Hello, everyone. Welcome to our webinar, Connecting K-12. Sorry, a little technical difficulty there. Sorry. Hello, everyone. Welcome to the webinar, Connecting K-12 and Higher Education through the use of performance assessments. Thank you so much for joining us. Well, we have a few minutes to make sure everyone gets logged in and online. I'd love for some of those who are on the webinar right now to use the chat function to let us know who you are. If you've attended one of our webinars before, maybe identify your organization or who you are, and just kind of start practice and kind of warming up our chat room as we wait for others. As many of you are probably aware, you can engage in discussion in the chat throughout the webinar. And please choose panelists and attendees from the dropdown in the chat box so everyone can see the responses. Hey, I saw Mike Riley, one of our partners. Welcome, Mike. We'll be listing resources we share in the chat throughout the webinar. In fact, the slides are currently available in the link at the link in the chat box. If you have questions, please submit them using the question and answer button at the bottom of the screen as well. I'd also like to let the audience know that this webinar is being recorded. A video recording along with a summary of the webinar content will be emailed to you in a few days. So this means my stumbling over words will be well recorded at this point. This is the third in the series of three reimagining college access and success webinars. Today's webinar will build on the first two webinars. The first webinar described performance assessment and highlighted the outcomes for students who scored below the admissions cutoff for standardized college entrance exams and were admitted to City University of New York based on performance assessments. The webinar was based on a study LPI is releasing today, assessing college readiness through the use of authentic student work, how the City University of New York and the New York performance standards assessment are collaborating towards equity. The study was conducted by Michelle Fine and Karina Priyanka and can be found on our website starting today. We're really excited about this report provides the evidence that a lot of folks are looking for in this field. Our second webinar shared how the higher education institutions have integrated performance assessment in their admissions process. It included our partner with a common app who works with Slide Room for students to submit student work through a portal. Wheaton College, one of the five RCA piloting sites in New England and MIT who has been using student work as part of their admissions process for almost a decade now were featured. The institutions shared in detail the how tos and the lessons learned, as this is a very iterative process admissions officers take on. Today we are concluding this three part series with a focus on K-12 as we explore why and how secondary schools can align their performance assessments for their use in higher education to advance college access and success. We now begin the formal part of our presentation. My name is Monica Martinez and I am the director of strategic partnerships where one of the initiatives I support is reimagining college access. A partnership of the Learning Policy Institute and Education Council. Dan Gordon and Joan Fretwell from Education Council helped create and support this webinar. For those of you who are not aware of RCA, we began in 2017 when LPI and Education Council brought together a group of individuals and organizations in higher education admissions, placement, advising, and performance assessment to explore the value of using K-12 performance assessment to improve the decisions around quality and equity by providing better information. As you can see from the slide, partners include the National Association for College Admissions Counseling, the American Association of Collegiate Registars and Admissions Officers, State Department leaders, school networks like link learning, envisions, great schools, partnership, the mastery transcript, the coalition for college, and making caring common. Following this 2017 exploratory meeting, three task force were created to shape the initiative. As this slide shows, through a combination of task force meetings and convenings with a network of interested individuals and organizations over the last two or three years, a specific set of recommendations were made aimed at achieving RCA's vision. Ed Council and LPI enacted these recommendations over the past few years, including Ed First supporting us in launching a pilot program last fall, 2019, to use performance assessment and admissions at Castleton University, Clark University, Pine Manor College, Southern New Hampshire University, and Wheaton College through the Common App in partnership with Slide Room. With the increase in the number of higher education institutions that have gone test optional, RCA seeks to connect two trends in education, the use of high quality performance assessments in K-12 to drive deeper learning and better post-secondary preparation, and the use of more holistic approaches to increase college access and success for students, particularly those who are most underrepresented. As I referenced when we began this webinar, today's webinar addresses performance assessment and higher education. But we are also releasing the report, Assessing College Readiness Through Authentic Student Work, that describes the teaching assessment systems of schools in the New York Standards Performance Consortium, and how the work that students produce through these schools can inform college admissions. And more specifically, how CUNY uses performance assessment for admissions to their four year colleges for students who do not meet the cut score for the SAT. The report presents evidence that shows students admitted to CUNY based on their performance assessment, on average, achieved higher first semester college GPAs, earned more initial course credits, and persisted in college after the first year at higher rates than peers from other New York City public schools. We're really excited to release this report today. Today we have three experts in college admissions to explore how to use and align performance assessments to higher education. We have David Hawkins, who is the executive director for educational content and policy at NACAC, where he has worked for the past 20 years and will bring a perspective from college admissions counselors. NACAC represents college admissions counseling professionals dedicated to fairness, equity, transparency, and professionalism in college admissions. David has been working with RCA from the very beginning, as he really helps rethink college access and success. Clea Joseph is the manager of college readiness for international network. Clea is responsible for building the capacity of school staff across the international network schools to support college access and success. And last but not least, Chris White, an educational coach for High Tech High Graduate School of Education's Carpe College Access Network, an executive director of college counseling for High Tech High Network for the past 19 years. Additionally, Chris has served on the external admissions committee for the University of California San Diego since 2004. So how this will work today is I'll pose some questions to the panelists to kick off the conversation, and then we'll also turn to address questions from the audience. As a reminder, if you have any questions, please click the Q&A button at the bottom of your screen. If you'd like to engage in discussion, you can click the chat button at the lower right side of your screen and type in the chat box to everyone and panelists. It'd be great if you identified your institutional affiliation, if possible. With that, as context, I'd like to welcome my panelists for today. Great. Thank you all for joining us today and thank you for the time and preparing for this and being part of this today and taking an hour out of your day. I'm going to start with Chris and Kalia. And to ground us, I want to start by asking about the student competencies that are developed the teaching and assessment practices at High Tech High and international networks for schools, and also talk with David about what higher education could be looking for or are looking for. Chris, we'll start off with you. Tell us a little bit about your students at High Tech High, who comes to your school, how do they learn, and how do you know they are learning. Thank you. Certainly an honor to be here. Welcome everyone and hello from sunny San Diego. Mandy, if you could just throw up the first slides there, just to provide a little bit of the context of the High Tech High Network and our learning environment. We have four design principles, personalization, equity, authentic work and collaborative design. I won't go through all four of them. I will highlight for the purpose of this today's conversation, two of them in the essence of equity. You can see from a member's perspective about 50% of our students are eligible around the pre-reduced like program. 47% first generation and a majority are students of color, 44% Latinx and 10% black. But beyond just the numbers, we are also culturally responsive in terms of like teaching pedagogies and a part of the abolitionist teaching network and then the authentic work piece to provide a little bit more detail. The project-based learning is the core of our work and so students engage in projects that matter to them, to their teachers and to the broader society. And then just to dig one layer deeper, if you could go to the next slide. We ascribe to the deeper learning competencies so our students are assessed in areas and you can see the six competencies here. And again, I might reference them later on as maybe we kind of look at or answer some of the specific questions, but how these competencies are assessed. Currently, qualitative comments every quarter, our students receive comments from their teachers and of course they're kind of assessed relative to the six deeper learning competencies. They do provide letter grades. Students do have presentations of learning where they present quarterly about the work that they've mastered and then through student-led conferences. So in a nutshell, that's the high tech high network and as I mentioned earlier, I may reference some of these points later on. Great. Thank you so much, Chris, for grounding us in the work of high tech high. Clea, would you do the same for the international network? Sure. So our students are recently arrived immigrants. They're multilingual learners. And so one of our schools in New York City can have, you know, maybe 42 native countries represented, 22 languages spoken. Our students are first generation first, you know, to go to college. But I think what's really unique is that our classrooms and what's up is our core principle. So I'll speak to just the first two. Our classrooms are heterogeneous. So our students are grouped by language, English level, grade level, a lot of activity based and group based learning. I really emphasize students home language and cultures being integrated into the curriculum.  And so students are demonstrating that through literary essays, research papers, scientific lab reports, reflections, or even we have a native language proficiency sheet proficiency. That really kind of demonstrates, you know, what students are learning. And, you know, so I'll continue to talk about that throughout the talk as well. Great. Thank you so much to both of you. Let's take a little bit deeper into some of the work you all do and tell us how this kind of learning and assessment practices that your students engage in at your school, prepare students for college. Another way I like to say it is what will make them successful in college because they attended a school like yours. I'll go and go first. Go ahead. Thank you. Sorry. I think when I so I'll the first one I'll mention and I'll kind of refer to our deeper learning competency of learn how to learn and kind of reform kind of support that with an example. I do think that learning learning how to learn and our students when they're approached with difficult content and challenging and rigorous learning. Our students are really trained on how to learn. And so example of that actually, I just kind of reconnected with a graduate from last year. First generation student went on to Pitzer College, and he shared with me he just said Chris chemistry was so so hard. He got through it and actually did well, got an A in the class, but it was very, very difficult. So I just asked him, obviously, how did you get through that class? What were the things that you, you know, did and and it's things that we would naturally kind of want a student to do but he really put them in practice. So he was one of facilitated small groups. He kind of looked around. This is a difficult thing kind of leaned on his project based learning and collaboration. He got the students groups together. And of course brought in the faculty really felt comfortable and engaging faculty. And so he really felt that through that experience and learning how to learn got him through a very difficult course. Thank you so much, Chris, can you tell us a little bit more about some of the competencies that you guys developed that really enable your students to be successful in higher education. I actually agree with Chris, you know, for us, similar our students ability to advocate for themselves, I think, especially because students are coming in newly arrived immigrants they've been in the country for years or less. And so the advocacy part is really important who to go to, you know, when you need help. And, you know, I've seen that we have we hope interns and our interns are graduates from the network and so, you know, being able to engage with them and talk to them about their college experience as they're in it. In that moment I always see that the advocacy piece shows through even as they they're interning for us and need support, which is, which is important to see, you know, to see them taking an internship be serious about this internship but then also have the ability to recognize like how to grow. And I think that those things are very important and things that they're learning at our schools again with the group learning as well collaborating with others. I think it's just such an important factor in when attending college.  Yeah, I mean, I hear this time after time schools like yours around the ability to learn how to learn, and the fact that you take your students through such an intense feedback and learning loop where they're constantly getting feedback from teachers and from outside members. So they're constantly improving their work. I can hear how comfortable they are to advocate like what you said clear, and, and Chris how comfortable they are to approach a faculty member because they're used to integrating asking for feedback and support so the agency as well as the learning to learn is amazing. David, what are you higher education members. What are they looking for higher education institutions in admissions and, and how could they know more about these types of competencies that Chris and clear have just talked about First of all, thank you, Monica for having having me on this on this webinar. I'll answer your question by noting how how significant what clear and Chris just said is it in that is that in college admission, you know, they obviously look at a range of factors. They look at factors like the high school grades and the college admission test scores and essays and recommendations and such. And that gives them a pretty good overview of what a student has has accomplished but what most admission officers will tell you at selective admission colleges is that there's a lot we don't know about what makes students successful in college and I think that if I had to share what, you know, over the last decade or so what what admission officers have have most been looking for actually this extends well beyond the last decade but it certainly reached a point in the last decade where I think we've gotten some critical mass. We've seen it labeled a number of ways we've we've we've heard about non cognitive factors we've heard about grit. We've heard about moxie we've heard about character and all of those things are important. Advocacy is incredibly important self advocacy learning how to learn you know all of these sort of paint a much broader three dimensional multi dimensional picture of students that we really don't get through the paper online application process. So I think that that it's it's that unexplained variance that a lot of admission officers have really been trying their best to go after. And the way we hear we hear it talked about is, you know, holistic admission and and and you know sort of comprehensive review. But what what I think you'll hear most from admission officers is that really what students do in high school is the single best predictor of their success in college and it's also the most most important thing if you really think about it, you know it's it's it's what a student actually learn and how they engage with their educational experience. That is where I immediately Monica you mentioned I was have been in this RCA initiative since the start. It's where I immediately recognized that performance assessments provide a lot of that they really provide a lot of the depth that a straight up transcript or GPA doesn't provide about what a student is capable of doing. And of course, college admission ranges from just minimally, you know, ensuring that a student can succeed, all the way up to making more nuanced decisions about you know well how do we craft the student body at this highly selective college. And in any of those contexts, having access to this depth of information is going to help, particularly as it adds depth to the to the high school record. And the last thing I'll say is that another thing that they want. They want to come from high school students, but they want something that they can demonstrate to others so I'm thinking campus leaders alumni legislators and policymakers about how these things actually do correlate to student success in college, because it's easy to show correlations between quantitative measures, but what's what's better in a way is being able to say well look at how this set of skills aligns with success at our institution. So that in a in a nutshell I think is is is what we're after these days. Thank you so much clear and Chris I wonder if you want to build a little bit more on that hearing what David has suggested about kind of this arc of conversation with admissions officers about what they're looking for. And I also wonder if you could address how you develop the core content we had a question about that from one of our participants. So I'll start and David, thank you for that summary of kind of what colleges are looking for, you know, beyond, you know, the grades and the test scores. And I think I would just build upon it and having had experience and admissions and then now the last 19 years on the high school side. And I guess I would summarize my experience in this way, I wish colleges knew the students stories, not how they write about them, but how they live them I mean it's a, it's an aspirational statement clearly. But again, having served on both sides of the desk. That's that's that's truly what we as we support our students in the college application process and of course their learning experience is what we're trying to aspire these students to do you know in their kind of one dimensional application. And so that's the challenge that's the that's the bar that we set for our students. In terms of the learning environment and again obviously high tech high is not, you know, the original project based learning school and of course the only one that offers, you know, obscribes to the deeper learning competencies. We do feel though that is those competencies really serve the students best. And again, not just not just obviously as a transition to high school to college, but obviously college into life and beyond oftentimes our alums will come back and reaffirm a statement that we say, you know, high tech high. You know, traditional schools prepare students for the first year of high up college, or high high tech high prepare students for the last two years of college and beyond. And again, that's where those deeper learning competencies come in and we're going to stand strong on those and really kind of make sure that our students are walking away from from our school and our education with those competencies. Yeah, clear. Do you want to add before we move on to the next question. Sure, I definitely really liked what Chris said about, you know, wishing that colleges new student stories and how they live them and I think that with our students, again, being newly arrived immigrants English language learners. It's a set up for them to learn English, which is hard in itself. And so it's a lot of native language integration and our classrooms. And so I think that is important. And I wish that colleges can, you know, really understand how students are tackling this task right of graduating high school in New York City but also learning English, which is a big deal and and should be rewarded. And it's a competency in itself, right, because it's not hard to learn another language. So, you know, that's something I would add. Yeah, I appreciate that. And I'll just add to the person who answered the question. Everything that Chris and clear said, but also content is not taught and you can hear this from clear in isolation. It's really taught across all the courses and through an interdisciplinary integrated way so that students are able to have conceptual understanding of academic knowledge and to be able to apply that to different situations as well as other disciplines. So I just wanted to add that in there because sometimes you guys just don't brag enough about the work you do and and how well you prepare students around agency and learning to learn and collaboration. And I hope that you guys are able to accept feedback and to grow but also they come out as as true intellects who engage in in serious discourse within these schools at all these levels. I want to keep moving us along and I hope that folks have a good understanding or some understanding of both of these designs, because this one is a little bit more, I guess about an opinion in some ways but how do you think that the use of performance assessment in higher education or this kind of teaching an assessment that you both do can really kind of help and facilitate and support college access and success for students who are traditionally underserved. And this could be students of color English language learners low income students. Chris you talked a little bit about the one dimensional application so let's talk, let's lead with you and ask about and talk about how this can really provide equity in college access and success. I love it. I'm being a first gen student myself. Thank you for this question and it truly is what fueled me day in day out to do this work. And so if I can have our high tech I elevate by shared with a group. So we've been fortunate the high tech I network, you know, six high schools, 2700 students. We, we established a college access initiative called high tech I elevate. About three years ago, we started it. And within that, obviously we have some very strong relationships with universities and we're growing this partnership with universities to, to kind of really look at and pilot right performance assessment in the college admissions So this slide here is you'll see our three partners and University Redlands University Richmond and Gettysburg College have we've worked closely with them to to of course support for specifically for first generation low income students. And to your specific question, you know, what are those elements that we add into this admissions process, beyond the grades and test scores, and really encouraging these colleges and these colleges coming to a thing. We want to emphasize and put more weight on these elements of essays, interviews, recommendations, specifically a resiliency statement from the students and digital portfolios. And I want to highlight there's five, five comments from our partner colleges here but to I really want to highlight one being the first one there and the kind of the left corner learn so much more depth to their student stories, than an application or essay prompts could And what what's behind that statement is, you know, essays and the prompts and common app obviously does great work and really being mindful and top five was able to serve on the common app board of directors and and understanding the thought that goes behind the essay prompts. However, from a first generation student perspective they don't always they, it doesn't come natural to them to really kind of put out their stories of resilience. So it's oftentimes how you couch what you want them to respond to and be more explicit in what they're responding to so we actually have resiliency statements that we share with the group. And then the other one is I am so at the bottom left, I am better prepared to talk about some of the challenges and differences coming to Gettysburg, Pennsylvania, from San Diego, California. To David's point, right, like through the traditional application and admissions reader won't really kind of get those things out of an application to truly understand what some of the challenges that a student has experienced in their K-12 education. And one of those challenges that they may experience as they leave San Diego and go to Gettysburg, Pennsylvania, and the support systems that are needed in order for that, that to successfully that matrication to successfully happen retention of course graduation. So, so this has been a wonderful program that we've been able to work and really implement a performance assessment and and hopefully kind of grow and expand from what we've learned in these relationships with these higher education institutions. Great. Thanks, Chris. Clea, how do you think the use of the teaching practices that your school and performance assessment lead to equity in college access and success. So, I think that one of the things that we try to do in terms of building partnerships is really offering students and programs and teachers and programs and opportunity to understand our model and have that reciprocity. So, you know, for instance, CUNY has a program called CLIP, which is their language immersion program where students oftentimes may place into because they still need to develop their English language skills. And so one of the things that we did was, you know, have an opportunity to invite people from CLIP from the different CUNY campuses to internationals and get a chance to experience the international model. Visit the classroom, talk to students, talk to teachers, look at our rubric, look at examples, exemplar work of RPBAT, but then also give our teachers an opportunity to learn about the CLIP program and what CLIP is expecting our students to do. At the same token, wanting CLIP to understand what our students are learning, what are they doing in the classroom, how are they prepared to enter into a CLIP program, and what can we do differently on both ends. And so wanting to take this a step further and continue this work and allow for our teachers at some point to be able to visit the CLIP program and visit the classrooms and see how their classes are grouped, how they're doing collaborative work, how their students are learning, and to be able to really take that back and sort of promote success in these programs. Great. Thank you so much. And I don't mean to leave David last, and he is not least, but we'll move over to the higher ed admissions side. And David talk to us a little bit about how you think the use of performance assessment can lead to equitable practices around college access and success. Well, what strikes me most probably is that the use of performance assessments is not bottled up in a certain segment of schools. It is truly being implemented in all sorts of schools across the US and in different geographic regions with different demographics. And I think that that right off the bat shows that there's something happening in the secondary schools that is more evenly distributed than a lot of the other metrics that college admissions offices look at are. So that's the first thing. The second thing is, again, we know that we being admission officers know that the inequities in our education system lead to fairly calcified and predictable outcomes with regard to the measures that we currently use, grades, test scores, GPAs, all that kind of thing. So we're painfully aware of the limitations there and I think it's my hope, but I think it's also, I think it's been borne out as a side effect or a main effect of performance assessments is that we uncover more about what makes people engaged in education and what makes them successful. Because that is different in almost every person, but we certainly have enough evidence to see that it is it can be affected by where you live or what your income is or things like that. So the performance assessment I think adds enough depth and enough ways to demonstrate capacity talent you name it that that it can broaden the field and give us more as admission officers to hang our hats on. And we make these decisions and sometimes in very high stakes circumstances. So that's how you know that's the promise that that I certainly see and I think a lot of our institutions would see as well. I love the language you're you're using around depth and expanding and broadening the measures and again Chris using the word that right now we have kind of a one dimensional application to use the word calcified which is great. I wonder David if we can just stick with you for a little bit and and maybe you can help us as K 12 folks think about how we help higher education understand students and their experiences who 10 schools like those in the New York Consortium new tech big picture high tech high and international schools all these schools that engage in these inquiry based approaches with the more robust assessment system. How do we help higher understand that. Sure. Well, I mean there's a there's a few ways and I apologize if I cross over questions but but this is, I think there's a third I would say there's three really important things number one is that higher ed admission officers need to be educated about this phenomenon. I'm not suggesting that there's any deficiency there it's just that this is relatively new to them. And I think that that what what is really important is just to familiarize everyone because at the obviously at the high levels, the deans the vice presidents there you know they may have heard of this they may understand it pretty well, but what you also have is a lot of young people working in college admission offices and they're doing two really important things. One they're talking to students and families, and they're interacting with the schools that are doing these performance assessments so they need to understand what this is all about. And then on the back end they're reading applications so they need to know what this this phenomenon is so that they can understand it when they see it in an application. The second piece is, and that's a long slog I'll say I've been saying that since the very beginning that is something we have to do, because there's a lot of turnover and admission and it just takes any population of people, a long time to learn a new concept. So that's a, that's, we're in this for the long term. The second thing is that school counselors can play a particularly important role and right now. School counselors are quite overwhelmed in a lot of areas, particularly in areas where you have a lot of underrepresented underrepresented students disadvantage students in higher education. So the role of the school counselors potentially important, or if you don't have a school counselor, someone who can fulfill the role of a school counselor to articulate to colleges and universities, what this program is all about what your students are picking up how it helps you get yourself down the road and what your objectives are there, that that conversation between K 12 and higher ed is very important. And in an organization like NACAC, it's sort of what we do it's it's those conversations come to life in these spaces. The third and final thing I'll mention and and Monica you can signal me if we're not ready for the school profile question yet. Go for it. Well, the school profile is something that's been around for a long time, but not all schools have them and not all schools have them in a way that really helps college admission officers. But this is the school profile is literally the first line of I don't think it's line of defense but it's the first piece of information a lot of college admission offices will see about your school. And when we're talking about performance assessments, it's really important for us to be able as high schools to be able to articulate to college admission offices, what it is our schools all about. So NACAC has just put out a set of recommendations for school profiles and I see the link is already there in in the chat but what a couple of important things number one is to have one and to make it easy to find and that sounds really basic. But 60 only 62% of schools in the high free and reduced price lunch category even had a school profile so you're talking about, you know 40% of schools don't even have one of these documents. The key elements that we really recommend you obviously want to provide context about your school. You want, you want to provide staff contacts, because you'd be amazed at how many schools don't have a staff contact so that the admission officer can pick up the phone and call. But what's really central to this discussion is that we want schools to be able to describe the curriculum that they use and the grading system that they used that will that will be so helpful to a college admission officer who who really doesn't have very much time to process a lot of the information that's coming their way. So if you look at that document you'll see I think a lot of tips about how to lay that out in the case of performance assessments just really critical to be able to convey all of the different skills that that Chris and Kalea have talked about in a way that that admission officer can easily reference and that's those those things all combined I think K12 has a very affirmative and very important voice in that conversation. Yeah, thank you so much for that David and and it might seem like a small thing to some folks but as David said school profiles are so important. Envision schools who has been part of RCA for some time when David told them about the use of school profiles and how important it is to admissions officers. And he was like you know I'm going to go back and make sure all my schools are doing this, and there's a there's a great comment in the chat as well about a recovering admissions officer who has nightmares finding school profiles. And the fact that we need to think about best practices. The other thing I want to call out that both Chris and Kalea talked about were partnerships and relationships with K12. That's really what made the CUNY and consortium pilot work is that the admissions officers reached out to the consortium schools, and they started thinking more about this in a deeper way, but also then they began to trust this the school and how they were preparing students and begin to trust the assessment system. Because it goes back to David's point that they need to know what to look for, but it's all about relationships partners and and trust and so clear let's start with you I'll actually break break my habit here of leading with Chris and start with you Kalea and talk about how you help higher education understand your students, the kind of learning they have the assessment they do. Is there anything you do to help admissions officers or higher institutions understand your students at a deeper level as well as your schools. David hit a lot of the key points are you know the school profiles, you know for our schools that will submit PBAC to universities or you know for even something like a posse scholarship. It's important that they do share the school profile, share the rubric, but then also what really helped us is inviting admissions officers, you know, you know I know the schedule is pretty crazy but inviting them to the school to really get a chance to sit in the classroom and really experience it firsthand, because I think that there's something, you know, just, just, just very unique in that experience and again because our students, you know, for them to be able to see the immersion that we're doing as well. I think it's really hard to kind of thumb it up in a school profile, it really kind of takes it a notch. If, if an admissions officer is able to come to a school so our partnerships definitely gets forged, but it takes it up another level. If they're able to come and visit the school, come and speak to students, then they really, really get it. And really, you know, to your point Monica want to engage with us and trust our assessment process. So important. Chris, can you share some of the ways that you've really kind of opened up this black box of a deeper learning to higher institutions so they understand your students and what they bring. Absolutely. And the through line through all now my third comments adding on to David and Kalea is that is that relationship and partnership and specifically nothing new to what Kalea I think I would just add in terms of the visit. Again, having been that what we would call road warriors and admissions and visiting high schools. I understood the business of admission. And so, coming to the high school side, and perhaps maybe that's one suggestion for a system or school or district looking to move towards performance assessment is really look to NACAC to help connect with higher admissions professionals who want to make the jump to the K12 side, because there obviously is so much information and knowledge and experience that comes along with them. And when you make that jump to the other side. And specifically I'll share a specific example of the height the high school visits when the college representatives come. What I specifically do and this is 1718 years ago when we started high tech high and bringing those admissions representatives. Yes, the goal was for that admissions counselor to present their information about the University of the college, but more importantly for me. It was for them to walk away with a deeper understanding of our learning environment, the deeper learning competencies and of course project based learning. So what I would do have the admissions representative present or introduce themselves, but then also allow the students in the room to introduce themselves and talk about a project they're 30 minutes 30 second elevator speech about a project that they're working on. And so, this is a big example and this was again 17 years ago. We're 30 years into the world with high tech high we're a brand new on the scene. We hadn't seen any student admitted to Stanford up until that point. I knew Stanford was visiting the local San Diego private schools, but they weren't visiting us. So I knocked on their door knock knock knock, they finally came did that kind of protocol with the visit as I walked admissions representative She was I remember it vividly she told me, Chris, well, your students are doing graduate level research. I said, absolutely. That same cycle we had three students admitted to Stanford. No coincidence to Kalia's point under got a deeper understanding of the level of work that the students were accomplishing and doing. And, and, and, and when you see that one dimensional application come through all the sudden it's no longer one dimensional. So they have to David's point they have the profile. They have that trust now in the environment that that these students are coming from without AP courses we don't. We don't. Our students don't take advanced placement courses so so again it's just kind of that reaffirming of understanding of what our students are graduating with. Yeah, getting lots of kudos in the chat Chris for bringing that admissions role to high school so that you can really kind of bridge and connect that the two systems like what we're talking about today. So I appreciate you you're sharing that. And, and I remember Chris you said like Stanford again was like looking at your students and saying this, these are the kind of intellectual kind of students who want to be challenged by the rigors of college these are the students we want by showing them how students are problem solving and applying what they learn and so really using deep critical thinking skills I appreciate that we're going to start moving to the questions from participants and we have a few. And one of the questions that has continuously come up at these webinars is around then the potential inequity of performance assessments and some folks wonder if performance assessment higher ed can actually exasperate or continue in equitable admissions practices. And so I'll just kind of look to see who takes himself off mute to see who wants to kind of address the question around the potential performance assessment to continue to to lead to inequity and admissions David. Sure. And I think, you know, Monica that the reason the question comes up is that we've had enough experience with college admission over the course of its modern lifetime to know that you know money and socioeconomic issues and, and all sorts of other cross cutting phenomenon tend to find a way to. I'm going to use the word corrupt at risk of sounding, you know, maybe a little hyperbolic but, but, but, but they do exercise an outsized influence on college access. I mean we saw it in vivid relief with the with the University blues scandal last year and I think it even though that was clearly a bribery problem that was against the law it just unearthed this this whole locked up not necessarily locked up but, but just a very common concern so that the to answer your question I do think that we have to be careful we have to make sure that as we institute performance assessments in our secondary schools that we equip the schools to do what they need to do. I do think that it has a democratizing effect only because if we can get it into the admission process. You can just have access to this information I mean if the information becomes, you know, sort of a habitually accessible thing. Then it's it's in some ways bound to democratize but we but it's it's it's not going to probably fully realize its promise unless we address a lot of systemic issues like equitable funding right off the start you know right off the bat. So that staffing and resources and things like that, but it is I think it is more difficult for school districts to game the system as if you will that if you don't implement performance assessments well, it's probably going to show. So that would be my initial volley and I'll sort of step back and let others weigh in if they'd like. Great. Chris. Thank you David and I, for me, I think the question and Mandy if you don't mind showing up the state of cause admission slide. Just to kind of provide some context here. I think what when that where that question stems from is associating in what traditionally has been known in the college admissions world as as a portfolio. Right, as we learn from common app in the last webinar right like fly room and the implementation of a portfolio. But what I what I think the conversation would I feel the conversation needs to transition away from is it's we're not talking about a portfolio that can be quote unquote curated right we're talking about a learning and communicating for example in high tech case a deeper learning competency in a way that's just as systemic as as grades in all the courses right so so what you're looking at here if you haven't seen it and actually I was honored to to know that David Hawkins back in the beginning he initiated and started the state of cause admissions in which they certain act surveys admissions offices and they kind of associate their levels of importance of each of the components of a college application so that's what you're looking at here. In 2019 and what I'm looking forward to seeing and David you know we're we're putting you on the spot right like as testing test optional grows and grows in this next year, it will be fascinating to watch and see the percentages of that as you look down. And of course, admissions test scores is fourth ranked there in terms of considerable importance, seeing how that might shift but most importantly, what is going to be taking its place in terms of percentages. Right. Is it going to be the essay is it going to be the recommendation and then of course as you see down their extracurricular activities. So, so I just want to kind of maybe say like yes it's that question is a very good question. But I think what we're also talking about here is how college admissions currently worse and what colleges emphasize in terms of importance. And how we are going to be seeing the shift and now is a great time for RCA and LPI to really put it push to say, Okay, here's performance assessment. And now how does that fit college admissions offices into this into this graph here. Yeah, and Chris, I think you actually just kind of previewed some of the questions that we've been getting. Before I move to some of the questions from our participants clear. Did you want to add anything else around this question of exasperating inequities or anything else related to use of performance assessment higher education. No, I think everyone really hit some good points. I really just echoed. Okay. All right, well, we're going to open it up to some folks and looking at some of the questions. Many folks have asked really kind of what Chris hit on towards the end is how can we get higher education to agree to use performance assessment and admissions placement and advising. And some have even asked how do you get large institutions to do that right and and and so this is really kind of the problem that RCA is proudly taking on is how can we open up the different types of admissions submissions that students can provide to really show this robust set of competencies that they have in addition to understanding content and being ready for the rigor of college. And so that's one reason why we have the CUNY report it shows how a large public school system that has something like 25 colleges. Who have who are not open to missions how they use performance assessment specifically for equity to say okay if you did not meet the SAT cut score, we're going to look at performance assessment. We also have you know many schools and networks like the two of the represented today that are creating high quality performance based assessment. We have groups in New Hampshire and in Maine who are working with schools who are doing competency based learning and other organizations like the coalition for college and mastery transcript. So there's a lot of folks out there that are working on this independently and we're trying to really bring all this together to have some synergy, particularly with the test optional movement happening. We want to be able to provide higher education in K-12 some other alternatives of what they can think about in terms of what they could submit. So that that's my long answer about why we're here today and why we've brought David and Clea and Chris and we have another webinar where we had MIT Wheaton and the one before that where we released the findings from the study with CUNY. So, so I kind of answered that for all of us but there are at least six different people who who answered that. And then I kind of want to ask David this question that came through, and that are what are more holistic approaches to college applications and admittance. Well, let me let me first say that there was a question in the chat to about related to your last the answer that you just gave which is the question in the chat was to the effect of, you know, our admission office is aware that if they start adopting this more, it can signal to high schools that that this might be a good thing to check out this this being performance assessments and project based learning. So from the very beginning that's the question that we've posed the RCA posed to me when when I first met with them is that, you know, if admissions could just do this, it would help get us over the hump and I think that's absolutely correct I mean if we can, and this is one of the reasons why NACAC and ACRO have been involved in this. We also think though that by adopting these these systems secondary schools have more power than they realize they're actually if you all are doing this and doing this well. Colleges are going to have to adapt. So it's a it's a bit of an ecosystem a circular process so I want to make sure that those folks who are on this call who are high school members understand that you have a lot of power and then I encourage you to keep keep keep up the movement Now, Monica in terms of what are more holistic practices. You know you mentioned the MIT approach of looking for school work. I think that probably pops to mind first. The other thing that I look at is you know the coalition what led to the coalition for college and their concept of the locker was years of discussion about how do we get more authentic work were authentic representations of students learning into the process. So that's a big, I mean that's a big coalition example literally. You also mentioned that the common app is involved in this process. So, is in the RCA process to deliver that kind of information through the common apps tools. The bottom line is that when you when you think about holistic admission, it's really about looking beyond the factors that were on that table that we just showed so the, the possibilities are literally endless and some institutions, depending on the institutional mission might look at one set of characteristics and another institution might look at an entirely different set of characteristics, but what is common about it is that they're looking beyond the paper beyond that one dimensional look at students. So in the short time we have to talk about it. I think that's how I would generalize about it and then note that each institution might practice it in a separate and a slightly different way. Yep. Now thank you so much and clean Chris this is going to be our last question because we're down to just a couple of minutes so we can't make the answers too long. But we've got a few questions where I think there's still some folks who are not sure what performance assessment can show in terms of student preparation for higher education. So one of them, I really want to honor our OS or OUSD superintendent who chimed in today, and she wants to know how can they be, how can they really demonstrate college readiness. What are someone else asked, you know, what about the academic skills and these other skills you've talked about how, how does performance assessment show that is what people are questioning. So big question for for like two minutes so one minute each. All right, it's Chris or Clea or maybe they want me to answer. Chris. I'll take a stab at it. I mean, how do they demonstrate it and and and and honestly, it goes back to that holistic review question and how we demonstrated it through bringing literally bringing admissions officers into our building I think, and I guess I'll just highlight the work that you've already referenced Monica. And specifically, I've been able to have conversations and I believe they're on the calls well but the Mastery transcript consortium is doing great work in summarizing right the deeper learning competencies and putting it into what the transcript showing mastery of the of these deeper learning competencies and connecting with higher ed institutions of higher education to really put it in a format in a way that is essentially as quickly to read as as looking at a traditional transcript of courses and great. So, so I guess we we stumble in answering that question because of course there isn't a format out there yet to what I what I feel can accurately and quickly demonstrate the learning. So what we're doing is working within the current system to demonstrate those learning competencies again is bringing those colleges to campus. And all the things that David mentioned, in terms of educated admissions counselors like we're doing a lot of that groundwork, so that before an application shows up from a high tech I or an international school. They have the context of that and that deeper understanding of our environment so that's maybe a long-winded way of showing our environment and that our students are caught ready. Well, thank you so much, Chris and David and clear and we're going to transition a little bit to kind of some of the takeaways from from this really great webinar with the rich information and we have lots of questions and we always feel terrible that we can't get to all of them. But it's clear that schools like high tech high and the international network schools produce cultures of care and achievement. They educate high rates of students living in diverse circumstances. They produce graduates of great great promise and they build students experience with academic inquiry feedback revision and persistence. The study we're releasing today assessing college readiness through authentic student work shows the academic knowledge and dispositions developed by students who attend schools that are part of the New York Standards Consortium, which the international schools as part of and high tech high shares the same practices. When students learn in this way and you guys have heard us talk about the word deeper learning. This is where they are developing multiple competencies including content to be ready for college. So for high schools are recommendations for you guys are listed here on this deck right here and you've heard us talk about creating meaningful work, creating a school profile develop partnerships with a set of higher education. And we didn't get to talk a lot about this but provide the one on one support to juniors and seniors for college counseling. And again NACAC has a good resource about that. And David says it's not about the roles about the function who is helping your students be prepared for college. And then for higher education, what we suggest for folks to think about this is the next slide. Is it just like we talked about before is you can partner with high school systems that use performance assessment to better understand how students are prepared. You can identify specific set of knowledge skills and abilities that you want to know about students and then think about those best resources for this information. So again it gets back to the single dimensional application process. And then we can determine how requested supplemental materials such as performance assessment will be transferred received and reviewed for admissions. Consider who will review the supplemental materials or performance. Look at our last webinar about MIT and Wheaton talked about that. But for now, I know we're really short on time so I want to be able to thank everybody. So if you have any questions, first of all, do not hesitate to reach out to us. We couldn't cover everything today. A recording of this webinar as well as all of our resources we've shared today will be sent out via email. Please visit our website in a few days to get a summary of this webinar as well as the video. The paper college readiness through authentic assessment is also available on our website. And we hope you'll join us for continued programming in the reimagining college access series this fall. Yes, that's my dog you're hearing to stay up to date about future engagements. Please join the RCA mailing list. Thank you again to our presenters for sharing that valuable information about how to connect performance assessment to our education and success and another big thanks to our partners Education Council. I'm Gordon and Joe Fretwell created this webinar. Our partners and presenters also have some resources available outside of this chat and my deepest apology to end the webinar like this. We have to count on one big zoom bomb and it seems to be my dog and somebody knocking at the door deepest apologies and thank you very much for today.


So, I am not going to talk anything much about big data or anything because projects are very small and I just like to leave a very brief introduction of our lab with a very small video of last year internships. So, I just like to tell you few things. The project right now here what we are going to introduce is nothing different than much as you see as a co-opter or a medical general health management system and all that thing. But this time what we are going to introduce is more of our educational software that we would like to introduce. So, I hope everybody must have used this kind of software MATLAB in your course curriculum. So, a supplement to MATLAB is what we are trying to indicate this year and many other educational software which you may or may not be using as a IT or WE background. But other background students will be definitely be using. So, I will just hand it over to one of my colleague. She will start giving the presentation for various projects which are going to be covered in the idea. Thank you.


Okay, this is the closest to the Crimes of Grindelwald we're ever gonna get in this series. I don't like this one. Ooh, that's a hot mug, guys! Hey guys, this is my review for Harry Potter and the Deathly Hollows Part 1. This was the big game changer, not only in terms of coming to the conclusion of the series. This film is also the one that introduced the plethora of Part 1s and Part 2s that would come. Was it a necessary choice? Possibly?   This film follows Harry, Ron, and Hermione as they go off on their own quest now to try and take down Voldemort by going off their horcruxes. It starts off with a pretty big banger with the seven different different Harrys and them trying to get to the Weasley House.  I feel that what they were trying to do in this film is they were trying to squeeze in as much of the novel, at least the main plot points that were in the Deathly Hollows novel. And they try to shove it, all of it, into this film because in the second one there's not as much. There's much more action, there's much more drama rather than exposition because holy shit, there's so much in it. I read the books you could blink and miss that Grindelwald was in this movie. I did when I watched this movie and I had read the book. It's so stressing to try and keep up with all of the information that's happening in this film. I was constantly asking my wife, hey, what is going on here? Because she had recently listened to the audiobook so she knew more about what was actually going on because there's so many tidbits in this film that if you haven't read the book at all, if you aren't familiar with anything at all, you are out to lunch for a majority of this film. Sure there are some kind of interesting tidbits here and there. Dobby has a great moment in this film but that's not until the goddamn end. The Deathly Hollows animation is very good but again that also isn't until nearly the goddamn end. There's a lot that happens in this film that is just kind of circumstantial and it's all building up to what the Horcrux is. But there's also a lot that doesn't even kind of explain itself. Also the kids are just, I don't know, I just found the whole idea of them sharing the Horcrux. Like, oh god, keep an eye on it. I was like, guys, you could just put it on like a stick or something. You have that tent, just put it on something in the tent. It's not like it's going to go anywhere, it only seems to act out for dramatic purposes in this film. It's a really hard watch because there's so much being shoved on you. There's so much information being not even spoon fed to you. It's being dumped into you from a fricking dump truck. So they can clearly focus on what's important is that having a dramatic conclusion which is going to be part two. I don't think Deathly Hollows is badly shot. It's not badly acted either. Everyone's really decent in this film.  And obviously it's because of the Horcrux but I thought the part was stupid in the book too, admittedly. But it is setting up a lot of stuff.  Which it's a little bit surprising to me that Warner Brothers didn't screw this series up at all in the slightest. Maybe this film like a little bit. Again that's more so just how the film was put together. It was their choice obviously to do the one part one and part two and maybe maybe it's not an unfounded choice. Maybe they could have made like a three and a half hour long film. They did it with Lord of the Rings. I don't understand why they couldn't have done it with Harry. It would have cut out also a lot of stuff that is just kind of unessential. Like the whole Grindelwald thing is just so circumstantial. Again it is just right in there. Just like how Snape was really just at the very very end of the last movie. Yeah I'm the Half-Blood Prince. That's it. That's it. That's all you're gonna get. I feel like that's what's happened with this film. It's my least favorite out of all of the movies in the entire series. I could watch every single one over this one. It's setting up rather than actually being its own thing. And that is probably the biggest crime of the most unfortunate loss that this film suffers. So in the end I'm gonna give Harry Potter and the Deathly Hollows part one a three out of seven. One movie below the bar. That's not too bad. But now we're going in to Deathly Hollows part two. So far the highest rating I have given is Prisoner of Azkaban. Which I was kind of reluctant to give it that score. Because I've always been hesitant to appreciate this film as much as everyone else does. Because everyone loves this movie. Everyone loves the book. But it's hard to deny at least from the filmmaking perspective that it is as good as it is because it is honest. So part two is now the last one to try and contend with the highest rated film in this entire series. At least in my own opinion. So make sure to check that review out. That will be coming out next. I hope you guys have been enjoying this series. It's been really fun to do. About to watch part two right now. So make sure to subscribe if you like this video. Leave a like as well if you did. And I will be seeing you for our final Harry Potter review. To see any and all updates about the upcoming Undergrads movie, be sure to check out and like the Bring Back Undergrads Facebook page. And with any luck, we'll see you guys soon.


Everybody, won't you get over there? How many are you gonna get over? One, two, three! One, two, three! One, two, three! One, two, three! He goes for a Canada spin. Y'all look real good out here. Four!


Welcome everyone to the next lecture on, so what I plan to discuss today is what is called transformations of optimization problems. Now, we should relate this to what we did when we were talking of optimization over equality constraints. So remember we were talking of this problem where we had this ellipse and we wanted to find the inscribed rectangle with maximum area and we said we can take a point like this x star, y star on the ellipse, suppose that gives you the maximum area and then what we did was we said you will use implicit function theorem to around x star, y star in a neighborhood of x star, y star solve for y in terms of x, so every y that was in this, every x comma y in this neighborhood was written in such a way that y could be obtained as a function of x. So, if I give you an x in this region here, you could give me a y that lied exactly on the ellipse. So, this helped you transform, this was the case of basically transforming a problem, a problem of which is in two variables x and y, problem in x, y to a problem only in x. Now, this is a very sophisticated transformation and it was affected by the use of implicit function theorem and moreover because of the nature of the implicit function theorem, the limitations of it, we can only say that it holds in this neighborhood, it was a locally valid transformation. Now, there are certain transformations you can make which hold on the entire region but do not change the solution of the problem, that is why I will be focusing on today. And there as a result of them being such general purpose transformation, they are also in some sense very simple, but sometimes they are not easy to notice and you may not, it is not, it may not be a priori obvious to you that this could be done, so this, so I want to spend some time discussing this. So, suppose we consider, let us consider an optimization problem like this, you are minimizing the function f of x, the decision variable is x over you have inequality as well as equality constraints. So, you have constraint like this, g i of x less than equal to 0 for all i from 1 to m and h j of x equal to 0 for all j ranging from 1 to p. So, this will be my canonical optimization problem and I will write this in a different equivalent form. So, first thing is to, let us take the first form. So, do you notice that this is actually equivalent to this optimization problem is equivalent to this problem. So, what I have done is I have multiplied the objective by alpha, multiplied the inequality constraints by beta, ith inequality constraint by beta i and the jth equality constraint by gamma j. Now, are these two equivalent alpha, betas, gammas are all scalars, these are all scalars. Are these two equivalent? For equivalence, you need that you need some constraints on the signs of these. So, alpha, beta, gamma, these are all scalars, I am going to take alpha as positive, all the betas also positive. And gammas, I will make sure that I need that gammas are not 0. So, if I do this, what happens as a result of this? So, the objective function scales, the objective function is being scaled by alpha when I do this. So, earlier whenever you are getting one unit of objective, now you get alpha unit of objective. Now, what happens to the feasible region? The objective function is scaling, what about the feasible region? There is a feasible region scale. So, the feasible region is this, the individual functions that define the feasible region are scaling. These functions, the constraints that define the feasible region, they are scaling. So, your gi of x is being scaled by beta i, scaled up or down depending on whether beta is greater than 1 or less than 1. Similarly, h j of x is being scaled by gamma j, they are all being scaled. But the x is that satisfy the constraint, they are still the same. So, what that means is, if there is any x, if there is any x that solves these constraints, that satisfies these constraints, let us call them, let us denote these by star. If there is any x that is feasible for star, then it is also feasible for the optimization problem here in 1. Likewise, if there is any x that is feasible for the optimization problem 1, it is also feasible for star. So, the search space, the space over which you are searching, the x is over which you are searching has not changed. So, the feasible regions of both optimization problems are the same. Let me note this, they have the same feasible regions. What about the objective? The objective of 1 is being scaled by, the objective of 1 is alpha times the objective of star. So, the objective value will be scaled. So, if you send these two problems into a subroutine that solves them, what are you going to get as same for both? Suppose they both have one unique solution, what would you get? What would be the same in both? The solution would be the same, the optimal x would be the same. What about the objective that comes out of it? So, the objective that comes out of 1 will be alpha times the objective that comes out of star. So, when I say equivalent, we have to be precise what we mean by equivalent. So, equivalent by broadly speaking, we mean that if you solve one, you should be able to solve the other or you should be able to recover the solution of the other. This is why what we mean by equivalent. Equivalence can mean something more specific that the solution of one is exactly the solution of the other. But sometimes it is not just that. It is not just that the solutions are the same. Through some transformation, you should be able to get from one solution to the other. So, in this case, it does happen that the solutions are actually the same. So, if you take the solution sets of both optimization problems are the same, just that the objective value is scaled. So, we are I am thinking of these as equivalent this transformation as these two optimization problems as equivalent because essentially what has happened is there is a simple way of going recovering the solution of one from the other. All right, let us look at another problem. Suppose consider this problem, you suppose you have consider a problem that looks like this. So, minimizing a function f of some phi of z where and gi subject to the constraint gi of phi of z less than equal to 0. Decision variable is z sorry and hj of phi of z equal to 0. Now, what is phi here? Phi is just let us say if my x is in here x is suppose in Rn and my phi is a function that from Rn to Rn and let us say it is 1 to 1. So, phi is some 1 to 1 mapping from Rn to Rn. So, now what do you see about what do you notice about problem 2? So, what do you notice? What can it is a function of a function? So, f has been composed with phi, all the gi's have also been composed with phi, all the hj's have been composed with phi. So, what do you notice about this? See what is going on here is if you think about this. Yes, you are searching over z's. You are searching over the search, the optimization problem is now written in the space of z. You are searching over all values of z, but the way z enters into the problem is always through phi of z. So, the way z enters into this is in terms of in the constraint is that what matters is not the value of z per se, but the value of phi of z. Similar in the in the that is there in the inequality constraints and likewise in the equality constraints, what matters is the value of phi of z. And similarly in the objective also what matters is the value of phi of z. So, what this means is effectively although the problem 2 does not have the same feasible region as problem 1. These are 2 very different space of x and space of z are different spaces. It does not have the same feasible region as 1, but you can still say or transform 2 back to 1, 2 back to star, I mean not 1 star. You can transform problem 2 back to problem star. And how do you do that? Yeah, what you what we need here is a change of variable is something like what you do in calculus integration and so on. You suppose I just denote x as phi of z, then what is happening when I change my z, I am as I as I vary my z, I am spanning over the entire all possible values of x. Why am I spanning over all possible values of x? It is because the function is 1 to 1. Every x has a z associated with it and every z has an x associated with it. Is this clear? So, because this is 1 to 1, as I range over the values of z here, I am also effectively searching also over the values of x. So, consequently I can just do this substitution, do this substitution. After this substitution, I get back to problem star. Is this clear? So, problem 2 is actually another way of writing problem 2 is simply that I am doing something like this, f tilde of z subject to g tilde of z less than equal to 0 and h tilde of z equal to 0, where f tilde is simply f composed with phi g tilde i is also g composed with phi and likewise h tilde is h composed with phi. Is this clear? So, if I had shown you a problem in this sort of form without it being made explicit that these are actually all composed on the right hand side on from the right by phi, it may not be immediately obvious to you that there is such a function, there is such a function lurking there. But this is one of the tricks to notice that is, you know, for example, changing x to minus x or changing, doing some sort of a transformation to change or your coordinates or the way the x is represented, all of these are one to one transformation. So, those can, they do not, they basically give you an equivalent problem. So, in what sense are these two equivalent?  Notice the, I meant, I want to emphasize once again that phi is one to one. Without that, this is not going to work. So, for example, if phi is not one to one, if it is many to one, so there are multiple z's that give you the same x, then what will happen? How would 2 and star be related? So, when you want to establish the relation between optimization problem, there are two things that you need to look at. One is the feasible region, second is objective. So, if well point at every value of, if I make this transformation x equal to phi of z into, what I am doing is I am just evaluating f of x at some other point. So, objective is not so much of a concern here. What happens to the feasible region? If phi is not one to one. So, which has the larger feasible region or are they not related at all? Why does someone saying here is that 2 has a larger feasible region? Why is that? There are many values of z that can map to x. Is that a correct answer? So, if phi is many to one, what is happening here? This is actually something that does not need much mathematics. You just need to notice what is going on. So, you are of course, what the way z enters into the problem is through its value under phi. What matters is phi of z. So, as z varies over this range, you get to a certain ranges of in the values of phi of z. Now, when you make this substitution and get rid of the connection between x and z, when you substitute phi of z by x and get rid of the connection that x is equal to phi of z, that connection is gone now. You have just substituted x equal to phi of z and what you are saying is you are now solving star. Now, you may be searching over x's that do not have a corresponding z. So, the search space, the feasible region of star includes all the values of phi of z that could have come from the feasible region of z, of 2. So, you take the feasible region of 2, feasible region of 2 as z's. This is in the space of z's, z that satisfy, this is the feasible region of 2. Now, look at what, but look at the, look at phi of the feasible region of 2. Look at the values of phi of z, such that z is feasible for 2. All the phi of z for which z is feasible, in which z lies in the feasible region of 2. And this is obviously contained in all the x's that x is feasible for star. So, when we search over, when we search in star, in the problem star, when we are optimizing over all the x's, we are including those x's that for which there is a corresponding z, but also those that for which there is no corresponding z. So, this will, this feasible region is larger. So, the optimal value that you will get from here will be lower than the optimal value you will get from problem 2, less than equal to the one from problem 2. So, if phi is not 1 to 1, phi is many to 1, optimal value of star is less than equal to the optimal value of. Now, this is a canonical mistake that many people make, where they make these changes of variables without checking if the function is 1 to 1. Yes, because you are now, so the optimization problem star is an optimization of all x's that lie in the feasible region of star. But the feasible region, so if you look at the phi of z's that are coming in the feasible region of 2, they are included in this. So, you are searching over a larger region in star, then you are searching over in 2. So, you will get a, and you are minimizing. So, you will get a lower value. You are looking to minimize the function over a larger region. So, you will get a, you will get in general a lower value. If you are maximizing, then the inequality will go in the opposite direction. You would get a higher value for star than you will get for 2. So, if phi is not bijective, yes, that is what I am saying. You cannot, these are not equivalent, there will be an inequality. And it is, so many things can happen here. One is that, one possibility is that by chance it can happen that the solution of star also happens to be, so your x star just happens to be such that there is a corresponding z for it. There is a corresponding z star for it, in which case you will get equality here, if that happens. It can happen that the solution of star is such that, so maybe I will list these out for you. So, x star can be such, is such that, so first simple case is x star is such that there does not exist as a z, so there is no corresponding z. In which case there is no way you can, there is nothing, there is no way you can get back to a solution of 2. All you can say is that, all you can say is that optimal value of star is less than equal to the optimal value of 2. This is the only thing you can say. Second case is suppose if x star is such that there exists a z such that phi of z is equal to x star. So, you get to a solution and it just happens that you can actually recover the right z for it. In that case, you will get inequality. These two have to be equal. Now, the optimal values are equal. Now, it can also still happen that x star is such that there is no, so it can also happen that it can also happen that the optimal values turn out to be the same. But the solution of star is such that there is no corresponding, does not correspond to the solution of 2. So, I will explain what this is before I write this in the form of an equation. So, suppose it can happen that, so let me write it this way. Third case is that you can have that this is equal to this. You solve, phi is not 1 to 1, but yet you solve star you get and you solve 2, you get the same optimal value.  You solve 2, you get a solution z star. But x star is not equal to phi of z star. Is this possible and why would this happen? Why would this happen? So, the objective values are the same, but the solutions are not in correspondence with each other under phi. So, the issue is that this is one solution x star likewise z star is one solution there may be other solutions that are in correspondence with you here. So, x star need not be the only solution there could be other solutions which you have not discovered. And in particular phi of z star this point phi of z star let us call this x hat this point is actually another solution necessarily. This is a solution. So, this sort of case can also occur. But be aware of this particular possibility because I have seen this happen multiple times where you make a substitution without checking if it is 1 to 1 and then you get an what you get is an inequality.


Is NEO a buy at $35? Hmm, I'm Zeke and welcome to The Dream Green Show. In this video, I'm gonna do a complete marketing analysis just based off of price and price movement. I'm gonna pull up with charts and do a complete technical analysis over the stock NEO. Now NEO is a company that is a competitor towards Tesla in the EV community, electric vehicle community. Now they make batteries that power the electrical vehicles that are planning to switch out that you can just drive in, drop out a battery and then they're gonna drop in a brand new battery and you could drive out with a completely charged battery. It is an EV company that has been gaining a lot of buzz lately just because Tesla price is so high that a lot of buyers are not able to get in at that price but NEO sitting right at $35 might be an opportunity for a lot of investors to get in on an electric vehicle company that they missed out on on Tesla way back in the past. Now NEO has been on the steady incline over the last couple of months, gaining almost 600% since June. Now this company is fairly new and they've beginning a lot of buzz in the news so this company price goes up a lot based off of good news that comes out but we're gonna take a look into a technical analysis on NEO just to see if there's any pattern in this to see if buying at $35 is a good option or not. So before we check out if it's a good option or not make sure that you guys hit the thumbs up button on this video, it helps out this channel more than you can even imagine. Also this video is brought to you by Weeble. Sign up now by clicking the link down in the description deposit $100 and receive three free shares valued up to $1,600. Who knows you could receive three free shares of NEO if you sign up and deposit $100. But enough talking, let's go on heading down straight into the video.  Here is NEO tickle symbol NIO right now that prices at $34.94 so pretty much $95. Right now we're on the four hour chart that mean if we zoom in every bar, let's zoom in even more, every bar right here represents four hours of the trading day over the last 180 days. So let's zoom out so I can show you guys how much NEO has gained. So right here on June 1st, if we click right there all the way up to this current high of $34.94, there you go, NEO has gained over 755% over the last couple of months. Now let's do a technical analysis. Here we are, I'm going to draw trend lines and then we're going to look at the volume MACD and then we're also going to look at the RSI. All right, so here we are in June. If we draw out this line right here, it is a resistance line. When it first had this boom, it went up, had a resistance line and then it traded sideways. So let's draw that one out right there to see if we see a pattern, a high and a low. And then it ended up breaking that pattern and shooting all the way up to a high right there. Let's draw that out. And then it traded in this channel right here of the low. All right, so it trade, it goes up, it trades sideways, it get close to the green line. The green line is the simple moving average line. That is the direction of which the stock is going in the average line. And once it get close to that line, it looks like it wanted shoots for a boom and then it reaches a hard time high, pull back and then trade in between those two channels. It almost touches right there again, goes back to the green line and then boom, it shoots up again. Let's draw that line one more time. Right there, there's a high and then there's another channel for the low. So it shoots way up high away from the green line, comes back closer to the simple moving average and then shoots up again. So bam, it broke right there. Let's zoom in. It broke right here. All right, trade in between there. Got closer to the green line again and then boom, it shot right back up. Let's draw that one more time. It started to get closer to the green line again and then boom. So right now, this is where we are at $34.94. Let's zoom out. Now, just looking at the patterns based off of all the good news that's coming out and a lot of investors investing to EV companies. It looks like to trade, some good news come out, it shoots really, really high and then it pulls back to a resistance level. It trades sideways until almost touching the green line. Good news comes out, it shoots really, really high and then trades sideways again. Good news come out, trades really, really high. Then go sideways again, good news come out, goes really, really high, trades sideways. Great news that came out, went really, really high. So now, is this the new high? I can see Niyo going from anywhere between $36 trading sideways from here on out all the way over to it pulling back to anywhere between the $29 to $30 price range, trading sideways. And to eventually the price points catches up to this green line right here. And then you can see Niyo preparing for when some good news come out, it's gonna shoot up really, really high again. But that's just based off the patterns of what Niyo has been doing over the last couple of months. Now, the volume has been really, really good. It shoots up super high when good news comes out and then it comes back down and then it shoots up really high. So if the MACD end this up coming back and crossing back over and selling off, it is gonna trade in between these two channels right here and to eventually catches up to the simple moving average line. Some great news could come out. And if it does, I could see Niyo shooting from $34, $35 all the way up to $38, $39 to the $40 price point just based off the patterns of what Niyo has been doing over the last couple of months. Now, the RSI let us know when the company is overvalued or when it's overbought and then usually when it's overvalued like super high way up here, it usually pulls back a little bit. So, but it's kind of different when company have some great news come out that Niyo has been coming over the last couple of months. So right now it is overbought. So it could pull back if it does if the RSI does pull back to where it's oversold like right here, that might be a great buying opportunity. So if you got in right here when it's oversold and pulled back to its old resistance lines and then it shot off again when some great news came out. So that could be the play on what's about to happen. Right now Niyo is around $35. If it does pull back, it might be a good time to pick up some shares and hold it all the way up until $40. Now, if we zoom in a little bit more, that is the four hour 180 day chart. Now let's zoom into the one hour 20 day chart. You can see it even more true. It comes very, it touches the green line and shoots up. It touches the green line and then it shoots up. That's how it's been over the last couple of months with Niyo. So you can see Niyo trading sideways until it eventually touches the green line. Good news come out and then it's gonna shoot up again based off the patterns that it's been having the last couple of weeks. So yeah, you can see it even more clearly when you zoom in only one hour 20 day chart. Once again, every bar on here represents one hour and this whole chart represents the last 20 days of Niyo. And there we go, dreamers. Let me know down in the comments section what are you planning to do on Niyo? Did you miss out on Tesla? And this is your opportunity to pick up an electric vehicle stock that you missed out on with Tesla. Let me know if you're already an investor of Niyo and will you be a supporter of their products? Would you drive their cars? Or would you get the Tesla Cybertruck or the Model X or the Model Y? Let me know down in the comments section down below. Or let me know what price point would you be comfortable picking up Niyo at down in the comments section. And while you're down there, make sure you hit the thumbs up button and it helps out this video more than you can even imagine and also subscribe to the channel so you don't miss out on any future videos. But other than that, I'm Zeke, bringing you to Dream Green Show. I'm out, peace.


Okay, so let's do a summary of our significant zero rules where they pertain to zeros, okay? So, if we look at this problem or this number, it gives us a lot of information regarding zeros and significant digits. If we see we got three different types of zeros in this number, okay? We've got these two, which are before any non-zero digit, okay? Those kind, we call leading zeros. So, it doesn't matter if they're before or after the decimal place. If they're leading, they're never significant, okay? So, then we have zeros that are in between two non-zero digits, okay? Those are called captured zeros, okay? Those are always, okay? So, the question comes when zeros are significant and not to trailing zeros. So, I'm going to write another number that also has trailing zeros, okay? So, is everybody okay with all of those being trailing zeros? Okay, notice this number has a decimal place, or decimal point in it, okay? Whenever the trailing zeros are in numbers with decimal points, they're always decimal. So, when they're without the decimal, like this one, they're never significant, okay? So, that's kind of the overview really quick. If you were to put these two numbers into scientific notation, it would really reveal the significance of the zeros, okay? So, whenever you put something into scientific notation, you only put the significant figures into that scientific notation number, okay? So, let's just do that scientific notation really quick, and then you can ask that question, okay? So, let's put them both into scientific notation, and you guys can do this on your own while I'm doing this up here. So, this one's going to be 1, 2, remember? Put the decimal after the first known zero digit, okay? So, 1, 2 to the right, that's negative, right? So, this first one's going to be 1.5010, right? Because we're going to keep all the significant zero digits times 10 to the negative 2, like that, okay? This one down here, right? What do we say about the significant digits? Yeah, those don't count, and we're not going to bring, we're only going to bring significant digits into the scientific notation, right? So, how many digits is this one going to have? One, just one. So, it's going to be 2 times 10 to the, we got to pretend there's a decimal there, and say 1, 2, okay? Does everybody understand now? So, that kind of is revealing about significant digits when you put them in the scientific notation. Do you have a question? Yes, like in the 200, what would have happened if we had a decimal at the end? So, what is any number with a decimal? With a decimal, the trailing zeros are always significant, okay? So, if we put a zero there, what would they be? Oh, 200. Would they be significant or not? Yes. They would be significant. Of the difference, okay? So, let's do that. Yeah, let's do that one really quick. Yes, it's a number with a decimal, right? So, they're always significant. The arrows are, sorry, the zeros are there and there, okay? So, let's put this into scientific notation. So, are we going to leave those zeros in there when we put it into scientific notation? We're going to keep them. Keep them.


Good afternoon, I'm Olamideh Adeyemi. This is the news brief. We begin from a quiet bomb state where rescue operations are still ongoing at the site of a four-storey building which collapsed on a bungalow in the plaza area of Ubon Aka Road. It was guarded that the four-storey building was under construction when it caved in at about 6.30pm with some peasants fed trapped. The National Emergency Management Agency, while confirming the incident, however, said four peasants have been brought out of the Robola Life during a search and rescue operation by its officials in orders from the State Fire Service and the Federal Route Safety Corps.