mathematics Archives - The Jose Vilson


Chancellor Dennis Walcott Visits School of the Future

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.


Jose Vilson


An excerpt from my latest (highly shared) Edutopia article:

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 …

India Power Outage

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
x3 x · x · x n/a
x2 x · x n/a
x1 x n/a
x0 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 …


A Future Too Big To Fail: Using Corporate Thinking Corrupts The Classroom

March 29, 2011 Jose

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, […]

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The Real Purpose of Math Is …

April 21, 2010 Jose
Because the difference between six and five can be very damned important

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 […]

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Whenever You Get Those Moments, You Blog About Them

February 23, 2010 Jose
Blogging Requires Passion and Authority

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 […]

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