Why I’m not THAT worried about the future of math education…

A New York Times article by Elizabeth Green has made its social media rounds lately. “Why Do Americans Stink At Math?” has been tweeted/shared a couple million times by now, with good reason.

It’s actually a really good article with some good story-telling and relevant history, and all the data and examples to back up the title. It’s worth a read. (It isn’t a quick read, mind you, but a good read.)

As far as I can tell, the thesis of the article is in the middle of the piece:

The new math of the ‘60s, the new new math of the ‘80s and today’s Common Core math all stem from the idea that the traditional way of teaching math simply does not work.”

The “traditional way” that Ms. Green speaks of is summed up a bit later in the piece.

Most American math classes follow the same pattern, a ritualistic series of steps so ingrained that one researcher termed it a cultural script. Some teachers call the pattern “I, We, You.” After checking homework, teachers announce the day’s topic, demonstrating a new procedure: “Today, I’m going to show you how to divide a three-digit number by a two-digit number” (I). Then they lead the class in trying out a sample problem: “Let’s try out the steps for 242 ÷ 16” (We). Finally they let students work through similar problems on their own, usually by silently making their way through a work sheet: “Keep your eyes on your own paper!” (You).

Green goes on to say that quite often teachers recognize the limitations of the traditional model, but have a hard time reforming it largely because of poor resources and ineffective training. From later in the piece:

Sometimes trainers offered patently bad information — failing to clarify, for example, that even though teachers were to elicit wrong answers from students, they still needed, eventually, to get to correct ones. Textbooks, too, barely changed, despite publishers’ claims to the contrary.

So, here we go. Sounds like a big problem, right?

Well…

I’m not that concerned. Ya know why?

First off, I don’t want to give the impression that I think that Green is writing untruths or is exaggerating. That isn’t where I’m taking this. American math education needs some serious work. But see, that’s where I get encouraged.

Let’s look at a specific bit of content. How about volume and surface area of prisms?

So, my textbook provides this:

Prism Clip

taken from Holt’s Geometry, 2009 Edition, Pg 684

 

These practice problems fit in with the “I, We, You” model that Ms. Green described in her article. Right on cue, the textbook appears to be pitching to our education system’s weaknesses.

But those weaknesses have entered a brave new world where teachers who have found models that work are not only willing, but also able to share them freely for anyone and everyone who might be looking.

For example:

Andrew Stadel’s “Filing Cabinent” is, by content standards, just another prism surface area problem. But, the situation he sets up is anything but ordinary.

Timon Piccini’s “Pop Box Design” asks a relatively simple question in a context that is approachable by practically everyone.

Dan Meyer’s “Dandy Candies” pushes the envelope on video quality, pushes the same content, and includes it in a blog post that discusses a competitor to “I, We, You.”

All those fantastic resources are available… for free. And the creators can be reached if you have a question about them.

A movement has begun. An (ever-growing) group of math teachers decided that it was one thing to discuss reforming math education and it was quite another to effectively reform math education. The group is getting larger. It’s inclusive. It’s welcoming. It’s free to join. And it doesn’t expect anything from those who join. Everyone does what they are able. Some share lots. Some steal lots. Some do both. The bank of resources is growing.

And this isn’t legislated reform. There is a genuine desire for this. I spoke in Grand Rapids, MI this past spring and was amazed that the crowd that was willing to gather to hear someone talk about reforming math education. Nearly 100 folks crammed into a room to have, what ended up being a rather lively, discussion about how to engage all learners, push all learners, and keep as many learners as possible interested in meaningful mathematical tasks.

2014-03-14 12.38.33

They had to turn people away from a talk on effective math lesson planning.

So, Ms. Green is certainly right. Americans stink at math. But there is a growing group of teachers who are aware of the problem, interested in seeing it solved, and now, more than ever, there are places they can turn to, people they can reach out to (and who are reaching out to them). And it is all available for free on technology that practically everyone already has.

So, forgive me, but I am quite optimistic about where this might take us.

 

Testing at the speed of… change.

I have a question:

Will the problems the public education system be solved by employing standards-based solutions like Common Core (or some other standard-based curriculum)?

This seems like an interesting question. A lot of follow-up questions would be needed.

1. What are public education’s problems?

2. What’s causing the problems?

3. What do we do about problems that aren’t solvable under current law?

4. Are certain standards-based solutions better than others?

5. What will education look like when all its problems are solved?

 

I don’t want to sound like a skeptic, but, here in Michigan, we’ve been at this for a while.

In Novemeber 2005, the National Governor’s Conference decided that high schools weren’t rigorous enough to prepare students “for an increasingly competitive global economy.” In Michigan, this led directly to the development of the Michigan Merit Curriculum.

The results weren’t good. By 2011, the state set the proficiency “cut scores” at 39% of the MEAP Test questions correct. (Got that? The Michigan Department of Education was cool writing a test, giving to every student in the state, and calling “proficient” any student who could get 40% of the test right.) This, of course, showed that 90% of 3rd graders were proficient in mathematics statewide. By 2012, when the cut score was raised to 65%, statewide proficiency dropped to closer to 40%.

So, after all this, apparently, the people of Michigan wanted Common Core. So, along with that, we passed some other laws to try to get Arne Duncan’s Race to the Top money (We failed, by the way. Then we failed again. Then we failed for a third time.)

After all that, we’d changed a number of laws, including approving the Common Core standards. However, a lot of those laws were designed to appeal to Arne Duncan and his several billion dollars, which never came.

So, we have a department of education that has approved Common Core. By January of 2012, the state was gearing up for the Smarter Balance Test. We even had school districts running trials and pilot testing situations (my district included), even as the state legislature determined that it didn’t have the funds to support Common Core.

Bear in mind, these changes had all come quite quickly. If this upcoming junior class (class of 2016) is to take the Smarter Balance Assessment, it would have done so after an education that included no standards (from kindergarten to 2nd grade), Michigan Merit Standards (3rd grade until 7th grade), and Common Core Standards (since 8th grade). Keeping in mind the implementation dip that is going to accompany the transition periods, it’s really any wonder why we have any expectations for this group beyond simply finishing the test.

And the speed of change wasn’t being lost on people. Common Core dissent is gaining publicity and some think that is makes for some pretty compelling television. So, Michigan is stuck having blazed a trail that isn’t exactly popular and isn’t exactly funded.

Moreover, in the past month, a new set of questions is brewing in Michigan: What test will those students be taking next year? The public pressure is mounting. Business leaders and education groups support it, but there is a lot of apprehension over the online nature of the test. (And Bill Gates suddenly isn’t a huge fan of high-stakes testing anyway.)

So, it looks like we’ll stick with MEAP another year, except we might steal some of the Smarter Balance questions. We currently don’t have a test written, or dates to plan on. The only certainty we have is that we can rest assured, there will be some test we will have to give.

I started teaching in 2006. This has been my experience for the entirety of my career. All of this flurry over which standards, which test, which questions. For what? People are yelling, negotiating, quitting their jobs over all of this. But we still don’t have an answer to the original question.

Will the problems the public education system be solved by employing standards-based solutions like Common Core (or some other standard-based curriculum)?

Oh, and don’t forget. We need to grow consensus on those five questions BEFORE we get to the original, bigger question. Here’s the problem. We aren’t prepared to try to build consensus on those five questions, at least not in the right way. Discussions like these require cooler heads. (Every been in a meeting when people start to get worked up? All progress stops until everyone calms down.)

Oh, and there’s these other questions that are going to come into play.

6. Should kids who fail to meet a proficiency standard move on with support and accommodations? or be held back to start the program all over again?

7. What are the academic grounds on which a student should be eligible to be a varsity athlete? What level of participation is acceptable if the student doesn’t meet all the standards?

8. What is the acceptable age at which a young person, or their family, should be able to freely opt a student out of the state’s preferred education program without penalty? What are the conditions on which an opt-out application is accepted?

All of these questions I have seen people yell and scream in disagreement with each other. Yelling. Over athletic eligibility and the disagreement over social promotion vs. retention.

Education is filled with passionate people. We don’t need any more passion. We need more wisdom. We need calmness. Patience.

I would love to see the State of Michigan (or any state) just stop all of this madness until it can issue a research-based negotiated document answering those 8 questions with rationales, just so that we know that those answers have been factored into any plan to move forward.

I hate to sound like a skeptic, but until we are prepared to clearly build consensus on those eight questions, all of our “fixes” are much more likely to make the problems worse, not better.

 

My (imaginary) conversation with a baseball sabermatrician

Baseball’s gets most of the benefits of a very talented group of statisticians. They spend their times trying to figure out the value that each action of a baseball player adds to their team’s chance of winning a game. Every possible action. In fact, ESPN just issued an article regarding the value of a catcher who frames pitches well.

So, I’ve been wondering why education can’t get in on a little bit of that action. A while back, I appealed to Sabermetricians hoping to get some of that talent to play for our team.

Today, through some Twitter conversation with school data aficionado Andrew Cox (@acox) I got an idea of what the conversation might look like if a Sabermatrician responded to my appeal.

We’ll call our statistician Timmy. I’ll play the part of Andrew.

Andrew: Thank you for calling. I have been looking forward to this conversation for a while now.

Timmy: It’s no problem. I’ll do whatever I can to help. But first, I need some information from you.

Andrew: Anything. Just name it.

Timmy: Well, I need to know the goal of the education system?

Andrew: The goal?

Timmy: Yeah, the goal. You know, like baseball’s goal is to win games. The most successful team is the team that wins the most games.

Andrew: Yeah, well, that sort of depends on who you talk to. This article lays out 11 goals (some more explicit than others). President Obama says this. Thomas Jefferson says this. These folks say we should teach entrepreneurship

Timmy: Well… okay. So, you’re saying that education as a whole doesn’t have an agreed upon goal?  Who makes the decision of what a school goal is?

Andrew: Well, school boards make a lot of decisions. Increasingly, it seems like legislators are getting a larger say.

Timmy: I see, well, Okay, okay. So, are schools doing anything to measure how strong the long-term retention is for it’s students?

Andrew: um… while I can’t speak for schools nationwide, I am not aware of any K-12 school districts that are doing anything to measure the long-term retention of the content.

Timmy: Well, that makes it tricky to figure out the practices that contribute to that.

Andrew: I agree.

Timmy: Well, okay. Goals might be tough to define. I understand. It’s a diverse system. What about the means?

Andrew: The means?

Timmy: Yeah, like, in baseball, the means of reaching your goal of winning is to maximize the runs you score and minimize the runs your opponent scores. So, what are the means of reaching the goals of the educational system?

Andrew: Yeah… the means.

Timmy: Yep.

Andrew: Well, it kind of depends on which goal the school has.

Timmy: I’m sorry, I know I come from the baseball field, but isn’t learning the goal?

Andrew: Yes, absolutely.

Timmy: So, what practices maximize that?

Andrew: Well, these people say effective use of formative assessment and differentiated instruction. These folks have all kinds of advice. Some of that advice matches these folks’ advice.

Timmy: Okay, there some things to work with there. Some of that’s teacher stuff. Some of that is student stuff. Some of that is parent stuff. Some of that is administrator stuff.

Andrew: Yup. That is pretty much true.

Timmy: How can you tell if those things are actually happening in a classroom or in a student’s home?

Andrew: That can be tricky business. Principals have a hard time get into the classrooms to support instructors. And you can’t really ask to do walkthroughs on students’ homes. 

Timmy: So, what data do you have?

Andrew: We have TONS of demographic data. We have attendance and behavioral data. We have test scores.

Timmy: I’m sorry, do you really need to contract me so that I can tell you that there is value added to a kid’s experience by showing up to school and not getting in trouble?

Andrew: No… no, we knew that one.

Timmy: One thing that helps baseball statisticians is that every play is recorded from at least 3 camera angles. So, why don’t you just put cameras in each classroom to get a real sense of what teachers and students are doing?

Andrew: Some think that would be usefulLawyers say that’s risky. 

Timmy: Well, Andrew. If you don’t have a goal, you can’t really isolate the means, and we can’t really observe any of the practitioners in any real detail, then what do you expect do get done with your statistics?

 

Doggone it, Timmy. That’s a great question.

Perception and Reality – (Lean not unto thine own understanding…)

In Basic Economics, Thomas Sowell tells a story about a decision made by a New York politician who was attempting to address the homeless problem in New York City. The politician noticed that most of the people who were homeless were also not very wealthy. The politician moved forward with the idea that the apartment rent prices were simply too high for these people to afford a place to stay.

So, he decided to cap the rent prices… and the homeless problem got worse. How could this possibly be?

Well, according to Dr. Sowell, lowering rent prices, while making the apartments more affordable for those in need, did the same for everyone else. The suddenly cheaper rent prices decreased the rates of young folks sharing apartments. Also, people who have several places they call home throughout the year might not have found it reasonable to pay a high rent price to keep a NYC apartment that they might only stay in a few times throughout the year. Lower rent prices made that seem more reasonable.

Evidence also suggested that there was an increase in apartments being condemned. Lowering rent costs meant that landlords found themselves with fewer resources to maintain buildings, repair damages, pay for inspections, etc.

While the decision made the apartments more affordable, it also made them more scarce. There was a disconnect between a decision-maker’s perception of a situation and the reality. That disconnect led to a decision that ended-up being counterproductive.

I may have just done the same thing… maybe.

Perception-Reality

 

Sometimes things make so much sense. If we did this, it would HAVE to produce that. It make so much sense. How could it possibly not work?

This perception was in place among some in my community. It led me to decide to try The 70-70 Trial, which I’ve been at for about 10 weeks now. The perception in place goes like this:

a. Formative assessments prepare students for summative assessments.

b. Students who struggle on formative assessments are more likely to struggle on summative assessments (and the inverse is also true.)

It’s with these two perceptions in mind that we assume that the if we can ensure a student achieves success on each of the formative assessments (regardless of the timeline or the number of tries), we improve their chances of success on the summative assessment.

The 70-70 trial did what it could to ensure that at least 70% of the class achieved 70% or higher proficiency on each formative assessment. (There were four.) This included in-class reteach sessions and offering second (and in some cases third) versions of each assessment. With all of those students making “C-” or better on each formative assessment, how could they possibly struggle on the unit test? That was the perception.

50% of the students scored under 50% on the summative assessment. That was the reality.

Now, I am not an alarmist. I understand that one struggling class in one unit doesn’t discredit an entire education theory. But it sure was perplexing. I’ve never seen a test where, after 8 weeks of instruction on a single unit (Unit 4 from Geometry), half of an entire class unable to successfully complete even half of the unit test.

And when you consider that this class was the one class I had put the most effort into defeating just that kind of struggling, well it seems like the intersection of my perception and the reality wasn’t nearly big enough. I just got a better view.

And I’m having a hard time making sense of what I’m seeing.

Conversation starter: Is failure an option?

Let’s talk about students failing classes, specifically in high school.

Let’s suppose a teacher spent the last ten years teaching high school math. Let’s suppose further that the same teacher hadn’t had a single student fail his or her class for that entire span. This teacher is going to have that data met with a fair amount of suspicion, whether it is fair or not.

Let’s suppose a different teacher spent the same ten years in a comparable district teaching high school math. Let’s suppose further that for that time span 3 out of every 4 students who started that teacher’s math class left with a failing grade at the end of the year. This teacher is going to have this data met with outrage (and in all likelihood would never have made it 10 years like that.)

So, ten years without a failing student is suspicious, it’s potentially evidence of a rubber stamp course. 10 years at a 75% failure rate is outrageous. It is potentially evidence of a course that is unnecessarily difficult for a high school math course.

So… what’s an acceptable number of failures?

Actually, let me ask this question a different way…

How many students should be failing? It seems a little strange to suspect that anyone should fail a high school course, but is there an amount of failures that demonstrate a class is healthy and functioning properly? Is that number zero? Is it 5%? 10%? 20%?

I’ll tell you what motivated this post: I am aware that some schools impose mandatory maximums of failure for their teachers. It might be 12% or 7% or 2%. In these districts, each teacher in the district needs to make sure that at least 88% or 93% or 98% of students earn passing grades for their class each semester.

The implication is that if more students than the accepted maximum fail to earn passing grades, it is a reflection on the inadequacy of the course, the instructor or the support structures. But, I’m not sure if that’s true. And besides that, how does a district or community decide the acceptable percentage of failures?

There is another side of this argument that says that a school should be prepared to fail 100% of their students if the students don’t meet the schools requirements. This is the only way to motivate students to reach for the standard of proficiency that the community has agreed upon. There would certainly never be an instance where a teacher had to fail 100% of his or her class, but if the students didn’t meet the requirements, the teacher would have the support of the school and the community to every student, even if that meant 100% of them.

We should probably figure this out because failure numbers are starting to work their way into the mainstream, as demonstrated by this Op-Ed from the New York Times which asserts that perhaps Algebra should be reconsidered as mandatory for high school graduation because nationwide, math provides a stumbling block and the subsequent failures are leading to increased dropout rates. (This seems like a highly contentious point in itself, but it doesn’t mean that it isn’t driving decision-making in some communities.)

Here are the issues in play here:

What portion of the responsibility of a single high school student successfully earning a high school credit is the school’s and what portion is the student’s?

What are the costs of high standards? If we want to increase rigor, there is almost certainly a trade off in that there will be an increased number of students who are unable or unwilling to go through the more rigorous process to earn the credit.

What are the implications of community with class after class of students who know that the teachers are pressured to pass a certain percentage of their students? Is this effect overstated?

Has this ever been studied? I’m not sure if there’s ever been a comprehensive, research-based statement made on the topic of student failures and what the optimal percentage are. And if that’s the case, then should we be making decisions based on “what seems too high” or “what seems too low”?

I am looking for some conversation on this topic. Let me know what you think. Links to posts or articles by people that you trust are appreciated, too.