In this article, the author explains a new method being used that allegedly makes the use of VAM more reliable and valid than ever before.

As a brief background summary: VAM is a method whereby statistical analysis of standardized tests is used in combination with demographic backgrounds of students and teachers in order to calculate how much a teacher

One of the best pieces of evidence is the graph to the left. It shows the correlation between teacher ratings in 2008 (x-axis) and 2009 (y-axis) in New York City. If teachers were consistent year-to-year, one would expect the ratings to be fairly linear. As can be seen here, that is patently false. In fact, the correlation is rated as 0.35, something incredibly low for us to think about. If you read further into his report, you will find out even more scary pieces of data and graphs for those who might want to use this method for evaluation.

What the FiveThirtyEight author argues in this article, however, is that there are new method to get around these issues of consistency because there are more randomized trials that can be performed. Even though students are not randomly selected and sent to classrooms across the USA, teachers move somewhat randomly (or, at least, in a way that can be calculated as random) so that the difference in one class and the next can be quantified in connection with the teacher. Unfortunately, because of the myriad studies demonstrating the lack of consistency of tests and students, it is impossible to designate the teacher as the sole reason for student achievement.

The top comment on this article comes from a gentleman named BIll Honig, who accurately states (and cites):

The top comment on this article comes from a gentleman named BIll Honig, who accurately states (and cites):

Studies have shown that under current tests, a teacher who tests rank her at the 50th percentile could be anywhere from the 85th percentile to the 15th A significant number of teachers bounce from top to bottom or vice versa from year to year. (Reseach cited below) A recent report from the Federal Department of Education (of all places) found very high misidentifications even with three years of data per teacher. One fourth of teachers identified as needing special treatment were actually at the mid-range of performance and one-fourth of teachers who were deemed as average were actually in need of special treatment. http://ies.ed.gov/ncee/pubs/20104004/pdf/20104004.pdf

I really hope that those advocating value-added modeling read these studies carefully and spend some time in a classroom to see the effects of these policies.

]]>The article discusses a policy enacted by an elementary school in the US stating that in order to continue to the next grade students must fluently recite or calculate based on rote memorization. There is a ubiquitous tweet from Jo Boaler (mathematics educator and author) lamenting this school's policy. Check out the replies for some interesting argument and discussion.

Mathematics is much larger than simple computation and rote memorization. As the example in the article says, if you just multiply 2 x 2 you should yield 4, but that is only in the Base-10 number system. For a Base-2 number system, same computation has an output is 11. So we really need to train our youth to understand the origin of this content so they can build on it and recognize whatever patterns come out.

Mathematics is the science of patterns. Analyzing weather patterns; looking at increasing tile patterns; and more. Keith Devlin wrote an interesting introduction to his mathematics course coming up in Fall 2015 that elicits some light on this subject as well as the history of mathematics overall. In it he describes the origin of certain pieces of mathematics and how important it is to know where it comes from so that we can use it better. I hope I am able to teach my students the same way.]]>

What I want to do here is share some of my thoughts about the techniques that he writes and how I view their outcomes in my classroom. I'll be sure to include information for some I agree with and some that I don't.

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At close to the beginning of his book, Lemov discusses the nuanced idea of what is actually

The major example he gives in the book is that of

This one seems fairly obvious to a teacher attempting to get more depth out of conversation with his or her students: instead of taking a simple answer and moving on, ask deeper and deeper questions so the student needs to explain him- or herself. Asking things like "how" or "why" or to "explain your reasoning" are good examples of this. They do get to a higher level of question and will foster longer-term memory and thought.

In this section Lemov discusses how it is important to have a good classroom layout and have supplies organized, desks in proper locations, etc. While I agree that the classroom layout should change based on what kind of lesson you are doing (group work, gallery walk, testing, etc) I don't rely on the method he mentions as his primary: desks in paired rows. As part of our curriculum, College Prep Math recommends using teams of four at tables so that there is more discussion and analysis. One of his arguments is that you don't want groups like this so the teacher is the center of attention in the room; since I disagree with that sentiment (the content should be the center of attention) I don't think the layout is necessary.

This is not necessarily a technique he offers but the beginning of chapter three discusses the importance of the teacher as the center of attention and crafting lessons that begin with a demonstration, group practice, and then individual practice. I used to do a lot of this until I realized that investigation and discovery would create longer-lasting learning and didn't need to focus on me. I could give some instructions and the students could start their work without me. Instead, I use a method coined as "You, Y'all, We" and explained by Elizabeth Green in her NY Times article last year. Students essentially investigate on their own, then in a group, then we discuss as a class. This gives more work time and deeper understanding long term.

I'll continue analyzing these methods as I go along in the book.]]>

This past week the standardized test scores of Pennsylvania students grades 3-8 were released, much to the dismay of people paying attention. Scores overall dropped precipitously, only increasing with the age of the students (notice how higher grades had larger dips than lower grades). Those in the PA state government are attempting to make excuses, stating how these scores should be the new baseline, despite previous secretaries saying the same thing three years ago after a cheating scandal had erupted.

All this is happening as an opt-out movement is forming across the state and the country. Even though Pennsylvania state law allows for a child to be opted out of a state exam, there was a large controversy at the end of the 2014-2015 school year when teachers at the Feltonville school in Philadelphia were sharing that information. To me, that seemed rather wrong.

Luckily, though, the reauthorization of the Elementary and Secondary Education Act (aka the No Child Left Behind act) is moving forward in the House and the Senate with a proviso solidifying parent's rights to opt out of tests for their children. While not everything in this act will be beneficial to children, in my opinion, this is a signal that we are again moving in the right direction.

]]>All this is happening as an opt-out movement is forming across the state and the country. Even though Pennsylvania state law allows for a child to be opted out of a state exam, there was a large controversy at the end of the 2014-2015 school year when teachers at the Feltonville school in Philadelphia were sharing that information. To me, that seemed rather wrong.

Luckily, though, the reauthorization of the Elementary and Secondary Education Act (aka the No Child Left Behind act) is moving forward in the House and the Senate with a proviso solidifying parent's rights to opt out of tests for their children. While not everything in this act will be beneficial to children, in my opinion, this is a signal that we are again moving in the right direction.

One of the first books that I read regarding education from a first-person teacher view was Rafe Esquith's *Teach like your hair's on fire.* Through the story he explores myriad topics related to education: arts, funding, math, inequality, poverty, etc. It is a great narrative that explores how a good teacher can sometimes focus *so* much on a student that s/he may miss the fact that his hair has caught on fire from a bunsen burner.

Well, a few weeks ago he was removed from his classroom in the LA Unified Schoo District (LAUSD) under allegations of misconduct. While I do not know the man personally, from what I've read about him and from him I do not imagine this could be true. I am open to the possibility but there are so many people coming to his defense already I doubt it is. He is even filing a class action lawsuit against the LAUSD over this situation.

I hope this situation is dealt with swiftly and in a moral manner but I do not have high hopes it will be figured out soon. In the meantime, the plays he directs with his students have been put on hold for the first time in years.

Well, a few weeks ago he was removed from his classroom in the LA Unified Schoo District (LAUSD) under allegations of misconduct. While I do not know the man personally, from what I've read about him and from him I do not imagine this could be true. I am open to the possibility but there are so many people coming to his defense already I doubt it is. He is even filing a class action lawsuit against the LAUSD over this situation.

I hope this situation is dealt with swiftly and in a moral manner but I do not have high hopes it will be figured out soon. In the meantime, the plays he directs with his students have been put on hold for the first time in years.

In other news, back in Philadelphia, an arbitration regarding the school counselors in the school system has been officially settled, arguable in favor of what the Philadelphia Federation of Teachers was demanding. School counselors were laid off and then placed back in schools after 2013 but not in order of seniority. The arbitrator found the School District of Philadelphia (SDP) to be in violation of the contract and ordered them back. The issue has been said not to be one of desire, but one of finance.

]]>The idea is simple: there are differently-sized infinities.

But the explanation can get complex:

So let me explain (For deeper reference on number types, click here). Imagine you are in a hotel where there are an infinite number of rooms that are numbered 1, 2, 3, 4, 5....

Then say you have guests with number badges to make assigning rooms easier. With Group A, the number badges are the set of Natural Numbers (counting numbers that begin with 1). So, according to the image above, 1->1, 2->2, 3->3, etc. Each person is given a room. Great - that seemingly makes sense.

But now say you have Group B, whose number badges are the set of Even Numbers (only positive integers divisible by 2). Now you have Person #2 going to Room #1. That's okay, right? And Person #4 goes to Room #2. That's also okay. This continues with 6->3, 8->4, etc. And it goes to infinity. The kicker here is that it is the**same infinity as Group A.** That usually confuses people but the idea is sound. All members of Group B get a room at the hotel, and it is the exact same rooms as Group A.

Now you have Group C whose number badges are all the Integers (positive, negative, and zero). There is no "beginning" of this list like with Group A and B because they go on forever in both positive and negative directions. So the best way to assign them rooms is to start with 0, then alternate 1, -1, then 2, -2, and so on. As it turns out, this mapping is the**same size** **as Groups A and B. **This gets *really *confusing to many because they say "but there are SO many more numbers with the negatives involved!" Sorry, folks, but since each person in Group C **can** get a room, and they are the *same* rooms as the other groups, then technically, **Groups A, B, and C are all the same-sized infinity.**

There are a lot more examples that could be done to show the same size, so now let's see a*differently* sized one. Take the **real numbers**. Group D has people with numbers like 1.01, 1.001, 1.001, 1.0001, and **all numbers in between.** So if you try to assign room numbers using the system in place, we could take 1.01->1, 1.001->2, 1.0001->3, etc. So, technically, if we continue the pattern of adding a 0 in between the ones, we would use up all the rooms. The problem comes in when you realize there are *other numbers in this sequence*. Case in point : 1.009. Where does that person go? Since all the rooms are used up already from the pattern identified, then this set of numbers **must be a bigger infinity.**

If you want to get more in depth on the subject, there is a short article in Scientific American from 2007 that describes this phenomenon with mathematical language.

]]>Then say you have guests with number badges to make assigning rooms easier. With Group A, the number badges are the set of Natural Numbers (counting numbers that begin with 1). So, according to the image above, 1->1, 2->2, 3->3, etc. Each person is given a room. Great - that seemingly makes sense.

But now say you have Group B, whose number badges are the set of Even Numbers (only positive integers divisible by 2). Now you have Person #2 going to Room #1. That's okay, right? And Person #4 goes to Room #2. That's also okay. This continues with 6->3, 8->4, etc. And it goes to infinity. The kicker here is that it is the

Now you have Group C whose number badges are all the Integers (positive, negative, and zero). There is no "beginning" of this list like with Group A and B because they go on forever in both positive and negative directions. So the best way to assign them rooms is to start with 0, then alternate 1, -1, then 2, -2, and so on. As it turns out, this mapping is the

There are a lot more examples that could be done to show the same size, so now let's see a

If you want to get more in depth on the subject, there is a short article in Scientific American from 2007 that describes this phenomenon with mathematical language.

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This summer is particularly novel since I have no formal international travel plans organized. I spent so much time planning out my wedding that there just wasn't time (or money) to go that far. And, with recent personal events affecting us, any potential plans may be delayed even further.

That being said, I have some specific plans already organized for the summer that are somewhat exciting and definitely interesting. Since my school is a member of the Performance Assessment Consortium, I have access to a host of workshops run by consortium teachers, staffers, and so on. I ma particularly excited about the ones related to STEM or technology - including one about Arduinos coming up soon.

But more so this summer I am looking forward to reading more and hopefully finding some small tutoring gigs to sustain me with some extra income over the summer months. I will not be going far but hope to find some solace in my local community and taking some breaks with them.]]>

Probably the most important two experiences of my end-of-year were the Algebra 1 Data Analysis Round Tables and my Applied Math 3D Modeling Competition. Let's take them one at a time:

ALGEBRA 1

Over the past 2.5 months we have been working in class on analyzing data and making inferences based on graphs, tables, and lines. Each student had to determine two variables for which to collect data and then compare them to see if there was any strong correlation. We discussed strong, moderate, and weak associates as well as positive vs. negative linear relationships. The students (mostly) came out with a strong understanding of this work. It is truly amazing to listen to a student present in a small team about his or her work and feel confident in answering questions.

At the end of the unit we had the students gather in teams of 3-4 along with a teacher facilitator from the rest of our staff. We guided them through a process to understand who was to present and when as well as what questions they should be able to answer. Their final product - a poster - was used during the presentation to showcase their research. The feedback we received from staff was incredible. Not only did they share the fact that students truly understood their work, but they were also impressed at how organized we were. I really appreciate that feedback.

APPLIED MATH

My Applied Math students have been working on crafting business plans and presentations based on a 3D model of an object they want to sell at the school. There were so many different designs - keychains, cup holders, iPhone stands - I was not sure which one would win in the end. They spent 2.5 months learning how to use the software options and then developing their final designs, writing the plans, critiquing each other, and practicing their presentations. I was more hands-off because they were in 11th and 12th grades and it was still successful.

The students presented in front of a group of five judges: our principal, a representative from Makerbot (the company that makes our 3D printer), a staffer from DonorsChoose (the non-profit that helped us get the 3D printer), a marketing employee, and my wife. They were all very impressed by the detail of most of the plans as well as the responses the students gave to their questions.

In the end, the iPhone stand won, and we realized it could be used for a variety of different purposes (tablets, books, etc). I am happy to report we are going to start printing shortly.

My Applied Math students have been working on crafting business plans and presentations based on a 3D model of an object they want to sell at the school. There were so many different designs - keychains, cup holders, iPhone stands - I was not sure which one would win in the end. They spent 2.5 months learning how to use the software options and then developing their final designs, writing the plans, critiquing each other, and practicing their presentations. I was more hands-off because they were in 11th and 12th grades and it was still successful.

The students presented in front of a group of five judges: our principal, a representative from Makerbot (the company that makes our 3D printer), a staffer from DonorsChoose (the non-profit that helped us get the 3D printer), a marketing employee, and my wife. They were all very impressed by the detail of most of the plans as well as the responses the students gave to their questions.

In the end, the iPhone stand won, and we realized it could be used for a variety of different purposes (tablets, books, etc). I am happy to report we are going to start printing shortly.

hese two end-of-year products were long and time-consuming but showed the depth of thought and writing these students can aspire to when pushed. I hope to continue this kind of work in the future and am supported very well by the administration and leaders at my school.

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As the school year comes to an end there is always an uphill battle with a number of students to make sure they are passing their classes. As a teacher who has instructed mostly 9th graders over the last few years, it has been easier for me because the stakes have been a bit lower. If a student fails Algebra 1, they still have three more years to make up those credits and graduate.

But this year I have a course that involves seniors, adding its own issues for the past 10 months and currently offering plenty of challenges. As I finish preparing them for their final presentations and projects, what qualifies as a passing grade? For students who have 17 unexcused absences for the second semester, should I even bother giving them a chance? Does it depend on recent trends (were those absences in February and since March they have been here every day)? What if they were spread out and the student completely understands the outcome of his/her actions?

These are major questions we all deal with as teachers and sometimes butt heads with parents and administrators about the outcomes. If a student who has been a behavioral deficit to the class and recognizes that s/he was not putting forth the best possible version of themselves for the entire semester, maybe the deserving thing is the fail and learn a lesson about effort? Or, will that cause the student to spiral downwards and never life themselves back up to graduate high school?

On the other side of this are the students who are upcoming seniors - if they hear the story of these students who were not in class and eventually passed anyway, what does that tell them? Does it encourage a culture of lax focus in the school for years to come?

I am pained by these questions right now because I have to deal with them and make decisions in the next two weeks. I hope others can empathize and that these questions are some you are thinking of for your students as well. It is not easy to make them, but whatever we decide will be right because we have dug deep and are attempting to make sense of a crazy situation.]]>

Over the past few weeks I have been in touch with one of the folks at DonorsChoose because I sent a group of students there on a field work visit to learn how they use data (the students are now knee-deep in their own project on their own data). This turned out to be one of the best locations to send the students due to their focus on using data to analyze what they do and make their work better.

Yesterday I decided to visit their wonderful headquarters in Manhattan and was pleasantly impressed by their work, their vision, and how they use their space to support teachers and students across the country.

Yesterday I decided to visit their wonderful headquarters in Manhattan and was pleasantly impressed by their work, their vision, and how they use their space to support teachers and students across the country.

Their physical layout is similar to the Internet startups: very open with modular spaces that can be used for a variety of tasks. The space shown in the photo to the left can be use for meetings, small gatherings, lunch time, or repurposed for their projection screen (probably more options exist also). The two doors on the right open into various conference rooms with names like "The Art Studio" and "Homeroom" to mimic class at school.

In the rest of the office there are rows of calming desks with an open design that is not claustrophobic in the slightest. The organization of the desks matches the process you go through to make, craft, and get projects approved. They even has space for teacher and student interns/volunteers to help out. It's quite innovative and inclusive to have those folks come to assist.

In the rest of the office there are rows of calming desks with an open design that is not claustrophobic in the slightest. The organization of the desks matches the process you go through to make, craft, and get projects approved. They even has space for teacher and student interns/volunteers to help out. It's quite innovative and inclusive to have those folks come to assist.

Probably my favorite part of the office is that the suppliers often send examples of what they can offer teachers. These examples are strewn around the space in shelves and on desks to motivate the workers there. I saw a 3D printed model of the DonorsChoose text and then noticed the Makerbot Replicator 2 3D printer right next to it.

The folks at DonorsChoose are truly amazing. They have various levels of experience in education - some from the Peace Corps, some from inner-city schools, and elsewhere - and are all dedicated to the cause of helping teachers and kids get what they need to learn. While I sometimes question the need for an organization like this to exist because I wish all schools had the funding they needed, this is a great way of making sure we can all support future generations.

The folks at DonorsChoose are truly amazing. They have various levels of experience in education - some from the Peace Corps, some from inner-city schools, and elsewhere - and are all dedicated to the cause of helping teachers and kids get what they need to learn. While I sometimes question the need for an organization like this to exist because I wish all schools had the funding they needed, this is a great way of making sure we can all support future generations.