So far I’ve covered a technological and an ideological problem. This one’s logistical.
Specifically, in a discipline where one question can have many answers, it’s easy to set up a traditional forum discussion where every student’s contribution is meaningful and a springboard for further interaction. One student’s opinion does not make moot the opinion of anyone else.
With mathematics, even if the question is applied and relevant, quite often there is only one correct answer. So the traditional forum method can fail, since once one student posts the answer, there is no incentive for further discussion.
This can be solved by splitting — having only individual answers or collaboration in small groups — but this removes the very thing that makes social technology exciting: collective intelligence on a scale above what is possible with in-person interaction. Imagine, for instance, having a problem not just group-solved by your individual algebra class, but by every algebra class in a school.
There’s ways around this, like:
1. Personalized data: Students might figure out the square area of a room in their house. So every student does their calculation on something different, and then statistical methods can be applied to the data as a whole.
2. Required estimates. In a mathematics modeling problem, students try to match real-world data with an equation. While there are "best-fit" equations this can be done by hand, so that there isn’t one correct answer.
Unfortunately, neither method fully taps into the power of the group dynamic. The individual contributions don’t rebound and augment each other like an open-ended discussion. So I’ll ask: what are the best ways to set up a collaborative online assignment in mathematics?
The best solution I can think of is to get students to explain process. The class could essentially write its own textbook with a wiki; the assignment one week might be to finish the online explanation of graphing parabolas, and every student has to pitch in. I have yet to try something like this, so if anyone has, drop a line in the comments.
The use of a graphing calculator is considered an integral part of the AP Calculus course, and is permissible on parts of the AP Calculus Exams. Students should use this technology on a regular basis so that they become adept at using their graphing calculators. Students should also have experience with the basic paper-and-pencil techniques of calculus and be able to apply them when technological tools are unavailable or inappropriate.
Yesterday’s post was about a sticky tech issue. This one’s more about ideology.
Fierce debate raged in the 1990s over whether graphing calculators should be used in mathematics education at all. Proponents thought graphing calculators opened new vistas of understanding, as students could play and experiment, and see instantly how functions are affected by different tweaks. Detractors said graphing calculators killed the ability to work things out by hand; that they’re a crux, and true understanding is only obtained by pencil-and-paper repetition of the proper methods.
Arguably, the issue ended (in the United States) with the AP test adoption of the graphing calculator. What resulted was a deeper and more difficult test; not only did students still need pencil and paper methods, but they had to apply the calculator to answer higher-level questions.
(No, not every student will make it to AP classes, but I believe curriculum should be written with the assumption that some will.)
However, the issue never truly died, because there was (and still is) a hidden ideological struggle going on:
Should our primary focus in algebra be on symbolic manipulation, or is visualization and synthesis an important aspect?
In other words, are graphical methods and applications just an afterthought?
While this doesn’t seem to relate directly to social technology, the interesting enhancements computers can offer don’t attract the interest of a symbolic-manipulation-only teacher. Alternately, graphing calculators can be thought of as the gateway application — take a teacher comfortable with them, and it’s easy to hook them on related Internet apps. For the Internet to be truly useful, teachers need to see there is a world beyond factoring binomials.
So, if you’re a technology coordinator with a resistant math department, there’s one question you might ask: are there teachers who haven’t taken their class set of calculators out of their boxes? If so, there might be more going on than mere tech resistance.
Don’t get me wrong: there are options to put equations on a computer. Most computers have at least Equation Editor if not MathType. Scholarly papers in mathematics often use LaTeX and it’s also possible to blog LaTeX equations using WordPress. I have used these before (my Pre-Calculus students are currently working on blog posts with LaTeX equations) and they are fine in their own context.
However, I consider these typesetting solutions. What I mean is most closely analogous to the difference between a word processor and a desktop publisher. In a word processor the text can be played with, experimented with, refurbished and remodeled in a manner easier than even pencil and paper. The layout of the text, however, is secondary. With a desktop publisher the placement of text is key, or at least a distraction to a student still trying to figure out their sentences need verbs.
In the course of a normal math class, parts of equations need to be crossed out, circled, arrowed, underlined, and spaced out. When I laid out my solution to a general conic, I couldn’t use just an equation editor; I had to manipulate the parts in an image editor.
To put it another way, it’s difficult to think the equations directly to the computer screen; sometimes I have to work things out on paper first and then translate them visually. That’s hardly conducive to a live collaboration. It’s certainly still possible, but the pragmatic teacher has to ask if the loss of fluidity is worth the gain of remote interaction.
(Before you post about your brilliant online class and how everything is done on computer, keep in mind I am simply trying to explain where objections are coming from. I’m hoping it’s clear at least why the hurdle for mathematics is different than for language-based curriculum. Now, if you’ve seen these problems and have found neat ways for getting around them, post away.)
There are ways with technology to translate writing directly to digital form; on a SMART Board or a digital writing device. Some teachers will upload their SMART Board presentation to the Internet immediately after class, including any writing that happened. If anyone has done a particular lesson with these tools, feel free to share your ideas.
The ideal would be for the word processing equivalent of an equation editor. I’m not sure how that’d work; somehow it have to include the crossing out, circling, arrows and so forth we have students do in an entirely natural manner. There wouldn’t just be the ability just to write equations line by line as in a textbook, but to drop a single row and move a variable by using the inverse without any worry of typesetting. Take a look at my general conics example again; if that sort of layout could be done easily, with just natural typing, mathematics teachers would flock to your door.
Before I go on, I need to clarify something: I am addressing the use of social technology, not technology in general. (Although an aversion to technology in general is related to my graphing calculator point.) My example of a tech cynic is not a technophobe by any means. I am referring to what is supposedly the "new wave" of blogs, Twitter, wikis, and so forth. Additionally while it could be argued math teachers in the United States don’t use enough of it, I am not discussing project-based curriculum. That’s been around for a long time and while it can be augmented by new technology, being a technophobe (by any definition) doesn’t mean shunning it either. So while a comment like (courtesy Glenn)
If the something that you’re asking them to do is take a test. Well. Never mind. Sorry, didn’t mean to waste your time.
might apply to some teachers, I am presuming a faculty past that point but yet fussy about all the new gadgets being thrown at them. I am trying to explain why they’re fussy, and that it’s not just because their teaching isn’t Modern enough in an overall sense.
So, you’re making your technology pitch to the school. You’ve just been to the conference and still feel the warm buzz of The Future, and you want the teachers to embrace the blogs, the wikis, the collaboration with schools in different cities, different states, different continents.
You up your game: you set up workshops, seminars, buy new software, buy new hardware, try to convert a few followers hoping entire departments will follow.
Maybe you grab the English department and suddenly have every student in school with their own blog. Perhaps the technology people are putting student-produced videos on YouTube. You hear the foreign language folks are using Skype to call Mexico and work with a network of 5 classes.
(Ok, ok, idealism here. But these things are at least possible.)
But hit the math department –
And all I’m saying is, look, I’ve got some math to teach over here. And until I can count on two fingers the number of math teachers who are building a meaningful practice out of tech, until this stuff begins to approximate the importance of a cash register to a grocery store checker . . .
A lot of technology-coordination-types seem puzzled by this – why should math be any different from other subjects when adopting modern tech? – but it is, and there are (at least) three major reasons why.
The difficulty in working with equations on a computer
Sure, high school math teachers do statistics, and graphs, and even the occasional art project, but the meat of the content is working with equations. Even something easy to type like
Solve for x: 2+x = 3
can be a bear to demonstrate the steps on, and maybe could be done with fixed fonts and a fiddle like
2+x=3 -2 -2 x=1
but this is a post-understanding sort of kludge, and it’s not simply possible to work with things as easily as paper.
Students 3.0
The first graphing calculator was introduced in 1985, and it’s been a battle ever since.
One camp is fundamentally opposed to the notion of using graphing calculators, while the others think graphing calculators should be used at every level. This is still ongoing even though the AP Calculus tests require a graphing calculator and college expects students to arrive with the skills. (At one university I know of, they give incoming students a list of calculator tasks and say “if you don’t know how to do these, figure it out, because we’re not going to teach you.”)
Because the acceptance of graphing calculators is nearly a prerequisite for many modern math apps, arguments get stalled at the door. In other words, upgrading to wikis and the like is version 3.0, and 2.0 is still in beta.
Sometimes there really is only one right answer
With disciplines where multiple viewpoints are all equally valid, it’s easy to have a collaborative discussion where every contribution is valued and important. When solving a problem with only one right answer, snarls can hit. Maybe one student dominates the discussion, or things shut down too early, or everyone is stuck in a way that requires massive teacher intervention. These issues often aren’t discussed, and the edict to focus on process rather than solution gets messy in practice. (Although it’s a start, and even if there’s only one solution there may be multiple ways to get there.)
How this week will roll
I’m going to switch between general assessments of what’s going on and specific examples. I’m going to make a wish list for what I’d like to see in modern technology, because my sentiments match closely with the quote above.
I’m going to need your help. Some things I’m wanting really don’t exist, but I’m hoping there’s hidden gems out there I haven’t come across yet. If nothing else, maybe a developer will take notice and fill the gaps.
My run officially starts tomorrow, but I wanted to get my standpoint up.
I’m a high school mathematics teacher, and I focus on my class. I spend most of my time thinking about curriculum, not theory. I take a pragmatic approach and always ask, primarily: does it work?
However, I’m willing to try anything once. So I’m going to break open this week and take on one of the Big Issues: why is it so hard for mathematics teachers in particular to use social technology, and what’s needed to fix the problems? Mathematics teachers are often frustrated, because the generalizations about social technology don’t answer the question: so what do I do with it? There’s a lot of technology coordinators out there (greetings!) and I want to bridge the gap, so you understand where we’re coming from.
I believe both tech optimism and tech pessimism are dangerous. Too much optimism can blind one to failure, and too much pessimism can cause something to be discarded after only a single failure (when all it needed was a retooling). I’ll be aiming at the middle road, trying to balance practical reality and unrealized potential.
I’ll be out of my element, but feel free to compliment or criticize or add or subtract. I’m not going to have all the answers alone, but maybe together we can work this out.
Aside from serving as one of two Assistant Principals in my high school, I am also lucky enough to supervise three departments, one of which is Special Education. I do not manage IEPs, conduct testing, or get involved in the legalities of Special Education. I merely manage the day to day happenings with the Special Education staff, work with the scheduling and budgets, and assist the Director of Special Services and Child Study Team. I wish I had time to do more.
I have worked in three school districts in the last eight years. I am embarrassed to say that the Special Education programs have all been rather disappointing. I’ve seen watered down curriculum where handouts and worksheets are the standard of classroom practice. I’ve had conversations with Special Education teachers and heard some sad educational philosophies regarding Special Education students. I’ve seen and heard some unethical things in the highest offices of public school districts – things that would cost people their careers.
On the flip side, I’ve met (and currently work with) some of the best people for Special Education students; they are supportive, encouraging, and serve as life coaches and mentors for their students. They desire to be the best teachers they can for their kids. I’ve also been blessed to have strong school leadership role models in my life who keep me hopeful and guide me through the rough waters of Special Education law, practices, and education.
Since this is my last post for Dr. McLeod, I thought it would be helpful and intriguing for all of us if we left an open thread (a la Beyond School’s popular one). Open threads seems to me to be chock full of good advice, insight, and some remarkable stories.
So here it goes…
What practices have you seen in your experiences with Special Education? You can discuss a Special Education program that is worthy of publicity, or a teaching practice that deserves attention. If you are tempted to expose the troubles of Special Education, you may – but I would like this post to be helpful, not critical. So please, with a criticism, offer a potential solution.
It’s been an honor to share with all of you. Mike Parent, Guest Blogger
Mike Parent has done a fantastic job this week of guest blogging. If you like what you’ve read from Mike, check out his blog, The Schoolhouse Dissident.
Jason Dyer will be my next guest
blogger in 2008. I asked Jason for a short blurb about himself. Here’s what
he sent me:
Jason Dyer started out with a degree in Fine Arts Studies, intertwining
music, media arts, and computer science. After the dot-com crash of 2000, he
picked up a mathematics degree and now teaches high school in Arizona. He still
has a soft spot for his multimedia roots and has movie posters hanging on his
classroom wall. The school mascot is the Warriors and his normal blog of
residence is The Number
Warrior.
Jason has an ambitious series of posts for us next week and I’m looking
forward to reading his thoughts on math, education, and leadership. If you’re
interested in being a
guest blogger, let me know!
Thus far, I have posted about educational conspiracy, challenging the competitive nature of schools, and assessing assessments. What follows is a topic near and dear to everyone's career and workplace. This is a post I have been looking forward to sharing with all of you. It's a bit lighthearted, but a serious topic for school leadership.
Let me begin with a disclaimer. A tantalizing and possibly offensive word will be used throughout this post. The word is not common to the professional language of Dr. McLeod or his readers. However, since I will be using the word in the context of a theory, it should be understood that I am not trying to be edgy or shocking. I am merely using the word for purpose of clarity.
The day before Christmas break I am browsing through a book store looking for a good gift for my principal. In the management section I spot a small book with an intriguing title – The No Asshole Rule. I first think this must be some kind of gag gift. But a ten-minute perusing of the book tells me something else. The author, Robert Sutton, is a well known and respected writer. He's not joking here. He is only using the lay terminology for "difficult people", "hardened hearts", or "combative individuals". I bought The No Asshole Rule (TNAR) for my principal, and a copy for myself. Now we're both equipped to handle this obnoxious faculty member.
TNAR is a much needed common language leadership book. I know many of as are fans of many different education leadership authors (Fullan, Heifetz,Wheatley, and Gardner) . These books are chock full of ideas, principles, and theories that are sound, sensible, and applicable. But Sutton is onto something different here. His deliberate use of the word "asshole" to describe those – well, assholes – that we work with, sit through meetings with, receive directives from, and must collaborate with every day, is refreshing.
Though TNAR is written mainly for those employed in the private sector (where hiring and firing is fast and furious – unlike public education), it does have some practical applications for schools.
For instance, how many administrators, teachers, or staff members have you worked with or encountered that have indulged in Dr. Sutton's "Dirty Dozen" list of actions that assholes use?
Personal insults
Invading one's personal territory
Uninvited personal contact
Threats and intimidation, both verbal and non-verbal
Sarcastic jokes and teasing used as insult-delivery systems
Withering e-mail flames
Status slaps intended to humiliate their victims
Public shaming or status-degradation rituals
Rude interruptions
Two-faced attacks
Dirty looks
Treating people as if they are invisible.
Check out Dr. Sutton for yourself.
A few things anyone can take from this book are Sutton's suggestions on dealing with assholes you can't get rid of:
Deal with their asshole behavior immediately and make it known that you did. Don't let asshole behavior go on. Even if it hurts to confront an asshole, do it for the greater good of the organization. People are watching to see how you react to the known asshole.
Marginalize them. Make them irrelevant and their influence minimal.
Don't be confrontational with assholes, but don't be a doormat either.
His final word of advice is one that we should all take to heart. Don't hire assholes. Those of us in positions of authority to hire faculty, administrators, and staff must seriously consider candidate's personality as much as we consider their knowledge and ability. I'll remember that as we begin our annual hiring carnival this Spring and Summer.
Lastly, Sutton's book will give you some great tips on how to deal with those pesky, pernicious, parents whom we lovingly call (in the copy room) "assholes".
This is not an advertisement for The Education Trust, nor is it an endorsement of all that The Education Trust stands for. This post is merely my commentary on one aspect of The Education Trust’s practices – assessing standards in practice.
In 2003, I was working at a semi-urban high school near Paterson, NJ. Our school was seeing a major transition in demographics; more ELL students, Hispanic students, and first generation Muslim-Americans were enrolling. It was a regional high school, so we did not have a handle on the K-8 curriculum. Basically, what we were sent, we had to deal with. Literacy rates were suffering and our students were in need of more basic reading and math skills. In short, we were aware of the achievement gap that was present in our building; the honors courses and AP courses were completely Caucasian and the general level classes were nearly all minority. We weren’t ready for this. We had no plan other than to offer the mundane BSI courses. But a crafty Assistant Principal, Jim Jencarelli (who is now the Superintendent of a NJ high school) had the novel idea of bringing in The Education Trust to help us with our achievement gap problem, curriculum redesign, and shifting of paradigms.
One of the first things The Ed Trust does when they come in to your school/district is to meet with the teachers and administration to discuss their Standards In Practice protocol. I can remember the meeting very vividly – teachers were appalled at the presenters statement that one reason an achievement gap exists is due to the pity parties that teachers have for minority students and students who have less than stable home lives. In essence, teachers and schools do no students favors when they lower the expectations based on the perceived inabilities or emotional concerns that teachers and schools have for struggling students. What the Ed Trust ultimately condones is the practice of teaching every child as if they were college preparatory material.
Standards In Practice consists of the following (you can view Ed Trust’s presentation below):
Creating teams of teachers to review, analyze, and critique assignments
Having these teams honestly look at the standards (usually state standards) and see if their assignments reach the expectation, or fall short. (NOTE: you would be surprised how many tests and quizzes are comprised of recall and rote questions.)
A rubric is followed whereby the assessment is measured. If need be, the assessment must be redesigned to meet the standards.
The teams meet regularly and each team member is on the "hot seat" – no one is immune from the clinical exercise.
What I found most intriguing about Standards In Practice was not the protocol. Of course I learned a lot from the exercise (I disappointingly found that my assessments were far too "dumbed down") and gained insight into how to construct rigorous assessments, which, in turn, forced me to redesign my approach to students, lessons, and teaching. No, what intrigued me most was the philosophy of the Education Trust.
Ed Trust is committed to narrowing the great divide between minority students and others. I can’t tell you angry I get when I see school leadership revel in the glory of "beating" other schools at high stakes testing. I take no pride in the following facts:
32% of White adults (ages 16-65) read at the Basic or Below Basic proficiency in Prose literacy. (2003)
67% of Black adults (ages 16-65) read at the basic or Below Basic proficiency in Prose literacy. (2003)
53% of Hispanic adults (ages 16-65) read at the basic or Below Basic proficiency in Prose literacy. (2003)
Notes: Prose literacy refers to the knowledge and skills needed to search, comprehend, and use information from continuous texts. Source: NCES Table 379.
What I have come to understand is that while we scurry to find new ways to meet AYP, get our students over the hump, and keep our schools out of the editorial pages, there is a quiet epidemic of illiteracy spreading in our urban schools. The Education Trust (while not completely perfect) is trying to address the issue through their programs and protocols. They seek to shift the paradigm of teachers and schools, not throw money at the urban schools and hope that a miracle happens.
For my part, I can say that The Education Trust shifted my paradigm. I now see the problem and a potential means of addressing the problem.
Whatever happened to that high school I worked at in 2003 where we brought in the Education Trust? The Principal and Superintendent though it was too expensive and unnecessary. Jim and I left for brighter futures and more open minds. Yet, we are both committed to bridging the achievement gap… however, I now know that the achievement gap is a symptom of nothing more than institutional racism. When any school thinks that a curriculum must be watered down in order to help the minority student, simply because that student comes from a family or neighborhood that is less desirable, then that school is acting in a nearly criminal manner.
Please examine your state’s literacy rates. Is there a widening literacy deficit? Are you in a school or district that seems to have more than a fair share of minority students either classified as LD or stuck in Basic Skills? Once you have that answer, ask yourself if your school or district assesses students to the standard set forth by your state or county? How much rote and recall do you see in your classrooms?
