The post Open Letter To Chancellor Dennis Walcott and Others on The Idea of Assessment appeared first on The Jose Vilson.

]]>To Chancellor Dennis Walcott, David Coleman, Merryl Tisch, and McGraw-Hill Publishers:

First, I’ll mention that, since the discussions of the Common Core Learning Standards came to the fore, I’ve had a plethora of chances to immerse myself in the new vision for a quasi-nationalized education paradigm. In NYC, as usual, education policy makers feel the need to set the standard for the nation, from Bloomberg’s mayoral control dictates to the plethora of interim, field-testing, and high-stakes standardized assessments from third grade onwards. On the surface, one might think I’m at the forefront of the work done around the Common Core.

Yet, my earlier concern about the chaotic approach to transforming education via the Common Core concerns me still.

We can obviously start with Dr. Diane Ravitch’s contention that we haven’t actually field-tested whether the standards would actually get our students “college and career ready.” From a teacher’s perspective, I’d like to get more focused, coherent, and yes, rigorous about my argument.

We can talk all day about these standards and the three tenets of focus, coherence, and rigor, but without the means to make pedagogy more viable and focused on the whole child, we miss out on yet another opportunity to do something important: growing better *people*.

For instance, yesterday and today, New York City elementary and middle school children had to take an English-Language Arts and Math test (respectively) as part of the NYC Benchmark Assessments, with the assumption that these tests will give stakeholders a chance to see how much students learned in the past few months.

After a careful glance of the material along with conversations with students and teachers, these assessments seem to do more to assess what students *don’t* know than anything else.

If the intent is to help teachers, principals, and others get a feel for the tests in April / May, then why not let these parties into the assessment process rather than excluding them? If the intent is to show growth from today to the tests, then why give a test where you know the majority of students haven’t even covered all of this material? If the intent is to signal to everyone that they must raise their expectations, then why must we let them down so frequently with our *lack* of clarity?

From people I’ve spoken to throughout the city, we’ve had almost three re-arrangement in priorities in the last five months. At first, people thought we would have to address both New York State and Common Core Standards, specifically because the Common Core in New York State’s eyes was a draft. Then, people thought we would teach according to the first testing schedule given sometime in late August / early September.

For eight grade teachers, that meant we would teach exponents first. Sometime last week, however, the state sends out a document shifting priorities on topics again, giving some topics greater emphasis over others after almost three months of teaching.

We’re almost begging for schools to fail.

Even when schools had a clear roadmap like in the state of Kentucky, schools still dipped by as much as 35% in scores, and for good reason. Anyone familiar with the standards already sees the forestand the trees.

But we continue to perpetuate the myth that higher accountability will improve schools, no matter what the cost. After today’s interim assessment, I am convinced that, if we cannot make our school system more focused on children and their communities’ needs, we will continue to fail them, with or without a state test.

We can do better.

I’m not angry; I’m simply seeking answers. While I don’t speak for all teachers, I do speak because of them, and a plethora of other concerned citizens. Hope to hear from you soon.

Best,

Jose Vilson

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]]>The post Allow More Mistakes, And Other Advice for Getting Kids Into Math [Edutopia] appeared first on The Jose Vilson.

]]>## 1) Allow More Mistakes

I would suggest this to just about every teacher, but specifically math teachers, especially those of us who use the word “wrong” a lot. We should strike a balance between using direct instruction and exploration, leaning more on the exploration piece. Once we allow more mistakes, we let students into the process that our earliest mathematicians used in developing the axioms we believe today. Also, by admitting that we all make mistakes, it sends a clear signal to kids that they can be mathematicians, too. Surely, I’m not suggesting that we let the mistakes be. Yet, when I make a mistake on the board (intentionally or otherwise), I hope my students catch onto that, thus putting them in the position of expert. Speaking of which . . .

For more, click here. Read. Comment. Like. Share. Thank you.

**Mr. Vilson, who can’t believe his luck …**

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]]>The post Teaching Exponents In Eighth Grade, Part 1: [Old To The Now] appeared first on The Jose Vilson.

]]>Every so often, I’m inserting some posts on pedagogy, especially for those of us who aren’t as math-inclined. If you find this helpful, just let me know in the comments.

Today, I’m differentiating between the old way I used to prepare the students for a lesson on exponents and the way I do it now.

**Old Way**

1. Ask “What’s an exponent?”

2. Here are the five mail rules you need to know.

3. Apply them.

**New Way**

1. Ask “What’s an exponent?”

2. Use their definitions with a bit of refinement.

3. Get their thinking about a few cases involving exponential, expanded, and standard forms.

4. Have them deduce what 3¹ and 3° power would look like.

5. If they can see the operation of division, then prompt them to ask if this works for every case in general.

6. Use the same thinking from 3-4 to get the values for 3¹ and 3°.

7. Let them establish the (real) first two laws of exponents.

8. Use similar tabular thinking to deduce product, quotient, and power of a power laws.

Usually, when students are just given the laws, there’s rarely reason why we give it to them. It gets shoved on their laps, especially x to the zero power. Some of it might be because of a lack of understanding on the part of the teacher, but I also suspect it’s because we don’t see the importance of taking them through similar steps that an actual mathematician would go through.

But I changed that last year, and into this year.

My main objective was to make sure to establish the foundation for every argument we will make about exponents from here until October.

Here’s a sample of what I mean:

Exponential | Expanded | Standard |

x^{3} |
x · x · x | n/a |

x^{2} |
x · x | n/a |

x^{1} |
x | n/a |

x^{0} |
1 | 1 |

I’m hoping for a couple of things here. First, I hope they see that, as the exponent decreases, the amount of x’s in the expanded column decreases, just to solidify our definition of “exponent.” Also, I hope they see some sort of division (making the connection between multiplication and division matters here). I use a specific case first, and it’s usually a positive base, just so they’re familiar with the numbers, then work my way towards this.

By the way, once they see the 1 at the end, they should also be able to see that Icould have had a multiplication of 1 all along since 1 times any number equals that number.

Hope that helps. Best,

**Mr. Vilson, who will have a post like this about once a week …**

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]]>The post A Future Too Big To Fail: Using Corporate Thinking Corrupts The Classroom appeared first on The Jose Vilson.

]]>A few years ago, I read an article in Wired Magazine detailing the events that led up to the Market Crash of 2008-2009, wherein they pin down much of the blame on an elegant and seemingly infallible formula created by world renown mathematician David X. Li. Recounting the events that led up to the crash, the Wired article reads similar to every other well-intentioned idea: the creator thinks he or she is solving a problem, assumes no one will tamper with the few good assumptions within the creation, and hands it to the people entrusted with its longevity .

Only for it to fall into wrong hands and get adulterated for other, more vile purposes.

This formula created by Li assumed, essentially, that the market would continue to grow, and if it didn’t, it wouldn’t lose too much ground. It also meant that those who abused the formula, and didn’t understand the maths behind the formula, would continue to push it to validate selling and reselling pieces that essentially had no value or ground behind it.

That’s how VAM (value-added modeling) threatens to dice the teaching profession.

Proponents of VAM remind me of the proponents of the market’s wild success before the market crash. The mathematicians may have had the best intentions for using test scores as a means of determining how much the students are learning. The value-added model tries to control for external (socioeconomic) factors which differentiates it from a strictly evaluative model (taking the average of all test scores as is). It also tries to emphasize the growth a student makes from year to year, another boom for proponents of VAM.

What we have then are governors, mayors, newspaper heads, corporatists, and education celebrities (who have come under fire for massive erasures across their former school supervision) trying to tell the public that this formula is the only way by which we can hold teachers accountable. Policies like No Child Left Behind and initiatives like Race To The Top both implicitly and explicitly push schools to use student test scores as the most accurate way to evaluate teachers in the classroom.

Yet, it just doesn’t work. By many accounts from statisticians, financiers, and other vested mathematicians, students’ test scores used in this form are wildly undependable in all sides of the spectrum, and full of errors used as a continuous product of teacher quality.

What really shocked me was the ridiculous margin of error: 35% over 4 years, 11% over 10 years. As a measure of the teacher, it means that those who make it to the 4th year of teaching (*if* they do) with a 47% percentile on their Teacher Data Report may either be a terrible teacher at 12%, an excellent teacher at 82%, or anything in between. If they make it to their 10th year, and go up to the 53rd percentile, they’re still a below average teacher at 42%, a pretty good teacher at 64%, or anything in between. Let us guesstimate here and say that the margin of error by the 20th year is 5%, the same margin of error for many major political polls. Wherever the teacher is, frankly, won’t matter much because the teacher may be ready to move on to another career or retire.

How is using VAM a way to help a teacher as they grow in the profession with staggering numbers like that? For that matter, how does that help the school as a whole? It *doesn’t*.

It’s the equivalent of having to wait for someone a few hours too early or too late when you asked them to meet you at 8pm, a plane flying from Chicago to DC ending up anywhere between Massachusetts to North Carolina (give or take), or Ross Perot possibly getting the majority of votes in the 1992 Presidential Election or no votes whatsoever. (he won 18.9% of the votes that election year.)

Also worth noting that many teachers don’t stay in the same exact place and time, and neither does the neighborhood in which they work. With the fluctuation of populations in the places using these formulas, we can’t rely on the same type of students staying in there. How do we know that teachers aren’t teaching students how to take a test by means of mastering test methods taking or aren’t getting “help” from certain individuals?

With dangerous elements like VAM, we’re practically begging teachers to teach to the test, narrow the curriculum, and hope the child had breakfast that morning. We also have to limit creativity, assure students get the right answer on a particular question instead of getting the right answer on all types of questions involving that learning standard. I believe our solution lies in multiple forms of assessments for teachers and students, mainly formative, without repercussions or punitive scare tactics. If we want real professionals, we should find more professional means of treating everyone in this business we call “teaching students.”

Not that it’s a corporation. It’s a lifestyle for us.

Proponents of VAM couldn’t have possibly read up on using formulas for things they weren’t intended to measure and still think they’re benevolent. Public education is a future that’s too big to fail.

**Jose, who read the briefing papers and statistics, so you could get back to lesson planning …**

P.S. – For more on this, please check this paper by Darling-Hammond, Ravitch, Baker, et. al. …

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]]>The post The Real Purpose of Math Is … appeared first on The Jose Vilson.

]]>Anyone who’s ever had to fill in this blank understands my pain:

“The real purpose of learning math is _____”

I have a variety of answers, but usually, it’s straight-forward: much of the math you learn is applied to real-life situations, and the ability to do it yourself with no need for a calculator makes sure you’re independent of technological devices to a point. Also, even if it’s not necessarily math you’re using day-to-day, it activates a part of your brain that other subjects aren’t as adept at doing. Problem solving, using the tools in your hypothetical toolbelt, and applying the skills you’ve learned and strategies you’ve acquired to solve the problem leaves you in a better place to create, not simply ingest.

That’s my story and I’m sticking to it. However, the other definitions often laid out for us confuse the hell out of me. Two years ago, for instance, one of the questions read:

“Counselo is grocery shopping and sees that the price of 4 melons is 7$. Write a proportion that Counselo can use to find the price of one melon.”

followed by:

“Use the proportion to find the price of 1 melon.”

At first glance, this seems trivial. However, notice the way it’s phrased. Why does it require that students use a proportion if this problem implicitly requires proportional thinking? For that matter, what’s the purpose of writing a proportion if the student already knows what they need to find and how to find it? Why limit the students’ ability to find their answer by any (valid) means necessary?

Why even taut differentiation if this is the kind of question we’re posing?

I strongly believe in having as many ways of arriving at an answer as possible. Efficiency is key, but so is understanding. If the method that a child chooses is valid, consistent, and useful for the student, then why limit the child to “the way?”

As a test grader, I heard the uproar from teachers who all agreed. Generally, the people who make these tests always have to deal with subjectivity, but more often than not, it’s a question of error and pedagogy. And with the big test coming up soon, I’m in “catch ’em all” mode. I’m seeing how the preparation I’ve given my students has paid off dividends, but I have those few students who have their own methods to their madness, and it’s valid. I’m concerned that their methods won’t be validated, as correct as they are.

Then again, what is the purpose of math? I hope it’s not this.

**Mr. Vilson, who’s reviewing percent usage, hoping to remember some of these pieces himself …**

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]]>The post Whenever You Get Those Moments, You Blog About Them appeared first on The Jose Vilson.

]]>This morning, Bill Ferriter on Twitter ranted a bit about an e-mail from a disgruntled hater who called his blogging an exercise in self-fellaciating (if that’s even a word). Naturally, Bill was quick to distinguish between those who believe that their blogging not only becomes a central part of the reflective process for their practice and those who simply use it to show off a little. Do edubloggers really reflect in these given venues? How much of it would we consider constructive and fructuous labors that push the national agenda for the teaching profession and how much of it do we see as an exercise in futility and self-serving, looking for pats on the back for doing what they’re supposed to do?

I thought I had a real answer to this question until I finished teaching the morning. Topic: angle relationships with two parallel lines cut by a transversal. Yesterday, I prepared them for the topic by introducing a visual glossary for them to use, reminding them of all the names of the angles they’d seen since 6th grade. They were sharper than I thought they’d be, actually using words like complementary and supplementary to discuss the relationship between some of these adjacent angles. Of course, we had to work through some of the harder problems, like when the sum of two adjacent angles was equal to one whole vertical angle, but then they were steam-rolling through these relationship. Even with the little annoyances, I was rather satisfied with how it went today.

So satisfied, in fact, that I stopped with about 2 minutes to go, where my students started annoying me (in a good way this time). They discussed some of the images they found of me on Google Images, and the social networks I might be on, including Twitter.

One of my smart-asses said, “Yo, Mr. Vilson, I got 100,000 followers.” I told him, “Maybe you should watch your house.” Laughter ensued.

Moments like this make me wonder what teaching was like when we didn’t have to worry about some little curmudgeons and sycophants crunching in numbers, making equations, and churning out pretty pamphlets for mass consumptions trying to establish a firm relationship between standardized test scores and true teacher effectiveness. These moments I share with anyone willing to subscribe to my rants, or accidentally run into this mess through a string of search terms or a click from a referral.

And I guess that’s the whole point of blogging. In spaces where critical feedback and camaraderie may not exist within a school (for various factors), the ability to make one’s own network of professionals willing to discuss critical issues has become paramount for growth.

In other words, blogging isn’t about us specifically.

That’s the whole point of doing what we do. Even when it’s completely non-sequitur, there’s an understanding with edubloggers who take this seriously that there are people of like minds and interest willing to share in their experiences, often hoping they’ll get pushed further in their profession.

Even if the moments are ridiculous. At least I know someone’s reading it. And nodding along.

**Mr. Vilson, who has mannerisms even my kids are starting to imitate well. Ugh …**

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]]>The post Time May Change Me, But I Can’t Trace Time [An Explanation of Slope] appeared first on The Jose Vilson.

]]>For those who’d like a very fundamental and rudimentary explanation for slope and how to understand it as a function of two given variables, (and naturally, a correlation between that and real life), imagine the following:

Start walking for a good minute. Pick up the pace for another minute. Stop for a minute. Walk backwards for a couple more minutes. Then, walk forward for a few more.

In this scenario, as time (your x) increases, the line drawn will have different pieces varying on your movement or distance traveled (your y):

- it’s “going up” (in a positive direction, sometimes at a larger angle depending on how quickly you walked)
- it’s “going down” (in a negative direction, again depending on whether you paced or moonwalked)
- it flattens out (a representation of not moving whatsoever)

Even with that last one, your x variable time doesn’t actually stop, so your line doesn’t just cut abruptly away. The pencil keeps moving.

In the fourth case, and this is probably the best way one can explain in real terms the difference between no slope and undefined slope, the line just drops straight down or straight up. In other words, you moved to a certain distance … without respect to time. It’s as if you teleported in less than an instant.

And for now, that’s impossible.

In this life, we make many choices. Sometimes, our lives take divergent courses and other times they escalate to levels unforeseen. However or wherever we move, or even when we don’t, time will move on without us.

Maybe we should invest in making our slope positive. Continuously.

**Mr. V, watch the ripples change their size, but never leave the stream of warm impermanence …**

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]]>The post Abstracting the Concrete appeared first on The Jose Vilson.

]]>So instead, I decided to pull out the hardest questions from their predictive assessments (I’m a rebel) and help them understand how to do it. Let me show you. I took a problem like this:

and actually made it more multi-dimensional.

Nothing too shabby, but it’s interesting to see the kids’ faces of bewilderment. At first, only the more spatially inclined got how to do it. Then, as I started to show how the whole picture is nothing but a bunch of rectangles, the rest of the kids who were paying attention from the previous week’s lesson on the properties of a rectangle (it took a little reprogramming) were able to decipher the code on their own (for those not geometrically inclined, a hint: all parallelograms, including rectangles have 2 pairs of parallel and equidistant sides).

Of course, then I got really off-the-wall and gave them a similar figure and gave them completely off dimensions. Just to use the diagram above, the 10 was where the 7 is, and I mixed it up with some decimals, so the smart-asses in the class quipped, “But Mr. V, why didn’t you just put the measures where they belonged?”

I laughed, and like the quixotic teacher we’re used to seeing in the movies, I retorted, “It’s not about what you see. It’s about the idea behind what you see. Yes, the lengths are totally mixed up, and you’re already distracted by the mis-measurements. But if you understand that the longest length is the sum of the 2 shorter lengths parallel to it, then this should be no problem for you. Same goes with the the widths. Now, on the test, none of the lengths will be drawn to scale, so are you going to break out your ruler for every problem? I really hope not. I’m just making it obvious that you need to use your arithmetic skills to figure this out.”

Of course, one or two of them were still incredulous, but the rest understood. I was making them think for once. They couldn’t take anything for granted, and that’s important. Instantly, I found buy-in. I even differentiated by breaking the kids up in groups, and handing them cards with specially-made problems. Then they took it upon themselves to break out some chart paper and deliver how they did it to the rest of the class. I allowed for it only if I got to ask them critical questions to each and every student. Done and done.

**jose**

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