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This post also had several great ideas for summer reading. I incorporated some of the ideas in my lesson by reminding them why it is important, sharing my summer check out form, helping them plan in lesson above, and sharing my social media accounts, where I plan to do some book giveaways and book talks over the summer.
I altered the lesson a bit with my upperclassmen and added a moment to share reading memories, time to explore some Best of YA lists, and asked them to create a Summer Reading Bucket List graphic on Google Slides or Google Drawing.
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I thought of Ed as @solvemymaths for years, with great resources, dead clever problems and, of course, the math Mr. Men. Check his blog for all this and insightful writing on teaching and curriculum. He's inspired some GeoGebra work from me, too.
So I was very positively predisposed to like a book from the two of them together, and I was not disappointed.
For more of a preview of the book, check Ed's Twitter feed, or an Alex Bellos introduction. But probably you should just go ahead and eat it, er, order it. Snacks this good will make you hungry for more.
These puzzles and problems are so good. It is composed of five sections, with the somewhat surprising order of What Fraction Is Shaded?, What's the Angle?, Prove It!, What's the Area? and Sangoku. Each section is followed by solutions. Not just answers, but real solutions that guide the reader through the thinking of one way to solve each problem. And these problems tend to admit multiple solutions each, so knowing way to solve a problem does not make it worth much less for thinking about.
The problems are all visually presented, in beautiful black red and grey, almost crossing the border into pop art. Often they are stark in their simplicity. "This can't be enough information to solve it!" But then one relationship occurs to you, then "if that's true, this must be the case, and what if I..." In other words, the visual problem posing invites connections and problem solving. In my classes, one of my favorite definitions of math is "Math is the study of what else do we know?" and this book exemplifies it. I am not sure about this, maybe it's just me, but there is almost a sense of humor in these problems. Maybe it's whimsy? Maybe just the authors' sense of delight in the mathematics coming through.
While I can conceive of another book of problems that are this accessible and engaging, what would still set this book apart is the organization. The sequencing of the problems is intuitive, almost curriculum-like, but in a good way. The principle that helps solve one problem is often applied in a new context in the next problem, or needs to be extended in an upcoming puzzle. The fraction problems familiarize you with the shapes in the angle problems. The sequenced reasoning about angles is a lead into the idea of other sequenced reasons in the proofs. The proof reasoning prepares the reader for computation with measurements in the area section. The Sangaku problems are not the classical how do you construct the image precisely, but problems posed about measurements and relationships in those harmonious arrangements.
A nice indicator of how accessible these problems are is that a similar problem of Ed's blew up into an internet sensation, the Pink Triangle. What fraction is shaded?
So obviously I'm recommending this book. For yourself, for your role as a teacher or parent, or as an appreciator of the mathematical aesthetic. You will snack to satisfaction and return for more.
It was that or end with Bon Appetit, which I'm sure has been used in a healthy fraction of reviews for this book already.

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As I continue work on my forthcoming book on school finance, I find myself reflecting on the state of the field. Where we stand, and how we got here, and perhaps most importantly, how we should move forward.
I personally began studying school finance around 1994 and completed my doctoral work in 1997 at Teachers College at Columbia University in New York. In 1995, while a doctoral student, and still largely unaware of the breadth of literature in my field, I received (actually, I went in someone’s place) an invitation to attend a symposium sponsored by the New York State Regents. The symposium was on the topic of Cost-Effectiveness in Education and included research papers presented by academic researchers from universities across the state. The papers were released as a report to the New York State Board of Regents in March of 1996.[i] These were state supported research studies, including research advancing the application of conceptual models and statistical methods for studying cost-effectiveness and efficiency of local public school districts. The studies were at the highest levels of empirical and conceptual rigor, and conducted by leading researchers in the field (something I totally didn’t get at the time as a cocky and naïve doctoral student). These studies were part of an ongoing research consortium among scholars from Cornell, Syracuse, SUNY Albany and NYU, supported by the Regents of the State of New York. Over time, research emanating from this group would serve to break ground in analyses of equity,[ii] efficiency,[iii] resource allocation and the use of state longitudinal data systems to study teacher labor markets.
Similar efforts on similar topics were occurring in the State of Texas, where state agencies and academic researchers were collaborating to better understand variations in labor costs, in order to inform re-calibration of their state school finance formula. In early 2000s, the Texas legislature established the Texas School Finance Project, in which I was involved with researchers from Texas A&M University.[iv] State supported efforts in Texas, like New York served to significantly advance our knowledge of education costs, cost analysis, cost variation and efficiency through the production of numerous prominent and frequently cited reports.[v]
Research emanating from these states also found its way into national symposia sponsored by the U.S. Department of Education and released in two different recurring report series – Developments in School Finance and Selected Papers in School Finance. These reports have long since been discontinued, occurring mainly between 1995 and 2005. These reports like the state efforts in New York and Texas, tackled with empirical rigor, issues including the development of national indices to capture variation in teacher wages from region to region, labor market to labor market and district to district, [vi] the application of statistical modeling techniques to estimate costs of achieving common outcome goals,[vii] and statistical tests of the reliability and validity of estimates of school performance and efficiency.[viii]
These were the very types of analyses needed to inform state school finance polices and to advance the art and science of evaluating educational reforms for their potential to improve equity, productivity and efficiency. But these efforts largely disappeared over the next decade. More disconcerting, these efforts were replaced by far less rigorous, often purely speculative policy papers, free of any substantive empirical analysis and devoid of any conceptual frameworks.
This shift was largely brought about under the leadership of Arne Duncan. Kevin Welner of the University of Colorado and I explained first in a report for the National Education Policy Center and subsequently in shorter form in the journal Educational Researcher, that Secretary Duncan had begun to give lip service to improving educational productivity and efficiency, but accompanied that lip service with wholly insufficient resources. Kevin Welner and I explained that:
“the materials provided on the Department’s website as guiding resources present poorly supported policy advisement. The materials listed and recommendations expressed within those materials repeatedly fail to provide substantive analyses of the cost effectiveness or efficiency of public schools, of practices within public schools, of broader policies pertaining to public schools, or of resource allocation strategies.” [ix]
Among other issues, the materials provided on the web site failed to acknowledge even the existence of the relevant conceptual frameworks and rigorous empirical methods which had risen to prominence in state supported and federally documented research in the years prior.
Not surprisingly, a similar shift occurred in the states. In 2011, John King, New York Education Commissioner, close ally of and eventual replacement for Arne Duncan took a “different” approach to the annual Regents Symposium. Prominent researchers were invited to sit in the audience and be subjected to presentations by the authors of many of the materials from Duncan’s productivity web site, including but not limited to, the baseless graph I have presented in several previous posts. Here it is again (as much as it pains me):

Researchers in attendance that day forwarded to me their critique of that graph:
Maguerite Roza made claims that the service delivery programs she discussed could increase the productivity of educational spending several fold and illustrated this point with a graph. It is hard to know where to start in responding to this claim. First, she did not explain how the productivity of current spending was measured, so it is difficult to assess the claims she made about that. However, we are familiar with the literature on educational productivity and do not believe the productivity of current service delivery models can be estimated as precisely as she claimed, and suspect that the basis for the figures presented is questionable. Concerning the productivity of the innovations she was advocating there are several problems. It is not at all clear what the innovations are that she is claiming would create such large productivity improvements. Also, it is not clear what research those productivity estimates are based on. During the Q&A session, she indicated that these innovations were less than a year old. How can the productivity gain produced by service models used in a very small number sites for a very short time be determined? They can’t. It is not an overstatement to say that the claims about productivity improvement were simply made up. [emphasis added]
Below is a second, equally problematic graph that was presented in that same symposium, also later used by John King in presentations to school administrators across New York. Here, the presenter (using a graph from an organization called Educational Resource Strategies) argues that only a very small share of teacher salaries actually goes into “responsibility for results.” Thus, all of the salary differences above base salaries – and by extension much of school funding in total – is squandered inefficiently and can and should be reallocated, presumably toward “responsibility for results,” whatever that may mean or however that should be measured.

Researchers in attendance that day forwarded to me this critique:
Dr. Fisher [the presenter of this graph] made the claim that 30 to 40 percent of school district dollars were spent on resources that had no relation to student achievement. Again, the basis for this claim was not presented, so it is difficult to assess. However, the little explanation that was presented suggests that the analysis suffered from serious conceptual errors. Arguments can be made for a flatter teaching salary schedule, however, those arguments are more complicated than the speaker acknowledged. Particularly, the suggestion that any spending on teacher salaries above the starting salary is unproductive is, well, wrong.
It is likely that most of the people in the audience did not take these claims very seriously. Nonetheless, it was disappointing to see such claims being made by researchers in a forum like this one.
I raise these issues because:
To reiterate a take home point of many previous posts, equitable and adequate financing are prerequisite conditions for our education systems, regardless of how we choose to deliver those systems. System delivery may alter what’s equitable or adequate. But without rigorous and relevant analyses, we can never know how or to what extent.
NOTES
[i] Berne, Robert. Study on Cost-effectiveness in Education. University of the State of New York, State Education Department, 1996.
[ii] University of the State of New York. Board of Regents. Supporting Cost-effective School Reform: New York State Board of Regents 1996-97 Detailed Proposal On School Aid. Albany, N.Y.: University of the State of New York, State Education Dept., 1996.
[iii] Duncombe, William, and Jerry Miner. “Productive Efficiency and Cost-Effectiveness: Different Approaches to Measuring School Performance.” Study on Cost-Effectiveness in Education: Final Report, ed. R. Berne (Albany: State Education Department, New York State Board of Regents, 1996) (1996): 141-156.
[iv] http://bush.tamu.edu/research/faculty/TXSchoolFinance/
[v] Alexander, Celeste D., et al. “A study of uncontrollable variations in the costs of Texas public education.” A summary report prepared for the 77th Texas Legislature, Austin: Charles A. Dana Center, University of Texas-Austin. Available at http://www. utdanacenter. org/research/reports/ceireport. pdf.(Last accessed on 3/4/04.) (2000).
Taylor, Lori L., et al. “Updating the Texas cost of education index.” Journal of Education Finance 28.2 (2002): 261-284.
Taylor, Lori L., and Harrison Keller. “Competing perspectives on the cost of education.” Developments in School Finance 2002–2002 (2003): 111-26.
Baker, Bruce D., Lori Taylor, and Arnold Vedlitz. “Measuring educational adequacy in public schools (Report prepared for the Texas Legislature Joint Committee on Public School Finance, The Texas School Finance Project).” Retrieved August 17 (2004): 2006.
[vi] Chambers, Jay G. “Public school teacher cost differences across the United States: Introduction to a teacher cost index (TCI).” Developments in school finance (1995): 19-32.
[vii] Reschovsky, Andrew, and Jennifer Imazeki. “The development of school finance formulas to guarantee the provision of adequate education to low-income students.” Developments in school finance 124 (1997): 121-48.
[viii] Bifulco, Robert, and William Duncombe. “Evaluating School Performance: Are we ready for prime time?.” Developments in School Finance, 1999–2000 (2002): 9.
Rubenstein, Ross, et al. “Distinguishing good schools from bad in principle and practice: A comparison of four methods.” Developments in School Finance: 2003 (2004): 53.
Stiefel, Leanna, Hella Bel Hadj Amor, and Amy Ellen Schwartz. “Best schools, worst schools, and school efficiency: A reconciliation and assessment of alternative classification systems.” Developments in School Finance: 2004 81 (2005).
[ix] Baker, Bruce, and Kevin G. Welner. “Evidence and rigor: Scrutinizing the rhetorical embrace of evidence-based decision making.” Educational Researcher 41.3 (2012): 98-101.

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The influenza epidemic of 1918 first emerged without warning in late spring of 1918, and was known as the "three-day fever." Few deaths were reported and victims recovered after a few days. When the disease surfaced again that fall, it was far more severe. One fifth of the world's population was attacked by this deadly virus. Within months, it had killed more people than any other illness in recorded history.
Read more at The Deadly Virus
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As an educator and speaker I have often used pictures and images to underscore comparisons of education to other professions as a very effective tool to demonstrate the great need education has as a system to change. The most effective comparison was to show pictures of an operating room in the 19th century followed by a picture of a 21st century operating room. Step two is simple: Make the same visual comparison using pictures of a classroom. The difference in evolution of each set of pictures is a dramatic comparison. The early operating room was sparse, dark, and obviously not so sterile. The modern OR is packed with medical technology, brightly lighted, and an obvious sterile environment. The classroom pictures from early on had a teacher standing at the front of the room with a chalkboard behind and facing rows of students. The modern pic had a teacher standing at the front of the room with a whiteboard behind and facing rows of students.
Of course not every classroom in America is that stark, but I would venture to guess that description is probably closer to an accurate portrayal of a majority of classrooms. What should concern us even more than the environment of the classroom is the preparation, the mindset and the relevance of that educator standing in the room.
Of course we must assume that hospitals would not invest in medical technology if it were not being successfully applied to what doctors are supposed to be doing with it. Doctors are constantly being trained on the latest tech, and the newest drugs, and the latest methodology in their areas of expertise in their profession. Relevant knowledge to apply the proper methods and strategies for healthcare is essential. As a society we would not expect less of our medical profession. After all we depend on those doctors to do their jobs to the best of their ability to provide us with the best care possible and we won’t settle for less.
As an observer of student teachers, I visited many classrooms in many different schools giving me a unique perspective. In addition to observing my student teachers, I also made observations on the system of education. I was always astounded to see four computers collecting dust in the back or on the side of the room. It was however, a great opportunity to discuss education with many practicing educators. I found most of these educators wanting to be effective influencers on their students. They wanted to make a difference in the lives of their kids. They showed willingness and an openness to learn in order to evolve as educators. How are the motivations and concerns of these teachers different from those of our doctors? What are the differences in how doctors and teachers hone their craft?
The two greatest concerns we have in life are our kids and our health. We put our health in the hands of doctors and expect and pay for them to be not only educated enough to obtain a license in order to practice, but to pursue a continual path to maintain relevance in order to provide the best and latest procedures and methodologies to protect us. We show respect and teach them as adult professionals. They are provided assistants, technicians, mentors and mentees to feed into and perpetuate their support system. They develop as professionals on a continual basis.
We put our kids in the hands of educators and expect that they are educated enough to meet state standards while paying the most local taxes will afford. We support their relevance by providing sporadic training days once or twice a year. We have few standards to guide the education of educators and they vary state-by-state and district-by-district. We depend on pedagogy, the methods in teaching children, to teach adult learners about their profession. We require seat time in classes as the quality check on PD. The list goes on. There are many aspects of professional development that create a culture that does not support best practices for professional development.
Our kids are our most important asset and most valuable treasure. Why would we settle to place them in the hands of educators who could be better educated and more relevant on a continual basis if we were to prioritize the education of our educators. Most teachers are ready and willing to work on their craft, but they lack the thoughtful sources to do so.
There is no single solution that will fix our education system, because there is no single problem that is holding it back. It is a complex problem. There is however one thing that will most effectively and efficiently address most of the necessary changes we need. If we prioritize and rethink the way we allow and provide professional development for educators, we can enable them to continually hone their practice in their profession.
If we are to better educate our kids, we need first to better educate their educators.

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Access the Word of the Day course in Transparent Language Online, where you can listen, speak, read, and write each new word until you really memorize it.
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I recently attended the 4th annual CrossRoads conference organized by Infosys Foundation USA. It was filled with some great speakers and panels, but the most profound moment for me was a single statement made by Kipp Bradford, “failure is for the privileged.”

I have written about failure before in The Over Promotion of Failure:
Almost daily I see posts on social media by educators promoting the benefits of failure. It often seems that there is a push to intentionally embed failure into instructional activities. This always rubs me the wrong way. Failure has almost universal negative connotations. It doesn’t feel good and sometimes it is extremely difficult, if impossible, to recover from big failures.
For the past several years we’ve been bombarded with advice about the “wisdom of failure.” Books by business giants and self-help gurus tout the importance of learning from mistakes. The problem with the focus on failure is that failure is a weak process when put up directly against its counterpart: success.
I want to be clear that I’m not against learning from failure. It’s certainly useful that humans have the rare biological luxury of being able to learn, non-lethally, from our failures — we can remember them, share stories about them, even laugh about them. And all the stories and lessons about what you can learn from failure represent real opportunities to do better. The problem is that none of the advice and literature on failure fairly compares learning from failure to learning from success.
We have to ask how abundant or common are useful failures compared to useful successes? If opportunities for learning are rare, it’s hard to make a practice out of them. Unfortunately, truly useful failures that change our thinking (as opposed to merely stupid failures that just confirm what we already should have known) are relatively rare. (http://www.businessinsider.com/we-learn-more-from-success-than-failure-2014-6)
Mr. Bradford added another angle or perspective that I had not considered when he stated that failure for the privileged. This prompted me to see what others might have said about this. Here are some of my findings:
Not everyone “gets” to fail. If you are a student of color you have to be perfect. Think about the standardized test that plays an over-sized role in determining an accelerated or remedial course. You better not fail. Think about the rates of suspension and expulsion. You better not fail. Think about use of force incidents on campuses. You better not fail. Think about using a word the teacher doesn’t know. You better not fail. Think about hiding the fact your parents are undocumented. You better not fail. (Failing is a Privilege)
It also important for teachers to realize that failure in classrooms is an exercise of privilege. The effects of failure aren’t the same for everyone. For students who are marginalized in any way, failure has the potential to reinforce every negative image, bias, or stereotype they are facing. For students who struggle academically, failure can tell people they aren’t smart enough. For students who are marginalized socially, failure can tell people they aren’t cool enough. For students of color, failure can reinforce racist beliefs that they aren’t good enough. (When Failure is a Privilege)
Failure has become a trend in the past decade. As a society, we increasingly say “Failure is OK” or “Failure is essential to success.” But in this process of normalizing failure, we ignore the fact that failure affects people differently, and that privilege plays an important role in who is allowed to fail — and who isn’t.
“It’s OK to fail,” one professor told the class. “Students worry too much about their GPA.” And while I was never one to panic about grades, I did lose a key scholarship after finishing my freshman year with a 2.5 GPA. Unfortunately, this is the reality for many low-income, first-generation students — those who are in college only because of the scholarships that got them there. If those scholarships are lost, their dreams may be lost as well. More-privileged students don’t have those concerns. If they fail courses one year and require an extra year in college, they can afford it. (When “Failure Is OK’ Is Not OK)
While a first-gen/low income student is out there taking risks, their families may be struggling to put food on the table, All of this is assuming the student would have somewhere to live and at least be self-sustaining, which may not even be the case. “It’s not like you have the luxury of saying, ‘If this doesn’t work out, then I can find another means of providing for myself pretty easily, or I have my parents to fall back on, or have some source of wealth to support me while I go through this very risky process,’” Rodriguez said. (The privilege to fail)

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1. rostro [n] (face, human_face) the front of the head from the forehead to the chin and ear to ear.
2. rostro [n] (expression, look, aspect, facial_expression, face) the expression on a person's face.
3. rostro [n] (face) the general outward appearance of something.
4. rostro [n] (countenance, physiognomy, visage, kisser, smiler, mug, phiz) the human face (`kisser' and `smiler' and `mug' are informal terms for `face'; `phiz' is British).
5. rostro [n] (face) (synecdoche) a part of a person that is used to refer to a person.
6. rostro [n] (face) the side upon which the use of a thing depends (usually the most prominent surface of an object). |
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The resting places of Second Lieutenant (2Lt) Norman Frederic Surry and Private (Pte) George Skilbeck have been marked a century after their deaths in the Great War. The rededication service took place on 10 October at the Commonwealth War Graves Commission (CWGC) Montay-Neuvilly Road Cemetery near Cambrai in northern France.
The service was organised by the MOD’s Joint Casualty and Compassionate Centre (JCCC), part of Defence Business Services, and was conducted by the Reverend Tim Flowers CF, Chaplain 4th Battalion The Mercian Regiment.
Rosie Barron, JCCC said:
Tony Skilbeck lays a wreath on his grandfather's grave, crown copyright all rights reserved.It has been a privilege to organise this service and to have this opportunity to honour the sacrifices of 2Lt Surry and Pte Skilbeck 100 years after their deaths. As we mark the centenary of the armistice which ended the First World War next month, it is important not to forget the individual stories of these men who left their families and gave up everything to fight for the peace and freedom that we now enjoy.
The Reverend Tim Flowers said:
It is wonderful that we are finally able to give both these men the recognition that they deserve, and that their families now know the exact location of their final resting place. Now known to the family as well as known unto God.
2Lt Surry was serving with 16th Battalion The King’s Royal Rifle Corps (KRRC) when he was killed on the morning of 12 October 1918, aged 25. The Battalion had been ordered to capture german positions on the Le Cateau to Solesmes railway line and had marched north east of Troisvilles to their assembly point west of the River Selle. 2Lt Surry was killed early in the attack which was ultimately successful.
2Lt Surry’s first child, Madeline, was just 5 weeks old when her father was killed.
Pte Skilbeck was killed on 11 October 1918 whilst serving with 53rd Field Ambulance, Royal Army Medical Corps (RAMC), aged 34. It is believed that he was killed between the front line at Neuvilly and the village of Inchy.
The service was attended by Pte Skilbeck’s grandson Tony and his family.
Members of the RAMC, The Mercian Regiment and The KRRC Association, at the graveside of Second Lieutenant Surry, crown copyright all rights reserved.Tony Skilbeck, grandson of Private Skilbeck said:
We are extremely grateful to the MOD’s JCCC, CWGC and the researcher, Michael Lowe, whose research and hard work have made this service possible. We thank all those whose efforts ensure that the sacrifice made by George Skilbeck, and those like him, will never be forgotten.
We are pleased that my grandfather, having been an “Unknown Soldier” for a 100 years, is now identified and properly recognised for the brave man that he undoubtedly was.
Also in attendance were representatives from 16 Medical Regiment, RAMC, and the KRRC Association. Both men are commemorated on the Vis-en-Artois Memorial to the Missing and left behind young families who were faced with the uncertainty of not knowing where their loved ones were buried.
The final resting places of these 2 soldiers came to light after a researcher submitted evidence regarding their whereabouts. Further investigation was undertaken by the JCCC and the National Army Museum to corroborate the submitted evidence and the identification of the ‘Unknown Soldier’ graves were finally confirmed by the JCCC.
David Avery, CWGC Commemorations Officer said:
Second Lieutenant Surry and Private Skilbeck were recovered from the battlefield and buried in the Commonwealth War Graves Commission’s Montay-Neuvilly Road Cemetery. Thanks to the dedicated efforts of a researcher, we are privileged to be able to mark their graves with headstones bearing their names and personal inscriptions chosen by their families.
Two new headstones bearing the names of 2Lt Surry and Pte Skilbeck have been provided by the CWGC, who will now care for their final resting places in perpetuity.

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