Common Core: The Blessed Textbook Conflict


We started working because the textbook stopped.

When we started the process to realigned our curriculum to the Common Core, we noticed that our textbook, which previously aligned to the Michigan Merit Curriculum, stood no chance against the Common Core State Standards. This forced us to make several decisions: First, were we going to replace the textbook with a new one? Second, were we going to keep the textbook and, in a sense, align the CCSS to the book?

After much discussion, we decided to do neither.

And it was the best decision we ever made.

It forced us to meet, research, collaborate, decide, create, experiment, reflect, analyze, adjust, and all sorts of other verbs that show up on the top of Bloom’s Taxonomy.

We are fighting through this year. We have reflected on the lesson’s we’ve learned. It hasn’t been easy. But our geometry team, which includes three teachers, has invested in a product that has resulted in some of the most intense and effective professional development that has forced us to have real conversations about student engagement, assessment, grading procedures, class structures, and all sorts of other goodies.

And none of it would have happened if we went with the textbook.

Mainstream Media Flips Out over Flipped Classes

Well, it seems the secret’s out…

Right on the heels of a series of decent Twitter conversations I had regarding blended learning, I noticed two articles on the benefits of Flipped Class structures, oddly enough, in mainstream news outlets.

Yesterday The Sacramento Bee published two articles: Flipping Class Gaining Momentum Among Educators which offers some praise for the blended learning model, and Khan Academy is a Flipped Classroom Pioneer.

So, this got me wondering how many other mainstream news outlets have done stories on flipping. The Herald Democrat (out of Texas and Oklahoma), The Columbus Dispatch, The News Messenger (A Gannett paper out of Ohio), all have recently ran pieces.

Then I noticed The Hawaii Tribune Herald picked up an Associated Press piece called “Teachers flip for ‘flipped learning’ class model“…

… which was printed… well… practically everywhere including USA Today, Yahoo!, and The Salon. The story, out of Santa Ana, California, was printed nationwide, from Hawaii to Maine. Here’s the Bing search results for the AP article.

Well, I know that I’ve only been in the game since 2006 when I got my first job, but I can’t say as I’ve ever seen a teaching model EXPLODE on the mainstream media quite like this.

It seems that I’m not the only one noticing the media’s infatuation with the flipped model.


So, the mainstream media is excited.

But see, according to much of the media fanfare, it was “invented” in 2007. That’s 5 years ago, folks. Elementary teachers who’ve embraced this haven’t seen their students graduate from high school yet. So, is this all fluffy frenzy?

Mark Frydenberg wrote a piece for The Huffington Post “The Flipped Classroom: It’s Got To Be Done Right.” From the middle:

With help from the Internet, word grew of the flipped classroom. Teachers tried it. Today, there are social networksblogsnewspaper columnsvideo contests, and websites to flatter flip fans, and flummox the flippant.

It would appear that the internet isn’t the only support that this movement has. Mainstream print media are jumping on the bandwagon, too. It’s starting to sound like the flipped model is the magic bullet that will solve all of education’s problems.

Which, of course, isn’t true.

That isn’t to say flipped model isn’t without its virtues. It has opened up conversation about the use of class time (especially in math) which was perhaps overdue. It has certainly energized some positive media coverage about the education sector which was also overdue. And, it has allowed equally as devoted new media bloggers and podcasters who aren’t sold on the flipped model to present conflicting, non-traditional viewpoints. There are worse problems to have.

Frydenberg offers some excellent advice mentioning that for this model to be effective, the proper amount of prep time is needed, the at-home piece must be short and to the point, and the in-class piece must be focused and well-designed. Which, by the way, is the same advice for any of a dozen other models of instructional delivery.

Eventually, the frenzy will die down and we will know the truth about flipped class. Is it a hip new trend? Is it a vision of the future? Is it the answer we’ve all been waiting for? Is it a way for traditional lecture models to find a niche in the 21st century?

Forgive me, but I am going to withhold judgement at least until 2008’s flipped out first graders become college freshman.

Algebra as Calculus’ Farm System

I was struck by a comment left on a recent post of mine by a person called “Rich”:

Algebra leads to Calculus, ask any professor and Calculus is the gold standard that leads to the fun stuff with mathematics.  Unfortunately, there’s no short-cut to go from arithmetic to Calculus.  Many people talk about “real world” problems, but most of them are calc based or need a deeper understanding of higher mathematics.  I see algebra as the foundations of calculus, kinda like what high school football is to college football, and what college football is to the NFL. (emphasis mine)

His reference to football makes for an interesting analogy. Let’s push this one. If Algebra I is high school football and calculus is the NFL, then I agree with the following points:

1. There are way more [high school football players/Algebra I] students than [NFL players/calculus students].

2. It takes more skill to successfully compete in the [NFL/calculus] than it does to compete in [high school football/Algebra I].

3. Some [high school football players/Algebra I students] will go on to the [NFL/calculus]. Many won’t.

Here are some ways that I would extend this analogy that seems to disagree with the commenter.

1. High school football exists for far more reasons than to produce NFL talent. In fact, I would go so far as to say that developing NFL talent is pretty much the last thing that most high school football coaches are considering when they coach their team.

2. High school football has players, pads, refs, marching bands, and all of the things that make it REAL football. It isn’t pretend football. It has the same rules. It is played on the same-sized field. Similarly,  algebra should stand on its own as a class that contains all of the elements of an effective math class.

Here is a big question in my mind right now: Are we concerned that algebra isn’t good enough? Does a rich understanding of algebra have any meaning of its own? Armed with an airtight understanding of basic high school algebra, is a person able to be a proficient, patient solver of life’s everyday problems?

Well, it seems to me that attempting to motivate and inspire high school Algebra I and Algebra II students by treating them like minor leaguers is probably not going to work. In order to draw these students out, we have to treat them to an experience that shows them the stand-alone value that being able to reason algebraically has.

“Rich” seems to be suggesting that algebra finds its value in calculus. Perhaps in that mantra lies the key to the disengagement problem for secondary algebra students. How many classes are taught as if “the fun stuff” was all somewhere else because engaging in “the real world” requires a “deeper understanding of higher mathematics”?

The Mixed Bag of Blended Learning

Math has taken to the computer. What now?

Math has taken to the computer. What now?

Thursday I read this from Dan Meyer (@ddmeyer): An Aggravating and Energizing Hypothetical. And I commented on it.

Today I read this from Adam Percival (@ampercival): Blending Learning will bring big changes. And I commented on it.

I’ve been pretty forthcoming about my thoughts about the needed shake-up in the traditional look of math classes for a while now. This blended learning phenomenon is really getting the discussion going. That can be healthy. Just so we are on the same page, I’m going to steal from Mr. Percival, that blended learning is “classes taught partially online, partially in-person.”

And in the mathematics field, the discussion is never… uh… healthier(?) than when we all get to talking about Khan Academy (@KhanAcademy): The one-stop, YouTube-based, fix-it-all for struggling learners everywhere.

Now, to put it mildly, the jury is still out on whether or not Khan Academy helpful or desirable. Robert Talbert’s Report “Does Khan Academy help learners?” casts a bit of doubt, but leaves it open. Also, for a good time, check out blog posts about Khan Academy and read the comments (this post, for example).

So, what about blended learning? Well, my teaching experiences, conversations I’ve had, reading I’ve done and talks I’ve heard have utterly convinced me of one incredibly important point.

When it comes to Algebra, students struggle because they are disengaged. DIS… EN… GAGED… period. They aren’t learning because we aren’t teaching them in a way that draws them in. There it is.

If blended learning is prepared to deal with that problem, then I think we may be onto something. My contention with Khan Academy (and similar services) is that they are assuming the wrong thing. They are assuming that students are inherently self-motivated (certainly true in some cases, certainly not true in other cases) and that we are trying to teach material too fast. (The YouTube lecture lobby gets a ton of mileage out of the ability to pause a presentation and rewatch.)

As I see it, those are not the problems. The problem is with engagement. From my location in the cheap seats, the biggest bang for the professional development buck comes from developing the means to engage students into algebra learning. Draw them in. Sell it. Make it interesting. The question of Khan Academy (and similar services) isn’t whether or not its cost-effectiveness is going to muscle out traditional classrooms.

Whether or not Khan Academy (and similar services) becomes the tool that finally breaks through the wall of disengagement that the 21st century teenager has built remains to be seen. I am not convinced Khan Academy (and similar services) can do that to the typical unmotivated student, but I’ve been wrong before.

In the end, it all comes down to this: If there is to be a magic bullet that solves the problem of the struggling American algebra student, then it will be the system/program/model/philosophy that solves the problem of the disengagement of the American algebra student.

What if this is actually true…?

Last August, Kelsey Sheehy (@KelseyLSheehy) published “Failing a High School Algebra Class ‘isn’t the End of the World’  in US News and World Report. In the article she discusses the arguments of a couple of critics who are essentially arguing that it is time to reassess the long-held tradition that algebra is an mandatory part of a high school mathematics curriculum.

From the article:

“Algebra requirements trip up otherwise talented students and are the academic instigators behind the nation’s high school and college dropout rates, argues Andrew Hacker, an emeritus professor at CUNY–Queens College and author of the much-debated article.” (Sheehy, 2012)

She continues:

“Hacker argues that students should understand basic arithmetic, but memorizing complex mathematic formulas bring little value to society. “There is no evidence that being able to prove (x ² + y ²) ² = (x ² – y ²) ² + (2xy) ² leads to more credible political opinions or social analylsis,” Hacker writes.”

Sheehy is referencing Mr. Hacker’s Op-Ed from the NY Times dated July 28, 2012, which has generated a rather strong response. The comments number 477 and are closed. Some of them are less than cordial. There have also been blog responses like this (which also got 20 comments).

The last paragraph of his piece makes no bones about his point-of-view:

“Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.” (Hacker, 2012)

It would seem that the policy-makers across the country would disagree with him, but I’m not sure our policy-makers are any more equipped to make that decision than Mr. Hacker.

I’m also considering Dan Meyer’s (@ddmeyer) rather engaging line: “I’m a high school algebra teacher. I sell a product to a market that doesn’t want it, but is forced by law to buy it.”

So what gives? If Algebra is driving up failure rates, driving down student motivation, and, as Mr. Hacker asserts, isn’t actually useful (a very debatable point but perhaps a debate worth having), why do we continue to insist that Algebra continue to be mandatory?

And if it is going to continue to be mandatory (which might be the right thing to do), what can we do to make it more universally accessible?

Perhaps the question of why algebra is mandatory should give way to the much more meaningful discussion: Why do kids hate it so much and how do we fix that problem?

Increasing Engagement Through Art

A half-hour of drawing might make the difference to whether or not the data table gets filled out...

A half-hour of drawing might make the difference to whether or not the data table gets filled out…

I have a teaching colleague to thank for this idea. He currently teaches all of our Algebra I students, mostly freshmen. We have noticed a struggle-disengagement cycles that is self-repeating and driven by inertia. The student begins to struggle, which leads to disengagement, which leads to more struggling, which leads to… you get the idea. However, my colleague created an art activity that might be a game-changer for some of these students.

It goes like this. First, create an image on a piece of graph paper. Whatever you want. Could be your name or a picture or whatever. But there are conditions. It must include at least 10 line segments. Endpoints must have integer coordinates. It must have one pair of parallel lines. It must have at least one pair of perpendicular lines. After the pictures were drawn and colored, then the students picked 10 line segments and found coordinates of the endpoints, slope, function rules in standard and slope-intercept form.

Doing all of those things ten times over is as good as a practice worksheet, except better! Better because, you activated the right side of the brain for those who need it (which is a healthy portion of our students). There is a greatly reduced temptation to cheat or shortcut because the products are unique (and the more competitive students will see to it that their picture isn’t copied). Plus, like a good billiards player, you are always thinking two shots ahead. By tossing in the parallel and perpendicular pieces, you are running the risk that the student might begin to make some conjectures about the look of lines and their slopes.

How much more Algebra is this student learning now?

How much more Algebra could this student be learning now?