A friend recently sent me an article written on the FiveThirtyEight blog (remember, Nate Silver's organization?) supporting the use of value-added modeling (VAM) in order to evaluate teachers across the country. I find it truly interesting that so many researchers continue to use this data despite such vilifying evidence against it. 

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 should improve a student's ability vs. how much they a actually do. I have found this method very tenuous ever since reading Gary Rubenstein's critique of it back in 2012. 

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):

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.

I've had an article in my to-read box on my computer for a while and finally got a chance to dig in today. While short and to the point, it discusses the idea that teaching "math facts" is dangerous and harmful to the youth of today. In fact, it goes so far as to say that explicit focus on memorization is harming our students rather than helping them. I understand the idea that memorizing certain things makes computation take place faster sometimes, but I wholeheartedly agree with the author that memorization does not yield true understanding, which is really the goal of any mathematics teacher (and also the goal of the Common Core Math Standards).

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.

I've had a lot more time to read this summer break (a fact for which I am immensely grateful) and decided to take the plunge and read Doug Lemov's Teach Like a Champion. Lemov's book dictates 49 techniques that he argues are essential to a top classroom in the country (possibly the world). This book has been somewhat controversial because of its messages (that we will dive into shortly) and also that its author has really only had experience in the charter school world (he is the Managing Director of Uncommon Schools and used to be an auditor of schools as part of the State University of New York's charter schools program). 

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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Technique 2: Right is Right

At close to the beginning of his book, Lemov discusses the nuanced idea of what is actually correct in a student answer. I know I've been guilty of this myself: letting an answer slide that is close-to but not the exact idea of what you are trying to get. Now, it is important to note that there could be many "right answers" out there, something his book does not really acknowledge very much. That being said, it is important that when a student provides an answer it is detailed enough for anyone to understand.

The major example he gives in the book is that of Romeo and Juliet and asking for background on the Capulets and Montagues. If a student simply says "they don't like each other," that is not in-depth enough but the teacher should not extend the answer and share the fact that they have been feuding for generations, that is something for the students to parse out together.

Technique 3: Stretch It

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.

Technique 11 - Draw the Map

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.

I, We, You

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.

New common core exams were implemented in Pennsylvania before I moved up to Brooklyn and have been defined as "common core aligned," with "increased rigor." From accounts of teachers across the state, these tests are not helping students learn and instead are a waste of time. A superintendent in Bethlehem area said "that students is spending a lot of time demonstrating things we already know that he or she can already do." As a former PA resident myself, I can tell you this is increasingly true. The tests I had to take growing up did not help me and were, instead, often used as a carrot or a stick in certain situations.

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.

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.

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. 

Just yesterday I was recapping a very interesting concept with my wife: the idea of "bigger" infinities. We have an inside joke that developed early in our relationship about how we love each other like the "bigger infinity" because I explained to her once the same idea that came out of a blog post from Math with Bad Drawings just two weeks ago. 

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.

I have unfortunately not been posting for the past two weeks due to end-of-school nonsense and personal issues that have kept me from my desire to share about education. That being said, I am carving out time for myself so that I can also have a catharsis at times. Hopefully I'll be able to write more here after this soon.

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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.