Let me just say up front that I know I’m hardly the first person to address this topic, and I’m sure I won’t be the last. In fact, so much has already been written on the subject of student blogging that I’m not going to spend time here talking about the basic reasons or the how-tos of doing it. Others have done that better than I.

What I want to explore today are a few of my thoughts about why blogging is a particularly powerful tool to give to gifted students. Gifted students have some unique needs that blogging can help teachers to address. Read the rest of this entry

Though it has taken me much longer than I planned to get back to this topic, I want to share with you today what I believe is an outstanding and probably very obscure tool that would be excellent for gifted students.

Think back a few years. No, further back. A little further. When home computers had memory measured in kilobytes, an 8-color monitor was high resolution, and disks were floppy.

The cutting-edge trend in computer entertainment was something called a “text adventure game.” Zork is the classic example of games in this genre, but there were dozens of them. They had no graphics and no need for a controller, because the entire means of interacting with the game was through text.

For those who have never played a text adventure, here is a typical sequence of moves you might see in one of these games (this is part of the sample transcript that was in the instruction manual for the original Zork): Read the rest of this entry

It’s a line you’ve probably seen on ads for sports equipment:

Better Tools for Better Performance

A debate is swirling among many people in my PLN about what’s more important: the tools and technology, or the teaching and learning. Before I begin exploring examples of great technology tools to use with gifted students, I thought it would be worth exploring, since it is directly relevant. The crux of it can be summarized in this exchange I had recently with Tony Baldasaro (@baldy7) on Twitter: Read the rest of this entry

It is important for teachers to get feedback from knowledgeable observers. A good supervisor will help you elevate your practice, hone the skills that are already sharp, and identify the areas where you have allowed lax habits to seep in.

Even the best supervisors can only visit a few times a year. Having peers watch us work is helpful, but making that happen is often a logistical challenge. We could videotape the lesson and watch it later, but that too is often complicated and time-consuming.

We often forget the team of observers that is readily available: our students. Ask your students regularly to tell you how you are doing. They’ll tell you. In excruciating detail.

Even better, do what a colleague of mine did the other day, perhaps without even realizing what would result: Ask your students to teach. It was fascinating to watch as students took on the persona of the teacher, then walked around the room, shushing other children, gesturing, and explaining. We saw, in sometimes frighteningly accurate mimicry, the precise methods and mannerisms that the teacher uses on a regular basis.

If you really want to find out what you do well—and will dare to find out what you don’t—put your students in the front of the classroom.

When I first moved to Bucks County, I knew the major routes to get around the area. I could, by rote, drive from my house to my in-laws’ house. I could also drive from my house to the school where I worked. I could flawlessly and efficiently travel those well-worn paths and arrive promptly at my destination.

One day, I received a simple phone call from my wife: “My parents are making dinner for us tonight. Just come straight from school and meet us there.”

Not a problem. I left work at my usual four o’clock and with traffic arrived a little after 5:30 PM.

“What took you so long? Did you have a meeting after school?”

“No, I left as soon as I could.”

“But it should only take a half hour.”

“That’s impossible. It’s more than that just to our house, then another 40 minutes to your parents.”

“Um, no, dear. There’s a more direct route.”

Read the rest of this entry

Students come to our classrooms with many assumptions and misconceptions, and it is the teacher’s job to anticipate them, recognize them, and correct them. Here are a few that I have seen or heard about:

• When you add or subtract, always line up the numbers on the right
• When you multiply, the answer is always bigger
• Rockets work because the exhaust pushes against the Earth
• Magnets stick to anything made of metal
• Christopher Columbus was trying to prove the world was round
• The American Revolution was fought over high taxes

Many student misunderstandings are simply a lack of experience. There is a scene in the 1982 movie, Star Trek II: The Wrath of Khan, where Khan, the villain, is trying to hunt down our heroes. Kirk flies the Enterprise into a nebula in order to obscure the ship from Khan’s scanners. After a few minutes, Spock makes an observation about Khan:

SPOCK: Sporadic energy readings port side, aft. Could be an impulse turn.

KIRK: He won’t break off now. He followed me this far. He’ll be back. But from where…?

SPOCK: He’s intelligent, but not experienced. His pattern indicates…two-dimensional thinking…

Kirk looks at him, smiles.

KIRK: All stop.

SULU: All stop, sir.

KIRK: Z-minus ten thousand meters. Stand by photon torpedoes.

Like Khan, our students are intelligent but have limited experience. I wonder, though, how often we reinforce misunderstandings instead of correcting them?

Often in the name of making our lessons accessible or understandable we simplify concepts and use stereotypical examples. Consider geometry, for instance. When we draw shapes, they always look essentially the same:

Standard pattern block shapes

Triangles are always equilateral and point up. Rectangles are always wider than they are long and are parallel to the ground. At the extreme, we even refer to shapes by different names depending on their orientation. I actually heard this statement during a math lesson once:

And if you turn this diamond, it will become a square.

The shape was always a square; the direction it faces doesn’t make any difference.

Try these suggestions to avoid reinforcing the misconceptions of your students:

• Know your own misconceptions. Begin with the assumption that you may have picked up your own wrong ideas in school or from popular media. Review the material ahead of time and look for places where you yourself didn’t quite get it right. (Incidentally, if you read any of the items in my original list and thought, “What’s wrong with that?” you may want to do a little research and find the subtle problems with them.)
• Plan ahead for student misunderstanding. Learn the places where your students are likely to get confused or have preconceived ideas about a topic. Many misconceptions are common and repeated, so it’s easy to prepare for them.
• Use a wide variety of examples. Deliberately choose examples that stretch students’ thinking. Use counterexamples to help them better define concepts in their minds.
• Let students construct their own definitions. By letting students build definitions and explanations around examples you use, you are encouraging them to analyze the examples and understand the concept deeply instead of just memorizing a sentence someone else has provided them. After they attempt to build a student-friendly explanation, you can come in and provide more precise vocabulary where necessary to give them a more concise way to express it.
• Expect students to explain and justify their reasoning. Sometimes students are able to apply a rote algorithm accurately and get a correct answer to a problem without really understanding what they are doing. Asking them to explain, even when their process seems obvious to you, will give you insight into whether their thinking is accurate or has flaws that need to be corrected.

Soon after Kirk changed his tactics to account for Khan’s misconception, he was able to sneak up behind Khan’s ship, ultimately winning the battle. While it is unlikely that the misconceptions our students carry through school will result in such life or death circumstances, we can make our own jobs easier by preventing them in the first place.

SPOCK
                             Sporadic energy readings port side,
                             aft. Could be an impulse turn.

                                           KIRK
                             He won't break off now. If he
                             followed me this far he'll be back.
                             But from where...?

                                           SPOCK
                             He's intelligent, but not experienced.
                             His pattern indicates two dimensional
                             thinking...

                   Kirk looks at him, smiles.

                                           KIRK
                             Mr. Saavik, all stop.

                                           SAAVIK
                             All stop, sir.

                                           KIRK
                             Descend ten thousand meters. Stand
                             by photon torpedoes.

Last month some colleagues and I ran a workshop for teachers at my school on differentiation. In preparing for it, I came across the idea of anchor activities. Unfortunately, many of the resources I found giving examples actually list a lot of the traditional time-filler busy work (extra worksheets, copy and define words from the dictionary, coloring pages, etc.) and slap the “anchor activity” label on them. In her book The Differentiated Classroom, Carol Tomlinson defines anchor activities as

meaningful work done individually and silently. This could be journal writing, free reading, foreign language pattern drills, seatwork in math, or sketchbook assignments. It’s something useful and important for students to do…. (p. 97)

The key words I see here are meaningful, useful, and important. We have to put as much thought into selecting what we ask students to do in their unstructured time so that it never actually becomes down time.

At the same time, it’s important to keep in mind that students’ brains cannot stay in high academic gear all day long. They need frequent short “brain breaks” (as Eric Jensen calls them) to be able to stay alert and focused throughout the school day. The real trick is finding the balance and making sure that the breaks are built into our instruction so that students are more able to continue academic work during their unstructured time.

As with many differentiation techniques, though, anchor activities should be just a starting point. Tomlinson herself explains that setting up anchor activities as a routine in your classroom should be a way to train students to expect that there will be times when different people are doing different things so that some students can break off from the group.

What do you do, then, when you have students who are ready to break off? Perhaps you have a few gifted students who have compacted out of part of a math unit. Or you have several students who routinely finish their work quickly and accurately. Here are a few ideas for ongoing, long-term activities they can do that are meaningful, useful, and important:

• Independent Study. This is of course the tried and true traditional approach, and much has been written about it. What I recommend is that you always give students a way to share their results or integrate it back into the classroom community. I had a student once who was fascinated with folk tales and fairy tales. Her fourth grade class was learning about Africa that year, so her independent study project was to find and study some African folk tales and adapt one into a play (another interest of hers). She then selected student volunteers and put on a very simple (just a few masks and props) production in the classroom.
• Classroom yearbook. Have your regular early finishers form a “yearbook committee.” Their job is to plan, design, and prepare a classroom yearbook to go home with your students at the end of the year. They would need to interview each member of the class, prepare a page about each, take photos, record important classroom events, and so on.
• About Our School video. Have your kids take snapshots of activities around the classroom (and around the school if your situation permits and your students are trustworthy). Use Animoto to put together an introductory music video that the principal could use during Back to School night presentations or post on the school website.
• Unit reconnaissance. Enlist the aid of your better researchers to help you find good materials for upcoming units. Tell the students what the next unit will be in one subject area. Give them some guidelines and some topic suggestions, then give them time to explore the library and the Internet for materials that will support what you will be doing. Use online tools like Diigo or a classroom wiki to gather the information in one spot.

What are your ideas for keeping anchor activities and bigger projects connected and meaningful? How will you work to eliminate busy work from your classroom and school this year?

References:

Tomlinson, C. A. (1999). The differentiated classroom: Responding to the needs of all learners. Alexandria, VA: ASCD.

Every year I stand in front of a group of new fourth or fifth grade students and face the most challenging teaching task I’ve ever had: training them to be telepathic.

I always begin with a magic trick. Each student chooses a two-digit number. Then I walk them through a series of simple calculations resulting in a new number. On that page in their math book, they choose a picture and memorize it.

Earlier in the day, a mysterious envelope had arrived in the classroom, marked “DO NOT OPEN…TOP SECRET.” I now open that envelope, revealing a duplicate of the photo they all have memorized. I can read minds!

Of course, it doesn’t take long for the class to realize it was a trick, and I don’t deny it. In fact, I remind them that I began the exercise by telling them I was going to do a magic trick. The point is why I had to do a trick: teacher’s can’t read minds.

“So what does this have to do with math?” they ask me.

“Ah, excellent question,” I reply. “When you put an answer down on a math test or a homework problem, how does your teacher know what you were thinking when you solved it?”

“Uh…she doesn’t?”

“Precisely. But for us to teach you, we need to know how you’re thinking so we can help you learn how to solve problems better. Since we can’t read minds, what’s the only way for us to know what’s going on in your head as you’re solving a math problem?”

If the lesson were outside at night, this question would normally be answered by the sound of crickets chirping. One brave soul usually raises a cautious hand: “Uh…we tell you?”

A simple concept. A difficult task. Actually getting the thoughts from their heads into words—and eventually onto paper—is something that takes much practice and many examples. Yesterday I talked about one of the ways to begin this process by teaching and using the correct vocabulary.

We need to teach students that math is not about rote manipulation of abstract symbols. Those symbols, and the terminology that goes along with them, are tools with two purposes: solving problems, and communicating ideas.

I’ve developed a structure that helps students organize their thinking and chunk the way they communicate it. I tell them, “Wear Your C.A.P.E.”:

The most difficult aspect of this, of course, is the explanation—describing the why, not just the what. In order to help with this, I teach them the Magic Words. Just like using clue words to identify the operation in a word problem (like “all together” signifies addition), these words can help to signify their mathematical reasoning when they talk or write. (This list is based on an article by Diane Hurst published several years ago in the PA Math Assessment Handbook, but no longer appears to be available):

Students who learn to use these words correctly will begin to unpack the reasoning that is going on in their heads.

How could you adapt this to your situation? What other subject areas might it work for? Do you have other ideas about teaching students to be “telepathic” and communicate their thinking to other people?

Teachers of mathematics need to recognize that there is a strong link between language, writing, and problem solving. In most of the assessments that states use to determine student and school success, a student must demonstrate math reasoning abilities through writing. This skill is not automatic, though. It develops through a recursive process:

Vocabulary & Language <—> Reasoning <—> Talk <—> Writing

Beginning with vocabulary and language, a student learns to reason, then to communicate those thoughts verbally, and finally to write. Each of the levels feeds back to the previous one, reinforcing and further developing it.

Thus if we’re going to teach reasoning skills effectively, it follows we need to carefully consider the vocabulary we use.

It isn’t uncommon, especially in the primary grades, for teachers to simplify the language we use with children to explain complex concepts. Although this is useful, it can also lead to sloppy language if we aren’t careful. It is particularly important that we don’t permit students to use precise math terms improperly and that we teach the “real” terms as quickly as possible. Even if students don’t use them right away, they should be hearing the correct terminology in context from the beginning.

Here are a few examples of sloppy math language that I often hear from older students. If these go uncorrected, students will have a very difficult time communicating well when they need to explain their thought process–a skill that is essential to upper level math.

I believe it’s essential to require students to be precise when they communicate. Often when students don’t use the correct term, or use a valid term improperly, it is a sign they just don’t have the right words.

I’ve heard teachers argue that young children just aren’t capable of such sophisticated language yet. My father, a retired professor of speech/language pathology, has often said, however, that if second graders can learn and correctly use terms like “Tyrannosaurus Rex” and “Diplodocus”, why on earth can’t we teach them to say “subtracted” instead of “minused”? Vocabulary instruction should be as much an integral part of mathematics as it is of reading, writing, and other content areas.

Tomorrow I will tackle a more challenging vocabulary-related issue in mathematics: verbal and written explanations of a student’s cognitive process.

(This article is based on material I originally posted in Grandé With Room.)

Here’s an interesting idea for a quick classroom activity that has potential for many discussions. This could certainly be applied in many different ways to students at all levels.

Begin by taking kids to this site: http://whereiwrite.org. It is a small site with one purpose: to showcase portraits of authors (they all happen to be in the science fiction genre) in the spaces where they do their writing.

A few thoughts come to my mind as I scan through the pictures:

• Nearly every space is a work space. Creativity isn’t about flashes of inspiration. It’s about doing. And effort.
• Almost every writer surrounds him- or herself with books. Dozens or hundreds of them. Writers read. A lot.
• Writers are ordinary people. They have pets. They even have stained glass thingies hanging in their windows.

I think there’s a great lesson for students, especially reluctant writers.

Some other ideas for follow up activities:

• Have students share photos of their writing spaces and talk about them
• If you could create a better space to write, what would it look like? Why not create it?
• How could we design our classroom space to make it better for doing our work?

What do you see in these photos? What questions would you ask of your students about these pictures? What else do they tell you about what writers do and how to be one?