Get Students to Argue in Math Class

I recently submitted my speaker proposals for both 2014 CMC conferences. One of my proposals is for the following session:
Title: "Get Students Arguing in Math Class with Number Sense Activities."
Description: Get students to productively argue about math situations. Participate in number sense activities requiring students to construct viable arguments, critique the reasoning of others, and use sense-making. Get ready to throw down.

I also had to answer a few questions justifying the session and connecting it to the CCSS and 8 Mathematical Practices. I provided the following connection:
The presenter will use number sense activities to get participants to construct viable arguments and share their reasoning like students. Using presenter-made tasks (Estimation 180) and other online resources appropriate for grades 3-8, attendees will be able to see the importance of student reasoning and creating productive discourse in the classroom. Teachers will also be provided with sentence frames and stems for all students, especially English language learners.

I'm really excited at the thought of this session getting accepted so I figured I would jot down a few ideas here and see what you all have to contribute. Even if I'm not accepted, I think every math class has to have students productively arguing at times. Doing estimation challenges with my students has been so beneficial for them to get better at the art of arguing. However, I know it could be better. I'm not sure if you've ever experienced it before, but it's a treat to stand off to the side or in back of a group of students arguing about a question in math. They have no idea you're nearby because they are so caught up in the argument. Don't get me wrong, it's not like they're swearing at each other and calling each other names. They are having a rich discussion, sharing conjectures, examples, counterexamples, etc. and I have the pleasure of spectating. I usually turn to an innocent bystander (nearby student) and whisper, "Awesome, look at them arguing. Isn't it great?" The student usually looks shocked that I'm happy their classmates are arguing. I love it!

I'd like this session to place a big emphasis on two mathematical practices:
MP 3: Construct viable arguments and critique the reasoning of others.
MP 1: Make sense of problems and persevere in solving them.

I plan to break these two practices down more in my session. For now, I feel I need to focus on three major parts to arguments: having excellent content, capturing the arguments, and indirect facilitation.

Content: There's a wealth of content available, but I think the more controversial the point of contention, the better. One of my favorite moments in math class was when we did Mathalicious' Datelines lesson. Students were arguing about which celebrity shouldn't date another celebrity because of the age discrepancy. Some students disagreed about the rule of (n/2) + 7, especially since I was teaching 14 year-olds at the time. It was awesome.
Here's my current list of resources that have given my students great things to argue about:

• Estimation 180
• Mathalicious
• Would You Rather 
• by John Stevens

My kids went nuts arguing about a similar question to this "Would You Rather" found here.

These don't have to be full-on lessons. They can be warm-ups, math talks, used during classroom transitions or to break up your direct instruction, etc. I'm really looking forward to using @MathCurmudgeon's site MathArguments180.com
Imagine your students arguing about which student should pack your parachute based on this data.

Another up and coming resource is Open Middle by Robert Kaplinsky and Nanette Johnson.

What resources would you add to my content list?

Capture: I need to capture these arguments for a few reasons. Students need to listen to other students argue, especially from different classes. My memory is very porous, and I can't remember what students say verbatim. Students can listen to the recordings and pick a side, or provide their own agreement or dissent. I'd also love to share student arguments with other teachers, especially at this session. How do I capture this?

I just downloaded Voice Memos for iPad onto my school iPad. I will test it out next week with students. Wish me luck. Here are the features I'm optimistic about:

• It will record in the background while another app is running.
• It was $1.
• I can pause the recording.
• I can trim audio clips.
• I can sync with Dropbox.

Have any tips for capturing student arguments?

Facilitation: Here's where I need to do a better job. For many of my students, English can get in the way of them articulating their point. I'd like for students to listen better to each other and respond accordingly. I want to hear what they have to say. I want them to be a contender in their disagreement, but I don't want them to be held back because of language deficiencies. Therefore, I need to provide them with sentence starters and stems. Fortunately, these can be used with any student. Here's a few:

• My opinion about this is _____________.
• I could argue that _____________.
• I disagree with your statement that _____________ because _____________.

Have any stems or sentence frames you're already using with students to help them articulate their thoughts?

Argue,
339

NCSM 2014 Day 1

Day 1 of NCSM was yesterday and here’s something I found interesting. Robert Kaplinsky, Dave Chamberlain, and I were walking back to our hotel room from the conference and I saw this clearance sign to the entrance of our hotel. I have been known to do estimation challenges before with clearance heights, not once, but twice.

I thought to myself, "There's NO WAY that thing is 6 foot 4 inches!"

I walked up to it and thought I should hit my head. Nope.

Okay, I’ll stand on my toes. Nope.

Okay, what’s going on here?

Why is this mislabeled? What’s your theory?

I’ll admit, this made me a little suspicious of the other clearance height challenges I’ve captured. Is this worthy of Estimation 180?

Photo bomb!

Suspect,

852

The Broadcaster and The Artist

We have a 30-minute intervention period four days a week at my school as part of our RtI program. Monday and Tuesday are slotted for math intervention. Thursday and Friday are slotted for Language Arts intervention. The students that report to me on Friday are supposed to participate in some type of activity that helps them improve with collaboration and/or communication. Here's a quick little activity we did last week you can try with your students. It's really cool to see how the students communicate with each other.

I made these two slides in Keynote.

I took my students to the outside lunch tables to sit across from their partner. One partner (artist) had a blank sheet of paper and their partner (broadcaster) had one of the sheets pictured above.

Job Descriptions:
Broadcaster: without showing the artist the sheet of paper, use descriptive language to help them draw the picture in front of you. You can't touch the artist's paper or point where anything should be drawn.

Artist: follow the directions of the broadcaster and ask any clarifying questions.

Add or subtract any rules you'd like. When groups are finished, have them compare their drawing with the original. After they see how accurate or inaccurate they were and have a good laugh, switch roles. If they had the yellow sheet during round 1, their group now gets the blue sheet during round 2.

The fun part is having each group pick their favorite drawing and we do a little competition back in class. I display their drawings using the document camera and we share some compliments and some good laughs. Hope you give it a shot.

Some Student work:

Broadcast,
1107

4!

Me: I need two volunteers. You have no idea what you're doing. Thanks Brianna and Jesus. Go stand in front of the whiteboard on the side of the room. You are the two contestants in today's Spelling Bee.

This is how I opened today's lesson. Wait. A Spelling Bee in math class? I address the audience:

Me: I need your help. I am going to ask you a question. The answer is a number. I am not interested in any categories like gender, height, age, birthday, first name, last name, etc. For my Spelling Bee, I need you to take my contestants and order them for me. What's the maximum amount of ways I could order these two contestants?

Students have time to think and some quickly raise their hand to say, "Two."

Me: Show me. Tell us what they are.

Student: Right now Brianna is first. Jesus is second. We could switch them and Jesus goes first.

Me: [looking at Brianna and Jesus] Do what she said.

Brianna and Jesus switch order.

Me: Have I maxed out all the possible combinations for ordering Brianna and Jesus?

Class: Yes!

For a little comic relief, I toss Jesus an easy word to spell.

Me: Jesus, spell "cat".

Jesus: C-A-T

Me: Wait. What?

I learned today that most kids don't know how a spelling bee works, so I call on a few kids to explain the three steps:

1. Say the word.
2. Spell the word.
3. Repeat the word.

Me: Jesus, let's try this again. Spell "cat".

Jesus: Cat. C-A-T. Cat.

Me: Bri, spell "discombobulate".

Brianna: Ughhhhhhh. What?!

Me: Okay, can I get a third contestant for our spelling bee? Jesus, since you're the winner, please pick someone. 

Standing in front of the audience, I now have Jesus, Brianna, and Garry.

Me: Okay, let's say their current order is one possible combination. Let's keep Jesus first. Can you get any other combinations with Jesus being first?

Student: Yea, switch Bri and Garry. 

I look at Bri and Garry.

Me: Do it! Okay we now have two possible combinations. Have we maxed out the possible combinations with Jesus being first or can we get more?

Class: We're maxed out.

Me: Okay, someone give me a new combination.

Student: Put Brianna first this time. Then Jesus. Then Garry.

Me: Okay, we now have three combinations. Can we get more where Brianna is first?

I repeat this process until the class has agreed we maxed out our combinations with six total. Great. I toss this information in a table like this to keep track of it.

Me: So what if I add a fourth contestant to the spelling bee? 

Sarah: No!

Me: Really Sarah? What? Are we going to have more or less combinations?

Sarah: More.

Me: Gimme some guesses everyone. Toss something out there for fun. How many combinations could we get with four people in the spelling contest?

Students tell me 8, 10, 9, 12, 16, 13 and I write all of them up on the board. I ask for some quick reasoning behind the guesses.

Me: Ok, thanks. You all can't be right. Instead of moving people around, let's do this instead. 

I gave each group a sandwich bag with four different colored snap cubes: red, green, blue, yellow. Students were to work in their groups to figure out all the possible combinations of four colors. They were to write it down in their notes for the day. I circulated the room, noticing student work.

For groups that think they're done, but wrong (like only 12 combinations):
I zone in on one combination and keep their two colors fixed, "Have you maxed out all the combinations with these two at the front?" Usually this is the only nudge they need to get closer to the correct number of combinations.

For groups that are on track:
I make it obvious I note their work, or ask for a quick explanation, or I quickly move to another group.

Groups that finish and have the correct answer:
I have them explain their work, organization, process, and reasoning. I ask if they feel confident and usually they do. I'm not going to string them along. I respond, "That makes sense to me." followed by:

Me: So what if I gave you a fifth color?

Student: [typical response] Ughhh. 

Me: Oh, what's wrong?

Student: That's a lot of work.

Me: I know, right? I'm right there with ya. I wouldn't want to write out all those possible combinations either. So, your job is to try and figure out a shortcut. In other words, if I just gave you four colors right now, how could we quickly get 24 combinations without writing them all out. If I'm now giving you five colors, what would be a quick way to figure out all the possible combinations?

Once I see that most groups have reached the magic number (24), I show them this and have them count.

Me: One clap on three for the closest guess. 

1-2-3 CLAP!

Many kids see that 4 groups of six combinations yields 24 combinations. I toss 24 into our table and ask the whole class about finding the possible combinations for five colors. Typically, the students want to avoid this nonsense and express some noise of rebellion.

Me: What's wrong? You guys don't want to write out all the combinations? Well, let's try and find a shortcut. Do we see anything from our table that might help us?

To my pleasant surprise, at least one kid in each of the three participating classes found the following relationship:

Abraham, Brianna, and Daisy: You take the previous "Combos" result and multiply it by the diagonal "Colors" amount to get the new amount of "Combos."

Me: Let's see if that works.

It does. Great!

Me: Okay hot shots! This is a great shortcut. What if our principal walked in and gave us 13 colors. How would I quickly figure out the total number of combinations since I don't have the number of combinations from 12 colors?

Here's where I introduced the use of factorials. Yes, I could have spent time getting the kids to look for this pattern, but I simply didn't have or make the time. I felt it was a good place to show them that putting the factorial symbol after a number means to multiply it by all of the natural numbers less than the given number.

4! = 4 x 3 x 2 x 1 = 24

Me: So if our principal walked in and said, "Find all the combinations of 13 colors." we'd go thirteen...

Class: ...times twelve, times eleven, times ten, times nine...

In reflection, this lesson created more successes for my students than I anticipated. Some include:

• Discovering patterns and relationships within a table,
• Creating a need for the factorial of a number,
• Adding another vocabulary term to our tool belt, and
• Finding combinations more efficiently.

This lesson started with a low-entry of two students and two combinations.
We built in the next part by finding six combinations for 3 students.
We built in a guess for the combinations of four students so they can invest in the question and look for patterns.
We manipulated four colors, organized our combinations, made conjectures, and arrived at a reasonable answer that maxed out the combinations.
We pushed those students who finished early to discover a shortcut on their own.
We created a need for avoiding excessive work with larger numbers and a need for some type of formula (factorials) that will get us the same result.

I came into this lesson with a rusty understanding of factorials, probability, and combinations. Anyone who is against Common Core State Standards, think again! It's making math teachers know their content better, so they can better serve their students. It's opening the door for students to reason their way in math class. I'm not blogging to get into the importance of CCSS right now. However, I'm convinced this was way better than me standing in front of the students telling them to put an exclamation point after 4 (like this 4!) and to just multiply 4 by 3 by 2 by 1 to get all the possible combinations of four somethings. Instead, the students discovered the relationship (pattern) within the table and felt confident in discovering the total combinations of five colors without drawing them all out.

Factorial,
848!

My Crush on Google Forms

No matter who you are, who you teach, what you teach, and what type of school demographic you teach, teachers always have to account for student behavior and classroom management. Likewise, you might be the most engaging teacher, have the most awesome lessons, and/or have a lot of students who adore your every sneeze, but we can all benefit from keeping track of student progress. Enter my crush on Google forms/docs/drive this semester for two reasons.

After-School Help
Nothing complicated. When students show up after school for math support (voluntarily or involuntarily), I have a quick way to keep track of who showed up and how long they stayed. The "miscellaneous notes" section is helpful for tracking students' skills or questions they might have, etc.

This can also be helpful when working with parents if you have an action plan for their child to receive additional support outside of class time. The last thing I want to do is create more work with these forms. When students show up, I have them write their name on the board and the time they depart so I can quickly enter their work time. This is a short and sweet form. Let's move on. 

Behavior Log
The purpose of the form is to log any interaction I have with a student as a result of being off-task, misbehaving, or anything else that disrupts the learning process. The purpose of this Google form is not to curb bad behavior. However, I will say it can be effective to fill out the form together with the student. Tread lightly: don't make a show of it in front of their classmates or project it up on the screen for all to see.

Behaviors:
This is not an exhaustive list of classroom (mis)behaviors. However, think how easy and efficient it is to check common behaviors. When filling this out with the student, it helps to have them identify what behavior disrupted the learning process. The "other" option takes care of anything you can't foresee your students doing. Always nice to have.

Action Taken:
My school expects teachers to handle as much classroom management issues as possible by having us layout a progressive discipline procedure with our students. As you can see, my list under "Action(s) Taken" seems pretty progressive, or at least I think so. For me, the most meaningful and effective action is the "Student-teacher conference." Whatever your fancy is, create a list of actions you usually find yourself doing and make them checkboxes. Don't forget the "other" section.

If this happens again...
I have a really porous memory so this section is a lifesaver. You're telling the future you what to do if a student repeats their behavior. I can't tell you how many times I just open the Google responses for my log, press Command-F (for find), type the student's name, and BAM! I have what they previously did and what we agreed on as the next step in progressive discipline.

Additional Notes
I sometimes use this to make a note about the student responding well to a warning, the details of a student-teacher conference, or the actual incident itself. It's there for what you need it for.

Final thought:
Create a shortcut in your browser for these Google forms. If you're out in the wild with an iPad, create a shortcut there too.

Don't get me wrong people, I'm not bragging about student discipline with this post. I believe that most student misbehavior can be prevented by providing students meaningful/engaging learning experiences, classroom boundaries, and routines. Mix this with a lot of preventative-maintenance teacher moves and students typically stay on task and out of trouble.  But we can do more than that.

PBIS
Our school has also required every teacher to include a Positive Behavior Incentive System (PBIS) in their classroom. Students earn some type of token for positive contributions to the learning environment and can cash them in for prizes that range from candy, to sitting in the computer chair, to a bag of chips, to an Expo marker, to picking something from the mystery box.

Students used to earn stickers in my class for positive behavior, where they could cash in the stickers for prizes. It was a hassle for all of us. Recently, a colleague went to a conference and shared a PBIS idea I've found to be pretty effective. I hand out small "Thank You" notes printed on scratch paper. Students save them and can cash them in. So far, so good.

My goal of this post was to encourage you to look into Google forms for efficiently keeping track of student interactions. If you have others, please share.

Crush,
1014

Carnival of Probability

This past week, my awesome partner, Hannah, and I hosted a Carnival of Probability for our 7th graders in our school's multi-purpose room. Let's get to it:

Station 1: Spinner 1

Pick a side. Will the spinner (arrow) land on the 5 or the 15? If you choose wisely, you win that many tickets.

Station 2: Spinner 2

No need to pick a section. You get three spins. Land on the 1, you get one ticket. Land on the 100, you win 100 tickets. BAM!

Station 3: Rolling a die

Pick a game. Grab the six-sided die and roll. 

• Roll an even number, win 8 tickets.
• Roll a multiple of 3, win 15 tickets.
• Roll a one, win 30 tickets. 

Station 4: Rolling two dice

Pick a game. Grab two dice and roll. 

• Roll two sixes, win 45 tickets.
• Roll an even number and a five, win 45 tickets.
• Roll two multiples of three, win 32 tickets.
• *Roll the same number on our twelve-sided dice (pictured below), win 70 tickets.

See the blue 12-sided die? There's a 12-sided die inside. Cool, right?!

Station 5: Bag of letters

Pick a game. Reach inside the bag of 26 chips chips (pictured above) and pick one chip. 

• Pick a vowel, win 25 tickets.
• Pick a consonant, win 21 tickets.
• Pick the first initial of your first name, win 40 tickets.

Station 6: Ball toss

Take a ball. Toss it in the direction of the cups. If it goes in any white cup, win 3 tickets. If it lands in the red cup, win 35 tickets. Just like that!

Station 7: Deck of cards

Decide on a game. Pick a card or two. Win tickets!

• Pick a red or black card, win 1 ticket.
• Pick a red card and a queen, win 40 tickets.
• Pick a Jack, Queen, or King and win 22 tickets.

Station 8: Coin toss

• Flip it once and land on heads, you win 8 tickets.
• Flip it twice and land on heads both time, you win 20 tickets.

You might ask, "Did you really pass out all those tickets?"

The simple answer is, "No!" You don't think we're that crazy, do you? We assigned one to two students as captains for each game. The game captains gave each contestant one ticket with the number won written on it. 

The math: we spent a few days leading up to the carnival talking about probability and identifying "and" statements along with "or" statements. Station 4 was all "and" probabilities which made your chances of winning more challenging. The 12-sided dice game had a less than one percent chance of winning. Station 7 and 8 had a couple of "or" probabilities. Our goal here was for students to have a concrete introduction and application of probability. To enter the carnival, students had to represent the probability of each game as a fraction, decimal, and percent. 

The students had a blast. It was fascinating to hear from them about the carnival the following day. They explained which games were the "easiest" and "hardest." The games (as you can see from the pictures) were nothing fancy, but they did the job. Students will get to cash in their tickets for prizes such as candies, pencils, pens, and Expo Dry Erase Markers. What would your carnival look like? Please share.  Head over here for the paperwork/handouts we used. 

Carni,

633

180 Ways to Use Estimation 180

New challenge: Find 180 ways to use Estimation 180. Wait a minute. That's seems a little extreme, yet I still love the idea. Here's one use I came up with this week: inequalities.  Click on any picture to enlarge.

Me: Hey guys, here's a piece of paper. Fold it into fourths for me like this.

Me: Great. Now, who remembers how tall I am?

I know, silly question, right? If these guys don't know my height by now, I'll send them back a few grades. Then I show them this picture and ask: What's the height of Mrs. Stadel compared to Mr. Stadel?

I take about 4-6 guesses and write them on the whiteboard. It’s been awhile since we’ve done this specific estimation challenge in class. Many have forgotten my wife’s height. Great! However, it’s quite obvious her height is less than mine.

Me: Let me step back. Let’s all look at these guesses. Is it safe to say that all of your guesses put her height less than mine?

Class: Yes.

Me: Okay, so before I reveal the answer let’s put this in our notes for today.

Me: Before I reveal the answer, who can remind me why we used an open circle?

Student: Because we know her height is not the same as yours.

Reveal Mrs. Stadel's height. Wait for it... Wait for it... Here it comes... Student responses: 

“Yes, I was right!” 

“Ohh, I was close.”

“Ohh, I was off by an inch.”

Next up, our beloved Mr. Meyer.

“Woah! He’s tall!”

“Someone is actually taller than you, Mr. Stadel?”

Again, toss 4-6 guesses up on the whiteboard. Step back. What do we notice? Yes, all the guesses should be greater than my height.

Walk through the notes on this new section with more student confidence and participation.

Ask students:

• What type of circle should we use this time?
• If we’re talking about guesses that are greater than my height, how will that affect the inequality symbol?
• What are ways to remember this inequality as greater than?
• Which direction will we shade now?
• Someone give me a variable we can use for Mr. Meyer's height.

Reveal answer. Same responses as my wife, but usually a different kid was right this time.

Okay, great. Now what? What about those other two inequalities, right?

Me: Before I show you this next picture, last year the 6^th grade English teacher (@mrkubasek) at my old school read this novel with his students and came across these two books he found interesting. I found it interesting too and took a picture so we could talk about it in math.

Show picture.

Me: How many pages in the book on the LEFT?

No need to write anything down. Just get 6-8 guesses out loud. Don’t spend much time here. Reveal the answer. Give some math love [one clap on three: 1, 2, 3, CLAP!] to the closest student. Seriously, it’s pure gut instinct here people.  

NOW, show this picture and ask how many pages in the book on the RIGHT.

They don't know it yet, but you just broke their brains for a bit. Yup, you’ll get a lot of guesses below 307. But wait for it. I guarantee in a class of 35-40 students like mine, one student will say 307. If you do, treat it like every other guess you've gotten.

...and if no one guesses 307, step back after about 6-8 guesses and...

Me: You know all of your guesses make sense to me. I'm curious though guys. This is the same novel here, right? What if? I mean, WHAT IF? What if these books had the same amount of pages? Do you think that's possible? Do I have your permission to add it to your guesses?

Step back again. Look at all those beautiful guesses. 

Me: So if I'm looking at this right, you guys think the number of pages could be equal to 307, or could be less than 307? I wonder how we could represent this mathematically?

BAM! Focus here on the circle. Why are we shading it in this time? What's up with that line under the less than inequality?

Me: Okay, before I reveal the answer, someone remind me why we shaded in the circle. 

Reveal!

Brains broken! Now repair. 

Me: What's up with that? Anyone have any ideas/theories why they have the same amount of pages?

Alright. That fourth and final inequality. Here are the goods. Repeat all the other moves from above. 

Initial guess of one bar.

Take some guesses out loud. Reveal the answer.

Toss up new picture.

Write down some guesses on the board. Play up the "what if" again. Complete the notes. Ask a few questions before revealing the answer.

BAM!

That was fun. Boy, I wish it didn't have to end. But it did. Okay, let's find other ways to use Estimation 180 in the curriculum. The full lesson will soon be is available on the lessons page at Estimation 180.

180 ways,

957

Presentations & Workshops

Last month I added the Lessons page to Estimation 180 so you can quickly access lessons I've made. I will continue to add lessons as I make them and host them in that space.

This month, I'm adding a Presentations & Workshops page to the site. Since last November, I've been fortunate to work with some amazing math teachers at conferences and workshops. I've learned a lot and have truly enjoyed doing math with teachers as we share instructional strategies and lessons. My goal is to help support math teachers in strengthening their instructional tool belt for the Common Core classroom. 

I'm excited about this new chapter. Drop me a line if you're interested.

PD,
945

Explain that, please.

Recently, I've given a few teacher workshops/conferences and have had the luxury of reflecting on teacher moves as I facilitate a lesson with the attendees. One of the many things we talk about are teacher responses to students.

Me: Did anyone hear me say, "No. That's wrong. You're wrong. I don't like your answer."

Attendees: No.

Me: Right. Instead, you'll hear me say things like, "Can you explain what you did here? Explain that, please. I noticed you did [this] here, please share how you got [that]. I'm curious how you came up with that. Walk me through what you did."  

I tell teachers that I'm taking the emphasis away from right versus wrong answers and placing an interest on the student's thought process and problem-solving. I continue with teachers:

Me: By telling a student they're wrong, a student can have the tendency to shutdown [I make the sound effect of a machine shutting down, "BOOOOvvvvvvvv"]. By asking a student to explain things, it shows that I'm more interested in how they arrived at their answer. 

As teachers, we know a student can be told they're wrong and it's easy for them to give up. On the flip side, when we validate a kid by telling them they're right, the student can also shut down and never reach the higher levels of Depth of Knowledge.

Recently, a workshop attendee asked me how I respond to students who have nailed the answer to a 3 Act task. First, I have them explain their problem-solving plan to me. Second, I question any details that were unclear, encourage them to be more precise, or have them explain their units of measurement. Third, I ask them if they feel confident in their answer after explaining it to me. Fourth, I validate them by simply saying, "That makes sense to me."

I don't tell them they're correct. I treat them just like as if they got the answer wrong. If that doesn't satisfy them, I respond with, "We'll find out soon if you're correct, but that (their explanation and work) makes sense to me." At this point, I offer them an extension to the task. I'd like to talk more about this later, but usually the extension revolves around the students creating something with the new knowledge or skills they have just recently gained.

After all that, please add your favorite lines when questioning students to this Google doc. I think it's also helpful we create a list of lines we avoid using with students as they explore math.

Here are a few people with other stellar teacher moves/lines to support students.
Max Ray: 26 Questions You Can Ask Instead
Dan Meyer: You Don't Have To Be The Answer Key
David Cox: Creating A Culture Of Questions
Steve Leinwand: Accessible Mathematics

BOOOOvvvvvvvv,
645