Morning reading – The Loudest Sound in the World

From the physics department, I started my morning with a fascinating bit of reading from FiveThirtyEight.

They hooked me with the intro line:

The questions kids ask about science aren’t always easy to answer. Sometimes, their little brains can lead to big places adults forget to explore. With that in mind, we’ve started a series called Science Question From a Toddler, which will use kids’ curiosity as a jumping-off point to investigate the scientific wonders that adults don’t even think to ask about.

You want to capture my attention? That’s a pretty good way to do it.

What follows is a really approachable discussion of sound energy that is designed to be understandable but doesn’t skimp on all the science-y goodies to do it. It also doesn’t shirk on the drama.

A sound is a shove — just a little one, a tap on the tightly stretched membrane of your ear drum. The louder the sound, the heavier the knock. If a sound is loud enough, it can rip a hole in your ear drum. If a sound is loud enough, it can plow into you like a linebacker and knock you flat on your butt. When the shock wave from a bomb levels a house, that’s sound tearing apart bricks and splintering glass. Sound can kill you.

Go ahead and give it a read. I’d consider using it in a high school physics course. Although, full disclosure: I can’t universally recommend FiveThirtyEight since I know they also write about a lot of other topics and not all of their writers stick to basic school-appropriate rules, like no swears.

It also mixes in a bit of history (some nice story-telling on the eruption of Krakatoa) and some nice unit discussions (hertz, decibels, some prefixes get in the mix, too.)

All in all, definitely an article worth checking out.

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 WWI. Andrew 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…

http://www.nationsreportcard.gov/reading_math_2013/#/comparisons

… and to perform mathematically at a high level.

http://www.nationsreportcard.gov/reading_math_2013/#/comparisons

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?

Okay…

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.

The Role of Reading in Math Class

My more recent endeavors have moved me away from exclusively math and allowed me to enter into the world of literacy, particularly elementary literacy. (Math teachers out there, if you haven’t gotten a chance to sit and participate in a conversation among elementary folks talking about kids learning to read, the essential components of curricula and classroom activities, the different types of assessment and support for struggling learners, etc. then do it. Such interesting conversations…)

But my math background led me to look at the new literacy experiences I’ve been having through the lens of the math classroom. Specifically, what are the elements of literacy education in a problem like this:

taken from Holt’s Geometry, 2009 Edition, Page 702 #25

What math content knowledge is this problem asking students to use? Volume of cylinders, volume of rectangular prisms, and simple probability.

But we need to keep in mind that the ability to read is a significant skill to being able to apply math to this problem. Especially when you consider that the typical high school student probably doesn’t read quite as well as we’d like them to. I want to be clear that I’m not saying that this is an excuse for us to eliminate reading as a way to accommodate this potential weakness in our students, but it is important that we recognize that we are asking students to exercise that skill when solving this problem.

When we are asking our students to read as part of a math experience, we should do so deliberately. There are times when one of our stated learning outcomes is helping students learn to read math. There is a lot of value in that skill. There are also times when we are much more interested in helping the students set-up and solve math problems in ways that may not require as much reading.

This requires us to be strategic about what we are expecting our students to be able to do by the end of a lesson. Consider the math problem from earlier in the post. Literacy doesn’t have to be a barrier to that math content.

Andrew Stadel provides an example of how volume of multiple solids can be integrated into a math problem in video form.

Dan Meyer integrates a fairly similar set of content in a much different (and more delicious) scenario.

Using video in your class is one way to provide access to a math problem without having student having to tackle the reading part, which can be a pretty significant barrier to some students. In the past, I certainly haven’t been nearly conscious enough of the literacy demands I was putting on the students when I asked them to explore math content. Here’s a perfect example of a handout from my geometry course. How many students would benefit from a video introduction to this handout? (Especially when you consider how many students aren’t real strong using a protractor…)

It just all goes back to us, as educators, having a clear vision for what we want our students to learn by the end of their time with us and being willing to do what it takes to help them get there.

Vocab: The Foundations of Math Talk

I want to talk about vocabulary for a minute.

Specifically, I want to describe one way that can support students struggling to learn vocabulary that is necessary for effective math talk. Often times, struggling math students are willing math talkers, but the math talk is filled with pronouns (that thingy right there, you know what I mean?), hand gestures, and rough sketches.

This can make communication a bit of a chore, especially if the student is talking to another student who is also still in the beginning stages of developing understanding in that topic.

So, here’s a way that you can change the conversation a bit.

Consider this handout combined with this Google Form.

In short, the students would take a few minutes exploring different formal definitions for the vocab words you are exploring. There are always differences if you go to different sources, so by forcing them to explore a variety of interpretations, you can really help the students see that this vocabulary is about describing an idea, not memorizing a specific wording. This is important, at least to me.

Pair the students up (or group them in 3’s) and have them consider the big ideas and develop their “own-words” definitions for each vocab word. Then they plug them into the Google Form.

At that point, you’ve got a nice collection of what your class currently has taken away from their time. (And by “time”, I mean about 20 minutes from start to submission.)

As you wander around listening to the conversations, you’ll likely notice a few definitions that are coming together more slowly than others. This is inevitable.

At that point, I’d bring in Wordle. Wordle is a free tool that build word clouds. Word clouds can have a nice visual appeal and change the way a block of text looks by changing the physical size of a word based on its frequency in the text. For confusing definitions, this tool has the potential to help the students hone in on the big ideas. For my students, it was often “circle.” Most kindergartners could draw a decent circle (or at least a shape that you would guess quite quickly was supposed to be a circle.) But, that visual understanding is often as far as students get.

Want to see how well your students understand what a circle really is? Ask them why this is a lousy attempt to draw a circle. See what they say.

If your students are struggling with an idea, though, go into the Google Form responses, copy all of their definitions and paste them into a Wordle.

My third hour Geometry last year, produced this word cloud.

This isn’t going to solve all of your problems by any means, but with a visual like this, your students will have the opportunity to see that the major idea of this concept of circle revolve around the notion of a center point, a distance, and points in a curved shape. Those are major steps in the right direction when we are moving students away from a purely visual understanding of what a circle is and helping them understand the geometric properties of a circle.

Remember, the goal of learning vocabulary is to facilitate student understanding of the content. Memorizing a definition only goes so far. We have to continue to develop the means to push students to internalize the bigger ideas within the vocab so that those words then become foundations to build more sophisticated ideas.

If you feel like you’d like a tutorial of how to use Wordle, I went ahead and made one.