lot, it was all very intentional. First of all, she planned today’s activities based on her formative assessment of the students after they did several lessons on counting by tens the previous week. She didn’t feel they were strong enough so she wanted to give them more practice. She also wanted to ensure they were comfortable doing it in multiple ways. This was such a smart move on her part because it would have been easy to think that her students “got it” early in the lesson, but when I played the matching game with one of her students, I was intrigued that the student knew 10 more instantly for some of the cards, but for others she had to consult the hundred chart.

The other thing I loved was how many opportunities she gave the students to get up and move around. It would have been very easy for her to set up shop at the front of the room and try to get through all of her planned activities. However, as we all know, students get very fidgety after sitting for a few minutes. While her students did sit for most of the class period, the constant change in locale got them up and moving and made the class feel very active, energetic, and fun.

And above all else, I was struck at how much respect the teacher showed her students by giving them the think time that they needed and how excited she was to hear their thinking and ideas.  Her respect has clearly rubbed off on her students because I heard numerous unsolicited compliments given out by students whenever a classmate was willing to go to the front to share their work or demonstrate counting by ten. It’s such a great mathematical community, and I’m so happy I got to visit even if just for a little bit.

Fraction Number Sense

This week I gave a presentation to grade 3-5 teachers from around my district. One of the points I wanted to drive home to them is that number sense does not apply to only whole numbers. Students can (and should!) have number sense with regards to fractions and decimals as well.

One area where I see teachers frequently take shortcuts and/or avoid number sense is with comparing fractions. Some teachers teach their students to use cross multiplication to verify whether two fractions are equal. Others teach their students to use one and only one strategy for comparing fractions: find common denominators. This strategy works, don’t get me wrong. However, it develops one skill, not number sense.

When comparing fractions, students should be mentally choosing from a variety of strategies. Why? Because students might notice they can make a comparison quickly and mentally. Why go to the trouble of creating common denominators, which likely involves making some notes on paper, if you can mentally make a comparison based on your understanding of fractions?

To that end, I put together three “books” that teachers could use to prompt some discussion and reasoning among their students. I’d love for their students to start realizing that fractions are something they can make sense of.

Each book focuses on comparisons around a particular strategy, but the strategy is never spelled out for the students. Instead, my hope is that by noticing, wondering, questioning, reasoning, and communicating, a class of students can make sense of the strategy in each book.

By no means are these books intended to fully develop students’ number sense with regards to comparing fractions. Additional experiences and practice are likely required. However, if you’re a teacher who wants a place to start this work with your students, give these a try and let me know how it goes.

Another Blog Post About Fraction Division

Person 1 mentioned on Twitter tonight that there aren’t enough blog posts out there about fraction division.

Person 2 recommended using rectangles to model fraction division.

I decided to help Person 1 using Person 2’s suggestion. Though the meat of this post is in this PDF I made and not in the blog post itself:

Fraction Division (1/29/2015 Stacked all fractions and made a cover page.)

Good enough, I say. I made a lot of examples fairly quickly, so I apologize if there are some errors here and there. Let me know and I can easily fix them and re-post the PDF.

And now there are n + 1 posts on fraction division on the internet. Woot!

Suck It, Gauss!

I’m a little bit embarrassed to share this story, but damn it, I’m so proud of myself I’m going to do it anyway. Apparently an extra hour of sleep on Sunday morning is all I needed to figure out the answer to a math problem that left me feeling dumb back when I was in middle or high school.

For the last hour or so that I was in bed, I dozed. At one point as I was going in and out of random dreams, an image flashed across my mind. It was a clever solution to a math problem I saw posted on Twitter a week or two ago. I can’t even remember what the problem was, just that the visual solution had this shape:

4-squared

There were numbers in the squares, maybe counting how many squares are in each column? All I remember is that this visual represents how the answer to the problem is 42.

Clearly my memory of this problem is not what I’m proud of. The important thing is that this random image triggered the line of thinking I continued on.

So after thinking about this image for a few seconds, I started to think about a math problem that has plagued me since I was in school: How can you quickly find the sum of all the numbers from 1 to 100?

I have no clue why this question popped in my mind, but it did, and since I was only semi-conscious, I just went where my thoughts took me.

I decided to try a simpler version of the problem to see if any insights struck me. I also tried thinking of a visual to see if it would lead me to a clever solution like the 42 image I was just thinking about.

I started with finding the sum of all the numbers from 1 to 5, and I thought of it like stair steps:

1-to-5

Then I played around with the squares in my mind to see if reconfiguring them would lead to an epiphany. My first thought was to redistribute the 5 squares to make columns of 4 which led me to this:

1-to-5-reconfigured

Having three 4s and a 3 made finding the sum a lot faster, but it didn’t seem generalizable. I decided to try summing all the numbers from 1 to 6 to see how my redistributing strategy would work.

1-to-6-both

Now I ended up with four 5s and a 1, which is easy to compute, but clearly showed me I wasn’t going to get anywhere satisfying with this strategy.

Feeling a bit frustrated, I started thinking about what it would look like if I made stair steps of all the numbers from 1 to 100. That’s when it hit me. The shape of the numbers from 1 to 100 is a jaggedy right triangle that looks kind of like this:

1-to-100

I thought to myself, if I duplicate that triangle, I can rotate it and fit it with the original triangle to make a rectangle. So long as I can find the number of squares in the rectangle, then all I have to do is half it to find the number of squares in the original triangle. All that was left was determining the dimensions of my rectangle.

1-to-100-rectangle

I knew the length had to be 100 because I was finding the sum of the numbers from 1 to 100, so it is 100 units long. From there I had to think about the width of the rectangle if the tallest portion (100) was set on top of the shortest portion (1), which got me 101. I tested out the next few columns that would line up to make sure I wasn’t making a mistake. The 99 column would rest on top of the 2 column to get 101, and the 98 column would rest on top of the 3 column to also make 101.

I felt pretty confident that the height of my rectangle would be 101. Then it was just a matter of multiplying 101 by 100 and halving the product to find the number of squares in the numbers 1 to 100.

I had no idea if 5,050 is the correct answer, so I decided to go back to testing out smaller numbers to see if this idea was solid. I thought to myself that the dimensions of my rectangle for anything I try have to be n and n + 1, where n is the final number in my series.

So going back to the sum of the numbers from 1 to 5, I would be creating a rectangle that is 5 by 6, and then halving it to get 15. Then I tested out summing the numbers from 1 to 6. This makes a rectangle that is 6 by 7, which gives me 21 when it is halved.

Success!…followed by grabbing my phone and consulting the internet to make sure I was actually correct. When I saw that I had derived the same equation that I had been shown when I was a student years and years ago, I was beyond elated.

To give you a bit of back story, back when I was in school, I remember our teacher presenting us this exact problem, and I didn’t have a clue how to approach it. You may as well have asked me to sum all the numbers from 1 to 1,000,000. I hated challenges like this because I always ended up feeling stupid. Even after giving up and waiting for the teacher to share the solution with us, I still didn’t really get it.

The whole experience reinforced my fixed mindset thinking that I wasn’t actually intelligent at math. I may have been a whiz at learning procedures and following them, but when it came to doing “real” math, I was terrible at it. I think hearing the story about how Gauss solved this problem really quickly in elementary school didn’t make me feel any better about it either. Instead of being inspired about the power of looking for patterns, it only made me feel that much worse about myself.

It’s funny how many people see me today and hear what job I do and they automatically think of me as a “math person.” It’s true, today I am a “math person,” but only because I’ve put a ton of effort into relearning how to think about and do math for most of my adult life.

And finally, after all that hard work, here I am lying in bed at the age of 37, casually entertaining mathematical thoughts as I wake up, and I finally figured out that damn problem all by myself!

Numberless Word Problems

“They just add all the numbers. It doesn’t matter what the problem says.”

This is what a third grade teacher told my co-worker while she was visiting her classroom as an instructional coach. She didn’t really believe that the kids would do that, so she had the class come sit on the carpet and gave them a word problem. Sure enough, kids immediately pulled numbers out of the problem and started adding.

She thought to herself, “Oh no. I have to do something to get these kids to think about the situation.”

She brainstormed for a few moments, opened up Powerpoint, and typed the following:

Some girls entered a school art competition. Fewer boys than girls entered the competition.

She projected her screen and asked, “What math do you see in this problem?”

Pregnant pause.

“There isn’t any math. There aren’t any numbers.”

She smiles. “Sure there’s math here. Read it again and think about it.”

Finally a kid exclaims, “Oh! There are some girls. That means it’s an amount!”

“And there were some boys, too. Fewer boys than girls,” another child adds.

“What do you think fewer boys than girls means?” she asks.

“There were less boys than girls,” one of the students responds.

“Ok, so what do we know already?”

“There were some girls and boys, and the number of boys is less than the number of girls.”

“Look at that,” she points out, “All that math reasoning and there aren’t even any numbers in the problem. How many boys and girls could have entered into the competition?”

At this point the students start tossing out estimates, but the best part is that their estimates are based on the mathematical relationship in the problem. If a student suggested 50 girls, then the class knew the number of boys had to be an amount less than 50. If a student suggested 25 girls, then the number of boys drops to an amount less than 25.

When it seems like the students are ready, she makes a new slide that says:

135 girls entered a school art competition. Fewer boys than girls entered the competition.

Acting very curious, she asks, “Hmm, does this change what we know at all?”

A student points out, “We know how many girls there are now. 135 girls were in the competition.”

“So what does that tell us?”

Another student responds, “Now that we know how many girls there are, we know that the number of boys is less than 135.”

This is where the class starts a lively debate about how many boys there could be. At first the class thinks it could be any number from 0 up to 134. But then some students start saying that it can’t be 0 because that would mean no boys entered the competition. Since it says fewer boys than girls, they take that to mean that at least 1 boy entered the competition. This is when another student points out that actually the number needs to be at least 2 because it says boys and that is a plural noun.

Stop for a moment. Look at all this great conversation and math reasoning from a class that moments before was mindlessly adding all the numbers they could find in a word problem?

Once the class finishes their debate about the possible range for the number of boys, my co-worker shows them a slide that says:

135 girls entered a school art competition. Fifteen fewer boys than girls entered the competition.

“What new information do you see? How does it change your understanding of the situation?”

“Now we know something about the boys,” one of the students replies.

“Yeah, we know there are 15 boys,” says another.

“No, there are 15 fewer, not 15.”

Another debate begins. Some students see 15 and immediately go blind regarding the word fewer. It takes some back and forth for the students to convince each other that 15 fewer means that the number of boys is not actually 15 but a number that is 15 less than the number of girls, 135.

To throw a final wrench in to the discussion, she asks, “So what question could I ask you about this situation?”

To give you a heads up, after presenting to this one class she ended up repeating this experience in numerous classrooms across our district. After sharing it with hundreds of students, only one student out of all of them ever guessed the question she actually asked.

Do you think you know what it is? Can you guess what the students thought it would be?

I’ll give you a moment, just in case.

So all but one student across the district guessed, “How many boys entered the art competition?”

That of course is the obvious question, so instead she asked, “How many children entered the art competition?”

Young minds, completely blown.

At first there were cries of her being unfair, but then they quickly got back on track figuring out the answer using their thorough understanding of the situation.

And that is how my co-worker got our district to start using what she dubbed Numberless Word Problems – a scaffolded approach to presenting word problems that gets kids thinking before they ever have numbers or a question to act on.

Recently we shared this strategy with our district interventionists and several of them went off and tried it that week. They wrote back sharing stories of how excited and engaged their students were in solving problems that would have seemed too difficult otherwise. This seems like a great activity structure for struggling students because it starts off in a nonthreatening way – no numbers, how ’bout that? – and lets them build confidence before they ever have to solve anything.

Do I think that every word problem should be presented this way? No. But I do think this is a great way to prompt rich discussion and get students to notice and grapple with the relationships in problem situations and to observe how the language helps us understand those relationships. To me this is a scaffold that can help get students to attend to information and language. As many teachers like to say, standardized tests are as much reading tests as they are math tests.

Perhaps you can use this activity structure when students are seeing a new problem type for the first time and then fade away from using it over time. Or maybe you have students who have been doing great understanding word problems, but lately they’re rushing through them and making careless errors. This might be an opportunity to use this structure to slow them down and get them thinking again.

Either way, if you do try this out, I’d love to hear how it went.

Talking Up Talking Points

I have been talking up Talking Points ever since I got home from Twitter Math Camp in July. Don’t know what Talking Points are? No problem. You can learn more about them on the Twitter Math Camp wiki. We had a group led by @cheesemonkeysf who dove deeply into this topic and shared their work with the rest of us. When you have a chance, I suggest reading the document titled About Talking Points. In the meantime, here’s a brief summary:

Talking Points are simply a list of thoughts. They are statements which can be factually accurate, contentious, or downright wrong. They can be thought-provoking, interesting, irritating, amusing, smart, simple, brief or wordy.

That definition aside, it’s not so important to know what Talking Points are as it is to know what to do with them and why.

Often children (and even adults) are asked to discuss their ideas or work together in groups, but it quickly becomes apparent that those involved don’t really know what is being asked of them.

You have those participants who love to talk, but they don’t really know how to consider other people’s views. On the other hand, you have participants who are quiet. They find it hard to join in the conversation.

The role of the teacher is to make explicit the kind of talk that is useful, and that is where the Talking Points activity comes in.

The activity stimulates speaking, listening, thinking, and learning. It offers ways in to thinking more deeply about the subject under discussion. It gives everyone a chance to say what is on their mind, so that others can decide whether they agree or disagree.

If you want to try out the activity, you need to create small groups of about 4 people per group. Give each group a list of Talking Points. (You can write your own, or you can start by using some of the ones on the Twitter Math Camp wiki.) The group will engage in 3 rounds per Talking Point.

Round 1

  • One person reads a Talking Point
  • Go around the group. Each person says whether they AGREE, DISAGREE, or are UNSURE about the statement AND WHY.
  • The most important part of this is that there is NO COMMENT by anyone else in the group. Their job is to listen.
  • After everyone has had their turn, proceed to round 2.

Round 2

  • Go around the group again. Each person says whether they AGREE, DISAGREE, or are UNSURE about their own original statement OR about someone else’s statement they just heard AND SAY WHY.
  • Again, there should be NO COMMENT from anyone else in the group while someone is speaking.
  • After everyone has had their turn, proceed to round 3.

Round 3

  • Go around the group one final time. Each person simply states whether they AGREE, DISAGREE, or are UNSURE about the original statement. The group takes a tally and moves on to the next Talking Point.

When time is up, the facilitator can choose whether to have the participants complete a group self-assessment. (Check out the wiki for an example.) This gives them a chance to reflect on the discussion and how their group worked together.

The facilitator can also do a whole group debrief. I highly recommend doing this because it helps the participants reflect together, and it also gives the facilitator a chance to point out and emphasize to everyone behaviors and ways of talking that were effective. Here are sample questions that could be discussed:

  • Who in your group asked a helpful questions and what was it?
  • Who in your group changed their mind about a Talking Point? How did that occur?
  • Who in your group encouraged someone else? How did that benefit the conversation?
  • Who in your group provided an interesting additional idea and what was it?
  • What did your group disagree about and why?

You might be thinking to yourself, “Oh this activity is just like ___.” I’ve had several people tell me that, but once they have participated in their first Talking Points activity, they see how much deeper the conversation is than in the other activities they were thinking of.

The first time I tried this activity was with our district interventionists. This school year we are leading PD sessions with them about 10 times spread across the year, and one of the recurring themes is knowing their learners in general and using strategies to foster a growth mindset in particular. Before we dove into this topic, we created some Talking Points to get them talking with one another about their beliefs about intelligence and learning. Here is the set we used:

Talking Points About Intelligence and Personal Qualities

  1. Your intelligence is something very basic about you that you can’t change very much.
  2. You can learn new things, but you can’t really change how intelligent you are.
  3. No matter how much intelligence you have, you can always change it quite a bit.
  4. You can substantially change how intelligent you are.
  5. You are a certain kind of person, and there is not much that can be done to really change it.
  6. No matter what kind of person you are, you can always change it substantially.
  7. You can do things differently, but the important parts of who you are can’t really be changed.
  8. You can always change basic things about the kind of person you are.

The Talking Points were successful in getting the interventionists to start talking about ideas of growth mindset without us have to tell them anything. Many of them already felt strongly that intelligence can change (which made me happy considering the population they serve!) but I appreciated the discussion in a few of the groups where one person was able to point out some nuance in the language that made the others in the group consider the statement more carefully.

For example, in one group someone raised the point that she has an uncle with Down syndrome, and over the course of his life she doesn’t feel that his intelligence has really changed all that much. This personal experience made it difficult for her to fully agree with the Talking Points statements.

When the groups were finished discussing their Talking Points, we debriefed as a whole group. One of the recurring comments they made was how nice it was to have a chance to give their opinion and feel like it was heard by the rest of the group. Because of the “No Comment” rule, they knew that no one was going to interrupt them, and if someone tried, the other group members quickly reminded them of the rule.

A few weeks later, I was asked to share Talking Points with our district leaders at a Vertical Leadership Team meeting. This meeting consisted of all of the principals from all of our elementary, middle, and high schools as well as many other district leaders, about 120 folks in total. No pressure! I was nervous about what they’d think, but happy to have the forum to share the activity.

As with the interventionists, I was using the activity to lead in to a discussion of growth mindset research, but this time I revised the statements because I wanted them to each feel unique. In the first set I used, I felt like several statements said the same thing but in different ways. Here are the statements I finally settled on:

Talking Points About Learning and Intelligence

  1. You can learn new things but you can’t really change how intelligent you are.
  2. You are a certain kind of person, and there is not much that can be done to really change it.
  3. When you are learning something new, you should avoid making mistakes at all costs.
  4. You are smart when you can complete tasks quickly and accurately.
  5. The people who are the best in their field tend to be naturally good at what they do.

I only had 20 minutes to introduce Talking Points, share how to do them, have everyone in the room try them, and then debrief. It was a rush to get it all done, but it went smoothly enough. I definitely think 30-35 minutes is probably better for a first introduction.

I love walking around and listening in on different discussions while the groups are going through the Talking Points. While listening to the district leaders, I loved hearing one woman say, “Well, I did agree with the statement, but now I disagree because of what you two just told me. I just didn’t know that before.” It’s not required that anyone change anyone else’s mind during Talking Points, but it sure is powerful that it has that ability to happen based on just three short rounds of sharing opinions.

Someone in my department used Talking Points just over a week ago with a team of instructional coaches. While each grade level has some common ELA vocabulary that is used, the way it is used has not always been consistent across grades. Before the coaches started preparing for upcoming PD sessions, she had them go through some Talking Points about the vocabulary. She said it was such a quick and powerful way to gain clarity as a group before they started their planning.

Ever since I’ve shared Talking Points, it has started to slowly spread in my district, and I’m excited to see the creative ways it is used to deepen conversations among both students and staff.