 All right, you guys you're ready to smile everybody has their hair perfect and all that okay, all right say Pythagorean Pythagorean All right, I got us. Thank you One other thing I'm gonna be going just for a second. I've got to go fix I got my computer I got a different computer for this so that so when I present I can do it from that computer So if you see me in and out don't mind me Okay Thanks, Zach Sorry figuring out how to screen share Can you all see my screen? Yes, okay So I'm gonna talk about a prize that's available for math teachers It's called the Rosenthal Prize. It's for innovation and inspiration and math teaching which I think that PCMI is such a great place to Advertise this prize. If you want this presentation, I know it's gonna be available later, but there's the Bitly link if you want to find that that presentation. There's more about it, too I have the link to the Rosenthal Prize. It's offered through the Museum of Math in New York City So this prize is designed to recognize and promote hands-on math teaching in upper elementary and middle school classrooms It's a cash award and it's for you personally It's not for your school and it's for a single activity So it's it's just in a math activity that you have probably already done in your classroom So the winning teachers also get to go to New York and get to share their their lessons You don't need to be a middle school teacher But it should be a middle school lesson and if you have access to middle school kids to present that lesson, too So my first thought when I read this was I have nothing worth $25,000 And I thought there's there's no way I saw this on a link through Twitter and I my initial thought was that yeah This is this is really not for me My second thought was math teaching really Priceless, right? It's worth more than $25,000 actually. No, I didn't really think that How long is it gonna take and so I looked at the application and I thought okay So if I apply for this, how long would it really take in and you know, maybe it's a long shot But if it's easy enough, I think I'll do it So the initial application for this prize you just have to answer a series of questions So it's really really easy. It's just a series of short responses and it's You're you're likely The applications aren't open yet. They open near the end of March and they're usually due sometime in May I actually finished my application in one day. So I read about it and then I'm like, okay I'll just I'll just put that in because it's so easy Here these were my questions. They might be different I did go back and look up what my questions were and since the applications aren't open yet I don't really know what they are But as I go through those questions, think if you have something that might fit in that same category So the first question is describe an innovative activity which you implemented with your students Where that activity itself illustrates a relevant mathematical concept. We've all probably done that And then it says if your activity wasn't implemented through fourth through eighth Just include a description on how it would be modified To the age group and it's 200 words or less. So it's not long. So this this actual question is 56 words So like your fourth of the way done if you just write that much So it's small. It's a small amount when you're describing that the next question was write a brief essay and it is very brief Explaining how this activity represents your teaching philosophy. So this is just some sort of it's it's how we at PCMI think So this was a pretty this one was probably the easiest one for me to answer The next one is is this activity original to you? If so comment on when and how you developed it and it can be recent If this activity is when you borrowed from another source, you can explain that you do need to have adapted or changed the activity You can't just do someone else's activity and submit it They will actually Google your activity to see if other people have done it So when you think about it, you know, how you're modifying and whether you're using somebody else's activity They type it into Google to see what kind of results that they get The next question is Imagine another teacher. We're trying to implement your activity in the classroom If they start from scratch, what materials do they need? They're looking for easy materials How much time would it take to prepare and what would be the cost they're looking for low-cost? Activity materials they actually try your activity if it gets far enough, so they'll try it to see if it works When did you start using this innovative practice in your classroom? So that's just a simple answer And then that's it. So those are that's the initial application So it is fairly easy. It doesn't take a whole lot of time and it's well worth it There is a rubric that and it's kind of hidden information. I Googled it and found it so it can be useful when you're trying to decide like if you have three or four activities like which one would be A great activity in order to be able to submit it. So here's the rubric. I've included it So they the first one is innovation and these are not all weighted equally So innovation is a big one. Is it outside the box? Engagement is also a big one for them and then you can see that there's a link down here for the rubric copy That has the whole rubric copy on there What is the what is the math? So that's really important to them as well and can can you replicate it? The last one does the connectedness so if you have something where I know the last activity had Some sort of light and similar Triangles in there if you can connect it with something else They they like that a lot. Is it understandable the last one they said is actually the least important Is it well written? Just have somebody go through and edit it, but that they said it was the least important on them So there's this video that's on YouTube And it's got a lot of insight as to how the process works and what the judges are looking for I'm just gonna play just a little short clip of it and then stop it It's a long video, but if you're applying it's a good one to kind of look through it's So they introduce all the judges here these guys are the judges and these guys are past winners And so they'll talk about like how their lessons were developed and then some of the judging criteria So if you're interested in it, I would encourage you to just watch this video. I mean it's 46 minutes So I'm obviously not gonna play the whole thing But it is helpful in in as you're doing your application to know what they're looking Okay, whoops, sorry Okay so after you do that initial application and You filled it in and they've looked through it and they really like what you're doing They will ask you for other stuff when they ask you for this this other material It's well worth it because you know, you've made it far enough that that you actually have a chance of winning So after they look through it and they say oh, we really like these activities They'll ask you for a letter of recommendation a video of your class And so I videoed all six of my classes so I could get the best one because I was really nervous They weren't gonna turn out well and you can borrow what their class is to I had a couple people lined up in case my classes We're not we're not doing what I wanted them to do Just in case make sure you get parent permission for that and do that kind of early in the year So I handed that out of back to school night You will also have a short essay as to how the lesson Impacted your overall class and it is short. So I included my essay there. It's it's not great But just so you could see an example of that Also a detailed lesson plan So be really careful when you're applying for this prize because if you look at the polished ones It's really scary like I looked at them and I thought wow mine is nothing like this, but it becomes that so don't let those intimidate you it's it is It is a work in progress. It takes a while for them to get to look like that So this is a video of my class Doing the lesson And I'm just gonna play a little bit of it So you can see it's not like super professional Somebody's like videoing me and kind of turning around I think we had like one of the test tubes break as we were doing it So they they're not expecting perfection. They just want to see how the activity looks and mostly like what the students are doing They pay attention to what the students are doing And then this is another like quick video of another Rosenthal Prize winner and it's their activity. They're doing Flipping their coin heads or tails and deciding whether to walk forwards or backwards. So this is a random walk and Mine is not as polished as his video was But then he's showing the normal curve how it develops from that So it's just it's a very quick activity. I mean it didn't take long to do but that was one of the the prize winners So my activity the one that I presented was Okay Was on developing ratios with colors so they used colored water and then What does what do equivalent ratios look like for the same shade? So if you have 10 milliliters of blue And you have five milliliters of yellow. It's gonna make this shade of green Well, what if you have 20 milliliters of blue? How much how much are you gonna need of the yellow? So Yeah, sorry. I'm cutting you off. Okay Um, I love this idea. When do you hear? So you hear here's the timeline. Let me go down to the time. No, no, so that's that's my last slide So the initial application is March through May the finals notifications beginning of school You get revisions in November. So they give you back and they say we want this You get notification in December and the ceremony is in January or February. Awesome. Yeah, sorry I didn't mean to go too long. No, that's okay. Very exciting. I just saw I don't know if anybody remembers Matt angle He was at PCMI this past summer. He won the top Rosenthal prize He got twenty five thousand dollars and Tracy you mentioned it for using light and similar triangles So, yeah, that's pretty cool. I hope you win Tracy. Oh, I did You did win. Yeah Wasn't the one last year Matt angle So I won the year before the year prior you won the year before The twenty five thousand one. Mm-hmm. Oh You're like so humble about that. I'd be like, whoa, look at me Well, I think train one to train who is in the Awesome congrats Tracy. That's so exciting. Thanks Is your I didn't mean to cut you off. I cut you off right when you got to the most exciting of what was your lesson? It was just it was ratios. It was using color for ratios. So where they were mixing colors And that's in your slides. Yeah, it's in my slides Okay, awesome And I am gonna ask everybody at the end to send your slides to me And then I'll send them all to Suzanne to get everything posted up on our time when everybody can see all of those on our PCMI page Awesome. Thanks Tracy. Oh, congrats. That's so exciting. So you won in 2015 20 yeah the year before The year before no year it is anymore. Yeah, I don't know. I don't know All right, awesome. Okay, Christina your turn in 10 minutes So Tracy, can you turn off your screen sharing? Okay, can you guys see my stuff? Can you guys see my presentation? Okay, so my top Great. Um, my topic is implementing IB which is international baccalaureate I'm not sure how familiar people are with that But I just wanted to talk about what my middle school does and give some specific examples and see if people had any questions about it So this is my fourth year teaching 6th grade math at Albert Einstein academies which is a small charter school in San Diego and so I was gonna say what we did The first thing that you can see here is from the IB website and it just shows the continuum of programs Most people know about the high school program because that was the first one that was developed. You can see here that it was And 1968 that that started But since then there has been a middle years program and primary years program developed you can see those both happened in the 90s and Approximately the middle school middle years program is 6th through 10th grade it can be run in a smaller Range, for example, my school is 6th through 8th grade and we are able to run it We don't have 9th and 10th grade and then the primary years program Is typically run K through 5th like at our elementary school But you can see the age range is 3 through 12 so that they can also do it even earlier than that So I was gonna focus on a couple of key things you can see on the left hand side Right here. Those are the three things that I wanted to focus on today How our program is inclusive and holistic that connects to the whole child Which just definitely starts in the primary years program, but then also continues on into the middle years and also how IB education is supposed to be relevant those connections between studies and also to the real world and Then how it's rigorous or challenging So the first thing inclusive and holistic In high school a lot of times it's not the entire school that's IB It's just a select group of students who opt into it But at least at my middle school and I'm not sure how how much this is true but I think there are a variety of middle schools and elementary schools where the entire school is IB and so that makes it much more inclusive and Then also you can see in this image here all the 10 IB learner attribute profiles These are characteristics that we as a school emphasize and help the students to develop In sixth grade we've chosen to give monthly awards to students who display these attributes So there's 10 months in the school year So each month will select one of these attributes and give awards to students and we do give one to every student It's not supposed to be like oh have a trophy type of thing But it is supposed to help every student see in themselves One of these attributes so we give those throughout the year To students and also and our math classes We connect the attribute of the month to our unit so that we're emphasizing that within our lessons and student interactions as well So the next thing is that IB education is relevant and on the left right here You see an example of one of my unit boards. It's a requirement at our school and with all IB classes I believe to have a unit board for every unit that you do and this shows the broader aims and connections of the unit So that it makes it easier to connect to other content areas and then also to the real world So for us for unit two, this is connected to the CPM curriculum by the way So it's statistics arithmetic strategies and area and then this is all the IB stuff that goes with it the global context Orientation time space and space and time. This is kind of vague on purpose But you'll see that the same global context key concepts and related content concepts exist in other content areas so Later when you do interdisciplinary units, you are able to connect it and see those commonalities across the content areas This statement of inquiry here is We're supposed to write it in such a way that it is not tied to your content area So we shouldn't say math or anything very obviously mathy in it This one says we can make better logical arguments by modeling information in purposeful ways So you could see how that could be connected to an English class maybe so Examples of interdisciplinary units. Well, first of all one is required per grade level per year One that we piloted last year was where students create solar panel models to scale and that was through math and science class So there's a lot more here, but that's a taste of it And lastly IB education is rigorous So we give summative assessments which are usually tests but sometimes projects at the end of each unit These are graded on a rubric with a rubric that's a zero to eight point scale and Seven to eight level is intended to be above grade level so that it's not just like an easy eight for kids It's really hard to get seven and eight and so there's always additional challenge But all levels aren't just Giving a letter grade and that's it and you're supposed to feel bad if you get a certain letter grade or good with another letter grade They're supposed to be very specific with feedback You can see over here on the left the basic categories seven eight being excellent understanding five six strong which depending on the Exam in the content area grade levels considered somewhere between three and six And so on but there's usually a lot more detailed of a rubric as well And these are different categories that we have tests in so we need to cover all categories ABC and D At least once per semester Knowing and understanding is your tradition traditional procedures and skills type of test but all these other ones BC and D help us to Teach students to apply math to communicate with math and these go along really well with the SBAC Claims so it's really helping us to give students a broad math education And our teaching so I know I went pretty fast, but are there any questions? I think the pacing was perfect actually that was awesome Thank you And I my question is my head is spinning because you just gave us a ton of information and I am not familiar with the IB program at all and I don't teach it in a school that That considers all the things that you're talking about to the degree that you your school does Would it be weird for a teacher to request a visit like I teach it a public school. Could I request a visit to another school? It's like an IV school to see how it works I know that our school is totally open to that. I'm in San Diego. You'd have you're in where I'm in Philadelphia area I'm in New Jersey. I mean, I think a lot of schools are open to that You would just want to contact them directly as a charter school I think we're definitely open to that because yeah, we're just more open, but you can always contact the specific school They all do all of these IB schools have the same type of philosophy. That's like a common philosophy or Yeah, a lot of it is I mean not all schools will do awards every month for the IB attributes But all middle school programs should use the IV attributes And you can see right here There's the link for the IB website, which gives you more Information and that first thing that I took well basically all three areas I focused on were taken from the description and the description which was the first page image comes from the IB website So yes, they all should have the same philosophy people implement it differently, but in general, yeah Thank you Does anybody else teach at an IB school here, I don't I do not but I've always wanted to Christina, have you always taught in an IB or did you switch between the two? I've switched So I taught one year at a traditional High school 11th 12th grade kind of kids mostly and then I've taught at charter schools after that I taught at a traditional charter school, you know with letter grades and all that for two years And then four years here. Nice. And do you like this the best? I like this the best for Multiple reasons not just the fact that it's IB, but just it's a really great culture at the school where it's supportive of both students And staff I think charter schools a lot of times can be supportive of students But then not really care about staff, you know work you to the bone kind of a thing. So This one has a really great work-life balance and the people are awesome Great Awesome. Thank you and perfect timing any other questions or we will move on to sunny Okay, so if you can turn off your screen share and sunny Europe Okay, I think I'm ready Okay, and it's actually pretty oh Well, I got this I think okay, there we go. All right So That chair Okay, I see lots of thumbs up. So I assume that you're seeing just the slideshow with the decohedral dice on it Is that correct? Okay, so I This is one of my favorite lessons that I've Done in a variety of classes. It's great for algebra to but I also use it for pre-algebra as well when we're studying probability and Basically, it's a pretty simple lesson. It's interesting because I was thinking when when that when Tracy was doing the Rosenthal Prize Presentation this is not a cheap lesson especially if you want to have enough dice for multiple small groups to conduct the experiment Because you need 40 10 face dice for each group Or it could be any face dice But 10 face dice is a nice is a nice one that you get a nice exponential curve with and essentially you ask the students to Roll their 40 10 face dice a total of 20 times and they basically record that In in a data sheet so you can see there after So so I guess I guess step back here a little bit They don't just rolling dice after each roll you pick a number in this case I pick one and they remove those without Replacement at the end of each roll and so they basically record in their data how many dice are left over after removing that particular number and So after they do this 20 times Everybody in the class comes up to the board in their groups come up to the board and They recorded an Excel spreadsheet their individual Dice remaining after each roll and then we find a class average which we'll put in the third column here And then the students will do a regression in order to come up with An equation that models our class average and then you walk them basically through a series of Questions to help them come up with a theoretical model for it and what I like about this particular dice experiment is that It's a really good model like the X that what you what you get using a regret with the equation you get using a regression Model either on the TI 84 or some other program is usually typically really close to the theoretical model that You should get in this case and so You know some of the things that they do in addition to conducting the experiment depending upon the class You have them graph the data talk about the different characteristics Talk about the independent versus dependent variable variables domain range Talk about continuity versus discreteness and oh she was being so good. Sorry you guys I was like, yes, I can't believe I get to go next because she was being so good listening to all your presentations And of course now that I'm up. She's kind of whining So it also we also talk about whether or not there's an X and a Y intercept for this particular Problem and what those would mean and then of course they do come up with both an experimental and a theoretical model And so this is kind of the lesson that I did and I had like basically, you know Five sets of 40 dice. That's not a cheap lesson. All of the dice are not that expensive if you go through the right the right place But I started working with one of my MAT students when I used to train teachers at the University of Alaska Anchorage and He was really into spreadsheets and what he did is he helped me Write a spreadsheet and I think what I have to do is I have to stop sharing and Share and this time show you this one Are you guys able to see the spreadsheet and so he helped me Create this spreadsheet and on this one you can put in that you have 10-sided dice And it'll roll it for you that many times 20 times. It'll run the experiment for you It'll tell you how many dice are remaining here. You can see in this column After each time and this one does it 40 times not just 20 so you can also do it for a different dice and so You can do it for a five-sided dice if you guys ever seen one of those Or I'm just you know, just being a little facetious there an eight-sided dice and so on and so forth or you could have the kids use pennies and M&Ms for the two-sided Experiment you've probably seen that done before and you can also have this spreadsheet Generate it and so all this is to say that It's a really fun experiment that kids get a lot out of and it helps them connect It helps them connect some of the stuff they're doing in algebra to particularly the exponential regression with an actual theoretical model That's pretty easy for students to understand because you know with a 10-sided dice They understand that you're if you're only taking out one number each time You're going to be removing about a tenth of the dice each time and so they can see that growth modeled fairly easily and Let's see here So I think I have one more slide here Um So like I said you could do other than you could have different groups do different Give them different kinds of dice so you could give one group a 10-sided die set of 40 10-sided dice another one 40 M&Ms another one 46 Six-sided dice and so on or you could use the spreadsheet I like the actual motion of having them use the dice because the kids really enjoy that part And it's very noisy if you have all these groups shaking that these in a box but the spreadsheet could be can be nice to You know get more data to add to your class average So that's all I have. There's my cute little puppy on the beach here where I live in Homer, Alaska And if you have any questions Let me know and I'll send the materials along to Elizabeth So I'm going to stop sharing now Awesome. Thanks, Sonny. That's fantastic. I Like that it was using 10-sided die I've done the exponential growth with M&Ms an exponential decay with the M&Ms But I like seeing the change with the 10-sided dice as opposed to two-sided. Oh, thank you Anyone else have any questions or anything for Sonny? All right, Zach, you're up. What are you doing? Is this okay? You see it No, you can't okay now you can I Can see you right now Zach you can see me right now. That's not good. You look great. Let's try it share screen Here we go. Here we go. I think I found it Great. There you go. Yeah, there we go. Okay, so When I came to PCMI, I'm gonna share a quick story I was I was inspired by what I saw. This was a really cool experience for me and When I did the morning math The thought that I came to my mind was I need to bring this to my classroom And I didn't know how to do that. I was I was going on our charted territory All I saw was 14 problem sets and said I have to do something with this So I won't but I knew that there was there was some kernel of truth that I wanted to find So I just want to review with you what the morning map look like The morning map had these things. They had your opener. Yes, you're important stuff the neat stuff and the tough stuff, right and Very few people ever made it to the tough stuff. I think I made it once. I tried that stuff. That's tough stuff Okay, I but most of the time I was in the important and neat stuff And and it was really cool about it. I Read later about how Bowen and Daryl did a really good job of making sure that we had a very scaffolded experience that we could attack a problem that was unknown and Make it known in essence, you know, we could we could come to a consensus as a team to Gain an understanding in my year. It was on rate matrices But on other things, you know other years It's been on geometry and other things and we took these these topics and learn more about it so I Saw this experience is really cool because I said, okay Maybe I can do the same thing. Maybe I can bring in Start the class with something really simple and build some really cool ideas What I'm going to share with you is some Billy I've built from other people's ideas and some inspiration I received from PD that or other colleagues have talked to me about this So one here's here's a fault Here's a you know if we if we could have this be true all the time all students will complete all tasks every week I think as teachers we know that that's not always possible and I you know, it's it's a it's a sad reality that we We can't have students do everything every week Some kids are not as able some kids can do it some kids You know, I just need the extra support. Sometimes time gets the best of them And so what I what I wanted, you know, I had a colleague come up to me and say You know, I structure my class this way and this is what did it for me. This is what I saw this is the realism and He breaks his class down into three parts. He says a hundred percent of my students at the end of the week should be able to do this 70% of my students probably can handle this and you know for the advanced 30% they can handle this and You can probably take any sort of any Topic I'm gonna use completing the square here because I'm a secondary teacher But you can probably think of ratios proportions. I mean you can take anything and do it with this But I I realized that once once this guy said it to me. I was like, hey, you know, my class sort of fits in these groups They sort of naturally do it. They don't I don't have to force that. That's not something and I hate I Hesitated saying this because it makes it seem like kids can't do everything You know, I don't I don't want to send that message They can't do everything, but I also want to provide a challenge for those that can handle it so Sort of taking those two ideas together. Here's what I came up with For starters, I use a thing called MVP mathematics vision project, which is developed by the state of Utah I don't know if anybody's familiar with that great curriculum excellent curriculum. I'll put a link to it here Mathematics vision project org you just go there. It's for secondary one two and three in Utah Which is the equivalent of algebra and geometry and also to so you can you can get some really good stuff Even some pre-calculus materials in there as well Really cool stuff. It's all caught creative commons free stuff But what I decided to do is take some of their ideas and basically break the class into parts where you notice a pattern Then you reflect about that pattern and then you practice the pattern I have a few ways of doing this The noticing a pattern that's like doing a task. I'll show you an example like that with Completing the square, but we use algebra tiles for that So we'll have kids kids just say alright I'm going to build x squared plus 10x plus something and I need to make a perfect square out of that So I have kids experiment a little bit and then afterwards we ask some reflection questions I use a learning management system called canvas for that But you could use a journal you could use anything you wanted for that And then finally I have an online program called math space Which I don't know what you're available to but this is the equivalent of textbook problems You know, you could you this is where you practice the procedure if you will of completing the square and the cycle continues So, you know, I'll like I said, I'll explain that a minute How that how that progresses? So in Inspired by PCMI I sort of I did I was less creative I didn't go with the tough stuff the neat stuff, but I went more boring. Here's here's my boring version Okay But here's the basic idea Level one is essentially the opener, right? It's something that everyone should be able to do No one should feel left out Either review material in a very brief introduction to the new material in this case completing the square I'm gonna use that I'll show you a detailed version of this and Over the over the course of moving up each level you do a gradually more difficult thing with completing the square For example, maybe you have a is bigger than one Maybe you have B as an odd number Maybe you you do you have an incomplete square and you have to add or subtract something extra, you know that that kind of stuff And then I add an honors task because we have a we have an honors program at our school And if you want to give some of the honors credit, that's a great way to do it Just add a little, you know, here's an extra thing you can do So here's here's an example like as I mentioned here's here's some here's some practical. What does it look like? So it just so happened that the lesson before this was on complex numbers and rational exponents So I do a little review of that and then we we complete the square Like I said, you give them something that says x squared plus 10x plus blank fill in the blank And we have a mess with the algebra tiles see if they can make a square out of it ask some questions And then I and then we do some practice on it Then we move on to imperfect squares Complete in the square where there's not where there's more than one square Right and then finally doing it with an odd number because then you get the decimals and kids don't like decimals So, you know for those that really want to challenge themselves and really abstract the procedure they can And it just so happens that we had been talking about complex numbers There's an honors thing that we do with moduli The modulus of a complex number, which is basically a length That's how it looks like and I can show you the actual if you're interested in like the paper. I give out to students There's a link right here that I'll copy in Let me copy that in the chat So you can sort of see it Okay, if you want to look at it you can I'll pull it up here so you can sort of see what's going on And I'll put the mathematics vision project here to a oops. Did I add more crap? Okay, there's that Here's this Can everybody see this? Did you get it? Okay, so you scroll down a little bit. This is all the formal mumbo jumbo But what I do is I say here's my here's the stuff you got to complete this week I lay it out say okay level one if you are an honor student you got to do that part and then you've got the The cumulative review and complex number practice then we do some investigations You notice that the building a perfect square was a swell backwards here Sort of fun, but let's get into the details. So here you go they've got some practice review review and practice the building the perfect square and Then I have them do it backwards See right there and have what value of B that will make a perfect square trinomial So they have to think about the procedure a little bit and then afterwards I have them do a little reflection saying okay How does foil connect or you know that I hate foil sorry the distributor property connect to Here I am using the bad lingo right No, the the the distributor property has a connect to the expanded form and Then I asked them to write an algorithm for what they've just accomplished right so and then I give them feedback I'll write back to him and say hey, you know, have you thought about this? Have you thought about that? and So on so then level two builds on it Notice there's an almost a perfect square. I have them adjust right and then do a reflection They do some math space practice on what they had just experienced and so on and so forth Let's do you think this is a lot of time The thing that really takes the time is finding the tasks, right? That's why I use the MVP That's that's my go-to source you guys probably have your own sources you go to if you use a textbook for this You can just chop it up into sections and say hey if I'm covering three sections that are all related I Could split it up in a way so that kids can attack it at different levels and use the teacher No, right? You know what the the the content that's hard the content. That's easy you can use the You can use that knowledge to help develop this that's sort of how I do it. I know it's harder and easier for my students And I'll finish up I'll finish up here. I'm just about done Yeah, I was just about to finish I'm just like done so I just I'll ask any questions you have That was a lot I know but That's how I set it up That looks awesome, and you'll send us the slides with all those links so they'll all get posted just Yes, all there. They're all great resources. I love this stuff. So yeah That was fantastic. Thanks Zach. No problem. Okay. Just try to get back on time. Abby you're up Okay, hello, I'm gonna be doing Mastery-based grading I'm gonna try this So do you all see the slide that says what is it Okay, great so there's definitely a lot of definitions about mastery-based grading out there and These are the three most important characteristics to me. So the first is it's based on specific learning targets very discreet Content targets you could also do writing or reading targets We at my school do Democracy and work habit targets as well and another key characteristic of mastery-based grading is that there is multiple opportunities and revisions So in a traditional assessment method, you may say the unit test is happening on March 5th And that's the day you do it mastery-based grading one of the things that is Different teachers do this differently But one of the goals is to give students multiple opportunities to so to say maybe you don't know whatever We're assessing on March 5th, but maybe you know at March 10th, and you should get credit for that and then it de-emphasizes percentages and points To use a smaller number scale and different people do this differently, but my school does a scale of one to four So if you earn a four it means you've completely mastered the given learning target if you've earned a three It means you're on track But there's still some misconceptions a two means you've shown that you have an idea You're starting to understand some part of the concept and then one normally means you didn't It's kind of like blank or you have no understanding of this content learning target. So Let me go back to why Why okay So I teach at a transfer school and that means that students come from places where they have to have attended another high school First so they have a lot of anxiety about school and school has just not been something That they've been successful at in the past and a lot of students when they receive an assessment They are really anxious. They'll walk out of the room So this mastery-based grading is One way to reduce anxiety for students because students know that there's multiple chances, right? If you don't get it today, you can maybe get it tomorrow or the next day And there's no penalty for getting it later or for my class You can get it at the end of the semester and once I see that you understand this learning target You've earned a four in my gradebook Doesn't matter when or how you showed me that Another reason I really like this and it's really shifted my classroom is I understand more of what students know so in my first Years teaching I had very traditional assessments and I would say oh this student got a 70% on the test When I had no idea what that meant or an 80% on the project I didn't really understand what they knew or what they didn't know a lot of teachers use this with rubrics as well And then it's easier to give feedback So it's easier for me to know what my students are knowing and it's easier for students to know So something I hear in my classroom often is oh I understand how to solve theoretical probability But I don't get experimental probability yet And that's a really good thing for students to be able to talk about their learning in that way so like I said before teachers do this very differently and I've spent a lot of time looking at Different people's work to design this so this is modified and adapted from other people's work I give students this at the beginning of each case study right now in teaching probability My learning targets are broken into different big categories problem-solving representation um reasoning and proof communication and Connections and those are from a network rubric that we use for another type of assessment so I First as a teacher decide what learning targets are important So in my probability class for our first case study, which is the language we use for units I give them these um Learning targets. This is our goals for that first case study four weeks about and I give students this so our goal is to learn these three concepts we spend Three or four weeks learning these things normally through games and problem solving And then every Friday I give the students a mastery opportunity and this is to show what they know You notice a few differences from maybe traditional assessments. The first is it's learning targets at the top right so all the questions are broken up by learning targets and Students receive this every Friday For the four or five weeks of the semester or for the four or five weeks of the case study And then when that case study is over they can still work on this um This content we're moving on in class, but if they want to come after school and we take these that's great And again, there's no penalty. I take their best score And so I can see what students know and they have the opportunity to Feel confident about what they know as well Just a few challenges. Um, this process is really easy with discrete skills But it's hard to assess something like problem solving and I really don't know how to assess problem solving yet um So that's a big question for me It doesn't always measure retention or application You could design your assessments to be more of an application um I choose not to for this part of my assessment And then as with any assessment, it's only a sample of what students know or don't know So we're always getting incomplete. Um information when we're assessing and this doesn't fix that totally So I think I might have time for a few questions if anyone has questions I um, thank you abby. I just uh, one of the things I appreciated about your presentation is I don't know how Other schools operate, but our school board has a policy that you cannot factor behavior into a student's grade And so I what I like about your approach is that it's focusing on what kids know Not how they behave in class Um, we obviously know that at some point we will factor a certain level of behavior into a students grade Because if they don't show up we can't assess their their learning um, but it's neat that you're trying to Remedy or fix that that dilemma that that we have and that math teachers. I think in general fall into that whole You know 70 80 percent zeros in the grade book for every homework assignment miss that just kill a kid's grade And brings it down to a hopelessness, you know, and so your mastery approach is really It's just really refreshing to see I'll just add at my school. We have 60 attendance at transfer school. That's one of our challenges And so I have students who have maybe 30 attendance But actually know a lot of the content and are able to get it um, and I think in a traditional assessment System these students want it passed and that this is one of the reasons they haven't passed in their other high schools And they're not earning credit even though they know the content So I think it's really valuable to give credit to what students do know if these are the things I think are important for students to know and they know it. They should pass my class, right? Yeah, absolutely and um You know having taught pre-algebra for almost 20 years in the school. I'm in right now is 90 attendance rate Uh 95 attendance rates, you know middle to high income super easy place to exist, right? And when I taught pre-algebra At a low-income school for 10 years It was largely male and largely non-white even though that wasn't representative of the population And so I think that's an example of how some of these kids get all the way to high school and They're in a math class based on their behavior not on their knowledge is Is when and then they're putting that track and okay. Anyway, I'm not going to go off on on that tangent Your other thing was about problem solving and I think I've seen some good like observation checklists or rubrics out there um, you've probably seen as well, and I think that it's really time consuming to assess problem solving or anything via a checklist or an observation, but maybe it could be developed into a student's self assessment You know where they self assess themselves based on that checklist or rubric I have a question about how much time after school. I mean with 160 students thinking about them retesting um, or retaking things after school is kind of overwhelming to me Um, because a lot of them would choose to do that How do you how do you work with that? I think that's one of the reasons that I've embedded it So frequently into the class. So every Friday, it's another opportunity So they get three or four chances in class um I don't have that problem of too many students wanting to come after school. I have like maybe A few students who want that perfect for on everything each semester. So it's very manageable I think you'd have to maybe reconsider how to either structure it in class or Maybe you get I don't know. Yeah, I'm not sure how to deal with that problem or that that's a good problem to have but That situation cool. Thank you so much abby. That's our 10 minutes So more questions that people want to email our presenters if presenters are okay with that We can get that for more questions and if at the end we're done and we get everybody covering We still have time we can come back to it So abby if you can Stop sharing your screen and Irene you're up Can you see? Can you see can you see my screen? I can okay All right. Um, I did a little practice right here. So I'm a little bit nervous I started doing this in year 2014 and When I attended the PCMI I shared this And I got something from PCMI where We were focusing on structure So when I got this materials Yeah, the straws and connectors because I have a lot of slides. So I'm gonna Jump on to the straws and connectors, but my Really mean focus is how can I use these straws and connectors to develop algebraic thinking? And I use these Definitions as reference to what would be the evidence says that I should see from my students So that I know they are thinking algebraically Then I came up with this like I know when my students are thinking algebraically when they can search for a recognized pattern and structure Collect and organize data write equivalent expressions and equations Write ruling words and symbols grab and use equations to solve real problems Now I focus on one thing. How can I develop among my students the skill of being able to Generalize a pattern with fluency so This material is like In the beginning. I just was uh, fascinated with this Toys just to play Then I started using this with my middle schooler And the initial objective that I I had was to develop social learning skills because They don't know how to communicate with each other and they don't want to share space So I think up. Let me make them build, you know, something and let them share the space So they seem to be happy like, oh, they're not fighting sharing little space And then I just let them play and then I started Let me just show the picture before I show the slides. So I'm not going to be jumping with Other, you know, take time to jump to another slide. So I just I did this with the middle schooler And then I also did this with the adult this Our picture so my students in adult education the the ages are 21 and above. I have 60 year old 22 23 45 and It was amazing. Like I discovered like when they count It was not systematic. So they get confused But when I said if you can count systematically, you can develop the the pattern and the formula And then I let them build different, you know shapes and then later on They asked me to do this with adult ad teachers this time Because when they do workshop, they're always sitting down and they see that oh with that they can stand up and you know And work together as a team And social learning skills also among adults can be developed And then lastly I did this with the mat for america teachers And they seem to have fun too. So I started with the simple strokes and connectors That's line segments, but I use strokes and connectors. So my students can touch it Can disconnect it can connect them and they can hold it when they count it And then I focus on the way they should count the dots and the strokes Systematically and write the equivalent expressions When they write the equivalent expression, they can establish the pattern And then they can come up with a formula in the end So this one two dots Every stage has two dots in the beginning And then you're adding one Two zero first and then one two this one you You make the first that consistently there Make it like it's always there in every figure number stage number And you're increasing it by one two and three And in any way you count it as long as you are being consistent you can establish the formula And there are many patterns where my kids work and Later on they develop the skill of writing equivalent expressions They work as a group and then it is extended to Functions So there are a lot of concepts that can be developed with the use of this tools And it's so hard to count when you have three dimensional if it is just a drawing But if you have a tangible thing where they can systematically count and hold it They can develop the pattern and they can develop the formula And they can now perform Developing or generalizing for more complicated figures So these are the I develop worksheets. I have a lot of worksheets with different patterns And they keep on practicing and that and then we also extend it to Like if you have this equation here One quadratic and one linear And then we are developing the concept of a system of equations So Before I was just like looking at this as like simple pattern and now it becomes more complicated as I keep on working So this is still in progress and with the sixth grade student being able to come up with this work and I just wonder how These skills can help them when they go to high school And go to college like will they be able to Generalize a pattern if they can systematically count and represent this counting system in order And then develop the pattern develop the the formula And then I found the structure here and I saw my straws and connectors So I can connect now my straws and connectors solving a problem like this Like how many panels and how many connectors do I need in order to form? You know a cube square divider an organizer two by two three by three four by four And I saw this also on Uh the images from Uh a certain website and I saw this Kind of figure two. Oh, this is also something that I can connect with my straws and connectors So it's still in progress. I am seeing a lot of things. I am seeing a lot of math but I just don't have time to really work on it, but Maybe if I focus on it, I could see a lot of Mathematical concepts that can be developed so far. These are my findings That to develop formula A consistent systematic counting can help Objects may be counted in different ways, but as long as it is done systematically and consistently patterns can be stopped Scaling writing equipment expression numbers can be written in an infinite number of ways It can be interpreted as you as used in a context of real life situation It only makes sense when we're written in such a way that you can relate the number with the real objects and The operation symbol with the process in counting the objects And of course with the straws and connectors I think these are the skills that can be developed mathematical concepts and You know mathematical skills, processing skills, communicating skills Listening and reading skills, visualizing skills, manipulating skills, social learning skills And of course when you are working within a group leadership skills are also developed Thank you That was great Thank you I like that using the straws and connectors to build those I just finished going over Sequences and patterns with my I teach math for elementary education teachers So we go over, you know elementary school math and finding patterns and sequences and I wish I had seen this before to get them to actually do it and touch them as opposed to just looking at the pictures So awesome. Thanks Irene. Thank you You have any question Irene there was also a question in the chat if you are willing to share your worksheets. Yes I am I have a lot I can show you if we have time just one piece like this one Irene if you have like a link to share or anything you want to share or you want to share and I say new share, right? Yeah, yeah send anything to me and then we'll get it posted to the webpage for everybody to see Can you see it? You see something So so if Irene emails this to you this You can like have have it uploaded to the website. I'll have everything uploaded to the pcmy website It'll be under the reconnect sessions under today's will we'll put links for everything there. Yep Awesome, thank you so much Irene and gail. Thanks for waiting patiently. I know we're well behind schedule today But take it away. So Irene if you stop screen sharing and then gail you can screen share Just Gail you're muted you have to unmute yourself so we can hear you now can hear me. Yes Okay, um, these are for sunny. There's some pictures of five sided dice I thought you might like and What i'm going to do today is just share a game that I played with my students called building fences it builds teamwork and some math skills and it was Something that I used because I liked the game of 24, but um I wasn't as crazy about it as some teachers and it seemed like either you are really really good at it or you really weren't good at it and there weren't like multiple entry levels, so I developed this game Um, and the way you start is you choose four digits to fill the blanks And I usually played it first as a whole class kind of activity. So I had two different groups Um, usually boys and girls because they seemed to like that competition so they would alternate numbers and I used colors so that they could easily see Who did what on the board and the next step is you take turns using at least two of the digits To reach one of the numbers on the board Um, and you could use two or three or four of the digits So but you couldn't say like nine and find nine on the board So for example, the red team might say nine plus one plus two plus five equals 17 And they get points By how many numbers they use so if they use all four numbers they get a bonus point of five And the second team then said, oh, I want to do five times two plus one that gives me 11 They use three numbers. So they got three points And then the next group said, oh, I want to do nine minus five squared so they got three points however Because they have an adjacent square. That's their color It doubles their points to six So they there's a little strategy you have to try to get certain numbers and the purple team Didn't want them to get another double. So they found two plus one subtracted from five times nine to get 18 And that gave them five points, but they've also blocked the other team and The reason I liked this game better than 24 was There were multiple entry points kids that really were only comfortable adding and subtracting could try to do that Kids that wanted to use exponents or square roots could do that the ones that Had never thought about using square roots were like, oh And it was really neat when Somebody would use the square root of zero Or not the square root of zero the exponent of zero to get the number one Then everybody wanted to use that so um, they they became Pretty interested in which numbers they should choose at the beginning of the game as well Um, I think it builds computational fluency. I let them use calculators But some of them discovered that the kids that were doing it mentally Were doing it quicker than the ones that were using calculators So that was encouraging. Um, it provided order of operation practice because they wrote the Expressions down and then if it wasn't exactly written correctly somebody would point it out to them But that's you know, what you said It encourages strategic thinking And it supports teamwork um, I would after I'd introduced this and we played it and I I usually started with a small group who were interested in playing Um, maybe the last five minutes of class while we were waiting for dismissal to happen for the buses um And then more and more kids would sort of at first reluctantly and you could watch them all looking and Then suddenly they oh they had an idea and they wanted to share their answer So it got kind of cool the way they would talk to each other about what numbers they should choose Um, and it's really adaptable. I mean I put the numbers 11 c 34 on this grid But you could start with one or any number you wanted um Or you could even use negatives Or I I guess there's you know, there are no building fences police out there You could actually put any numbers you wanted on the board So that's it. Um That was longer than I thought it would be That's fantastic. I do something similar my mom years ago found us this game and it was I'll have to see if I can find a picture of it. I don't remember the name of it. It was like math forum or something Where the center dice is a 10 digit dice and there's there's two black dice And it's kind of like a yatsi and you shake the dice and you have to use the five dice on the outside To get up to whatever it happens to roll Sometimes there's multiple ways to do it sometimes there's only one so it's just like this And I used to have that sitting on my desk When I taught high school and if there were you know five minutes or a study hall The kids would fight over getting to play the toy with the toy to see who could figure it out And it was the same thing noticing like oh I can use exponents But they couldn't use a square root unless they could write it as an exponent So that awesome. I love that a lot. Thank you You're welcome I love your idea about using get at the end of a class for you know that if there's like a few minutes even that It's like well, you know, it's it's just a few minutes. I love that idea I may even do that with my higher level cat classes I was thinking oh, it would be perfect for seventh grade curriculum and such But then I was like shoot forget that I could do that with any class. They'll have fun Are we allowed to have fun during math? Every once in a while, huh? Every once in a while Thanks And gail, would you mind sharing that file as well? Is it? Yeah, I'm happy to thank you. You're welcome So I'm done Oh, this was the game. So you you shook it around and the black dice. It was whatever their sum is You have to use the other five dice to get there So magic mixer is what it was and I know you can still find it I actually wanted to order it when I taught at the high school And I was told because we didn't order it it didn't come from an official school supply store We weren't allowed to um, but if you guys have it my students absolutely loved this I've also used it for just a held a Information like we call it mathematics at the community college on one of our kind of convocation days and the groups of students that came in So they loved it. We did it with the faculty and staff So it's very similar to what gail was saying, but they can kind of do it on in their own as well I'm going to try to end my screen share And liz I just found it on amazon for 12 dollars and 51 cents. It does for amazon prime Don't everyone go at once though. It only has 11 left in stock And how what am I doing here? That's basically one for each of us though. So that's all right Good point. So if liz already has hers we're we're said Limit one each All right, awesome. Thank you so much everybody. This was I think a great fantastic session. I apologize. I know we got off late Um, I'll I'll blame myself because I had my little situation of running sprinting through the snow to get my dog So I was a little late getting everything started this morning as well So thanks for bearing with us and giving us your morning sunny. Thanks for being here so bright and early Cal we're glad you were able to come in and kind of spy on us Notice you didn't want a video with us, but that's okay. We're still happy to have you and beth I'm so happy you could come in and sit in as well And I will get all of this posted. There will be the recording will also get uploaded probably early next week If anyone has any questions just send us an email. Thanks so much everybody. Great day. Thank you. Thank you