[Van der Kloot]: 嘿，每个人都在这里吗？ 是的。 是的。 好的。 关闭。 抱歉，我有一些技术困难。 因此，让我起来。 好的，感谢大家加入我们。 我现在在手机上遇到了一些问题，但我们将从这里开始。 今天，课程小组委员会会议被召集。 这次会议的目的是在梅德福公立学校中审查数学课程K至12。 根据贝克州长的2020年3月12日命令，中止了公开会议法的某些规定，以及州长的3月15日命令对可能聚集在一个地方的人数施加严格的限制，梅德福学校委员会的这次会议将通过远程参与进行最大可能的范围。 可以在Medford网站www.medfordmass.org上找到具体信息和远程参与的一般参与指南和参加此次会议的要求。 对于希望听或观看会议的公众会议成员，可以通过访问此处包含的会议链接来做到这一点。 将不允许与公众举行会议的面对面参加，但是将尽一切努力确保公众可以通过技术手段实时充分实时访问诉讼。 如果我们尽了最大的努力，我们将无法做到这一点，我们将在会议结束后尽快在梅德福市社区媒体网站上发布音频或视频录制笔录或其他诉讼程序。 会议结束后。 因此，梅德福（Medford），如果您需要打电话，该号码为312-626-6799。 Zoom Meeting ID是965-1022-5227。 好吧，谢谢。 我们可以代表效忠的承诺吗？ 我承诺效忠美利坚合众国的旗帜，并以自由和正义为所有人。 谢谢。 抱歉，我有点困惑，因为我遇到了一些问题，所以请原谅。 我们可以开始吗？ 和校长，如果您可以将其带走。
[Edouard-Vincent]: 下午好，大家。 感谢您加入我们今天的课程小组委员会会议。 今天，我们将仔细研究数学指令。 我们的数学总监，女士。 法萨·汗（Faiza Khan），将带我们穿越幻灯片甲板，这将真正谈论 您知道，给我们快速概述数学，发生的变化，我们所在的位置，必须在州一级必须满足的特定标准，然后她将潜入数学指导。 以及在小学，中学和高中级别使用的节目。 在演讲结束时，她将为数学系分享一些目标和下一步，以及他们希望继续做的工作。 所以我要把它传递给女士。 可汗现在。 而且您应该分享屏幕。 您应该有能力分享您被列为CO主机。 谢谢。
[Khan]: 谢谢。 谢谢你，文森特博士。 感谢今天在这里的每个人。 你能听到我吗？ 是的。 好的，完美。 因此，我将开始分享我的屏幕。 让我们来看看。 好吧，我不太确定它在哪里。 我把它拉了起来。 让我看看。 出色地。 因此，我将其拉到了Safari中，但这不是，这使我经历了系统的偏好和其他内容。 是别人 - 我可以分享。
[Edouard-Vincent]: 我会问库欣博士只是为了让我成为主人。 给我一秒钟，我可以分享。 谢谢。
[Khan]: Great, thank you. Thank you, Dr. Vincent. So here we are. Welcome. I'm happy to be doing this presentation because I feel like it was long overdue. So as Dr. Vincent said, I will be talking about how math looks like right now in Medford Public Schools. What have we done over the last two years? and how Massachusetts curriculum frameworks have led to a district curriculum, and then the syllabi that we are working off of. So we can move on to the next slide. Thank you. This is another just title slide. Thank you. So as I mentioned, the outline is that we'll talk about Common Core, the curriculum frameworks for Massachusetts, the district curriculum that we have adopted and that we have, and then the district program that we have adopted. The Medford Public Schools Mathematics Department curriculum and instruction, I'll be discussing that over the last two years because I assumed this role late August 2018. We'll be talking about elementary grades and we will also be talking about secondary grades, middle and high school. And then we will close off after talking about equity in mathematics and our future goals and what I have in mind for the next steps for the department. So I'm going to take a step back and It's really important that we look at this visual and really try to understand, you know, where our mathematics district program that we have adopted as a district is coming from. Any program that has been adopted by the mathematics department has been in line with whatever the district approved mathematics curriculum has been at that time. And the district approved mathematics curriculum has always come from Massachusetts, mathematics frameworks, which has been based on Common Core. And it's really important that we distinguish between Massachusetts mathematics frameworks, mathematics curriculum, which is approved by the district, and the district-adopted mathematics program, because I feel that more often than we should, we cross-reference them, and also that we somehow get mixed up between the three different pieces. As you can tell, I'll go to the next slide. Thank you. It's important to understand what is it all based on. So what is Massachusetts Curriculum Frameworks? Massachusetts Curriculum Frameworks for Mathematics has two different kinds of standards, content standards and practice standards. Content standards, they vary with grade. I will not be teaching the same content in grade one as I'll be teaching in grade two. But will I be teaching the same practice standards from different, you know, from grade one to grade three? Yes, I will. They will take a slightly different shape when I look at them in the classroom, but they are the same eight. that have been set from 2011 to 2017, there have been very minor verbal changes, but they have stayed as eight. Whereas content standards have changed, they have varied, they have been, they have modified verbally and in content as well. Massachusetts Curriculum Frameworks for Mathematics, as our previous visual explained, is the superset of district mathematics curriculum. So basically we are deriving our district math curriculum based on Massachusetts frameworks. And one thing to keep in mind is that Massachusetts curriculum frameworks for mathematics is based on common core standards. They were put together by a consortium of states several years ago. Massachusetts as a state has added a few at different grade levels, its own standards, and we'll see it in a slide that's about to come. Massachusetts curriculum frameworks. Actually, I'll still stay on the same slide. Thank you on the previous one. Thank you. They are approved by DESE here in Massachusetts, and it's important that they are approved by DESE. That's the only way we get them. The programs that the district approve and district's own curriculum does not need DESE approval, but it's important that public schools stay in line with DESE's Massachusetts curriculum frameworks. And again, I can't emphasize on this enough that the Massachusetts frameworks are not tied to any particular mathematics programs. DESE provides guidance in choosing programs, but they do not endorse any program either. Thank you. So here's the timeline. Before 1993, states were kind of teaching whatever they wanted. So for example, Massachusetts would get together with another state that they will feel are more in line with their learning priorities and teaching priorities and will you know, form a set of standards and go from there. But with the Education Reform Act of 1993, everybody started thinking about what have we been teaching and are all different states teaching different standards. So when they got together and they discussed it and they kind of had a common baseline that was called the mathematics state curriculum frameworks, it came around in about 1995 1996. Revisions happened in November 2000. More revisions happened in May 2004, but it only happened for grades three, five, and seven. Yet again, another set of revisions, March 2011. And then the final set, the final frameworks that we are dealing with right now is the one that's based on December 2017. And we got it in 2018. So here are the 2010 and basically with minor changes 2017 practice standards. So these are the 2017 one and 2010 were slightly different, but basically they emphasized on the same pieces. All students shall be able to make sense of problems and they need to persevere in solving them. Second one is reason abstractly and quantitatively. Explain reasoning, model through applications, use appropriate tools strategically. That would be tools that students use with hands and any other kind of tools. that we introduce to students. They should attend to precision. They shall be able to look for and make use of structure and they should be looking for repetitions in patterns and calculations. These again, And I'll show you where they're all located. You can look at them at different grade levels, how they look like. But those are the guiding principles when we go into the classrooms or when teachers are teaching to see our students persevering and how are they being encouraged to persevere. One important thing to note about Massachusetts Curriculum Frameworks 2017 is that shifts from 2010 happened at a bigger level at the higher grades of 6 through 11. 12 seemed like it was pre-calculus, so it was not modified much. And the example is that the new grade 8 standards are now more rigorous and incorporate some standards that traditionally have been taught in Algebra I. And because I was teaching mathematics at that time from 2010 to 2018, I have witnessed these shifts my very self. So, and I can talk more about these later, but we can go to the next slide. So the Massachusetts Curriculum Frameworks 2017, there are a few highlights about it. It's a much well-rounded curriculum. And there's a lot of emphasis on literacy now. So basically, we now are giving students a lot more word problems than they have seen in the past. And that actually, ties in with procedural fluency as well. And I'll talk about it later. There's a big emphasis on coherence, focus, and rigor. So basically, the curriculum should be coherent with each other from grade one to grade two to grade three. So we are talking about progression in grades here. It should be focused. In grade one, I should be focusing on such and such. In grade two, I shall be focusing on certain things and then so on and so forth. So, for example, in grade one I shall be talking about integers, in grade two I shall be talking about, you know, divisions of certain numbers, for example, and in grade four instead of just modeling, students shall be able to do fractions by hand. So this is where it is. I have given a link right here. It is right from the Massachusetts curriculum framework. Again, it's a very well-rounded curriculum as claimed by DESE. And yes, in teaching also, it sure is as compared to the 2010 curriculum. Here, again, when we go back to the same slide, it's important that the conceptual understanding, one more slide up, please. Thank you, right here. Conceptual understanding, procedural fluency, and application, they stay together. So in this triangle, you will see the purple one is saying make sense of mathematical concepts. And then procedural fluency is there. And then the third one is application. And the three of them together, basically, the foundation of all of it is rigor. So there's a lot more emphasis on rigor then there was in the 2000 frameworks and it was quoted by the mathematicians that it was a mile wide and only an inch deep. But this one is that the depth of the mathematical concepts increase as you go up in grade levels. And we are not totally discrediting the procedural fluency. It needs to be there too. But it needs to come after conceptual understanding. And the third piece will be now we are able to apply it. So it starts from understanding, goes to procedural fluency, and then it should be application. But the way the visual says it is that all three of them are equally important, and they need to form the mathematical rigor at each grade level. Thank you. So this is the chart where I mentioned that Massachusetts has put in some of their own standards, as you can see in counting and cardinality and operations and algebraic thinking. Massachusetts has some standards in pre-k, it also has it in measurement and data and geometry. Also at fifth grade level, Massachusetts has introduced a couple of standards in the number system. And you can see clearly over here what is being taught at what grade level and how it progresses. As you can see, geometry is extremely important, which it wasn't in the 2001 and in the 2000 curriculum. And we recognized that it's really important. It's a very logical concept and it's not just gonna happen if we start teaching students at the high school. So a little bit of it is spread out through all the grades. These are our high school course offerings and pretty much the 17 courses that are offered at the high school level are here. I can come back to this if needed, but here they are. They are also on the mathematics department website. Thank you. So these are the initiatives. This is what we have been doing since 2018 up until now. We have conducted several math learning walks. They are on pause for this particular school year due to COVID. We saw where we need improvements where we can support our teachers. And I can't wait for these to start back up again because they gave us some very good data. The middle school program review and adoption was completed and elementary school program review and adoption has been paused. We had a committee formed of teachers and we had barely started, you know, just looking at different programs when COVID hit in March. That's when the presentations from the vendors had started. We had formed a rubric as to what will be our criteria. It was in line with DESE, and we have been in talks with DESE to kind of get an idea of when the next curriculum frameworks will be coming in. They don't know yet. So we looked at different rubrics that were used in the towns. And with the teacher input, we basically went with one rubric. That work had started in October of 2019 and it took us good five or six months to get to a rubric, but we were in good place because a lot of that rubric development also needed a little bit of professional development because we want to have an elementary school program that is in line with the middle school program. It is a problem-based, inquiry-based program. And then we were going to go ahead and pilot it. So again, it is paused for this year, but we know where we are at and will hopefully resume it under better conditions. Evaluations of curriculum and instruction, they are ongoing. The inventory of current resources. That's ongoing as well. Transition to inquiry-based, hands-on instructional resources. We are always on the lookout. We are always open-minded. We always encourage people to give us thoughts, give us ideas, because, you know, as I see it, as we see it, It's not just on to the teachers. It's not just up to me. We need parent input. So if any parent or any teacher comes across a tool, a program, we are more than happy to look into it and make them partners in our teaching and learning. Elementary school summer math calendars were given out in June of 2019. And in June of 2020, we had a good success rate with the collection of the summer calendars. Last year in 2020, we did not have that much luck this year, but they were there in case anybody was interested. So for elementary grades, under programming, we have the envisions program that was adopted in 2014. As the core program, we still have it. And what we also got was envisions 2020 as a supplemental resource at no cost. Of course, when you get a program at no cost, there are pros and cons to it. But we decided to say yes to that offer because it is a more robust and clearly has a few advantages over 2014. Additional considerations is that we renewed hand visions this year for a cost of $50,000 plus paper materials. anticipated budget request for 2020-2022 will be approximately the same. So I would say budget request for 2021 and 2022 will approximately be the same. My apologies for that mistake. Program Review Committee October 2019 goals and status. I believe I mentioned it. The goal is that we need to stay with the procedural fluency, but before that comes the conceptual understanding and after that comes the application. We want to make sure the new program is in line with that and that it's coherent time to time we hear from our teachers that you know it's just not tying in it's just not connecting and that's why teachers at all different grade levels from different schools. are on that committee of about 20 teachers and administrators are as well so that they can give us the feedback. Our final goal is to make a recommendation to the school committee for adoption of the new program and we are hoping to do it for June 2022. So for the middle school grades, we adopted a new program. The name is illustrative mathematics and it was in June 2019. Before that, the status of the middle schools was that we were using at least three to different middle schools. And one thing was very important for me personally as well was that we are on one platform because we have a goal of having one Medford. And then when we looked at different programs, we saw that illustrative mathematics clearly has major advantages over other programs, which seem to be more procedural. This one was very inquiry-based, and that's how it was from the beginning. It wasn't cut out to pass a certain criteria. The authors wrote illustrative math. They put examples and questions and activities in illustrative math, and then it passed the criteria. So it's like, basically, are you teaching to the test kind of scenario that I was seeing with different programs. There is definitely lots of emphasis on problem-solving, inquiry-based, hands-on activities, and that's for our standard 6th, 7th, and 8th grade classrooms. About 85% of our students fall in that category. The big ideas is for the accelerated program. Additional consideration at the middle school level is that professional development was done in illustrative math two full days in June 2019 before the teachers were going to start using it in end of August beginning of September in 2019 and then we followed up with two hours in the same school year 2019 and 2020 to launch the program. We spent about $25 per student per year on the paper book. The program itself is free and it's all available online for families, for students, and for teachers. It has lesson plans and condensed lesson plans and many resources for the teachers. Um, one thing to keep in mind is that when I say online, uh, people assume, uh, we assume that a lot of it is, uh, that students are doing all the work, um, online. Um, that's not the case. Students still need paper and pencil. They still need to show their work by hand. And teachers use nowadays in during COVID conditions, they are using different technology tools to make that happen. program itself is not just you are constantly working on the computer. Now we can take it as a pro or we can take it as a con but that's where we are with illustrative math. So approximate paper cost per teacher per set is $125. It's a one-time investment. We bought it for all of our special education teachers and all of our English language teachers as well. Approximate PD cost was about $15,000 for the program adoption and coaching. That included my coaching as well. and the coaching of our EL teachers so that they can modify the program as need be for their needs. And then now we can go to the high school. So for the high school grades, the program that we are using that comes as a set of Algebra 1 Geometry and Algebra 2, when we adopt a program for the courses at the high school, we usually look for the sequence that the program offers the sequence of Algebra 1 Geometry and Algebra 2. We have Houghton, Mifflin, Harcourt. And the reason why we do it is because these three courses, of all the others, are the foundations. And we want to make sure they're coherent and they're focused, so we don't go with Pearson in one and Houghton, Mifflin in another one. That was adopted in 2016 and we paid for the program. It's all paid for. The remaining courses use Pearson, McGraw-Hill, HMH, Addison-Wesley, BFW, Prentice Hall, Desi's own binder, and Skylight Publications. for different programs. Additional considerations is that we have invested in new statistics books. These ones come with an online interactive book. So we have the paper book and we have the online version. And it was bought right in time because our students are using it very nicely and teachers are getting used to it in October 2020 we bought it. with $6,000. The HMH program renewal is due in June 2022. We have yet to get a quote on it, but this program that we have in, that we got in 2016, basically we will keep their paper books, but the online piece of it, of the Houghton, Mifflin, Harcourt, the Algebra I Geometry and Algebra II, we will have, we'll no longer have access to it after June of 2022. So we need to think about where we want to go and if we want to renew, you know, what will be the dollar cost associated with it. So the program review committee for that one needs to be formed and the plan is to form it in June 2022 because that's when the elementary school program committee will be ending its work and hopefully will be adopting a program. And I feel that it'll be a good time to start working on this. It usually does not take this long, but because of COVID, the elementary school program review committee we had to put it on pause. So hopefully this will be done by June of 2023 and we will either have a new program or we'll stick to the program that we have. So equity in mathematics. We are fully compliant with the Office of Civil Rights regulations. We do a yearly program curriculum bias sign-off sheet for racial, religious, and gender equity. We do an annual discussion on how to deal with unconscious bias in program and practice through targeted teacher feedback sessions. and in math department meetings. We are committed to an assumptions-free all-inclusive teaching and learning models. We promote co-teaching as much as possible and the professional development and modeling is done by better lessons at the middle school level and at the high school level because it was specially requested from them. In fact, the teacher that we had for our illustrative math program was a special education teacher who gave much feedback on how to include our special population. Our future goals and next steps. We would like to continue the learning walks K through 12 starting in September 2021. We would like to develop a department mission statement because I believe it's important that we have a mission and we keep it in mind. Continued work on developing and updating the core syllabi. As we are adopting new books and as we have 2017 frameworks. The district curriculum was updated in line with the DESE Massachusetts frameworks, but we are working on syllabi of a few courses. We had some technical difficulty that some of them were only in PDF. Now we are working towards them. We are almost done. Continue to research best mathematical practices across the state to incorporate in our classrooms. One thing about the mathematics department, at least at the secondary level, because they only teach mathematics is their continuously researching best mathematical practices. Many teachers at the elementary schools are also constantly engaged in it, and they're very interested in what's happening in the mathematical world, and that's definitely good news for us. We are closely monitoring the new trends in mathematics. Teachers are eager to learn, continue to promote inquiry-based teaching and learning That's the way we see that learning is happening best. Those days are long gone when there was a traditional setup and now until students touch and feel the actual, you know, bits and pieces. And they don't play around with stuff or they don't discuss with each other. They are not where we would like them to be. We would like them to become competitive, more competitive in the world. And I believe that group discussion and inquiry-based teaching is the way to go and group-based learning. We will continue to research and incorporate data driven strategies to minimize learning loss due to COVID-19. I myself am constantly trying to research and look for things that I can give to the teachers. I again, hate to be the bearer of the bad news, but I was reading Education Week just very lately. And it mentioned that the loss in mathematics overall throughout the country is gonna be twice as much as the loss in literacy. So I just wanted to raise the red flag. And I mean, this is where we are right now. We'll continue to strive. But I just wanted to bring it to everybody's attention. And my last slide is saying thank you for your time. And please let me know if you have any questions.
[Van der Kloot]: 辉瑞，非常感谢。 这是一份非常全面的报告，其中包含了很多信息。 您最终真正地登上了我认为我们都担心的关键点是今年的影响。 尤其是，就像我能够的那样，如果我想到八年级的八年级课程，我们已经多次谈论了很多次。 因此，现在那些孩子已经进入了九年级，我想知道老师告诉您什么以及到目前为止看到了什么。
[Khan]: 因此，老师以这种方式挣扎。 我的意思是，他们负责。 他们手中有很多资源。 他们正在努力工作。 但是事实是有下降。 学生不是应该从任何标准的地方，但他们不在那里。 他们想确保学生订婚，并为下一个年级的水平做好准备。 有很多老师，实际上所有的老师都担心他们将不得不做很多追赶，他们担心他们将要做多少年级的教学。 但是他们相信自己会尽力而为。 他们愿意为学生加倍努力，我愿意为他们提供帮助。 我很高兴帮助他们。 但是事实是，下降已经很明显。
[Van der Kloot]: 我很好奇您是否看到完全偏僻的学生与混合动力的学生有所不同。
[Khan]: 因此，在中学和高中阶段，这种差异尚不明确。 我相信，如果情况会如此 在这个冬季和这个假期期间，我们将能够在2月和三月初的时间范围内更好地谈论它。 目前，老师正在使用所有这些不同的策略，即jamboard，flipgrid和白板，所有这些都可以在网上保持参与。 但是我很担心 关于在冬季的这种参与度下降。 还有一些差异，但是肯定有一些非常有动力的学生很遥远，有些学生也没有参与。 但是我希望老师是 将继续与学生一起努力工作，您知道，学生也不会放弃。 他们中的许多人的反应非常积极。 所以我有希望。
[Edouard-Vincent]: 你在静音，女士。 范德克洛特（Van der Kloot），您正在静音。
[Van der Kloot]: 是的，我有一些问题。 除了在太空吧，我不能静音，而且我无法进入画廊的视野，所以我看不到别人的问题。 所以，珍妮，我要问你是否可以，你能看到，如果你能看到每个人，你能问别人吗？
[Ruseau]: 珍妮，你很迷惑。
[Graham]: 我很迷惑。 好的。 Ruseau成员，我想我看到您的手在空中。 我也有一些问题。
[Ruseau]: 是的，我做到了。 谢谢。 这里有很多消化。 而且，没有涉及大流行的问题，我对计算机科学和计算机编程在列表中的位置感到好奇。 我知道数学系中有一些课程，有些没有。 我也很好奇我们将如何使用实际的计算机科学课程？ 我认为有很多证据 幼儿园很好。 我们可以从幼儿园开始。 而且，如果我们等到高中或中后期，那么我们就知道的是知道如何上课的人，以便他们可以获得轻松的A。 这并不是真正的目标。
[Khan]: 鲁索先生，这是一个很好的问题，这与我的心非常接近。 在担任这个角色之前，我正在教授AP计算机科学课程。 是的，管道将是很棒的。 会很棒。 学生可以很早就开始了。 DESE最近所做的是，他们创建了数字扫盲标准集。 不再属于数学。 他们说的某些课程说，数学学分或科学学分是可以的。 因此，属于数学部门的两个课程，他们位于数学系，但是如果学生要求科学学分，我们很乐意将其提供给他们。 他们留在数学部门的原因是 传统上，一位数学老师教授了这些课程，也是因为根据Desi的指南和许可条款，教师可以在他们的外部教书的时间有一定时间 内容区域。 因此，老师将在高中任教，这三个级别的数学和一部分计算机的三个级别。 我就是这样做的。 但是最近他们改变了标准和要求。 所以现在有点流畅，但是您知道，这就是我们所处的位置。 是的，创建管道很棒。 我知道莫莉·拉丁（Molly Ladin）付出了很大的努力，以使其脱颖而出。 我很高兴成为她的伴侣，但是由于她在技术工作，我们决定最好为此服务。 她和她的船员。 她还介绍了计算机科学的一些课程，例如，计算机科学原理并不那么严格，但它仍然是AP课程，不是基于语言的课程。 该课程属于数学系，基于Java。 因此，您需要很好地了解Java才能教它。 再说一遍 我总是认为，作为那个课程的老师，让学生在进入这一过程之前很长的课程也很棒，但这又是我和莫莉正在谈论的事情，并且那是更好的时刻。 我们肯定会继续这样做。 但是，任何其他事情，我们彼此合作，我很乐意以任何方式，形状或形式支持她。
[Van der Kloot]: 谢谢。
[Graham]: 我也有一些问题。 因此，我现在要继续问他们，因为我没有看到空中的其他手。 所以Faiza，我知道您在小学数学上所做的工作 是为了评估替代设想的努力。 显然，这是有点行驶的，但是就像设想一样，在课程世界中获得了非常糟糕的印记。 到完成此操作时，我们将失去整个充满小学生的整个学校的课程，甚至不符合标准 最少。 因此，我只是觉得那样，老师必须努力工作才能弥补差距，对吗？ 因此，如果课程不能独自站立，那么老师将面临填补空白或您的差距。 而且我不太确定我们会做什么，除了我认为我们需要缓解我们的期望 除非我们愿意改变基础，否则任何数学成果都会改变。 所以我一直在考虑这一点。 根据课程小组委员会的这项工作，我们谈论的一件事是，我们最终将创建一个包括程序到期日期之类的目录，因为这绝对是我的感觉 在我们应该在更完美的世界中，我们应该在计划到期之前进行这些评估的情况，在我们应该在此期间，我们应该在此期间进行。 实际上，我们面临着我们面对的，我们将要求社区为明年不起作用的计划付费。 而且，你知道，这是一个大流行， 我不太确定我们在这一刻能做什么，只是说我们不想再次处于这种情况，以及我们如何有不同的严格性，以便我们到达一个更好的地方。 您知道我们谈论的一件事，作为批准动议的一部分，该目录不仅包括该程序，还包括那些到期日期，因此，这是一个非常容易的视觉效果，并说这是我们要努力的日期。 以及课程是否具有EL或IEP补充剂以及我们是否购买了它们，因为我的理解是在历史上，我们并不总是购买所有这些补充剂。 有时是它们不存在，有时是我们没有购买它们。 因此，只是要开始创建该目录，而不仅仅是在基础层面上，而且整体上，我认为这是很有意义的。 我想你有 在本演示文稿中，这里的开始和胆量。 然后，我认为我对一些高中东西的问题确实更倾向于 该委员会中的另一项批准的动议不一定是当今的主题，而是数学进步和数学进步的最佳实践的主题，尤其是当您喜欢从中学到高中时。 因此，我只是不想让我们忘记这一重要的对话。 我很想 举办一个专门讨论该主题的会议，因为我今天刚刚从一个朋友那里听说她有一名中学生，数学老师正在和她谈论她需要做的事情。 所以她的孩子最终进入了微积分，我立即想到了你。 所以我当时想，我真的很想喜欢圈子回到那个谈话。 所以我会，我认为我会对这次对话真的很感兴趣，这显然不是今天发布的原因，而是 我从这个演示文稿中无法分辨的是，也许就像我们创建该目录时一样，更明显的是，对于各种课程和教科书，我们在诸如更新之类的方面在哪里，如果续订是一件像高中教科书相比，与我们应该像我们应该像我们的优先顺序一样， 当我们考虑计划和预算时。 因此，我知道这就像很多想法，但我认为我的问题是什么样的，您对我们如何做更好的计划来积极计划的看法是什么 在可能会或可能不会为我们的学生服务时必须进行扩展。
[Khan]: 因此，我绝对同意您所说的话。 我确实相信拥有目录，拥有Excel表肯定会有所帮助。 它将一眼就我们所处的位置，这样我们就不是 您知道，试图在同一年赚取相同数量的钱，这将对我们有所帮助，对我们进行分类。 好的。 因此，您知道，这是完成此数学程序的时候。 因此，现在我们可以对某些部门进行投资，因为所有部门都同样重要。 我不想 破坏他们中的任何一个。 因此，是的，我认为这将是一个很好的起点。 我想说的是，如果这再次，这个大流行就不会袭来，那么您可能会在三月份看到我参加小学课程，因为老师准备好驾驶。 不幸的是，这就是我听到的。 他们准备好了。 他们真的准备好了。 而且，我们已经准备好这些演讲了。 然后我们不得不插上插头，因为发生了太多事情，这是我们无法控制的。 因此，因为我们没有来找您，所以我们不会在今年三月来找您，所以再推迟了一年。 是的，不幸的是，我觉得老师确实需要一个基线计划。 它可能不是我们想要的，但它还为学生提供了某种在线访问权限。 所以我们需要 给他们基础。 这是我们必须咬人的子弹，但我相信我们明年三月，您肯定会看到我。 嗯，就那个，然后对于高中时，嗯，嗯，我相信这是一个很好的计划。 嗯，教科书是教科书背后的主要目的，基本上是高中对代数一级几何和代数二的高中。 因此，我们在该统计数据中处于一个很好的位置。 嗯，老师们真的很喜欢它。 学生们正在享受它。 我们还需要审查其他一些。 因此，例如，先进的代数和三角学可能会出现在管道上。 离散的数学可能会升入管道。 但是，这些也是未由dese定义的课程。 一段时间以前，我们一直在寻找一本好的赛前书籍，我们一直在寻找一本好的赛前书籍，我们向出版商询问了这本书。 我们正在使用的确实很旧，但是它们很好。 他们有点让我们的学生准备好微积分。 因此，我们将所有这些都牢记，我们不断讨论它，但是我要说的是，如果有一本好书，我们的眼睛可能需要在接下来的两个程序中是高级代数和三角学。 我会说，您知道，离散的数学之一。 我们确实有一本书，但这与我们想要的不符 我们希望我们的学生取得什么成就。 这样我就可以按照课程并为您提供更多详细信息，但是我说，更大的块是代数一个几何代数来思考，我也只想让您陷入统计书时的循环中。 图书。 我意识到，实际的纸质书籍仅花费约20美元25美元，而这本书的六年订阅售价约为一百千万美元。 因此，这就是发布者将其切换的方式。 这些书是重型精装书籍，它们过去耗费了每件一百$ 20的部门，而不再是。 现在，我们看到了不同的趋势。 所以 我很高兴投资统计书，非常感谢您的慷慨，并为此做好了。 谢谢。 卢梭先生。
[Ruseau]: 谢谢。 因此，回到大流行造成的坠落的问题，我觉得有不同 小学的情况，住在小学的孩子，我觉得，我的意思是，你可以告诉我我错了，但是我觉得有机会把他们带到他们所在的地方，并推动他们前进，试图赶上他们，或者至少保持他们的进步是一回事。 但是，如果您要完成代数1，并且正在服用代数2，则代数2老师 不是教代数。 因此，我觉得这些临界值和后来几年的进展似乎更具挑战性。 您是否希望几何老师在那之前教典型课程？ 因此，您在部门正在谈论您将在那里做什么吗？ 你觉得员工吗 你知道，我不知道有多少老师。 我不，我不知道几何老师是否只是一名几何老师，也不知道如何教代数，但是您知道，您是否有这些对话，您的想法是什么？ 因为我今天刚刚读新闻。 这不是一个好场景。 看起来明年秋天，我们肯定不会有接种疫苗的孩子。 这真是令人恐惧，想像我们将进入下一个学年，无论是混合动力还是其他。 和 我只是有点担心选项是什么？ 您是否需要我们的东西来帮助老师？
[Khan]: 因此，这再次是一个很好的问题，我想说的是沟通是这件作品的关键。 因此，我一直在与老师进行不断的沟通。 我们有部门会议，我们也举行了15至20分钟的个人会议，以至于您真的在哪里感到 挑战。 在高中级别上没有帮助我们的是，Dese最初宣布他们将给MCAS，因为他们最近成为大三学生，因为他们没有在5月份参加MCA，他们现在将在一月份服用。 因此，我们在高中阶段担心我们将如何为孩子们做准备。 那么，代数2老师是大三学生和孩子的老师，学生现在将在一月份乘MCA，因为他们在五月份没有接受，他们是否应该停止教学代数2并开始教学几何学？ 因为几何形状，因为MCAS基于几何和代数1。 因此，我们进行了这些对话。 实际上，我们的下一次会议再次致力于它。 因此，危险已经消失了，因为它没有在一月份发生，但会发生。 他们没有说它消失了。 他们只是推迟了它，并没有告诉我们何时会发生。 我的怀疑是，这可能会在五月与大二学生发生。 我们正在奉献我们的部门会议，只是为了看看我们能做什么。 不幸的是，想要强调学生学习的老师，教育者，敬业的教育者将不得不留出一定时间。 教测试。 真的很不幸。 我觉得这不是一个好地方。 对于教育者来说，这是非常无动的，但这是现实。 这就是我们讨论的方式。 因此，是的，我们不仅为学习差距，还为MCAS制定计划。 因此，所有老师都记录了他们在起搏指南中的位置以及什么 导致延迟和或在任何主题中都有多少深度。 所以我相信这很重要。 因此，例如，如果我要教几何学，并且我是几何形状，则有很多嵌入其中的代数，并且学生无法在其中进行代数。 我该怎么办？ 我应该坐着并且应该在年初审查还是应该嵌入 中间的差距的教学。 因此，全国数学教师理事会一直与这些委员会保持一致，他们的建议是，目前，继续根据需要填补空白。 因此，您不知道，要花费前两个月在基本上进行审查，因为您将在教授自己的年级课程中落后，这将再次动机。 几何老师不想在前两个，三个星期内教代数，因为他们会遵守标准。 因此，请记住这些建议从专家出发到我们很重要。 我们必须非常现实地关注我们所处的位置和期望 来自此游戏的所有不同政党。 我们不高估了，我们要记住学生的参与并与学生建立联系，此后所有其他事情都会随后出现。 至少这是我的哲学。
[Ruseau]: 谢谢。 这让我非常高兴，我并不感到惊讶。 我真的需要听到您说的所有这些。 谢谢。
[Van der Kloot]: 我看到校长把她的手举起了。
[Edouard-Vincent]: 是的，在数学部门正在发生的工作方面，我稍早地举起了手。 在与Faiza及其在数学部门的领导下交谈和合作时，中学团队的方式 采用了说明性的数学，以及这是如何真正严格，动手实践和对学生深入参与的。 我们已经说过，您知道是否有一个初级版本可以喜欢可以在基础层面采用的说明性数学？ 我的意思是，我过分简化了，但是说，这就是我们想搬进来的方向。 因此了解发生的专业发展以及培训 由于收养是在学年结束时发生的，因此我们必须在6月挤压培训，就像您知道，几乎强迫喂食它，以使老师习惯或适应新课程。 所以，如 辉瑞（Pfizer）在今年解释说，考维德（Covid）让她踩了刹车，但这确实是希望。 她所做的另一件我非常兴奋的工作实际上是去其他地区 有了很强的数学成果，并研究了他们在特定地区使用的东西，然后试图说，嗯，在梅德福的背景下，类似的事情可以工作吗？ 为此需要多少培训？ 因此，在计划今天的演讲时，我知道格雷厄姆成员的观点是不幸的 我们不得不暂停小学，因为，你知道， 辉瑞无法前往其他地区，看看在气候期间的指导。 而且，如果您正在查看指令，我们不得不暂停学习步行的K-12，因为您不想有10名额外的管理员和员工在六英尺远处的教室里走进教室。 因此，所有这些事情确实迫使我们停止确实需要发生必要的重要工作。 因此，通过暂停直到6月的希望，希望有些人会在6月接种疫苗，但是要重新启动基础团队，以便他们可以查看将要在他们面前的不同课程，并希望能够在下一个其他地区进行一些观察，以证明这一点是有记录的方法 更好的编程及其背后的原因，因此，如果是时候在基础层面做这项深入的工作，我们知道最终被采用了，K-5将在22岁时将22岁的22岁设定给学校委员会。 所以在那个时间点， 您知道，辉瑞现在将能够将我们所有的额外关注集中在高中级别上，并且确实说，我们在哪里找到或在哪里确定了其他差距或区域，以便在高中级别上带来更好的课程，以便我们提出这一进步，并提出这一进展，并有类似的目录，这就是我们所在的地方，这就是我们的样子，这是什么样子 目前在数学方面的最高趋势。 因此，您看到了在次要级别使用的所有不同事物，但是为学生提供了大型课程。 因此，我只是想重申这是工作的意图，然后才能继续 借助数学学习步行，学校委员会成员和范德·克洛特（Van der Kloot）成员，其中一些人有机会进来寻找这些核心行动。 因此，我们确实在K-12中成长，但是，随着这些的限制，我们又一次。 因此，卢梭刚刚分享了什么， 由于我们真的不知道该疫苗会发生什么，但是我们作为一个地区非常非常乐观，我们必须开始思考 认真考虑明年，认真地认为，如果疫苗确实无法在秋季使用，您知道，我们需要开始思考我们是否有远程学习学院21、22，您知道，可能要小得多，但是我们需要开始思考哪种指导将是什么样的。 再一次，限制并试图找出有关，嗯， 病毒将会发生什么，这将影响我们进行更大规模的教学学习步行的能力。 您知道，它们仍然可以发生，但是现在，您知道，在他们分组工作之前，您知道，您可能会看到他们的位置，您可能会看到这些团体。 现在，您有一些在线，有些在突破室中，有些在独立工作中，这只是，您知道， 我们只是非常非常困难的位置。 因此，我只是想指出，这并不是说我们并不是要深深地关注教学，而是考虑到现在在这些共同条件下教学和学习的异常情况，我们需要牢记这一点，而是我们对21、22学年非常乐观 我们至少将转弯，至少能够回到更大的常态感。 因此，这些是我对今天所说的话的评论。 谢谢。
[Van der Kloot]: 珍妮，你看到其他手起来吗？ 或者，如果没有，我还有一些问题。
[Graham]: 我没有，但是这里有很多社区成员。 而且我只是不知道你们中的任何一个人是否对女士有疑问。 可汗。 如果您只想把手伸向空中，我们很乐意把它们拿走。
[Khan]: 我也有几个，我看到了几条给我的消息。 那么，您是否介意我阅读它们并回答消息中出现的那些问题？ 当然，请这样做。 谢谢。 因此，第一个来自克里斯蒂娜·麦戈尔迪（Christina McGordy），她说，当前的土耳其人调查版本如何？ 我很想知道这是否可以根据我在2000年至2010年的经验来列入列表。 非常感谢您领导这次会议。 是的，克里斯蒂娜，我试图回复。 好像您不在这里，但是如果有人知道克里斯蒂娜，请让她知道调查第三，第三版在我们的名单上。 它实际上是我们正在寻找的最重要的之一。 因为它与标题非常符合哲学。 因此，如果有帮助。 第二个是丽莎（Lisa），是我在去年冬季给您的电子邮件，如果可以的话，我重复我的报价以协助计划评论。 我是一所小学生的父母，在一所学校偏远三年级，在HMH的高中数学出版工作中花了25年的时间。 我一直在工作 几何教科书的编辑开发目前正在高中使用。 她给我发送了她的电子邮件地址。 谢谢。 是的，丽莎，我记得你。 我对当前的基本计划感到满意，尽管对实践和解决问题的工作簿的依赖意味着实践的机会很小。 是的调查。 这是正确的。 所以 调查在清单上。 绝对地。
[Graham]: 人们一定听说过我们今天在谈论的调查，法萨。
[Khan]: 调查很好，牛顿使用它。 我认为，我认为布鲁克林也是会采用它。 虽然他们确实飞行员 基础级别的alpha版本数学。 但是，您知道，我们需要一些更稳定的程序，该程序已经经过了足够的测试和尝试，却与我们的中学严格联系在一起，您知道，更强大的程序。 因此，是的，调查在清单上，所以每个人都知道。 谢谢。 我们确实包括，我们确实计划包括父母。 只是我们想逐步发展。 您知道，首先，老师看着它，看看它是否在教室里看起来如何？ 然后委员会肯定会有一些父母。 绝对地。 我们可能必须减少数字，因为我很高兴看到这么多参与，但是您知道，我们可能必须从每所学校中选择一个或两个父母，但绝对是计划的。 是的。
[Graham]: 伟大的。 Ingrid将她的手抬高了Ingrid。
[Ingrid]: 嗯，嗨。 嗨，英格丽。 嗨，阿米斯。 因此，您已经有点讨论了这一点，但是我只是想询问有关基本课程的更多细节，选择了基础课程。 在什么时候您必须停下来？ 我想到您已经选择了今年要试用的一些课程。 我不知道这是真的，我想对此有更多的了解。 是的。
[Khan]: 这是一个很好的问题，英格丽。 我很高兴您和我前几天谈过，似乎您的背景与我相似。 因此，感谢您在这里并抽出宝贵的时间。 因此，我们正在研究的五个程序是桥梁。 调查是其中的另一项。 当然，设想2020年，因为以前有发布者。 是的，为什么不吧？ 我的意思是，您知道，我们必须给所有人一个公平的机会。 我们不会把它拿出来，因为老师已经习惯了。 因此，我们必须使我们想成为整个最终游戏的好组合。 因此，基本上我们的说明性数学将是另一个。 我相信还有另一个。 为什么我忘记了它的名字？ 但是这是五个中的四个。 和调查，对吗？ 调查，桥梁，说明性数学，为什么我会忘记？ 无论如何，有五个。 其中有五个。 然后，我们将其降低到三个。 然后，我们将在父母的帮助下将其归结为两个。 然后，我们将研究成本，然后取决于我们提出的建议，学校委员会是您知道的一个，
[Ingrid]: 因此，该过程是选择两个，然后您想在学校中驾驶两个？
[Khan]: 是的，理想情况下，我们希望开始使用三个驾驶，但是随着时间的流逝，三到四个月后，我们会说这些是我们的决赛入围者，其中两个。 这就是地区通常这样做的方式。 或者他们从一开始就选择两个。 我只是认为三个是一个坏主意，因为我们确实有很多小学，我们想在整个年级中做一些人口。 这样一来，没有学校就被遗漏了。 要记住的另一件事是没有一个学校，只有一个课程。 一点， 所有不同学校的三个课程，以便我们了解不同人群如何处理它。 然后，您知道，在最后两个中选择一个，然后选择最后一个。 但是我们总是建议两个人最终推荐两个，因为我们必须牢记某些因素，并且会带来良好的竞争。 就是这样。
[Graham]: 和女士 卡恩（Kahn），我知道一些数学课程越来越依赖技术，这可能是当您做到这一初步观点时，我们的技术状况与现在大不相同。 因此，在这个大流行中，没有那么多的银衬里，但是能够评估课程 知道我们是一个一对一的设备区。 我希望那种可以打开大门，让大家真正说的 这就是我们的学生和老师所需要的，而不会像我们现在可能没有或可能没有的那样受到束缚。 因此，我这样做的要求是，您不会出于任何原因排除任何内容，即如果有一些资源隐含在程序的成功中，我们只是在谈论这些资源 我认为，就像我们在FOSS的科学课程中所做的那样，我知道，我坐在其中一些供应商访谈中，当时，人们对我们所在地区的削减能力愿意愿意喜欢购买消耗品的能力肯定。 我很高兴，这并没有妨碍我们做出的选择，因为从所有方面，您都知道， 该计划确实很强大，我知道这也受到大流行的阻碍，但是我很高兴，尽管有效且历史上的准确性，但我并没有妨碍Seery先生挺身而出，这是对我们的正确课程，让我们这样做。 因此，我只是鼓励您不要被 无论如何，什么都可能阻止数学课程。