The two key ingredients of real problem-solving

A quick word about dissent.

During a recent conversation with a teacher-friend I we stumbled into an area of conversation that allowed me to see dissent through the lens of leadership and problem-solving in a way that I hadn’t before.

Acceptance of dissent isn’t a new idea in leadership. Lots of writers talk about the need for leaders to appreciate it… here’s an example.

“Defining effective leadership as appreciating resistance is another on of those remarkable discoveries: dissent is seen as a potential source of new ideas and breakthroughs. The absence of conflict can be a sign of decay.”

– Michael Fullan (From Leading In A Culture of Change, 2001, pg 74.)

We were talking about problems that tend to have some pretty zealous advocates. For the sake of exploring a concrete situation, I’ll choose one for an example. How about student retention? This is a topic that can bring some energy out of some folks. It’s an important conversation, too. What happens when a student finishes a school year without meeting the minimum expectations to complete the grade/course they are in?

To push them forward would mean pushing the student forward into academic challenges that they likely aren’t prepared to tackle.

And making student repeat grades has just not been an effective solution according to ASCD, Education Week, John Hattie, etc…

So, when a district sits down to really solve this problem, they need to accept that they probably are going to need to choose a third option. Carelessly moving the student on is probably a poor choice. Making the student repeat the grade is also a poor choice.

The better option, the third choice, the one that will work better, is likely going to have to be crafted on site and with the resources available helping to guide the process.

This is where I began to see the need for two very distinct groups of people.

One group of people creates the boundaries… I’ll call them the idealists. These are the people who say, “We can’t retain them. We can’t. I don’t care what we do, but we aren’t retaining them. It doesn’t work.” Every issue has these people. Most of us can become these people when the issue at hand strikes us right. Luckily, they seem to be essential to the process. They also happen to be very frustrating to people who either disagree or just don’t see the issue as important.

The main issue with these folks is that zeal often doesn’t really solve problems. It creates boundaries for the solution, but (in the case of our example issue) simply eliminating retention doesn’t actually solve the problem of students falling behind. It just eliminates a series of potential solutions.

So, we need to bring in the dissenters… I think of them as the holders of the “yeah, buts…”

“We can’t hold them back.”

“Yeah, but they are still behind in their learning, so we can’t just move them on.”

Now… at this moment… as long as neither the idealist or the dissenter storms out of the room, the real problem-solving work can begin. The boundaries are set, the reality checker is in place and now the focus can turn to the ACTUAL problem In the case of promotion v. retention, it’s the fact that students are making it to the end of the school year not ready to move on.

And that takes some deliberate focus and patience. The zealous boundary-setters don’t want to hear about “yeah, buts…”. The dissenters tire quickly of the perceived inflexibility of the idealists. But I’m not sure real solutions to tricky, messy problems are more likely than when these folks can unify around a common goal.

American education (shoot, American culture as a whole) has a whole variety of problems that we are having trouble solving because the zealous idealists and the persistent dissenters have such a hard time embracing the valuable contribution that each other makes in the course of creating real solutions.

But real solutions… solutions that are effective and sustainable… probably require the active presence of both.

Changing the conversation about testing and data

What if I told you have I know of schools that run through their first grade students through just over an hour of math and reading exercises while recording their results to get a sense of their strengths and weaknesses? These exercises are done a little bit at a time in the first three weeks of school. They do this so that they can make accurate decisions about the ways that each of these students will be properly challenged. This way, each young person gets exactly what they need to grow as learners.

What are your thoughts about these schools? Would you say they care about their students? Would you say that this is a nice approach to education?

Pause here for a moment…

I’m going to start this blog post over again. This time I’m going to tell the same story in different words. I want to see if different words paint a different picture of these schools. Keep in mind that the second set of statements are equally accurate.


What if I told you that I know of schools that will give their first grade students eight different standardized tests by the end of September? They do this so that they can record a bunch of data about the students so that they can group them based on the data on those tests.

Sounds a little bit different, doesn’t it? Eight standardized tests sounds like a lot. (Even if the longest of them 8 minutes long. Some are as short as 1 minute.)

So, we’re faced with a decision. Is the first one unrealistically rosy? Or is the second one unnecessarily cold? Your bias will determine which of those viewpoints speak to you most. My bias certainly is.

What isn’t based on a bias is that “standardized test” and “data” have become hot-button, divisive words. And there’s been some backlash. That backlash is captured by posters like these.


Sharing encouraged by Marie Rippel

The message is that our young people are more than a few data points. And that, no matter how much data that we collect, there are important elements to these young people that no test can reveal. That is absolutely correct and if you don’t agree, I’m curious to hear your argument. Post it in the comments and we’ll explore it together.

But that doesn’t mean that the poster (and the related sentiment) are safe from push back. First, there are some things on that list that tests actually could measure. It would be fairly reasonable to collect some data on “determination”, “flexibility”, and “confidence” provided we could all agree on the definitions and manifestations of them.

But secondly, that poster includes items like “spirituality”, “wisdom”, “self-control”, and “gentleness”, which are items that different groups would argue aren’t really the job of the American public school system. That isn’t to say that these groups wouldn’t consider these valuable qualities, just qualities that the schools aren’t on the hook for teaching.

To me, this is an important point. Because there’s a variety of other things your garden variety standardized tests don’t measure. For example, they don’t test a student’s ability to drive a car, their ability to write a cover letter or resume, or their ability to cook a decent meal.

These fit largely into the same category as the items on that poster. Important qualities that are common among successful people, but not qualities that are tested on any of the standardized tests that the students take in the K-12 education. Yet, I’ve never heard anyone use their absence as a support to discount the value of the tests. What makes these qualities different that the ones on the poster?

It could be that the American public and teaching professionals agree that those things are not the job of our public schools. It isn’t their job to teach young people how to drive a car or write a resume, or cook a meal. So, clearly we should be inspecting their ability to do so.

So, would I be safe in assuming that if we could all agree on the job of public schools, then some of the fervor over tests would cease?

Would the authors of that poster be more satisfied if we were collecting data on students compassion?

What are the jobs of our public schools? Frame your answer from the context of what should all students be expected to do when they leave the educational systems after spending 13 years in it.

And how are we going to know if the system is doing it’s job? Listening to a discussion regarding those questions sounds like a huge upgrade compared to listening to hours of endless back-and-forth about whether or not to test, how to test, which tests to use, or what to do with the results of the tests.

What are our goals and how are we going to know if the system is doing it’s job? It’s fine by me if testing students isn’t part of that. But, our educational system has a vital job to play and somehow or another, we need to develop a way to inspect what we expect from the system.

Perhaps the first step of that is coming to consensus on what we expect.

Mathematical Reading – Wrapping my thoughts up.

I have spent the last couple of posts discussing the value, need, and potential of considering mathematical reading an essential learning target in all math classes.

Typically, this isn’t a tough sell in the elementary world because elementary teachers are teachers of all things anyway. They teach reading, writing, science, math, (and in some cases, art, music and phys ed, too.)

Secondary folks, on the other hand, tend to exist is a more compartmentalized world. This is largely a product of the increase in sophistication and depth of the content as the public education sequences progresses toward graduation. It is simply unreasonable to expect educators to have a teachers-level knowledge base of biology, economics, civics, algebra, and literature, as would be required if freshman year structurally looked like first grade. Compartmentalization (or silos as is becoming a popular term) has downsides as well. And many of those downsides can be wrapped up in the all-too-often uttered phrase “It’s not my job.”

And in my years in education, I’ve heard “it’s not my job to teach reading” from math teachers many times. And I forgive them for saying it. Math is a world that communicates differently. Graphs, charts, symbols, equations… we do that stuff so that we don’t have to read.

And they have a point. Consider these mouthfuls:

“The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse”.

“The slope of a linear function is the coefficient on the independent variable when the function is written in slope intercept form.”

There’s a reason people (both mathematicians and students, mind you) look to use notation to represent those two statements. it is quite a bit easier for a student to say “well, y = mx + b… slope is the m.” And what’s more, that statement will work effectively more often than not. So what’s the problem?

Through the lens of solving math problems on a test, there probably isn’t much of a problem. But consider reading to be an essential problem-solving skill, then there’s a risk to consistently easing the reading burden. We might be navigating our students strategically away from something they’ll need.

And while this thought process was instigated by the releases based around the redesigned SAT, I wouldn’t simply use the test as the primary motivator for updating our math classes. I would prefer to examine what message the College Board is trying to send by insisting that their materials insist on such a high degree of literacy for all subject areas, even considering that they have a reading and a writing test already.

And the message might be worth listening to. And possibly not. Remember, the very first post in this 5-part series started with the words, “This post has questions. No answers in this post. Just questions.”

Now it’s on all of you to help answer my questions and there was a lot. Ready? Go!

The Math Reading Classroom

In my previous post, I make a case for reading becoming a necessary component of the math classroom.

It’s interesting to consider what would it look like to integrate “the reading of mathematics” into a secondary math course as an essential learning target. “Essential” in the sense that we explicitly teach it, assess it and report out student status on it.

You’d start by creating a learning objective (or borrowing one that’s already written). Then you create some success conditions. Then you create an assessment (or series of assessments) so that you have a tangible experience in your mind when you are designing the learning activities.

In my mind, reading would need to be treated like one of the Common Core’s Standards of Mathematical Practice. It isn’t math content. The reading experience would be designed to a certain grade level, but in order to properly assess the reading, you have might need to back off the intensity of the math.

Obviously, word problems are nothing new. But this would be a different kind of word problem. Using the word problems as a READING assessment instead of a math assessment is not something I’ve seen before… or done before. Reading assessments look like a reading passage with some strategic follow-up questions designed to examine a student’s reading comprehension. Seems like a word-problem-esque scenario could take on that feel.

I imagine something like this:

“Danny and Sandy both collect bottle caps. Whenever they get together, they bring all their bottle caps with them. Danny has four Coke caps, three Sprite caps, five Mountain Dew Caps, and a Faygo cap. He’ll have more Mountain Dew caps when the 12-pack that his mom bought is gone. Sandy has nine Coke caps, five Pepsi Caps, and nine Mountain Dew Caps. Sandy wants more Pepsi caps, but that will have to wait because her Dad came home with a Pepsi 12-pack of cans yesterday.”

Okay, this is not perfect and people who write test questions for a living would probably come up with something much better. But, this a fairly standard word problem set-up. So, what questions would we ask if what we’re really trying to do is assess a student’s ability to read instead of assessing his/her ability to do compute? Maybe questions like these:

From the evidence, which of the two do you suspect drinks more pop? Why?

How many more bottles of Mountain Dew do you think are left to drink at Danny’s house? Why?

After Sandy finishes the 12-pack of Pepsi that her dad just bought, how many Pepsi bottle caps will she have? Explain how you know that?

The reading passage is written at about a 6th grade level, depending on which index you use. The math in the questions is probably first or second grade. So, giving that passage and set of questions to a seventh grade class would only be valuable as a reading assessment. How well are the students comprehending the details of the situation? Details like Danny’s 12-pack of Mountain is eventually going to yield 12 caps and he’s already 5 caps into it. Sandy’s 12-pack of Pepsi will yield zero caps because the pops are all cans.

Asking those questions gives you a window into the ability that each student has to comprehend the text. But considering the possibility of assessing our students in this way leads to a couple of confrontation points.

First, I don’t know of any math teachers who have learning standards written for mathematical reading. Those would have to be developed. That’s not a small or insignificant step. We don’t want to get in the habit of assessing without clearly defined learning targets.

Second, our students usually skip word problems in their practice sets. We would have to build in structures that change that. Whether it’s taking some pages from the #FlipClass playbook, or using some cooperative learning structures, somehow the attitude around word problems would have to change. We don’t want to get in the habit of assessing things that we know the students aren’t practicing.

Third, if a student begins to fall behind, or regularly is assessing at a low level on the math reading assessments, most math teachers are not well-equipped to provide appropriate curriculum-based interventions in the area of reading. These exist, but math teachers are typically not trained in their use. We don’t want to get in the habit of asking teachers to do things they aren’t trained or equipped to do.

Confrontations aside, there’s a lot of potential here. Potential for student growth. Potential for interdepartmental collaboration. Potential for more holistic math classes. But as with all updates, redesigns and revisions, it needs to be done strategically, thoughtfully, and with the best interests of the teachers and students in mind.

College-readiness, math, and reading… Part II

This is the third in a series of posts where I ask you for help understanding the idea of “college-readiness”.

The first post examines “college-readiness” as one of several competing ideas about the goals of a public school education.

The second post looks at math through the lens of reading and how some pretty influential people seem to support the idea of math and reading being combined for assessment purposes.

Math and reading both have the ability to act as gatekeepers. The ability to read is a classical form of empowerment. It was, for centuries, the primary way that powerful people controlled less powerful groups. In the last century a variety of different folks have suggested that math beyond basic computation is creating unnecessary barriers. (W.H. Kilpatrick was writing about this after WWIAndrew Hacker and Steve Perry are championing this cause in modern times.)

So, combing math and reading together could be troublesome. Kids are having to get through two gates with separate keepers in order to attain this “college-readiness” label that is so important.

And unfortunately, at least some data sets cast some doubt on whether or not our educational structures are properly preparing students to enter high school ready to take on the challenges of a system that is going to require to both read at a high level…

… and to perform mathematically at a high level.

So, we have reason to believe that the majority of our students are entering high school not proficient in math or reading… possibly both. (I am fully aware that this is just one measure… and one that isn’t universal beloved either.)

Let’s recap:

The College Board is writing college-readiness math tests that are written at about an 8th grade reading level to complement their college readiness reading and writing exams. And we are going to give this test to 11th grade students who have a better than 50% chance of entering high school below grade level in either reading or math.

Sounds like those of us in the education profession have a tricky task ahead of us.

I don’t want to make it sound like I’m the first person exploring this problem. Thanks to the work of those who are championing Universal Design for Learning (UDL) we are starting to discover that creating structures, supports, and access points for those who struggle either because of disabilities or lower prerequisite skills improves the experience for everyone.

The idea is that we can flex on the methods, the means, and the tools in order to keep the achievement expectations high. In math, this often means sticking to the learning objective without unnecessarily complicating the task by including areas of potential struggle. For example, students struggle with fractions. When you are introducing linear functions (a topic that doesn’t immediately depend on fractions), don’t use any fractions in your activities, materials, or assessments. In this way, you don’t create an artificial barrier to the learning of new content.

This thought process also applied quite readily to reading. If your students don’t read well, then why make them do it when we are trying to learn math? Dan Meyer suggests that there are student engagement points to be won by reducing, what he terms, “the literacy demand.” Rose and Dalton from The National Center on UDL discuss the variety of benefits of creating opportunities for our students to listen instead of reading. (One of which is creating better readers.)

And all of this makes so much sense…

… until our resident decision-makers decide that reading comprehension (in the traditional sense) is an essential component of a “college-ready” math student.

This puts math teachers between a rock and a hard place. On one hand, we can follow Dr. Meyer’s sage advice to reduce the literacy demand on our students. I’ve done this. He’s darn right about what it does for engagement.

But on the other hand, if the College Board knows what they are talking about (and I’d really like to think they do), do we risk eliminating an essential element from our courses if we work hard to limit the reading?

Perhaps this isn’t as tough a spot as we originally thought. Simply put, the work of the math teacher is complete when the student has developed the ability to solve a targeted set of math problems. This requires helping the students learn certain tools: Equation-solving, data collection and representation, strategic guessing and estimation… These (among others) are all essential problem-solving skills.

Most math teachers have mechanisms in place to support students who are in a variety of developmental levels on the  journey toward proficiency of any of those skills. They aren’t uncomfortable with a student who struggles to solve equations. We see it all the time. We know it’s our job to help support that student. So we do.

What if we looked at reading the same way? What is reading if not an essential mathematical problem-solving skill? A skill that our students are in a variety of different places on?

As math teachers, perhaps it is our job to teach reading.

In my next post, I’ll lay out what it might look like for a math class. I don’t mean a math class with a high literacy component. I mean a math class where the teacher and students all recognize that role of the math teacher is to help the students develop as math readers.

College-Readiness, math, and reading…

Consider this math problem:

In 1974, the state that had the highest population density was New Jersey with a population density of 1305 people/sq. mi. In the years that followed the decline of the auto industry, the populations began to shift away from the major industrial centers (like many of the cities in New Jersey). By 2015, New Jersey’s population density had dropped to 1210 people/sq. mi. If New Jersey has a total size of 8700 square miles, how many fewer people live in New Jersey in 2015 than in 1974?


The math of this problem isn’t really that sophisticated. Take your densities, multiply them both by the area to get total populations. Subtract the bigger population from the smaller population and there you go.

However, what is making me struggle with this problem is the undeniable literacy component. When I consider the reasons a student might get this problem wrong…

  1. Made computational errors
  2. Did computations correctly, but computed the wrong numbers.
  3. Didn’t know how to set up the computation because they got lost in the vocabulary or notation.
  4. Didn’t know how to set up the problem because the task was unclear.
  5. Got frustrated and skipped it because the US Census keeps records of state populations that can be referred to instead of having to crunch numbers.

From an assessment standpoint, what does a correct answer from a student reveal to us about what that student understands and is able to do?

  1. We know that student can work with rates and units in context.
  2. We know that student can multiply and subtract strategically and accurately.
  3. We know that student has the ability to accurately comprehend a piece of reading equivalent to about a seventh or eighth grade level.

I want to talk about that last one. The reading one.

If that question appeared on a math test, what would be the value of exploring their ability to read? It seems like we have tests for that. Won’t they reveal those things? Shouldn’t the result a math test be based simply on a student’s ability to do math?

Well, I’m going to go ahead an add a wrinkle. Michigan just adopted the SAT as the state-sanctioned offering to the legal requirement that all juniors in the state of Michigan will take a college-readiness test before they leave high school. (From 2008-2014 it was the ACT.)

The literacy component of the SAT Math test is quite heavy. The problem that I highlighted (which I made up… along with most the data in the problem) resembles the SAT Math questions pretty well.

So, the College Board (authors of the SAT and most the AP Tests) seem to be making the statement that college readiness includes the ability to read. I’m not sure there would have been much argument for that in general, however, there are SAT portions for reading comp and an essay. The literacy bases seem covered.

So, why put such a high emphasis on reading in math?

Perhaps The College Board is making the statement that math proficiency includes the ability to fluently read mathematical scenarios.

I’m of two minds on this issue, so I’d really like some reader participation in the comments. I’m not at all attempting to challenge the value of reading, but some students really struggle with reading. Does a reading struggle apply a ceiling to future math growth?

And if there is an essential connection between math and reading, what role do math teachers play in teaching reading? Should we be developing strategic interventions for math-based reading?

I hope you’ll feel comfortable adding a comment, idea, or question that I’m not thinking about.

In my next post, I’m going to further break down this idea with respect to my limited understanding of Universal Design for Learning.

What does “College Readiness” really mean for math class? I mean… really…

This post has questions. No answers in this post. Just questions.

I just spent the better part of a day exploring the SAT test (which Michigan has recently adopted as the test that all high school juniors will take as a “college readiness” test.)

I also read this Slate article which speaks to people who feel like they aren’t “math people.”

As I continue to listen to various groups chime in with that they think kids need with respect to the mathematics portions of our various educational systems, there seem to be a few ideas that are coming out.

The first two are usually close-to-unanimously agreed upon.

  1. All young people… ALL… young people have a God-given right to a high-quality education.
  2. A high-quality education includes a significant amount of mathematics beyond basic numeracy.

Beyond that, the overarching ideas push into value-based philosophies about what the author or speaker believes are in the best interest of American young people. These are definitely thoughts where two reasonable people could find areas of disagreement.

3.  An education earns the title “high-quality” when the receiver can use it to                    successfully take the desired next steps after it’s done. “Next steps” are                      generally considered one of the following: A. going to college, B. going to                    work, C. going into the military, D. starting a family or E. any combination                    thereof. No one necessarily more noble or challenging than the others.

4. The overseers of those areas are the authority on what is required to be                     able to successfully join those communities. College professors, business                   leaders, military leaders, and church leaders all have a reasonable                             expectation that they would influence the courses of study that lead into                     those individual arenas.

If we push these thoughts to the next level, it becomes reasonable to assume that college professors, business leaders, military leaders and church leaders are going to quite often disagree on the necessary requirements for an education to be considered “successful”. What’s more, there will be large segments of the general public who would prefer one or two of those get a larger say than the others. Certain groups of people would prefer that college professors should have the last say. The incredible number of religious private schools speak volumes to our public’s desire to allow their particular faith to have the ultimate say in the educational program.

And math doesn’t get a free pass in these disagreements. You will see wide differences in the types of mathematical content that are preferred as well as the instructional and assessment methods. The nationwide introduction of Common Core has demonstrated that math curriculum can trigger some very negative responses from significant portions of the American public.

And the fact that nationwide, our school systems are “public” empowers the general public to have a say. In fact, this is often a tricky balancing act for education professionals. There is a certain amount of background knowledge necessary to make sound decisions within the field of education. But, practically every single adult walking the streets has a decade (give-or-take a year or two) of experience within the field of education. There is a certain amount of boldness that that kind of familiarity breeds.

Result: Everyone has an opinion on how education should look. And that opinion is largely based on the relative satisfaction that the opinion-bearer feels when he/she reflects on his/her past experiences.

That is a very good thing with some inconvenient consequences. One of those inconvenient consequences arises when legislators get involved. The American public has an oddly-trusting, yet often cynical relationship with their elected officials. Most people have very few good things to say about them. But when it comes to their own personal beliefs about society, getting their views enshrined into law become the highest priority. You can see this on both sides of the political spectrum. These institutions disgust us and we don’t trust them, but we want them on our side. It’s an odd paradox.

This paradox extends into the fields of education where, at least here in Michigan, the state government has made several plays that are tipping the scales in terms of which of the aforementioned groups is getting the state favor. As a result, “College-and-Career Readiness” is becoming cliche.

But our familiarity with it doesn’t mean that we have any idea what to do with it. Moreover, it doesn’t even mean that the general public has agreed upon definitions of “college ready” or “career ready.” The state has just solidified those two arenas as the goals.

It’s our job as educators to figure out how we are setting up our classrooms, schools, and districts to maximize our impact on young people toward those goals.

In my next post, I am going to lay out the primary issue that is creating this inner conflict I feel…