{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":0.93,"endTime":4.38,"body":"Hey, fellow mathematicians."},{"speaker":"Pam","startTime":0.93,"endTime":4.38,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":4.38,"endTime":7.32,"body":"Math is Figure-Out-Able. I'm"},{"speaker":"Pam","startTime":4.38,"endTime":7.32,"body":"Pam."},{"speaker":"Ashley","startTime":7.56,"endTime":8.28,"body":"And I'm Kim."},{"speaker":"Pam","startTime":8.58,"endTime":11.91,"body":"And you found a place where"},{"speaker":"Pam","startTime":8.58,"endTime":11.91,"body":"math is not about memorizing and"},{"speaker":"Pam","startTime":11.91,"endTime":15.75,"body":"mimicking, waiting to be told or"},{"speaker":"Pam","startTime":11.91,"endTime":15.75,"body":"shown what to do. But it's about"},{"speaker":"Pam","startTime":15.75,"endTime":19.11,"body":"making sense of problems,"},{"speaker":"Pam","startTime":15.75,"endTime":19.11,"body":"noticing patterns, and reasoning"},{"speaker":"Pam","startTime":19.11,"endTime":22.26,"body":"using mathematical"},{"speaker":"Pam","startTime":19.11,"endTime":22.26,"body":"relationships. We can mentor"},{"speaker":"Pam","startTime":22.26,"endTime":26.52,"body":"mathematicians as we co-create"},{"speaker":"Pam","startTime":22.26,"endTime":26.52,"body":"meaning together. Not only are"},{"speaker":"Pam","startTime":26.52,"endTime":29.85,"body":"algorithms and step-by-step"},{"speaker":"Pam","startTime":26.52,"endTime":29.85,"body":"procedures not particularly"},{"speaker":"Pam","startTime":29.85,"endTime":33.6,"body":"helpful in teaching mathematics."},{"speaker":"Pam","startTime":29.85,"endTime":33.6,"body":"But rotely repeating steps"},{"speaker":"Pam","startTime":33.63,"endTime":36.96,"body":"actually keep students from"},{"speaker":"Pam","startTime":33.63,"endTime":36.96,"body":"being the mathematicians they"},{"speaker":"Pam","startTime":36.96,"endTime":37.35,"body":"can be."},{"speaker":"Ashley","startTime":37.74,"endTime":40.23,"body":"I'm really excited about"},{"speaker":"Ashley","startTime":37.74,"endTime":40.23,"body":"today's episode, Pam."},{"speaker":"Pam","startTime":40.26,"endTime":40.83,"body":"Woah! Yay!"},{"speaker":"Ashley","startTime":41.22,"endTime":44.22,"body":"So, this week, we want"},{"speaker":"Ashley","startTime":41.22,"endTime":44.22,"body":"to tackle something that is a"},{"speaker":"Ashley","startTime":44.22,"endTime":46.74,"body":"reality for so many of our"},{"speaker":"Ashley","startTime":44.22,"endTime":46.74,"body":"teachers."},{"speaker":"Pam","startTime":46.98,"endTime":47.4,"body":"Yeah, absolutely."},{"speaker":"Ashley","startTime":47.4,"endTime":50.85,"body":"This one is for you,"},{"speaker":"Ashley","startTime":47.4,"endTime":50.85,"body":"leaders, and coaches, and"},{"speaker":"Ashley","startTime":50.85,"endTime":54.75,"body":"administrators, on behalf of"},{"speaker":"Ashley","startTime":50.85,"endTime":54.75,"body":"teachers everywhere. So,"},{"speaker":"Ashley","startTime":54.75,"endTime":57.72,"body":"teachers have come to us saying"},{"speaker":"Ashley","startTime":54.75,"endTime":57.72,"body":"that they're working on building"},{"speaker":"Ashley","startTime":57.72,"endTime":60.72,"body":"a quote \"Math is"},{"speaker":"Ashley","startTime":57.72,"endTime":60.72,"body":"Figure-Out-Able\" classroom or we"},{"speaker":"Ashley","startTime":60.72,"endTime":63.6,"body":"could say a mathematizing"},{"speaker":"Ashley","startTime":60.72,"endTime":63.6,"body":"classroom. Where they have"},{"speaker":"Ashley","startTime":64.08,"endTime":68.31,"body":"students experience more and"},{"speaker":"Ashley","startTime":64.08,"endTime":68.31,"body":"more mathematics but also have"},{"speaker":"Ashley","startTime":68.31,"endTime":70.98,"body":"to be careful because they are"},{"speaker":"Ashley","startTime":68.31,"endTime":70.98,"body":"very aware that they have"},{"speaker":"Ashley","startTime":70.98,"endTime":74.01,"body":"administrators who will be doing"},{"speaker":"Ashley","startTime":70.98,"endTime":74.01,"body":"walkthroughs and they'll be"},{"speaker":"Ashley","startTime":74.01,"endTime":78.48,"body":"getting evaluated. And we have"},{"speaker":"Ashley","startTime":74.01,"endTime":78.48,"body":"heard, \"If only my admin or my"},{"speaker":"Ashley","startTime":78.48,"endTime":80.91,"body":"coach knew what I was trying to"},{"speaker":"Ashley","startTime":78.48,"endTime":80.91,"body":"do here.\""},{"speaker":"Pam","startTime":81.6,"endTime":84.63,"body":"Yeah, we have heard loud"},{"speaker":"Pam","startTime":81.6,"endTime":84.63,"body":"and clear from so many teachers"},{"speaker":"Pam","startTime":84.63,"endTime":89.67,"body":"that we really respect that if"},{"speaker":"Pam","startTime":84.63,"endTime":89.67,"body":"we can help administrators, and"},{"speaker":"Pam","startTime":89.67,"endTime":94.74,"body":"coaches, and anyone who's in"},{"speaker":"Pam","startTime":89.67,"endTime":94.74,"body":"sort of a position of doing an"},{"speaker":"Pam","startTime":94.74,"endTime":99.54,"body":"evaluation or helping teachers"},{"speaker":"Pam","startTime":94.74,"endTime":99.54,"body":"become better at their craft. If"},{"speaker":"Pam","startTime":99.54,"endTime":102.72,"body":"we could help them understand"},{"speaker":"Pam","startTime":99.54,"endTime":102.72,"body":"what are the kinds of things"},{"speaker":"Pam","startTime":102.72,"endTime":106.53,"body":"that you would see in a"},{"speaker":"Pam","startTime":102.72,"endTime":106.53,"body":"mathematizing classroom? What"},{"speaker":"Pam","startTime":106.53,"endTime":109.29,"body":"are the things that you want to"},{"speaker":"Pam","startTime":106.53,"endTime":109.29,"body":"see, and how could you actually"},{"speaker":"Pam","startTime":109.29,"endTime":113.1,"body":"help teachers get better at"},{"speaker":"Pam","startTime":109.29,"endTime":113.1,"body":"their craft in a way that's"},{"speaker":"Pam","startTime":113.13,"endTime":117.54,"body":"helpful and purposeful and not"},{"speaker":"Pam","startTime":113.13,"endTime":117.54,"body":"less helpful because you don't"},{"speaker":"Pam","startTime":117.54,"endTime":121.98,"body":"understand what the teacher's"},{"speaker":"Pam","startTime":117.54,"endTime":121.98,"body":"going for/where we're heading in"},{"speaker":"Pam","startTime":121.98,"endTime":124.74,"body":"a mathematizing or Math is"},{"speaker":"Pam","startTime":121.98,"endTime":124.74,"body":"Figure-Out-Able classroom?"},{"speaker":"Pam","startTime":124.74,"endTime":129.15,"body":"Totally. Often, we hear of"},{"speaker":"Pam","startTime":124.74,"endTime":129.15,"body":"instances. And for sure, Kim,"},{"speaker":"Pam","startTime":129.15,"endTime":132.12,"body":"you and I both had it when we"},{"speaker":"Pam","startTime":129.15,"endTime":132.12,"body":"were in the classroom. We had a"},{"speaker":"Pam","startTime":132.15,"endTime":136.95,"body":"sort of checklist systems where"},{"speaker":"Pam","startTime":132.15,"endTime":136.95,"body":"whoever was evaluating us would"},{"speaker":"Pam","startTime":136.95,"endTime":140.43,"body":"come through, and they had a"},{"speaker":"Pam","startTime":136.95,"endTime":140.43,"body":"certain kind of list of things"},{"speaker":"Pam","startTime":140.43,"endTime":144.6,"body":"that they were looking for. I"},{"speaker":"Pam","startTime":140.43,"endTime":144.6,"body":"had one principal that would"},{"speaker":"Pam","startTime":144.6,"endTime":147.9,"body":"script everything I did, but"},{"speaker":"Pam","startTime":144.6,"endTime":147.9,"body":"then he would go back and label"},{"speaker":"Pam","startTime":147.9,"endTime":150.48,"body":"everything according to a"},{"speaker":"Pam","startTime":147.9,"endTime":150.48,"body":"certain checklist. I had a"},{"speaker":"Pam","startTime":150.48,"endTime":154.2,"body":"different principal that had a"},{"speaker":"Pam","startTime":150.48,"endTime":154.2,"body":"real short checklist system."},{"speaker":"Pam","startTime":154.2,"endTime":156.42,"body":"There were just a few things"},{"speaker":"Pam","startTime":154.2,"endTime":156.42,"body":"that he was looking for at"},{"speaker":"Pam","startTime":156.42,"endTime":160.17,"body":"certain times, and sometimes"},{"speaker":"Pam","startTime":156.42,"endTime":160.17,"body":"that list would change. But I"},{"speaker":"Pam","startTime":160.17,"endTime":164.43,"body":"didn't have input into that"},{"speaker":"Pam","startTime":160.17,"endTime":164.43,"body":"list. Many of our teachers don't"},{"speaker":"Pam","startTime":164.43,"endTime":166.77,"body":"have input in the list. Many of"},{"speaker":"Pam","startTime":164.43,"endTime":166.77,"body":"our principals and"},{"speaker":"Pam","startTime":166.77,"endTime":169.92,"body":"administrators don't necessarily"},{"speaker":"Pam","startTime":166.77,"endTime":169.92,"body":"have input in that list. But if"},{"speaker":"Pam","startTime":169.92,"endTime":173.88,"body":"we had a way of having some"},{"speaker":"Pam","startTime":169.92,"endTime":173.88,"body":"common understandings of the"},{"speaker":"Pam","startTime":174.12,"endTime":178.35,"body":"goals of a Math is"},{"speaker":"Pam","startTime":174.12,"endTime":178.35,"body":"Figure-Out-Able teacher, I think"},{"speaker":"Pam","startTime":178.35,"endTime":183.0,"body":"we could all help each other"},{"speaker":"Pam","startTime":178.35,"endTime":183.0,"body":"understand how we can handle"},{"speaker":"Pam","startTime":183.0,"endTime":185.22,"body":"this. It's going to happen."},{"speaker":"Ashley","startTime":185.82,"endTime":186.18,"body":"Sure."},{"speaker":"Pam","startTime":186.57,"endTime":189.21,"body":"We're realistic. We're not"},{"speaker":"Pam","startTime":186.57,"endTime":189.21,"body":"saying, \"So, no more"},{"speaker":"Pam","startTime":189.21,"endTime":191.58,"body":"evaluation.\" Like, that's not"},{"speaker":"Pam","startTime":189.21,"endTime":191.58,"body":"even helpful. We're not"},{"speaker":"Pam","startTime":191.58,"endTime":194.79,"body":"suggesting it would be helpful"},{"speaker":"Pam","startTime":191.58,"endTime":194.79,"body":"to not evaluate. We actually"},{"speaker":"Pam","startTime":194.79,"endTime":198.21,"body":"want your help. We want to"},{"speaker":"Pam","startTime":194.79,"endTime":198.21,"body":"invite you that we can have a"},{"speaker":"Pam","startTime":198.21,"endTime":202.59,"body":"more productive help if we all"},{"speaker":"Pam","startTime":198.21,"endTime":202.59,"body":"have a more common understanding"},{"speaker":"Pam","startTime":202.83,"endTime":206.58,"body":"of what things mean... That's"},{"speaker":"Pam","startTime":202.83,"endTime":206.58,"body":"not quite the way I want to say"},{"speaker":"Pam","startTime":206.58,"endTime":210.54,"body":"that. Of what we are hoping for,"},{"speaker":"Pam","startTime":206.58,"endTime":210.54,"body":"and aiming for, and working"},{"speaker":"Pam","startTime":210.54,"endTime":212.67,"body":"toward. That's probably the best"},{"speaker":"Pam","startTime":210.54,"endTime":212.67,"body":"word I could say. What we're"},{"speaker":"Pam","startTime":212.67,"endTime":215.79,"body":"working toward in a math is"},{"speaker":"Pam","startTime":212.67,"endTime":215.79,"body":"Figure-Out-Able classroom. So,"},{"speaker":"Pam","startTime":215.79,"endTime":220.5,"body":"our goal is to help you"},{"speaker":"Pam","startTime":215.79,"endTime":220.5,"body":"understand what you might see or"},{"speaker":"Pam","startTime":220.5,"endTime":224.49,"body":"want to see in that Math is"},{"speaker":"Pam","startTime":220.5,"endTime":224.49,"body":"Figure-Out-Able, mathematizing"},{"speaker":"Pam","startTime":224.52,"endTime":229.56,"body":"classroom. And to do that, we"},{"speaker":"Pam","startTime":224.52,"endTime":229.56,"body":"are going to focus on the NCTM,"},{"speaker":"Pam","startTime":229.59,"endTime":234.36,"body":"effective teaching practices."},{"speaker":"Pam","startTime":229.59,"endTime":234.36,"body":"But we might do it with a little"},{"speaker":"Pam","startTime":234.36,"endTime":237.27,"body":"bit of a twist. So, if you're a"},{"speaker":"Pam","startTime":234.36,"endTime":237.27,"body":"leader out there, and you just"},{"speaker":"Pam","startTime":237.27,"endTime":241.08,"body":"tuned out. You're like, \"Oh,"},{"speaker":"Pam","startTime":237.27,"endTime":241.08,"body":"I've seen those.\" Maybe stay."},{"speaker":"Pam","startTime":241.29,"endTime":244.5,"body":"Stay focused a little bit. We're"},{"speaker":"Pam","startTime":241.29,"endTime":244.5,"body":"going to give you, definitely,"},{"speaker":"Pam","startTime":244.5,"endTime":249.15,"body":"our Math is Figure-Out-Able bent"},{"speaker":"Pam","startTime":244.5,"endTime":249.15,"body":"on those effective teaching"},{"speaker":"Pam","startTime":249.15,"endTime":251.79,"body":"practices. So, let's do it."},{"speaker":"Ashley","startTime":252.06,"endTime":254.31,"body":"So, there are eight"},{"speaker":"Ashley","startTime":252.06,"endTime":254.31,"body":"practices, and we're going to"},{"speaker":"Ashley","startTime":254.31,"endTime":258.72,"body":"take just a minute to talk about"},{"speaker":"Ashley","startTime":254.31,"endTime":258.72,"body":"each one of those and what we"},{"speaker":"Ashley","startTime":258.75,"endTime":260.46,"body":"think that they mean. So, the"},{"speaker":"Ashley","startTime":258.75,"endTime":260.46,"body":"first one..."},{"speaker":"Pam","startTime":260.459,"endTime":262.829,"body":"Ooh, Kim. I'm sorry. Can I"},{"speaker":"Pam","startTime":260.459,"endTime":262.829,"body":"just really, really fast?"},{"speaker":"Ashley","startTime":262.98,"endTime":263.25,"body":"Yeah."},{"speaker":"Pam","startTime":263.25,"endTime":269.01,"body":"Just for a little, tiny bit"},{"speaker":"Pam","startTime":263.25,"endTime":269.01,"body":"more background. The NCTM... No,"},{"speaker":"Pam","startTime":269.04,"endTime":272.43,"body":"that's not true. The Common Core"},{"speaker":"Pam","startTime":269.04,"endTime":272.43,"body":"State Standards came out with a"},{"speaker":"Pam","startTime":272.43,"endTime":276.33,"body":"mathematical practice standards,"},{"speaker":"Pam","startTime":272.43,"endTime":276.33,"body":"which describe standards for"},{"speaker":"Pam","startTime":276.33,"endTime":279.18,"body":"students in a mathematizing,"},{"speaker":"Pam","startTime":276.33,"endTime":279.18,"body":"Math is Figure-Out-Able"},{"speaker":"Pam","startTime":279.21,"endTime":282.42,"body":"classroom, at least (unclear)."},{"speaker":"Pam","startTime":279.21,"endTime":282.42,"body":"Those are practices that we"},{"speaker":"Pam","startTime":282.42,"endTime":284.58,"body":"would want to see in a"},{"speaker":"Pam","startTime":282.42,"endTime":284.58,"body":"mathematizing, Math is"},{"speaker":"Pam","startTime":284.61,"endTime":288.84,"body":"Figure-Out-Able classroom for"},{"speaker":"Pam","startTime":284.61,"endTime":288.84,"body":"students. And then, NCTM, NCSM,"},{"speaker":"Pam","startTime":288.87,"endTime":291.72,"body":"and leadership got together and"},{"speaker":"Pam","startTime":288.87,"endTime":291.72,"body":"said, \"If those are the kinds of"},{"speaker":"Pam","startTime":291.75,"endTime":295.2,"body":"student practices we want to"},{"speaker":"Pam","startTime":291.75,"endTime":295.2,"body":"see, what are the effective"},{"speaker":"Pam","startTime":295.2,"endTime":297.75,"body":"teaching practices to make those"},{"speaker":"Pam","startTime":295.2,"endTime":297.75,"body":"happen?\""},{"speaker":"Ashley","startTime":297.84,"endTime":298.05,"body":"Yeah."},{"speaker":"Pam","startTime":298.05,"endTime":301.2,"body":"And I think that was a"},{"speaker":"Pam","startTime":298.05,"endTime":301.2,"body":"brilliant move. Well done. And"},{"speaker":"Pam","startTime":301.23,"endTime":303.63,"body":"those are the teaching practices"},{"speaker":"Pam","startTime":301.23,"endTime":303.63,"body":"that we're going to focus on"},{"speaker":"Pam","startTime":303.63,"endTime":303.93,"body":"today."},{"speaker":"Ashley","startTime":303.96,"endTime":307.41,"body":"Yeah. So, the first one"},{"speaker":"Ashley","startTime":303.96,"endTime":307.41,"body":"is \"Established mathematics"},{"speaker":"Ashley","startTime":307.41,"endTime":312.3,"body":"goals to focus on learning.\""},{"speaker":"Ashley","startTime":307.41,"endTime":312.3,"body":"Which sounds fabulous, right?"},{"speaker":"Ashley","startTime":312.3,"endTime":313.68,"body":"So, so fantastic."},{"speaker":"Pam","startTime":314.07,"endTime":314.13,"body":"Yeah."},{"speaker":"Ashley","startTime":314.13,"endTime":317.4,"body":"But what I think a lot"},{"speaker":"Ashley","startTime":314.13,"endTime":317.4,"body":"of people take that to mean is,"},{"speaker":"Ashley","startTime":317.43,"endTime":324.27,"body":"\"Let me go through my standards,"},{"speaker":"Ashley","startTime":317.43,"endTime":324.27,"body":"and let me copy down the 3.2.a"},{"speaker":"Ashley","startTime":325.26,"endTime":329.16,"body":"standard onto the board, on a"},{"speaker":"Ashley","startTime":325.26,"endTime":329.16,"body":"chart, on a flip chart, on my"},{"speaker":"Ashley","startTime":329.16,"endTime":333.72,"body":"dry erase board, and maybe read"},{"speaker":"Ashley","startTime":329.16,"endTime":333.72,"body":"it aloud, maybe just posted each"},{"speaker":"Ashley","startTime":333.72,"endTime":334.35,"body":"day.\""},{"speaker":"Pam","startTime":334.38,"endTime":337.32,"body":"Maybe make students write"},{"speaker":"Pam","startTime":334.38,"endTime":337.32,"body":"it in their notebook for the"},{"speaker":"Pam","startTime":337.32,"endTime":339.72,"body":"day. (unclear)."},{"speaker":"Ashley","startTime":340.23,"endTime":340.5,"body":"Yeah."},{"speaker":"Pam","startTime":340.5,"endTime":343.02,"body":"\"So, at the end of today, I"},{"speaker":"Pam","startTime":340.5,"endTime":343.02,"body":"will...\" And then, they kind of,"},{"speaker":"Pam","startTime":343.05,"endTime":346.2,"body":"maybe even have written that"},{"speaker":"Pam","startTime":343.05,"endTime":346.2,"body":"standard in their own \"I will\""},{"speaker":"Pam","startTime":346.2,"endTime":347.94,"body":"language, \"I can\" language."},{"speaker":"Ashley","startTime":348.06,"endTime":348.57,"body":"Yeah."},{"speaker":"Pam","startTime":348.84,"endTime":352.77,"body":"And we're suggesting that"},{"speaker":"Pam","startTime":348.84,"endTime":352.77,"body":"\"establishing mathematics goals"},{"speaker":"Pam","startTime":352.77,"endTime":356.43,"body":"to focus on learning\" is a very"},{"speaker":"Pam","startTime":352.77,"endTime":356.43,"body":"necessary and important thing"},{"speaker":"Pam","startTime":356.43,"endTime":361.44,"body":"for teachers to do to focus"},{"speaker":"Pam","startTime":356.43,"endTime":361.44,"body":"their lesson. But that does not"},{"speaker":"Pam","startTime":361.44,"endTime":366.96,"body":"translate into proclaiming that"},{"speaker":"Pam","startTime":361.44,"endTime":366.96,"body":"standard in front of students at"},{"speaker":"Pam","startTime":366.96,"endTime":371.01,"body":"the beginning of the lesson. We"},{"speaker":"Pam","startTime":366.96,"endTime":371.01,"body":"do not find those to be"},{"speaker":"Pam","startTime":371.04,"endTime":374.76,"body":"equivalent statements. So, do we"},{"speaker":"Pam","startTime":371.04,"endTime":374.76,"body":"want to help teachers establish"},{"speaker":"Pam","startTime":374.76,"endTime":379.8,"body":"goals? Absolutely. Do we want to"},{"speaker":"Pam","startTime":374.76,"endTime":379.8,"body":"force them to write that"},{"speaker":"Pam","startTime":379.83,"endTime":382.59,"body":"objective on the board at the"},{"speaker":"Pam","startTime":379.83,"endTime":382.59,"body":"beginning of the class? We are"},{"speaker":"Pam","startTime":382.59,"endTime":385.08,"body":"saying no. We're saying that"},{"speaker":"Pam","startTime":382.59,"endTime":385.08,"body":"that actually can be"},{"speaker":"Pam","startTime":385.08,"endTime":387.69,"body":"counterproductive for"},{"speaker":"Pam","startTime":385.08,"endTime":387.69,"body":"classrooms."},{"speaker":"Ashley","startTime":388.2,"endTime":393.63,"body":"Yeah. So, what it does"},{"speaker":"Ashley","startTime":388.2,"endTime":393.63,"body":"mean is that kids walk away"},{"speaker":"Ashley","startTime":393.63,"endTime":397.14,"body":"knowing what they got out of the"},{"speaker":"Ashley","startTime":393.63,"endTime":397.14,"body":"time that you spent together."},{"speaker":"Pam","startTime":397.56,"endTime":401.73,"body":"Yeah. So, let's put the"},{"speaker":"Pam","startTime":397.56,"endTime":401.73,"body":"emphasis on, we need the teacher"},{"speaker":"Pam","startTime":401.73,"endTime":405.09,"body":"to know ahead of time what the"},{"speaker":"Pam","startTime":401.73,"endTime":405.09,"body":"mathematics goal is; we need the"},{"speaker":"Pam","startTime":405.09,"endTime":409.23,"body":"student to walk out of the"},{"speaker":"Pam","startTime":405.09,"endTime":409.23,"body":"classroom being really clear on"},{"speaker":"Pam","startTime":409.68,"endTime":412.23,"body":"the objective of the day and"},{"speaker":"Pam","startTime":409.68,"endTime":412.23,"body":"what they were able to"},{"speaker":"Pam","startTime":412.23,"endTime":415.29,"body":"accomplish, what the goal was,"},{"speaker":"Pam","startTime":412.23,"endTime":415.29,"body":"and what they're maybe still"},{"speaker":"Pam","startTime":415.29,"endTime":419.76,"body":"working towards. So, the goal"},{"speaker":"Pam","startTime":415.29,"endTime":419.76,"body":"could be a work in progress. But"},{"speaker":"Pam","startTime":419.79,"endTime":423.96,"body":"we do need students to have"},{"speaker":"Pam","startTime":419.79,"endTime":423.96,"body":"clarity around the fact that"},{"speaker":"Pam","startTime":423.96,"endTime":426.57,"body":"they were working... I don't"},{"speaker":"Pam","startTime":423.96,"endTime":426.57,"body":"want to say working hard. That"},{"speaker":"Pam","startTime":426.57,"endTime":431.31,"body":"sounds like it was all about"},{"speaker":"Pam","startTime":426.57,"endTime":431.31,"body":"effort. It's not. That they were"},{"speaker":"Pam","startTime":431.31,"endTime":435.93,"body":"developing something specific"},{"speaker":"Pam","startTime":431.31,"endTime":435.93,"body":"during that class, that day. So,"},{"speaker":"Pam","startTime":436.2,"endTime":442.59,"body":"we want to maybe help leaders"},{"speaker":"Pam","startTime":436.2,"endTime":442.59,"body":"and teachers flip the timing,"},{"speaker":"Pam","startTime":443.07,"endTime":446.25,"body":"that it's not about students...."},{"speaker":"Pam","startTime":443.07,"endTime":446.25,"body":"We want students to be really"},{"speaker":"Pam","startTime":446.25,"endTime":449.13,"body":"clear they're going to learn in"},{"speaker":"Pam","startTime":446.25,"endTime":449.13,"body":"class today. But we don't want"},{"speaker":"Pam","startTime":449.13,"endTime":452.91,"body":"to... I don't want to say \"spoil"},{"speaker":"Pam","startTime":449.13,"endTime":452.91,"body":"the surprise\", Kim. Help me put"},{"speaker":"Pam","startTime":452.91,"endTime":453.75,"body":"better words around it."},{"speaker":"Ashley","startTime":454.44,"endTime":457.68,"body":"Well, there are"},{"speaker":"Ashley","startTime":454.44,"endTime":457.68,"body":"definitely some standards that"},{"speaker":"Ashley","startTime":457.77,"endTime":461.55,"body":"if you announce ahead of time,"},{"speaker":"Ashley","startTime":457.77,"endTime":461.55,"body":"\"This is what we're going to do"},{"speaker":"Ashley","startTime":461.55,"endTime":468.03,"body":"today,\" then students are"},{"speaker":"Ashley","startTime":461.55,"endTime":468.03,"body":"deprived of the opportunity."},{"speaker":"Pam","startTime":468.12,"endTime":469.11,"body":"Of the sense making."},{"speaker":"Ashley","startTime":469.14,"endTime":471.72,"body":"Of the sense making that"},{"speaker":"Ashley","startTime":469.14,"endTime":471.72,"body":"they would be doing in class."},{"speaker":"Ashley","startTime":471.72,"endTime":471.99,"body":"Yeah."},{"speaker":"Pam","startTime":472.02,"endTime":474.51,"body":"Yeah, they're deprived with"},{"speaker":"Pam","startTime":472.02,"endTime":474.51,"body":"a sense-making, and grappling,"},{"speaker":"Pam","startTime":474.51,"endTime":479.16,"body":"and by definition, learning that"},{"speaker":"Pam","startTime":474.51,"endTime":479.16,"body":"they could be doing in class."},{"speaker":"Pam","startTime":479.19,"endTime":484.86,"body":"And it will also nudge them too"},{"speaker":"Pam","startTime":479.19,"endTime":484.86,"body":"much towards just doing. \"Oh, if"},{"speaker":"Pam","startTime":484.86,"endTime":487.38,"body":"that's the thing, then I'm going"},{"speaker":"Pam","startTime":484.86,"endTime":487.38,"body":"to do it, and get an answer, and"},{"speaker":"Pam","startTime":487.38,"endTime":492.3,"body":"be done, and I'm not going to"},{"speaker":"Pam","startTime":487.38,"endTime":492.3,"body":"engage in the grappling.\" It can"},{"speaker":"Pam","startTime":492.3,"endTime":496.68,"body":"have the effect of trivializing"},{"speaker":"Pam","startTime":492.3,"endTime":496.68,"body":"and making everything too much"},{"speaker":"Pam","startTime":496.68,"endTime":500.85,"body":"about getting an answer and not"},{"speaker":"Pam","startTime":496.68,"endTime":500.85,"body":"about developing the learner as"},{"speaker":"Pam","startTime":500.85,"endTime":501.63,"body":"a mathematician."},{"speaker":"Ashley","startTime":501.66,"endTime":502.05,"body":"Yeah."},{"speaker":"Pam","startTime":502.95,"endTime":506.94,"body":"Cool. Alright. So, that was"},{"speaker":"Pam","startTime":502.95,"endTime":506.94,"body":"number one. Number two, the next"},{"speaker":"Pam","startTime":506.94,"endTime":509.97,"body":"effective teaching practice"},{"speaker":"Pam","startTime":506.94,"endTime":509.97,"body":"is... Oh, by the way. Maybe I"},{"speaker":"Pam","startTime":509.97,"endTime":512.43,"body":"should just say it. We're not"},{"speaker":"Pam","startTime":509.97,"endTime":512.43,"body":"going to fully flesh all these"},{"speaker":"Pam","startTime":512.43,"endTime":517.74,"body":"out. Our goal of this podcast is"},{"speaker":"Pam","startTime":512.43,"endTime":517.74,"body":"to give you some ideas for each"},{"speaker":"Pam","startTime":517.74,"endTime":522.18,"body":"of these essential teaching"},{"speaker":"Pam","startTime":517.74,"endTime":522.18,"body":"practices to help you, help your"},{"speaker":"Pam","startTime":522.18,"endTime":525.66,"body":"teachers become the"},{"speaker":"Pam","startTime":522.18,"endTime":525.66,"body":"mathematician, the math teacher"},{"speaker":"Pam","startTime":525.66,"endTime":528.18,"body":"they want to be. So, we're just"},{"speaker":"Pam","startTime":525.66,"endTime":528.18,"body":"going to mention the ones that"},{"speaker":"Pam","startTime":528.18,"endTime":530.55,"body":"are sparking the most for us"},{"speaker":"Pam","startTime":528.18,"endTime":530.55,"body":"right now. We're not pretending"},{"speaker":"Pam","startTime":530.55,"endTime":532.56,"body":"that we're giving all of these a"},{"speaker":"Pam","startTime":530.55,"endTime":532.56,"body":"full treatment."},{"speaker":"Ashley","startTime":532.83,"endTime":535.5,"body":"So, can I just jump in"},{"speaker":"Ashley","startTime":532.83,"endTime":535.5,"body":"real quick? So, what that means"},{"speaker":"Ashley","startTime":535.5,"endTime":538.62,"body":"for leaders, and administrators,"},{"speaker":"Ashley","startTime":535.5,"endTime":538.62,"body":"and coaches is that you might"},{"speaker":"Ashley","startTime":538.62,"endTime":542.55,"body":"have teachers who have actually"},{"speaker":"Ashley","startTime":538.62,"endTime":542.55,"body":"thought about the fact that they"},{"speaker":"Ashley","startTime":542.67,"endTime":545.85,"body":"want kids to be thinking about"},{"speaker":"Ashley","startTime":542.67,"endTime":545.85,"body":"goals for the day, but they"},{"speaker":"Ashley","startTime":545.85,"endTime":550.05,"body":"recognize that writing it on the"},{"speaker":"Ashley","startTime":545.85,"endTime":550.05,"body":"board tells them what they're"},{"speaker":"Ashley","startTime":550.05,"endTime":552.9,"body":"going to do, rather than giving"},{"speaker":"Ashley","startTime":550.05,"endTime":552.9,"body":"them the opportunity to think"},{"speaker":"Ashley","startTime":552.9,"endTime":556.11,"body":"and process. So, rather than,"},{"speaker":"Ashley","startTime":552.9,"endTime":556.11,"body":"you know, \"Ding! You didn't"},{"speaker":"Ashley","startTime":556.62,"endTime":558.42,"body":"write 3.2.a\"..."},{"speaker":"Pam","startTime":558.42,"endTime":558.63,"body":"\"...on the board.\""},{"speaker":"Ashley","startTime":558.63,"endTime":562.74,"body":"Right. Maybe a"},{"speaker":"Ashley","startTime":558.63,"endTime":562.74,"body":"conversation will help give you"},{"speaker":"Ashley","startTime":562.74,"endTime":564.42,"body":"a vision for why they didn't."},{"speaker":"Pam","startTime":565.11,"endTime":567.54,"body":"Ah, so in other words,"},{"speaker":"Pam","startTime":565.11,"endTime":567.54,"body":"we're encouraging leaders, have"},{"speaker":"Pam","startTime":567.54,"endTime":570.78,"body":"the conversation with teachers."},{"speaker":"Pam","startTime":567.54,"endTime":570.78,"body":"\"Tell me about your goal for the"},{"speaker":"Pam","startTime":570.78,"endTime":571.05,"body":"day.\""},{"speaker":"Pam","startTime":571.0,"endTime":574.54,"body":"\"Help me understand that"},{"speaker":"Pam","startTime":571.0,"endTime":574.54,"body":"you had established a"},{"speaker":"Ashley","startTime":571.05,"endTime":571.26,"body":"Yeah."},{"speaker":"Ashley","startTime":574.54,"endTime":578.17,"body":"mathematics goal for this"},{"speaker":"Ashley","startTime":574.54,"endTime":578.17,"body":"lesson.\" Cool. And then, how are"},{"speaker":"Ashley","startTime":578.17,"endTime":580.6,"body":"students going to walk out of"},{"speaker":"Ashley","startTime":578.17,"endTime":580.6,"body":"here being clear on that goal?"},{"speaker":"Ashley","startTime":581.59,"endTime":586.27,"body":"Yeah, nice. Alright. Number two"},{"speaker":"Ashley","startTime":581.59,"endTime":586.27,"body":"\"Implement tasks that promote"},{"speaker":"Ashley","startTime":586.27,"endTime":587.74,"body":"reasoning and problem solving.\""},{"speaker":"Ashley","startTime":588.21,"endTime":590.37,"body":"Mm, that's a good one."},{"speaker":"Pam","startTime":590.7,"endTime":591.75,"body":"We like that one a lot."},{"speaker":"Both Pam and Kim","startTime":591.75,"endTime":592.44,"body":"Yeah."},{"speaker":"Pam","startTime":592.92,"endTime":595.38,"body":"But we also recognize it's"},{"speaker":"Pam","startTime":592.92,"endTime":595.38,"body":"not trivial. It's not trivial"},{"speaker":"Pam","startTime":595.38,"endTime":598.83,"body":"for teachers to find those"},{"speaker":"Pam","startTime":595.38,"endTime":598.83,"body":"tasks. It's also not trivial for"},{"speaker":"Pam","startTime":598.86,"endTime":605.61,"body":"administrators, evaluators to"},{"speaker":"Pam","startTime":598.86,"endTime":605.61,"body":"evaluate the task itself. So,"},{"speaker":"Pam","startTime":605.61,"endTime":608.58,"body":"that also might benefit from a"},{"speaker":"Pam","startTime":605.61,"endTime":608.58,"body":"conversation about why"},{"speaker":"Pam","startTime":608.61,"endTime":614.52,"body":"particular tasks were chosen."},{"speaker":"Pam","startTime":608.61,"endTime":614.52,"body":"Especially in what way were they"},{"speaker":"Pam","startTime":614.52,"endTime":616.86,"body":"going to lead towards that"},{"speaker":"Pam","startTime":614.52,"endTime":616.86,"body":"established goal that we just"},{"speaker":"Pam","startTime":616.86,"endTime":620.34,"body":"talked about. Yeah. We would"},{"speaker":"Pam","startTime":616.86,"endTime":620.34,"body":"suggest that a thing that you'd"},{"speaker":"Pam","startTime":620.34,"endTime":624.63,"body":"be looking for is, that it's not"},{"speaker":"Pam","startTime":620.34,"endTime":624.63,"body":"about direct teaching. Now, I've"},{"speaker":"Pam","startTime":624.63,"endTime":627.33,"body":"been reading some tweets lately"},{"speaker":"Pam","startTime":624.63,"endTime":627.33,"body":"that... I'm so clear that"},{"speaker":"Pam","startTime":627.33,"endTime":630.9,"body":"language is so tricky because"},{"speaker":"Pam","startTime":627.33,"endTime":630.9,"body":"there are some bright,"},{"speaker":"Pam","startTime":630.93,"endTime":634.32,"body":"articulate people who are"},{"speaker":"Pam","startTime":630.93,"endTime":634.32,"body":"pushing back on the pushback on"},{"speaker":"Pam","startTime":634.32,"endTime":637.29,"body":"direct teaching. Because they've"},{"speaker":"Pam","startTime":634.32,"endTime":637.29,"body":"said, \"Well, it depends on what"},{"speaker":"Pam","startTime":637.29,"endTime":640.14,"body":"you mean by direct teaching.\""},{"speaker":"Pam","startTime":637.29,"endTime":640.14,"body":"So, it does. It absolutely does."},{"speaker":"Pam","startTime":640.44,"endTime":645.03,"body":"We are suggesting that it's not"},{"speaker":"Pam","startTime":640.44,"endTime":645.03,"body":"about giving students a"},{"speaker":"Pam","startTime":645.63,"endTime":650.07,"body":"step-by-step procedure that you"},{"speaker":"Pam","startTime":645.63,"endTime":650.07,"body":"clearly outline, \"This is what"},{"speaker":"Pam","startTime":650.07,"endTime":654.87,"body":"you do. Here, here, here. Now,"},{"speaker":"Pam","startTime":650.07,"endTime":654.87,"body":"go practice it 29 times.\" That"},{"speaker":"Pam","startTime":655.23,"endTime":657.93,"body":"does not fulfill the effective"},{"speaker":"Pam","startTime":655.23,"endTime":657.93,"body":"teaching practice of"},{"speaker":"Pam","startTime":657.93,"endTime":660.24,"body":"implementing tasks that promote"},{"speaker":"Pam","startTime":657.93,"endTime":660.24,"body":"reasoning and problem solving."},{"speaker":"Pam","startTime":661.5,"endTime":667.05,"body":"We would look for kids"},{"speaker":"Pam","startTime":661.5,"endTime":667.05,"body":"grappling. We would look for"},{"speaker":"Pam","startTime":667.05,"endTime":673.32,"body":"kids working together. We would"},{"speaker":"Pam","startTime":667.05,"endTime":673.32,"body":"look for kids mimicking and say"},{"speaker":"Pam","startTime":673.32,"endTime":676.89,"body":"that's not a good... if we see"},{"speaker":"Pam","startTime":673.32,"endTime":676.89,"body":"mimicking, then we don't"},{"speaker":"Pam","startTime":676.89,"endTime":680.97,"body":"(unclear) the task hit the"},{"speaker":"Pam","startTime":676.89,"endTime":680.97,"body":"target. Is there anything you'd"},{"speaker":"Pam","startTime":680.97,"endTime":681.51,"body":"add to that?"},{"speaker":"Ashley","startTime":682.44,"endTime":686.07,"body":"Yeah. I would say that"},{"speaker":"Ashley","startTime":682.44,"endTime":686.07,"body":"if kids are really problem"},{"speaker":"Ashley","startTime":686.07,"endTime":691.53,"body":"solving, that's messy work, and"},{"speaker":"Ashley","startTime":686.07,"endTime":691.53,"body":"so there's probably going to be"},{"speaker":"Ashley","startTime":691.53,"endTime":694.41,"body":"some conversations. This might"},{"speaker":"Ashley","startTime":691.53,"endTime":694.41,"body":"come up again later. But some"},{"speaker":"Ashley","startTime":694.41,"endTime":698.79,"body":"conversations and some... You"},{"speaker":"Ashley","startTime":694.41,"endTime":698.79,"body":"said \"grappling\", but it might"},{"speaker":"Ashley","startTime":698.79,"endTime":703.83,"body":"not be so cleanly tied up with a"},{"speaker":"Ashley","startTime":698.79,"endTime":703.83,"body":"bow at the end of your five"},{"speaker":"Ashley","startTime":703.83,"endTime":708.24,"body":"minute bell ring, ding time. So,"},{"speaker":"Ashley","startTime":703.83,"endTime":708.24,"body":"like, some of it will spill"},{"speaker":"Ashley","startTime":708.24,"endTime":712.98,"body":"over. Some of it will provide"},{"speaker":"Ashley","startTime":708.24,"endTime":712.98,"body":"conversation. And that's"},{"speaker":"Ashley","startTime":713.43,"endTime":714.33,"body":"perfectly fine."},{"speaker":"Pam","startTime":714.42,"endTime":714.87,"body":"It's desirable."},{"speaker":"Ashley","startTime":714.93,"endTime":717.93,"body":"It's expected and"},{"speaker":"Ashley","startTime":714.93,"endTime":717.93,"body":"desirable."},{"speaker":"Pam","startTime":718.29,"endTime":721.2,"body":"And so, when we said that"},{"speaker":"Pam","startTime":718.29,"endTime":721.2,"body":"we want students to walk out at"},{"speaker":"Pam","startTime":721.2,"endTime":724.83,"body":"the end of the class being clear"},{"speaker":"Pam","startTime":721.2,"endTime":724.83,"body":"on what they learned, that might"},{"speaker":"Pam","startTime":724.83,"endTime":727.89,"body":"not be them saying \"I learned"},{"speaker":"Pam","startTime":724.83,"endTime":727.89,"body":"this procedure.\""},{"speaker":"Ashley","startTime":728.22,"endTime":728.55,"body":"Yeah."},{"speaker":"Pam","startTime":728.58,"endTime":730.5,"body":"We don't want it to be, \"I"},{"speaker":"Pam","startTime":728.58,"endTime":730.5,"body":"learned this procedure\" or \"I"},{"speaker":"Pam","startTime":730.53,"endTime":734.19,"body":"mimicked such and such.\" But it"},{"speaker":"Pam","startTime":730.53,"endTime":734.19,"body":"also might not. They might be"},{"speaker":"Pam","startTime":734.19,"endTime":736.59,"body":"able to say, \"I worked on this"},{"speaker":"Pam","startTime":734.19,"endTime":736.59,"body":"problem, and I worked hard on"},{"speaker":"Pam","startTime":736.59,"endTime":738.87,"body":"it, and there are some things"},{"speaker":"Pam","startTime":736.59,"endTime":738.87,"body":"that I'm grappling with about"},{"speaker":"Pam","startTime":738.87,"endTime":739.44,"body":"that problem.\""},{"speaker":"Ashley","startTime":739.56,"endTime":739.92,"body":"Yeah."},{"speaker":"Pam","startTime":740.22,"endTime":744.75,"body":"That could be not only"},{"speaker":"Pam","startTime":740.22,"endTime":744.75,"body":"acceptable, but a desirable"},{"speaker":"Pam","startTime":744.75,"endTime":748.56,"body":"outcome. At some point, yes,"},{"speaker":"Pam","startTime":744.75,"endTime":748.56,"body":"there'll be closure on that"},{"speaker":"Pam","startTime":748.56,"endTime":752.1,"body":"problem. But it might not be in"},{"speaker":"Pam","startTime":748.56,"endTime":752.1,"body":"that part of the lesson that you"},{"speaker":"Pam","startTime":752.28,"endTime":757.02,"body":"observed that day. But it would"},{"speaker":"Pam","startTime":752.28,"endTime":757.02,"body":"be good to have a conversation"},{"speaker":"Pam","startTime":757.02,"endTime":759.42,"body":"with the teacher. \"You know, I"},{"speaker":"Pam","startTime":757.02,"endTime":759.42,"body":"noticed that students left here"},{"speaker":"Pam","startTime":759.45,"endTime":762.15,"body":"still grappling with some"},{"speaker":"Pam","startTime":759.45,"endTime":762.15,"body":"things. Tell me about that.\" And"},{"speaker":"Pam","startTime":762.15,"endTime":765.81,"body":"then, that becomes a"},{"speaker":"Pam","startTime":762.15,"endTime":765.81,"body":"conversation that I think could"},{"speaker":"Pam","startTime":765.81,"endTime":767.7,"body":"be really productive for"},{"speaker":"Pam","startTime":765.81,"endTime":767.7,"body":"everyone."},{"speaker":"Ashley","startTime":768.12,"endTime":773.61,"body":"Yeah. Okay, number three"},{"speaker":"Ashley","startTime":768.12,"endTime":773.61,"body":"is \"To use and connect"},{"speaker":"Ashley","startTime":773.67,"endTime":775.65,"body":"mathematical representations.\""},{"speaker":"Pam","startTime":776.76,"endTime":782.34,"body":"Love! Models and modeling"},{"speaker":"Pam","startTime":776.76,"endTime":782.34,"body":"is such a huge thing for us."},{"speaker":"Pam","startTime":782.34,"endTime":785.91,"body":"Making thinking visible. We say"},{"speaker":"Pam","startTime":782.34,"endTime":785.91,"body":"that a lot. And maybe we'll just"},{"speaker":"Pam","startTime":786.42,"endTime":791.43,"body":"leave it at that. In a"},{"speaker":"Pam","startTime":786.42,"endTime":791.43,"body":"mathematizing, Math is"},{"speaker":"Pam","startTime":791.46,"endTime":795.06,"body":"Figure-Out-Able classroom, there"},{"speaker":"Pam","startTime":791.46,"endTime":795.06,"body":"should be modeling of thinking,"},{"speaker":"Pam","startTime":795.06,"endTime":796.95,"body":"making thinking visible. Yep."},{"speaker":"Ashley","startTime":796.95,"endTime":797.34,"body":"Yeah."},{"speaker":"Ashley","startTime":797.49,"endTime":801.18,"body":"I appreciate especially that"},{"speaker":"Ashley","startTime":797.49,"endTime":801.18,"body":"connection, the word \"connect"},{"speaker":"Ashley","startTime":801.3,"endTime":805.41,"body":"mathematical representations\"."},{"speaker":"Ashley","startTime":801.3,"endTime":805.41,"body":"Because it's not just about,"},{"speaker":"Ashley","startTime":806.22,"endTime":808.05,"body":"\"What's the one way you solved"},{"speaker":"Ashley","startTime":806.22,"endTime":808.05,"body":"it, and the one way you"},{"speaker":"Ashley","startTime":808.05,"endTime":812.31,"body":"represented it,\" but the"},{"speaker":"Ashley","startTime":808.05,"endTime":812.31,"body":"connection between student"},{"speaker":"Ashley","startTime":812.31,"endTime":816.81,"body":"thinking and seeing their"},{"speaker":"Ashley","startTime":812.31,"endTime":816.81,"body":"thinking in other people's work"},{"speaker":"Ashley","startTime":816.84,"endTime":820.65,"body":"that's so valuable. I think"},{"speaker":"Ashley","startTime":816.84,"endTime":820.65,"body":"maybe it doesn't get enough"},{"speaker":"Ashley","startTime":820.74,"endTime":821.28,"body":"credit."},{"speaker":"Pam","startTime":821.46,"endTime":824.28,"body":"Yeah, and similarly but"},{"speaker":"Pam","startTime":821.46,"endTime":824.28,"body":"slightly different is, it's not"},{"speaker":"Pam","startTime":824.28,"endTime":826.8,"body":"just about multiple"},{"speaker":"Pam","startTime":824.28,"endTime":826.8,"body":"representations. It's about the"},{"speaker":"Pam","startTime":826.8,"endTime":828.9,"body":"connections between multiple"},{"speaker":"Pam","startTime":826.8,"endTime":828.9,"body":"representations."},{"speaker":"Ashley","startTime":828.93,"endTime":829.32,"body":"Yeah."},{"speaker":"Pam","startTime":829.47,"endTime":832.8,"body":"Nice. Cool. Alright. The"},{"speaker":"Pam","startTime":829.47,"endTime":832.8,"body":"next one. Number four:"},{"speaker":"Pam","startTime":832.83,"endTime":835.86,"body":"\"Facilitate meaningful"},{"speaker":"Pam","startTime":832.83,"endTime":835.86,"body":"mathematical discourse\". Which"},{"speaker":"Pam","startTime":835.86,"endTime":838.29,"body":"you kind of brought up just a"},{"speaker":"Pam","startTime":835.86,"endTime":838.29,"body":"minute ago, Kim. Yeah."},{"speaker":"Pam","startTime":839.16,"endTime":839.7,"body":"Definitely."},{"speaker":"Ashley","startTime":839.88,"endTime":845.43,"body":"Discourse is so valuable"},{"speaker":"Ashley","startTime":839.88,"endTime":845.43,"body":"as a mathematician. And, you"},{"speaker":"Ashley","startTime":845.43,"endTime":848.34,"body":"know, we spend so much time, I"},{"speaker":"Ashley","startTime":845.43,"endTime":848.34,"body":"think, hearing about what"},{"speaker":"Ashley","startTime":848.34,"endTime":852.48,"body":"classrooms should look like. And"},{"speaker":"Ashley","startTime":848.34,"endTime":852.48,"body":"you and I are both not really"},{"speaker":"Ashley","startTime":852.48,"endTime":856.86,"body":"into compliance necessarily. You"},{"speaker":"Ashley","startTime":852.48,"endTime":856.86,"body":"know, we like community. And"},{"speaker":"Ashley","startTime":856.86,"endTime":860.97,"body":"kids want to be a part of the"},{"speaker":"Ashley","startTime":856.86,"endTime":860.97,"body":"community when we set those up"},{"speaker":"Ashley","startTime":861.09,"endTime":865.02,"body":"meaningful. And this \"meaningful"},{"speaker":"Ashley","startTime":861.09,"endTime":865.02,"body":"mathematical discourse\" does not"},{"speaker":"Ashley","startTime":865.02,"endTime":867.9,"body":"mean, you know, there's"},{"speaker":"Ashley","startTime":865.02,"endTime":867.9,"body":"arguments or there's, you know,"},{"speaker":"Ashley","startTime":867.93,"endTime":873.21,"body":"a riot happening. But kids"},{"speaker":"Ashley","startTime":867.93,"endTime":873.21,"body":"justifying their thinking, and"},{"speaker":"Ashley","startTime":873.24,"endTime":879.51,"body":"arguing their points, and"},{"speaker":"Ashley","startTime":873.24,"endTime":879.51,"body":"ruminating on what's going on in"},{"speaker":"Ashley","startTime":879.51,"endTime":882.63,"body":"their heads, and then grappling"},{"speaker":"Ashley","startTime":879.51,"endTime":882.63,"body":"with it out loud to others."},{"speaker":"Ashley","startTime":883.53,"endTime":886.2,"body":"Learning is happening in all"},{"speaker":"Ashley","startTime":883.53,"endTime":886.2,"body":"that."},{"speaker":"Pam","startTime":886.41,"endTime":888.87,"body":"Absolutely. And if you'd"},{"speaker":"Pam","startTime":886.41,"endTime":888.87,"body":"like more on that, we have an"},{"speaker":"Pam","startTime":888.87,"endTime":891.87,"body":"episode on Do, Say, Represent"},{"speaker":"Pam","startTime":888.87,"endTime":891.87,"body":"where we really talk about"},{"speaker":"Pam","startTime":892.77,"endTime":897.3,"body":"acquisition of language, and how"},{"speaker":"Pam","startTime":892.77,"endTime":897.3,"body":"language can help learning"},{"speaker":"Pam","startTime":897.33,"endTime":900.33,"body":"occur, and how it's the"},{"speaker":"Pam","startTime":897.33,"endTime":900.33,"body":"grappling with being able to put"},{"speaker":"Pam","startTime":900.33,"endTime":905.22,"body":"things into words that can. And"},{"speaker":"Pam","startTime":900.33,"endTime":905.22,"body":"then, representing that thinking"},{"speaker":"Pam","startTime":905.25,"endTime":909.57,"body":"and that process of... Well, we"},{"speaker":"Pam","startTime":905.25,"endTime":909.57,"body":"call it Do, Say, Represent. So"},{"speaker":"Pam","startTime":909.63,"endTime":912.3,"body":"(unclear) check out that"},{"speaker":"Pam","startTime":909.63,"endTime":912.3,"body":"episode, if you'd like more on"},{"speaker":"Pam","startTime":912.3,"endTime":915.0,"body":"why mathematical discourse is so"},{"speaker":"Pam","startTime":912.3,"endTime":915.0,"body":"important."},{"speaker":"Ashley","startTime":915.27,"endTime":915.54,"body":"Yeah."},{"speaker":"Pam","startTime":915.54,"endTime":915.96,"body":"Cool."},{"speaker":"Ashley","startTime":916.2,"endTime":919.68,"body":"Alright. The next one is"},{"speaker":"Ashley","startTime":916.2,"endTime":919.68,"body":"\"posing purposeful questions\"."},{"speaker":"Pam","startTime":920.34,"endTime":923.61,"body":"Yeah, that has been"},{"speaker":"Pam","startTime":920.34,"endTime":923.61,"body":"something that I've been"},{"speaker":"Pam","startTime":923.61,"endTime":926.79,"body":"thinking about for a very long"},{"speaker":"Pam","startTime":923.61,"endTime":926.79,"body":"time. I was always very"},{"speaker":"Pam","startTime":926.79,"endTime":929.97,"body":"interested in better questioning"},{"speaker":"Pam","startTime":926.79,"endTime":929.97,"body":"even before I knew about Real"},{"speaker":"Pam","startTime":929.97,"endTime":933.12,"body":"Math. But then, when I dove into"},{"speaker":"Pam","startTime":929.97,"endTime":933.12,"body":"the research, and into my kids"},{"speaker":"Pam","startTime":933.12,"endTime":936.0,"body":"classrooms, and figured out what"},{"speaker":"Pam","startTime":933.12,"endTime":936.0,"body":"it meant to do real math, all of"},{"speaker":"Pam","startTime":936.0,"endTime":942.0,"body":"a sudden, questions became this"},{"speaker":"Pam","startTime":936.0,"endTime":942.0,"body":"whole other gamut of, it's not"},{"speaker":"Pam","startTime":942.0,"endTime":945.48,"body":"just about me questioning you"},{"speaker":"Pam","startTime":942.0,"endTime":945.48,"body":"through a procedure; it's not"},{"speaker":"Pam","startTime":945.48,"endTime":948.3,"body":"just me questioning to see if"},{"speaker":"Pam","startTime":945.48,"endTime":948.3,"body":"you got the thing that I was"},{"speaker":"Pam","startTime":948.3,"endTime":951.48,"body":"having you mimic. In fact, it's"},{"speaker":"Pam","startTime":948.3,"endTime":951.48,"body":"not those things at all. Now,"},{"speaker":"Pam","startTime":951.48,"endTime":955.35,"body":"it's me questioning, so that you"},{"speaker":"Pam","startTime":951.48,"endTime":955.35,"body":"learn through the questioning."},{"speaker":"Pam","startTime":956.16,"endTime":958.35,"body":"It has everything to do with"},{"speaker":"Pam","startTime":956.16,"endTime":958.35,"body":"that discourse that we just"},{"speaker":"Pam","startTime":958.35,"endTime":962.49,"body":"talked about. Yeah. Kim, you"},{"speaker":"Pam","startTime":958.35,"endTime":962.49,"body":"wanted to say something about"},{"speaker":"Pam","startTime":962.52,"endTime":963.9,"body":"\"funneling\"? Do you remember"},{"speaker":"Pam","startTime":962.52,"endTime":963.9,"body":"what you were going to say about"},{"speaker":"Pam","startTime":963.9,"endTime":964.14,"body":"that?"},{"speaker":"Ashley","startTime":964.23,"endTime":966.84,"body":"Oh, gosh, no, I don't"},{"speaker":"Ashley","startTime":964.23,"endTime":966.84,"body":"think I do."},{"speaker":"Pam","startTime":966.84,"endTime":969.27,"body":"I think we were talking"},{"speaker":"Pam","startTime":966.84,"endTime":969.27,"body":"about the difference between."},{"speaker":"Pam","startTime":969.27,"endTime":973.56,"body":"And NCTM in the discussion about"},{"speaker":"Pam","startTime":969.27,"endTime":973.56,"body":"these standards does a very nice"},{"speaker":"Pam","startTime":973.56,"endTime":976.86,"body":"job of parsing out focusing"},{"speaker":"Pam","startTime":973.56,"endTime":976.86,"body":"questions versus funneling"},{"speaker":"Pam","startTime":976.86,"endTime":980.13,"body":"questions. Which actually, the"},{"speaker":"Pam","startTime":976.86,"endTime":980.13,"body":"first time I had seen that I was"},{"speaker":"Pam","startTime":980.13,"endTime":983.61,"body":"a young, super young teacher. I"},{"speaker":"Pam","startTime":980.13,"endTime":983.61,"body":"just started teaching. And it"},{"speaker":"Pam","startTime":983.61,"endTime":987.36,"body":"had come out in an article in"},{"speaker":"Pam","startTime":983.61,"endTime":987.36,"body":"The Mathematics Teacher, where"},{"speaker":"Pam","startTime":987.36,"endTime":990.87,"body":"they had parsed out those two,"},{"speaker":"Pam","startTime":987.36,"endTime":990.87,"body":"is where I really began thinking"},{"speaker":"Pam","startTime":990.9,"endTime":993.48,"body":"about the different kinds of"},{"speaker":"Pam","startTime":990.9,"endTime":993.48,"body":"questions and how we want to"},{"speaker":"Pam","startTime":993.48,"endTime":997.62,"body":"help students focus when we"},{"speaker":"Pam","startTime":993.48,"endTime":997.62,"body":"question. Focusing versus"},{"speaker":"Pam","startTime":997.62,"endTime":1001.07,"body":"funneling talk about patterns of"},{"speaker":"Pam","startTime":997.62,"endTime":1001.07,"body":"questioning. And so, it's not"},{"speaker":"Pam","startTime":1001.07,"endTime":1004.07,"body":"just about a single question,"},{"speaker":"Pam","startTime":1001.07,"endTime":1004.07,"body":"having the right question in a"},{"speaker":"Pam","startTime":1004.07,"endTime":1007.25,"body":"moment. But it's really about"},{"speaker":"Pam","startTime":1004.07,"endTime":1007.25,"body":"your pattern of questioning. So,"},{"speaker":"Pam","startTime":1007.25,"endTime":1010.79,"body":"if you picture... Focusing"},{"speaker":"Pam","startTime":1007.25,"endTime":1010.79,"body":"questions is all about helping"},{"speaker":"Pam","startTime":1010.79,"endTime":1014.42,"body":"students focus on the question,"},{"speaker":"Pam","startTime":1010.79,"endTime":1014.42,"body":"focus on what they're thinking,"},{"speaker":"Pam","startTime":1014.42,"endTime":1019.28,"body":"focus on the relationships."},{"speaker":"Pam","startTime":1014.42,"endTime":1019.28,"body":"Versus, a less effective pattern"},{"speaker":"Pam","startTime":1019.46,"endTime":1022.4,"body":"called a \"funneling pattern\"."},{"speaker":"Pam","startTime":1019.46,"endTime":1022.4,"body":"And a funneling pattern.... And"},{"speaker":"Pam","startTime":1022.4,"endTime":1026.21,"body":"it's funny, I'm doing it right"},{"speaker":"Pam","startTime":1022.4,"endTime":1026.21,"body":"now with my finger. I'm like"},{"speaker":"Pam","startTime":1026.21,"endTime":1030.56,"body":"swirling a tornado in to be a"},{"speaker":"Pam","startTime":1026.21,"endTime":1030.56,"body":"funnel in the air right now."},{"speaker":"Pam","startTime":1030.8,"endTime":1034.91,"body":"Because a funneling pattern sort"},{"speaker":"Pam","startTime":1030.8,"endTime":1034.91,"body":"of takes kids through this"},{"speaker":"Pam","startTime":1034.91,"endTime":1038.18,"body":"tornado, this funnel, where you"},{"speaker":"Pam","startTime":1034.91,"endTime":1038.18,"body":"ask a question, they answer it,"},{"speaker":"Pam","startTime":1038.18,"endTime":1040.25,"body":"and that leads to a next"},{"speaker":"Pam","startTime":1038.18,"endTime":1040.25,"body":"question, and the answer that"},{"speaker":"Pam","startTime":1040.25,"endTime":1043.04,"body":"leads to a next one. And by the"},{"speaker":"Pam","startTime":1040.25,"endTime":1043.04,"body":"end of it, you've reached the"},{"speaker":"Pam","startTime":1043.04,"endTime":1046.4,"body":"end of the funnel. They've"},{"speaker":"Pam","startTime":1043.04,"endTime":1046.4,"body":"gotten an answer. But without"},{"speaker":"Pam","startTime":1046.4,"endTime":1049.4,"body":"that funnel, the kids lost."},{"speaker":"Pam","startTime":1046.4,"endTime":1049.4,"body":"Like, if you don't re-funnel"},{"speaker":"Pam","startTime":1049.4,"endTime":1053.06,"body":"them through that, then the kid"},{"speaker":"Pam","startTime":1049.4,"endTime":1053.06,"body":"can't reason through the"},{"speaker":"Pam","startTime":1053.06,"endTime":1057.08,"body":"question. And so, we want to"},{"speaker":"Pam","startTime":1053.06,"endTime":1057.08,"body":"lean away from funneling"},{"speaker":"Pam","startTime":1057.08,"endTime":1060.5,"body":"patterning of questioning to a"},{"speaker":"Pam","startTime":1057.08,"endTime":1060.5,"body":"focusing pattern of questioning."},{"speaker":"Ashley","startTime":1060.53,"endTime":1063.53,"body":"Well, and I think. I'm"},{"speaker":"Ashley","startTime":1060.53,"endTime":1063.53,"body":"so glad that you talked about"},{"speaker":"Ashley","startTime":1063.53,"endTime":1068.33,"body":"that because I think that it"},{"speaker":"Ashley","startTime":1063.53,"endTime":1068.33,"body":"could feel like, you know, as a"},{"speaker":"Ashley","startTime":1068.33,"endTime":1070.67,"body":"teacher or as a leader, you're"},{"speaker":"Ashley","startTime":1068.33,"endTime":1070.67,"body":"watching your teachers. It could"},{"speaker":"Ashley","startTime":1070.67,"endTime":1073.19,"body":"feel like it might be helpful"},{"speaker":"Ashley","startTime":1070.67,"endTime":1073.19,"body":"because you'd see a teacher"},{"speaker":"Ashley","startTime":1073.19,"endTime":1076.49,"body":"circulating to a student,"},{"speaker":"Ashley","startTime":1073.19,"endTime":1076.49,"body":"talking with them for a few"},{"speaker":"Ashley","startTime":1076.49,"endTime":1078.92,"body":"minutes, then walking over to"},{"speaker":"Ashley","startTime":1076.49,"endTime":1078.92,"body":"the next student, talking with"},{"speaker":"Ashley","startTime":1078.92,"endTime":1083.75,"body":"them for a few minutes. But that"},{"speaker":"Ashley","startTime":1078.92,"endTime":1083.75,"body":"time that is so valuable in"},{"speaker":"Ashley","startTime":1083.75,"endTime":1089.42,"body":"every single classroom is maybe"},{"speaker":"Ashley","startTime":1083.75,"endTime":1089.42,"body":"helping a student get an answer"},{"speaker":"Ashley","startTime":1089.42,"endTime":1092.21,"body":"to a problem. But if they're"},{"speaker":"Ashley","startTime":1089.42,"endTime":1092.21,"body":"asking..."},{"speaker":"Pam","startTime":1092.66,"endTime":1094.43,"body":"If you're only funneling."},{"speaker":"Ashley","startTime":1094.43,"endTime":1096.92,"body":"...funneling type"},{"speaker":"Ashley","startTime":1094.43,"endTime":1096.92,"body":"questions. Then, yeah. That"},{"speaker":"Ashley","startTime":1096.92,"endTime":1101.51,"body":"hasn't grown the learner and"},{"speaker":"Ashley","startTime":1096.92,"endTime":1101.51,"body":"help them do anything other than"},{"speaker":"Ashley","startTime":1101.51,"endTime":1103.1,"body":"get an answer to that one"},{"speaker":"Ashley","startTime":1101.51,"endTime":1103.1,"body":"problem."},{"speaker":"Pam","startTime":1103.97,"endTime":1107.33,"body":"And what we are looking for"},{"speaker":"Pam","startTime":1103.97,"endTime":1107.33,"body":"is to help students develop"},{"speaker":"Pam","startTime":1107.48,"endTime":1111.41,"body":"their mathematical reasoning and"},{"speaker":"Pam","startTime":1107.48,"endTime":1111.41,"body":"their mathematics, so that they"},{"speaker":"Pam","startTime":1111.41,"endTime":1114.53,"body":"can reason through all sorts of"},{"speaker":"Pam","startTime":1111.41,"endTime":1114.53,"body":"problems, not just get an answer"},{"speaker":"Pam","startTime":1114.53,"endTime":1115.64,"body":"to one kind of problem."},{"speaker":"Ashley","startTime":1115.64,"endTime":1115.94,"body":"Yeah."},{"speaker":"Pam","startTime":1115.97,"endTime":1117.05,"body":"Yeah, nice. Cool."},{"speaker":"Ashley","startTime":1117.05,"endTime":1121.82,"body":"Alright, we got a few"},{"speaker":"Ashley","startTime":1117.05,"endTime":1121.82,"body":"more. So, the next one is \"build"},{"speaker":"Ashley","startTime":1122.87,"endTime":1126.41,"body":"procedural fluency from"},{"speaker":"Ashley","startTime":1122.87,"endTime":1126.41,"body":"conceptual understanding.\" And I"},{"speaker":"Ashley","startTime":1126.41,"endTime":1128.15,"body":"know you have lots to say about"},{"speaker":"Ashley","startTime":1126.41,"endTime":1128.15,"body":"this one."},{"speaker":"Pam","startTime":1128.36,"endTime":1131.18,"body":"And this would be the one"},{"speaker":"Pam","startTime":1128.36,"endTime":1131.18,"body":"that I completely disagree with."},{"speaker":"Pam","startTime":1131.42,"endTime":1135.29,"body":"So, I like the other eight,"},{"speaker":"Pam","startTime":1131.42,"endTime":1135.29,"body":"but... Or, the other seven."},{"speaker":"Pam","startTime":1135.29,"endTime":1138.98,"body":"Sorry. There's eight total. I"},{"speaker":"Pam","startTime":1135.29,"endTime":1138.98,"body":"like the other seven. So, I'm"},{"speaker":"Pam","startTime":1138.98,"endTime":1144.32,"body":"going to tweak number six, so"},{"speaker":"Pam","startTime":1138.98,"endTime":1144.32,"body":"that it works for us. I want to"},{"speaker":"Pam","startTime":1144.38,"endTime":1149.6,"body":"\"build fluency with conceptual"},{"speaker":"Pam","startTime":1144.38,"endTime":1149.6,"body":"understanding\". So, the standard"},{"speaker":"Pam","startTime":1149.6,"endTime":1152.27,"body":"reads \"build procedural fluency"},{"speaker":"Pam","startTime":1149.6,"endTime":1152.27,"body":"from conceptual understanding\","},{"speaker":"Pam","startTime":1152.27,"endTime":1155.36,"body":"and I think the word"},{"speaker":"Pam","startTime":1152.27,"endTime":1155.36,"body":"\"procedural\" gets in the way."},{"speaker":"Pam","startTime":1156.92,"endTime":1159.53,"body":"I've talked to the writers of"},{"speaker":"Pam","startTime":1156.92,"endTime":1159.53,"body":"the standards, and they're all"},{"speaker":"Pam","startTime":1159.53,"endTime":1162.02,"body":"like, \"No, no, no. We just want"},{"speaker":"Pam","startTime":1159.53,"endTime":1162.02,"body":"kids to, you know like, have a"},{"speaker":"Pam","startTime":1162.02,"endTime":1164.87,"body":"sense of what to do. We want"},{"speaker":"Pam","startTime":1162.02,"endTime":1164.87,"body":"them not to like sit there and"},{"speaker":"Pam","startTime":1164.87,"endTime":1169.37,"body":"have no no idea and just fumble"},{"speaker":"Pam","startTime":1164.87,"endTime":1169.37,"body":"around.\" Well, absolutely. I"},{"speaker":"Pam","startTime":1169.4,"endTime":1173.78,"body":"couldn't agree with that more. I"},{"speaker":"Pam","startTime":1169.4,"endTime":1173.78,"body":"don't want students to fumble"},{"speaker":"Pam","startTime":1173.78,"endTime":1177.14,"body":"unnecessarily. I don't want them"},{"speaker":"Pam","startTime":1173.78,"endTime":1177.14,"body":"to have no idea what to do. I"},{"speaker":"Pam","startTime":1177.14,"endTime":1179.9,"body":"don't want them to sit there"},{"speaker":"Pam","startTime":1177.14,"endTime":1179.9,"body":"stymied with no. And they're"},{"speaker":"Pam","startTime":1179.9,"endTime":1183.74,"body":"like, \"Yeah, see, we want"},{"speaker":"Pam","startTime":1179.9,"endTime":1183.74,"body":"fluency.\" So, I'm okay if the"},{"speaker":"Pam","startTime":1183.74,"endTime":1186.35,"body":"definition of \"fluency\" is, is"},{"speaker":"Pam","startTime":1183.74,"endTime":1186.35,"body":"that when students see a"},{"speaker":"Pam","startTime":1186.35,"endTime":1191.48,"body":"problem, they dive in, and then"},{"speaker":"Pam","startTime":1186.35,"endTime":1191.48,"body":"they let what pings for them"},{"speaker":"Pam","startTime":1191.51,"endTime":1194.93,"body":"work. They let relationships"},{"speaker":"Pam","startTime":1191.51,"endTime":1194.93,"body":"like, \"Oh, yeah. I could use"},{"speaker":"Pam","startTime":1194.93,"endTime":1198.83,"body":"that relationship.\" Or, \"Ooh, I"},{"speaker":"Pam","startTime":1194.93,"endTime":1198.83,"body":"could go that way.\" To me, that"},{"speaker":"Pam","startTime":1198.83,"endTime":1202.91,"body":"could define fluency. That"},{"speaker":"Pam","startTime":1198.83,"endTime":1202.91,"body":"students have the wherewithal to"},{"speaker":"Pam","startTime":1202.91,"endTime":1207.92,"body":"jump in productively using"},{"speaker":"Pam","startTime":1202.91,"endTime":1207.92,"body":"relationships they know, solving"},{"speaker":"Pam","startTime":1207.92,"endTime":1211.7,"body":"problems based on their"},{"speaker":"Pam","startTime":1207.92,"endTime":1211.7,"body":"understanding. Which then begs"},{"speaker":"Pam","startTime":1211.7,"endTime":1213.8,"body":"that we would have conceptual"},{"speaker":"Pam","startTime":1211.7,"endTime":1213.8,"body":"understanding. So, do I want"},{"speaker":"Pam","startTime":1213.8,"endTime":1216.53,"body":"conceptual understanding?"},{"speaker":"Pam","startTime":1213.8,"endTime":1216.53,"body":"Absolutely. The part that I have"},{"speaker":"Pam","startTime":1216.53,"endTime":1220.49,"body":"a problem with is that there"},{"speaker":"Pam","startTime":1216.53,"endTime":1220.49,"body":"would ever be a goal to get"},{"speaker":"Pam","startTime":1220.52,"endTime":1225.23,"body":"fluent with rote memorize"},{"speaker":"Pam","startTime":1220.52,"endTime":1225.23,"body":"procedures. And writers have"},{"speaker":"Pam","startTime":1225.23,"endTime":1227.81,"body":"said to me, \"No, no, no. That's"},{"speaker":"Pam","startTime":1225.23,"endTime":1227.81,"body":"not what we met.\" Except then"},{"speaker":"Pam","startTime":1227.81,"endTime":1230.9,"body":"that's what the paragraph"},{"speaker":"Pam","startTime":1227.81,"endTime":1230.9,"body":"underneath kind of says. And I"},{"speaker":"Pam","startTime":1230.9,"endTime":1235.7,"body":"understand. My bet is that when"},{"speaker":"Pam","startTime":1230.9,"endTime":1235.7,"body":"the writers got together... Can"},{"speaker":"Pam","startTime":1235.7,"endTime":1238.43,"body":"I say this? I'm going to say it."},{"speaker":"Pam","startTime":1235.7,"endTime":1238.43,"body":"I bet that when the writers got"},{"speaker":"Pam","startTime":1238.43,"endTime":1242.42,"body":"together. I'm well aware of the"},{"speaker":"Pam","startTime":1238.43,"endTime":1242.42,"body":"writing group that created these"},{"speaker":"Pam","startTime":1242.42,"endTime":1246.62,"body":"standards. And, ya'll, you did a"},{"speaker":"Pam","startTime":1242.42,"endTime":1246.62,"body":"fantastic job...almost, for all"},{"speaker":"Pam","startTime":1246.62,"endTime":1251.06,"body":"of it. But in this one case, I"},{"speaker":"Pam","startTime":1246.62,"endTime":1251.06,"body":"think this was a an example of"},{"speaker":"Pam","startTime":1251.27,"endTime":1254.99,"body":"negotiating. I think there was"},{"speaker":"Pam","startTime":1251.27,"endTime":1254.99,"body":"some negotiation, and some"},{"speaker":"Pam","startTime":1254.99,"endTime":1258.02,"body":"people didn't really want this"},{"speaker":"Pam","startTime":1254.99,"endTime":1258.02,"body":"procedural fluency idea in there"},{"speaker":"Pam","startTime":1258.02,"endTime":1261.38,"body":"and others did, and so they kind"},{"speaker":"Pam","startTime":1258.02,"endTime":1261.38,"body":"of compromised. And I think this"},{"speaker":"Pam","startTime":1261.38,"endTime":1264.14,"body":"one was the compromise. And I'm"},{"speaker":"Pam","startTime":1261.38,"endTime":1264.14,"body":"not going to compromise. And I'm"},{"speaker":"Pam","startTime":1264.14,"endTime":1268.01,"body":"going to say, \"Nope, we do not"},{"speaker":"Pam","startTime":1264.14,"endTime":1268.01,"body":"need to just start with a little"},{"speaker":"Pam","startTime":1268.01,"endTime":1270.86,"body":"conceptual understanding because"},{"speaker":"Pam","startTime":1268.01,"endTime":1270.86,"body":"our goal is to get kids fluent"},{"speaker":"Pam","startTime":1270.86,"endTime":1275.09,"body":"at the step-by-step procedures.\""},{"speaker":"Pam","startTime":1270.86,"endTime":1275.09,"body":"No. What we do want is"},{"speaker":"Pam","startTime":1275.12,"endTime":1279.23,"body":"understanding because we are"},{"speaker":"Pam","startTime":1275.12,"endTime":1279.23,"body":"developing mathematicians, and"},{"speaker":"Pam","startTime":1279.23,"endTime":1283.7,"body":"mathematicians fluently think"},{"speaker":"Pam","startTime":1279.23,"endTime":1283.7,"body":"and reason using relationships."},{"speaker":"Pam","startTime":1283.73,"endTime":1287.63,"body":"So, that would be my push on"},{"speaker":"Pam","startTime":1283.73,"endTime":1287.63,"body":"six. Alright, let's move on, and"},{"speaker":"Pam","startTime":1287.63,"endTime":1290.15,"body":"let's. Kim, do on anything to"},{"speaker":"Pam","startTime":1287.63,"endTime":1290.15,"body":"six or did I just pontificate"},{"speaker":"Pam","startTime":1290.15,"endTime":1290.72,"body":"enough about that one?"},{"speaker":"Ashley","startTime":1290.72,"endTime":1293.21,"body":"[laughs]. I think we're"},{"speaker":"Ashley","startTime":1290.72,"endTime":1293.21,"body":"good."},{"speaker":"Pam","startTime":1293.45,"endTime":1297.44,"body":"Okay, cool. So, the next"},{"speaker":"Pam","startTime":1293.45,"endTime":1297.44,"body":"one: \"Support productive"},{"speaker":"Pam","startTime":1297.44,"endTime":1299.18,"body":"struggle in learning"},{"speaker":"Pam","startTime":1297.44,"endTime":1299.18,"body":"mathematics.\""},{"speaker":"Ashley","startTime":1299.48,"endTime":1302.81,"body":"Oh, this one is so near"},{"speaker":"Ashley","startTime":1299.48,"endTime":1302.81,"body":"and dear for me. So, \"productive"},{"speaker":"Ashley","startTime":1302.84,"endTime":1307.01,"body":"struggle\" is, for me, this"},{"speaker":"Ashley","startTime":1302.84,"endTime":1307.01,"body":"idea...and we've talked about it"},{"speaker":"Ashley","startTime":1307.04,"endTime":1312.68,"body":"before...that we want kids to"},{"speaker":"Ashley","startTime":1307.04,"endTime":1312.68,"body":"grapple a little bit. But this"},{"speaker":"Ashley","startTime":1312.68,"endTime":1316.13,"body":"for me screams, \"Do you need"},{"speaker":"Ashley","startTime":1312.68,"endTime":1316.13,"body":"time or help?\" And we've done a"},{"speaker":"Ashley","startTime":1316.13,"endTime":1319.43,"body":"whole episode on that, and so,"},{"speaker":"Ashley","startTime":1316.13,"endTime":1319.43,"body":"you know, we don't need to take"},{"speaker":"Ashley","startTime":1319.43,"endTime":1325.01,"body":"a lot of time here. But kids"},{"speaker":"Ashley","startTime":1319.43,"endTime":1325.01,"body":"just stymied and going nowhere"},{"speaker":"Ashley","startTime":1325.04,"endTime":1328.85,"body":"is not helpful. But we don't"},{"speaker":"Ashley","startTime":1325.04,"endTime":1328.85,"body":"want to supply too much. We"},{"speaker":"Ashley","startTime":1328.85,"endTime":1332.06,"body":"don't want to give them too much"},{"speaker":"Ashley","startTime":1328.85,"endTime":1332.06,"body":"that they're not growing,"},{"speaker":"Ashley","startTime":1332.06,"endTime":1336.98,"body":"they're not learning. And so"},{"speaker":"Ashley","startTime":1332.06,"endTime":1336.98,"body":"that the key word for me here is"},{"speaker":"Ashley","startTime":1336.98,"endTime":1340.91,"body":"to \"support\", support the"},{"speaker":"Ashley","startTime":1336.98,"endTime":1340.91,"body":"productive struggle, to step in"},{"speaker":"Ashley","startTime":1340.94,"endTime":1345.98,"body":"in the right moment and help"},{"speaker":"Ashley","startTime":1340.94,"endTime":1345.98,"body":"guide, rather than give too"},{"speaker":"Ashley","startTime":1345.98,"endTime":1346.58,"body":"much."},{"speaker":"Pam","startTime":1347.06,"endTime":1349.31,"body":"And we like this one so"},{"speaker":"Pam","startTime":1347.06,"endTime":1349.31,"body":"much that we're going to"},{"speaker":"Pam","startTime":1349.31,"endTime":1352.97,"body":"actually spend a future podcast"},{"speaker":"Pam","startTime":1349.31,"endTime":1352.97,"body":"on this very idea, so stay tuned"},{"speaker":"Pam","startTime":1352.97,"endTime":1355.91,"body":"for more about \"supporting"},{"speaker":"Pam","startTime":1352.97,"endTime":1355.91,"body":"productive struggle in learning"},{"speaker":"Pam","startTime":1355.91,"endTime":1359.99,"body":"mathematics\". And then last,"},{"speaker":"Pam","startTime":1355.91,"endTime":1359.99,"body":"\"Elicit and use evidence of"},{"speaker":"Pam","startTime":1359.99,"endTime":1364.25,"body":"student thinking.\" And this"},{"speaker":"Pam","startTime":1359.99,"endTime":1364.25,"body":"might be the hardest one for"},{"speaker":"Pam","startTime":1364.25,"endTime":1367.49,"body":"teachers who have a background"},{"speaker":"Pam","startTime":1364.25,"endTime":1367.49,"body":"of being taught sort of"},{"speaker":"Pam","startTime":1367.49,"endTime":1369.71,"body":"traditionally, and it was all"},{"speaker":"Pam","startTime":1367.49,"endTime":1369.71,"body":"about memorizing step-by-step"},{"speaker":"Pam","startTime":1369.71,"endTime":1375.83,"body":"procedures. What does it mean"},{"speaker":"Pam","startTime":1369.71,"endTime":1375.83,"body":"for students to even think? And"},{"speaker":"Pam","startTime":1375.83,"endTime":1378.53,"body":"so, we look for in a"},{"speaker":"Pam","startTime":1375.83,"endTime":1378.53,"body":"mathematizing, Math is"},{"speaker":"Pam","startTime":1378.56,"endTime":1381.68,"body":"Figure-Out-Able classroom. We"},{"speaker":"Pam","startTime":1378.56,"endTime":1381.68,"body":"look for problems, like we said,"},{"speaker":"Pam","startTime":1381.71,"endTime":1383.66,"body":"implement tasks that promote"},{"speaker":"Pam","startTime":1381.71,"endTime":1383.66,"body":"reasoning and problem solving."},{"speaker":"Pam","startTime":1383.96,"endTime":1388.49,"body":"We look for problems that are"},{"speaker":"Pam","startTime":1383.96,"endTime":1388.49,"body":"worth thinking about. Meaning,"},{"speaker":"Pam","startTime":1388.52,"endTime":1392.09,"body":"students have access to them. In"},{"speaker":"Pam","startTime":1388.52,"endTime":1392.09,"body":"fact, can I just say? I heard"},{"speaker":"Pam","startTime":1392.51,"endTime":1395.15,"body":"something on Twitter the other"},{"speaker":"Pam","startTime":1392.51,"endTime":1395.15,"body":"day that...I want to do a whole"},{"speaker":"Pam","startTime":1395.36,"endTime":1397.28,"body":"episode about this, so I'll say"},{"speaker":"Pam","startTime":1395.36,"endTime":1397.28,"body":"a little bit about it"},{"speaker":"Pam","startTime":1397.52,"endTime":1401.48,"body":"now...where someone said, \"the"},{"speaker":"Pam","startTime":1397.52,"endTime":1401.48,"body":"most damaging idea in math"},{"speaker":"Pam","startTime":1401.48,"endTime":1404.66,"body":"education right now is that you"},{"speaker":"Pam","startTime":1401.48,"endTime":1404.66,"body":"can give students problems, and"},{"speaker":"Pam","startTime":1404.66,"endTime":1409.04,"body":"that they will then learn math"},{"speaker":"Pam","startTime":1404.66,"endTime":1409.04,"body":"on their own.\" And the teacher,"},{"speaker":"Pam","startTime":1409.04,"endTime":1412.37,"body":"the reply in the tweet was, \"If"},{"speaker":"Pam","startTime":1409.04,"endTime":1412.37,"body":"they don't know what they're"},{"speaker":"Pam","startTime":1412.37,"endTime":1415.52,"body":"doing, it's stupid to just have"},{"speaker":"Pam","startTime":1412.37,"endTime":1415.52,"body":"them sit there confused and"},{"speaker":"Pam","startTime":1415.52,"endTime":1419.51,"body":"frustrated, trying to figure out"},{"speaker":"Pam","startTime":1415.52,"endTime":1419.51,"body":"how to do it.\" And I so"},{"speaker":"Pam","startTime":1419.51,"endTime":1424.19,"body":"understand that perspective IF"},{"speaker":"Pam","startTime":1419.51,"endTime":1424.19,"body":"math is about memorizing"},{"speaker":"Pam","startTime":1424.22,"endTime":1427.94,"body":"step-by-step procedures that"},{"speaker":"Pam","startTime":1424.22,"endTime":1427.94,"body":"someone else gives you. But if"},{"speaker":"Pam","startTime":1427.94,"endTime":1433.76,"body":"Math is Figure-Out-Able, then we"},{"speaker":"Pam","startTime":1427.94,"endTime":1433.76,"body":"can give students problems that"},{"speaker":"Pam","startTime":1433.76,"endTime":1439.58,"body":"by thinking about them help them"},{"speaker":"Pam","startTime":1433.76,"endTime":1439.58,"body":"develop more mathematics, and"},{"speaker":"Pam","startTime":1439.76,"endTime":1444.83,"body":"that they can, that we can be..."},{"speaker":"Pam","startTime":1439.76,"endTime":1444.83,"body":"It's not about handing them"},{"speaker":"Pam","startTime":1444.83,"endTime":1447.98,"body":"random problems that kids have"},{"speaker":"Pam","startTime":1444.83,"endTime":1447.98,"body":"no idea how to do. At all!"},{"speaker":"Ashley","startTime":1448.07,"endTime":1448.31,"body":"Yeah."},{"speaker":"Pam","startTime":1448.31,"endTime":1451.01,"body":"It's about being very"},{"speaker":"Pam","startTime":1448.31,"endTime":1451.01,"body":"judicious about handing them"},{"speaker":"Pam","startTime":1451.01,"endTime":1453.44,"body":"problems that are just on the"},{"speaker":"Pam","startTime":1451.01,"endTime":1453.44,"body":"edge of their zone of proximal"},{"speaker":"Pam","startTime":1453.44,"endTime":1458.09,"body":"development. That by grappling"},{"speaker":"Pam","startTime":1453.44,"endTime":1458.09,"body":"with those problems, the"},{"speaker":"Pam","startTime":1458.09,"endTime":1460.55,"body":"students develop as"},{"speaker":"Pam","startTime":1458.09,"endTime":1460.55,"body":"mathematicians, and they develop"},{"speaker":"Pam","startTime":1460.55,"endTime":1464.0,"body":"mathematics. And the teacher is"},{"speaker":"Pam","startTime":1460.55,"endTime":1464.0,"body":"an active participant in that."},{"speaker":"Pam","startTime":1464.09,"endTime":1464.48,"body":"Yeah, go ahead."},{"speaker":"Ashley","startTime":1464.48,"endTime":1467.48,"body":"I'm so glad you"},{"speaker":"Ashley","startTime":1464.48,"endTime":1467.48,"body":"clarified that because I think"},{"speaker":"Ashley","startTime":1467.48,"endTime":1472.85,"body":"that it could be heard as, \"I'm"},{"speaker":"Ashley","startTime":1467.48,"endTime":1472.85,"body":"a new teacher. I've got fourth"},{"speaker":"Ashley","startTime":1472.85,"endTime":1476.99,"body":"grade students, and my job is to"},{"speaker":"Ashley","startTime":1472.85,"endTime":1476.99,"body":"just give them stuff and say,"},{"speaker":"Ashley","startTime":1477.02,"endTime":1481.16,"body":"'Go'.\" But I love that you said"},{"speaker":"Ashley","startTime":1477.02,"endTime":1481.16,"body":"it's just outside their zone of"},{"speaker":"Ashley","startTime":1481.16,"endTime":1483.23,"body":"proximal development. They have"},{"speaker":"Ashley","startTime":1481.16,"endTime":1483.23,"body":"something"},{"speaker":"Ashley","startTime":1483.23,"endTime":1483.5,"body":"There."},{"speaker":"Pam","startTime":1483.5,"endTime":1484.58,"body":"On the edge. Just on the"},{"speaker":"Pam","startTime":1483.5,"endTime":1484.58,"body":"edge."},{"speaker":"Ashley","startTime":1484.58,"endTime":1487.43,"body":"Just on the edge. That"},{"speaker":"Ashley","startTime":1484.58,"endTime":1487.43,"body":"you support, and nudge, and"},{"speaker":"Ashley","startTime":1487.43,"endTime":1490.07,"body":"encourage, and provide the"},{"speaker":"Ashley","startTime":1487.43,"endTime":1490.07,"body":"support that they need. And"},{"speaker":"Ashley","startTime":1490.07,"endTime":1492.89,"body":"then, you up the ante. Do the"},{"speaker":"Ashley","startTime":1490.07,"endTime":1492.89,"body":"next bit."},{"speaker":"Pam","startTime":1493.1,"endTime":1496.64,"body":"With very purposefully"},{"speaker":"Pam","startTime":1493.1,"endTime":1496.64,"body":"chosen problems. It's not about"},{"speaker":"Pam","startTime":1496.64,"endTime":1499.85,"body":"random frustration of trying to"},{"speaker":"Pam","startTime":1496.64,"endTime":1499.85,"body":"guess what's in the teacher's"},{"speaker":"Pam","startTime":1499.85,"endTime":1505.76,"body":"head. At all! So, in order to"},{"speaker":"Pam","startTime":1499.85,"endTime":1505.76,"body":"have those kinds of tasks. When"},{"speaker":"Pam","startTime":1505.76,"endTime":1508.85,"body":"we do, then as you're"},{"speaker":"Pam","startTime":1505.76,"endTime":1508.85,"body":"evaluating, as you're using"},{"speaker":"Pam","startTime":1508.85,"endTime":1511.01,"body":"these to help you have a"},{"speaker":"Pam","startTime":1508.85,"endTime":1511.01,"body":"conversation with the teacher"},{"speaker":"Pam","startTime":1511.01,"endTime":1513.83,"body":"that you're observing, you're"},{"speaker":"Pam","startTime":1511.01,"endTime":1513.83,"body":"looking for. One thing you're"},{"speaker":"Pam","startTime":1513.83,"endTime":1517.7,"body":"looking for is that they are"},{"speaker":"Pam","startTime":1513.83,"endTime":1517.7,"body":"eliciting student thinking. And"},{"speaker":"Pam","startTime":1517.7,"endTime":1520.73,"body":"then, they're using that"},{"speaker":"Pam","startTime":1517.7,"endTime":1520.73,"body":"evidence of student thinking in"},{"speaker":"Pam","startTime":1520.73,"endTime":1526.82,"body":"some way to move the math"},{"speaker":"Pam","startTime":1520.73,"endTime":1526.82,"body":"forward. Alright. So, the eight"},{"speaker":"Pam","startTime":1526.85,"endTime":1530.66,"body":"essential teaching practices are"},{"speaker":"Pam","startTime":1526.85,"endTime":1530.66,"body":"wonderful with a little tweak on"},{"speaker":"Pam","startTime":1530.66,"endTime":1535.04,"body":"number six. And we highly"},{"speaker":"Pam","startTime":1530.66,"endTime":1535.04,"body":"recommend that that could be a"},{"speaker":"Pam","startTime":1535.04,"endTime":1541.46,"body":"place for you to consider as you"},{"speaker":"Pam","startTime":1535.04,"endTime":1541.46,"body":"look for a mathematizing, Math"},{"speaker":"Pam","startTime":1541.46,"endTime":1542.66,"body":"is Figure-Out-Able classroom."},{"speaker":"Ashley","startTime":1542.81,"endTime":1546.92,"body":"Yeah. So, leaders and"},{"speaker":"Ashley","startTime":1542.81,"endTime":1546.92,"body":"administration, I would love to"},{"speaker":"Ashley","startTime":1546.92,"endTime":1551.33,"body":"invite you. We have a challenge."},{"speaker":"Ashley","startTime":1546.92,"endTime":1551.33,"body":"The \"You Can Change Math Class\""},{"speaker":"Ashley","startTime":1551.36,"endTime":1554.93,"body":"challenge is next week."},{"speaker":"Ashley","startTime":1551.36,"endTime":1554.93,"body":"Registration is currently open."},{"speaker":"Ashley","startTime":1555.08,"endTime":1557.87,"body":"You can register now at"},{"speaker":"Ashley","startTime":1555.08,"endTime":1557.87,"body":"mathisfigureoutable.com/change."},{"speaker":"Ashley","startTime":1560.69,"endTime":1563.51,"body":"Grab your teachers. Teachers, if"},{"speaker":"Ashley","startTime":1560.69,"endTime":1563.51,"body":"you're listening, grab your"},{"speaker":"Ashley","startTime":1563.54,"endTime":1566.84,"body":"leaders and coaches. You can do"},{"speaker":"Ashley","startTime":1563.54,"endTime":1566.84,"body":"it together and have some great"},{"speaker":"Ashley","startTime":1566.84,"endTime":1570.68,"body":"conversation about what a Math"},{"speaker":"Ashley","startTime":1566.84,"endTime":1570.68,"body":"is Figure-Out-Able classroom can"},{"speaker":"Ashley","startTime":1570.68,"endTime":1571.25,"body":"look like."},{"speaker":"Pam","startTime":1571.57,"endTime":1573.97,"body":"Absolutely. So, we will"},{"speaker":"Pam","startTime":1571.57,"endTime":1573.97,"body":"continue that conversation and"},{"speaker":"Pam","startTime":1573.97,"endTime":1577.6,"body":"help more and more make a Math"},{"speaker":"Pam","startTime":1573.97,"endTime":1577.6,"body":"is Figure-Out-Able classroom."},{"speaker":"Pam","startTime":1577.99,"endTime":1581.59,"body":"The dates are January 18th"},{"speaker":"Pam","startTime":1577.99,"endTime":1581.59,"body":"through the 20th with an extra"},{"speaker":"Pam","startTime":1581.59,"endTime":1586.45,"body":"bonus day on the 21st where we"},{"speaker":"Pam","startTime":1581.59,"endTime":1586.45,"body":"will meet in the evenings at 7"},{"speaker":"Pam","startTime":1586.48,"endTime":1589.84,"body":"p.m., Central time on Zoom."},{"speaker":"Pam","startTime":1586.48,"endTime":1589.84,"body":"People from all around the world"},{"speaker":"Pam","startTime":1589.84,"endTime":1592.9,"body":"will be joining in. If you"},{"speaker":"Pam","startTime":1589.84,"endTime":1592.9,"body":"register and can't make those"},{"speaker":"Pam","startTime":1592.9,"endTime":1596.71,"body":"times there are recordings"},{"speaker":"Pam","startTime":1592.9,"endTime":1596.71,"body":"available. It is a super fun,"},{"speaker":"Pam","startTime":1596.74,"endTime":1602.26,"body":"engaging, productive way for us"},{"speaker":"Pam","startTime":1596.74,"endTime":1602.26,"body":"to all make math more and more"},{"speaker":"Pam","startTime":1602.62,"endTime":1607.21,"body":"figure-out-able. That also means"},{"speaker":"Pam","startTime":1602.62,"endTime":1607.21,"body":"that registration for our online"},{"speaker":"Pam","startTime":1607.21,"endTime":1610.54,"body":"workshops is opening soon. We"},{"speaker":"Pam","startTime":1607.21,"endTime":1610.54,"body":"only open registration three"},{"speaker":"Pam","startTime":1610.54,"endTime":1614.29,"body":"times a year, and that's coming"},{"speaker":"Pam","startTime":1610.54,"endTime":1614.29,"body":"up, so get your funding ready."},{"speaker":"Pam","startTime":1614.86,"endTime":1618.07,"body":"Alright. Thank you for tuning in"},{"speaker":"Pam","startTime":1614.86,"endTime":1618.07,"body":"and teaching more and more Real"},{"speaker":"Pam","startTime":1618.07,"endTime":1620.44,"body":"Math. To find out more about the"},{"speaker":"Pam","startTime":1618.07,"endTime":1620.44,"body":"Math is Figure-Out-Able"},{"speaker":"Pam","startTime":1620.44,"endTime":1624.37,"body":"movement, visit"},{"speaker":"Pam","startTime":1620.44,"endTime":1624.37,"body":"mathisfigureoutable.com. Let's"},{"speaker":"Pam","startTime":1624.37,"endTime":1627.04,"body":"keep spreading the word that"},{"speaker":"Pam","startTime":1624.37,"endTime":1627.04,"body":"Math is Figure-Out-Able!"}]}