I just received the following email from my nephew, a conscientious and excellent student currently enrolled at an East Coast university costing $68,000/year – before textbooks, etc…

The subject line in the email was PISSED

Since I know how much you love Pearson…

I’m taking a math course and an accounting course this term, each requires the completion of weekly online homework assignments. In order to gain access to these assignments, each student must make an account using a course ID so that our scores will automatically be sent to the professors, and purchase access to the e-books online. The accounting textbook is McGraw-Hill, and the math book is Pearson.

Each e-book will cost me $100, only because we are required to use these websites for our homework. I’m literally buying homework.

I thought Pearson’s death-grip on my throat was over, but alas…

Click to enlarge image

It is worth noting that all of my nephew’s other coursework thus far has been project-based and authentic.

OF COURSE, a required math course and math-adjacent “Accounting,” rely on the same-old shitty “answer the odd numbered questions” alternative to an actual productive education experience. This is not a small point.

As Seymour Papert told me, [paraphrase] “If you are not concerned that not a single progressive development in education has had an impact on ‘math,” it means ultimately that no matter what else your school does to make education relevant, there is some part of the day or week where you introduce coercion, irrelevance, and misery into the system.” This coercion is corrosive and ultimately undermines any other learner-centered efforts. As I like to say, “the weeds will always kill the flowers.”

Any good school leader knows that they can’t keep piling  new mandates on teachers and kids. Yet, few school leaders and policy makers seemingly refuse to lighten the load. Editing is critical. Less is more.

However, there is an even more pressing failure of literacy than never getting around to taking out the curricular trash. While school principals continue to ask more and more of teachers, it is the rare school leader with the courage to tell a teacher to STOP doing something.

Allow me to describe a quite common scenario. A school community decides to invest  in a more progressive, creative, or learner-centered mathematics. Curriculum kits are purchased (even the ancillary materials) and professional development juice is sprinkled on the staff.

Later that school year one cannot notice the presence of arithmetic worksheets being used during class and for homework. The worksheets were not part of the “Big Box ‘o Fun” that came with the school’s math curriculum. The teacher purchased them behind the local laundromat or downloaded them off the Web.

You ask “Why are you using all of these awful math worksheets when our school has embraced a different vision of mathematics education?” Teachers almost always answer in the same way. “I’m supplementing the curriculum.” Implied is a concern that there will be life-altering gaps in a child’s eleven times table.

Ask the same teacher if she uses the manipulatives, games, or projects that came with the textbook and she’ll reply, “Nah. No time.” There’s always time for Frank Schaffer!”

I have worked in hundreds of schools over my career and I have yet to meet a principal who will go into a classroom and say, “Stop using those worksheets.” You purchased a curriculum because you didn’t believe teachers were clever enough to know what or how to teach. Why allow them to go rogue and make decisions that do violence to children’s learning?

Leadership is not only about subtraction, but having the integrity to tell a teacher to stop doing something.

This past Fall, one of my oldest friends, veteran mathematics educator Ihor Charischak, hosted me for a Math 2.0 live webinar.

The webinar featured a freewheeling discussion about the state of math education, the role of computers in mathematics learning, school reform, constructionism, Seymour Papert, Web 2.0 and a host of other topics. If you missed the original webinar, you can watch or listen to it now and read the comments posted by attendees.

Replay the webinar

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Dear School Leaders and Policy Makers:

Our university used to boast of a 100% job placement rate for MA students with a freshly minted teaching credential. The Class of 2010 faced nearly 100% unemployment. A remarkable portion of each of my recent pre-service class sessions was dedicated to questions of employment and unemployment. That’s a shame since the only thing bigger than these wannabe teachers’ graduate school debt is their desire to improve the lives of children. Despite the wholesale debasing of teachers by the media, foundations and political leaders, I am inspired by anyone who still wants to teach and am honored to help them develop.

Apprenticeship is a powerful way to learn. That’s why future doctors and teachers intern before being credentialed. The theoretical principle at work is that you learn best through the careful emulation, collaboration and supervision of a master practitioner. I remain staggered by the remarkable impact of student teaching on candidates – for good and bad. It does not matter what my colleagues or I teach in the ivory tower of academia. Those techniques, learning theories, even deeply held values might be shelved within days of becoming a student teacher. This is commonplace when student teachers apprentice with the best educators. The results are more catastrophic when assigned to less competent, generous or inspirational teachers.

A few of my student teachers report being paired with teachers who are hostile, mean or sleepwalking. That’s unfortunate, but not half as tragic as the lessons newbies are learning from the “good” well-intentioned teachers and principals. What are young teachers expected to learn from what they observe in today’s public schools? Are good teachers being required to behave in miseducative ways based on directives from school administrators?

Here are just a few of the common scenarios being reported from the field.

  1. I asked several dozen California student teachers, “Tell me about science instruction in your school?” The nearly unanimous response was that elementary science education is a lot like Big Foot. Teachers have heard it exists, just never seen it for themselves. The Sasquatch Effect may also be applied to art, music, drama, social studies or any other meaningful pursuit not reduced to a standardized test. The innate curiosity of young children is being squelched while learning is supplanted by being taught or worse – prepped. An archaeologist would be required to find evidence of thematic units, classroom learning centers, experiments or authentic project-based learning.
  2. Principals evaluate teacher efficacy based on the volume of their students. Students are taught to be quiet, compliant and work in isolation. Elaborate time-consuming systems are enforced for eating lunch in silence, walking down the hall and playing only with children in your own class, if your school is liberal enough to still condone recess. There is zero tolerance for joy, conflict, exuberance or the expression of any other human emotion. We then have the audacity to pretend that one of the benefits of schooling is socialization. Right, anti-socialization.
  3. Math and language arts instruction has been reduced to teachers delivering a script and students chanting. Neither teacher nor student is privy to the secret logic of the seemingly infinite and random list of concepts and skills being “covered” in preparation for the test. Second graders are forced to solve worksheet problems concerning half-dollar coins even if you can’t remember the last time you saw one in circulation and the chincy manipulative kit does not include them. That’s OK, because tomorrow’s lesson will be on perimeter or from the new “algebra in-utero” curriculum. Nothing connects. There is no big picture. There’s just more instruction, more quizzes, more tests and less learning.
  4. Reading is reduced to mechanical acts or a prelude to comprehension tests. Classrooms are devoid of books, except for the basal that interrupts each boring paragraph with a quiz and compels every child to read the same thing at the same rate, regardless of their ability. Strong early readers endure years of needless phonics instruction just because while struggling readers are poked, prodded and drilled. Students receive “credit” for books they race through, but only if the school purchased the computerized quiz for that title. Reading for pleasure, information or any other intrinsic reason has gone the way of butter churning. It’s now an unpleasant unrewarding chore without the yummy creaminess. Yet, in the golden age of publishing and dynamism of the information age, we pretend to be mystified by illiteracy and low rates of independent reading.
  5. Not only has the standardization of curriculum begot test-prep and boredom, but “pacing” is its toxic spawn. Teachers are not only forced to pretend that every student is “keeping up” with whatever the pacing guide throws at them, but students are forbidden from “going ahead.” My student teachers report that teachers are punishing kids for going ahead of the sacred lesson. Some teachers make these students sit in isolation outside of the classroom if they have the audacity to express understanding of what they are being taught. Make no mistake, this obscene teaching practice is a form of child abuse and demonstrates that teachers, even the best intentioned ones suffer from Stockholm Syndrome. At best, this phenomenon demonstrates that a primary lesson of contemporary schooling is helplessness. If you act helpless, your teachers will teach that lesson to their students.

Where will one find creative teachers when agency is deprived and compliance celebrated? Every subject at every grade level could be taught in conjunction with a current event like the oil spill in the Gulf of Mexico, but by whom? When?

Five years from now, will any teachers know how to seize the teachable moment and build upon student interest or connect the curriculum to the world outside of the school?

I realize that politicians and the media are kicking your ass, but it is morally reprehensible for you to compel teachers to behave in ways that harm or inhibit the natural potential of children. Invoking the Nuremberg Defense is unacceptable. Who will stand up for the children? For your profession? For what is right?

Let’s imagine that non-traditional paths like Teach-for-America are effective and recruit the best and brightest university graduates as they promise. How many of these teacher candidates would be willing to suspend their own expression what they know about learning and allow academic content to be forced through the narrowness of the standardized curriculum?

What would you have me say to the young teacher who chokes up and testifies, “I don’t want to become like that?” (referring to the terrorized, risk-adverse, authoritarians she sees in schools as a result of the high-stakes accountability movement)

Why should a young teacher work for you? After you remove all joy, creativity, freedom and individuality from education, who will teach your child?

Originally published in the September 2000 issue of Australia’s Hotsource online newsletter

Now that most of you can be considered advanced beginners in using MicroWorlds, this issue will explore a bit more of the language and data structures available to you.

The following activity explores probability while demonstrating how sliders, text boxes and even the screen may be used to collect and report data.

Who’s for two-up?
The core of this task will be to flip a coin numerous times and record the number of times heads and tails appear.

  • Start a new project.
  • Name the turtle, coin.
  • Create two coin shapes in the shapes centre. Name one heads and the other tails. Be sure to make them appear different in some way so that the user can clearly see which one side of the coin lands faceup.
  • Change the turtle’s costui-ne to one of the coin shapes. Create a Many Times button with the instruction, flip.

Recording data with text boxes
This part of the project will flip a coin in FLIP, and change the value in the textboxes, headscount, tailscount and totalflips. If you name turtles, text boxes or sliders with unique name you may change them even ii they are on different pages. This allows you to have some action going on between the scenes.

  • Make a Startup button on the first page.
  • Create a new page from the pages menu.
  • Create text boxes named, Headscount, Tailscount and Totalflips.
  • Show the names of the text boxes so the user knows what they are reading
  • Click the Startup button
  • Type the following procedures on the procedures page.

to flip
ifelse coin = ‘heads
settotalflips totalflips + 1

to coin
if 1 = random 2 [output “heads]
output “tails

to recordheads
coin, setsh ‘heads
setheadscount headscount + 1

to recordtails
coin, setsh “tails
settailscount tailscount + 1

to startup
everyone [settext 0]

Click the flip button to start and stop the experiment. You may wish to make the flip button run many times if you want it to keep flipping the coin.

Recording data with sliders
Sliders may be used as reporters (input devices) to change the value of a variable or they may be used as indicators (output devices) displaying the current value of that reporter. Let’s experiment with sliders on a second page of our coin flipping project.

  • Create a new page from the Pages menu
  • Create two sliders ‘heads and tails, with a minimum of 0 and maximum of 300 at the bottom of the new page
  • Optional: Create buttons to switch between the two pages of our project.
  • Make the following changes to your procedures.

To recordheads
coin, setsh ‘heads
setheadscount headscount + 1
setheads heads + 1

to recordtails
coin, setsh “tails settailscount tailscount + 1
settails tails + 1

to startup
settailscount 0
setheadscount 0
settotalflips 0
settails 0 setheads 0

Type Startup to init-ialise the variables, click oA the flip button and switch between pages.

Do you see the sliders changing their values?

Extra bonus! Adding a histogram to graph our data
It is easy to add simple graphing functionality to our probability lab with the creation of two turtles and a bit more Logo programming.

  • Hatch two turtles on the same page as the sliders.
  • Name one turtle, headsgraph, and the other, tailsgi-aph (for heads graph and tails graph)
  • Place those turtles above their respective sliders.
  • Create two different turtle costui-nes consisting of blue and red horizontal bars. Name the shapes hline and tline.

Make the following changes to your procedures.

To recordheads
coin, setsh ‘heads
setheadscount headscount + 1
setheads heads + 1
headsgraph, fd 1 stamp

to recordtails
coin, setsh “tails
settailscount tailscount+l
settails tails + 1
tailsgraph, FD 1 stamp

to startup
settailscount 0
setheadscount 0
settotalflips 0
settails 0 setheads 0
headsgraph, setpos [-170 1451]
tailsgraph, setpos [200 145] page2 clean pagel

Type Startup and click on the flip button to set the experiment in action! You may even want to figure out a way to stop the graphing when a bar reaches the top. How about a textbox reporting the experimental standard deviation?

The magic of MicroWorlds’ parallelism allows the coin to be animated, text boxes to change, sliders to report and a histogram to be created all at once. You can use lots of software to generate random numbers, but no other title allows all of these things to happen at once. I am confident that you can figure out exciting ways to integrate these programming techniques into much more complex simulations and experiments.

Originally published in the September 2000 issue of Australia’s Hotsource online newsletter

LogoWriter and MicroWorlds have done so much for interdisciplinary projects that it is useful to remember that MicroWorlds can play a major role in the development of mathematical knowledge. This issue and next will explore the numerical side of MicroWorlds.

First the Boring Stuff
MicroWorlds procedures come in two categories, commands and procedures. Most Logo-users are quite comfortable with commands such as CG, FD, RT and SETC. Commands may or may not take inputs and they always produce an action. Every Logo expression (line of code) must begin with a command. This is why typing HEADING in the command centre produces the error message I don’t know what to do with HEADING. SHOW HEADING, FD HEADING, RT HEADING * 2 will all work because HEADING reports the turtle’s current orientation and hopes a command is listening. Commands may have any number of hoppers, but they never have a spout. REPEAT is an example of a two input (hopper) command.

Every one input command beginning with the prefix, SET, has a corresponding reporter with no inputs. For example:

Command Reporter
SETTEXT1 TEXT1 (where text1 is the name of a textbox)

At the core of it all
Reporters are procedures that may or may not take an input, but they always output a result. Reporters are also known as functions or operations. Reporters are absolutely essential for most mathematical and interactive MicroWorlds projects. They pass information that can be used by other procedures or turtles. Reporters may have any number of hoppers, but they always have just one spout.

It’s your call
You can write your own reporters if you remember one simple rule. Every reporter procedure contains one output. When Logo encounters the OUTPUT reporter, the procedure is terminated. To create a new reporter you need to remember the rule about OUTPUT and decide how many inputs the reporter needs. For example, if we wanted to write a procedure to double a number, we would only need one input.

to double :number
output :number * 2


to double :number
output :number + :number

Type: DOUBLE 45 in the command centre and see what happens? Why did you receive an error message?

Many people who wish to double a number would write the following procedure.

To dumb.double :number
show :number * 2

Then if they type, DUMB.DOUBLE 45 in the command centre they will get what they think is the desired result. This is the result they need only if they want to see the number 90 appear in the command centre.

Try typing the following instructions in the command centre:

Now try typing:


Our DOUBLE procedure is much more flexible and versatile than DUMB.DOUBLE.

They can speak to each other
Reporters can perform a manipulation/operation on an input and then report that result to another reporter. Logo (MicroWorlds) reads reporters from right to left since you can’t type from top to bottom. The following graphic illustrates FD ADD5 DOUBLE DOUBLE 5.

Logo is a prefix language. That means that inputs always follow the procedures. Since humans like the standard arithmetic operators (+-*/), Logo will tolerate them, but often requires parentheses for grouping. These infix reporters tend to give the turtle indigestion. Logo much prefers PRODUCT 3 4 to 3 * 4. See how SHOW DOUBLE DOUBLE 3 + 4 behaves if you add parentheses, like SHOW (DOUBLE DOUBLE 3) + 4.

Make it simple
Young children can use similar simple arithmetic reporters to leverage their own turtle graphics. For example, a child incapable of calculating twice the distance for the turtle travel could use a DOUBLE or TWICE reporter and operate algorithmically. These procedures could be written by a teacher ahead of time or by the student herself.

Operation of fractions may also be explored with simple reporters.

To 3fourths :number
output :number * 3 / 4

to 2thirds :number
output :number * 2 / 3

to 1half :number
output :number / 2

To “play with” multiplication of fractions, try typing:
SHOW 3fourths 100
SHOW 1half 100
SHOW 2thirds 3fourths 100

You may of course use these fractional reporters to command the turtle. Type the following BAR procedure on the procedure page.

To bar :height
pd repeat 2 [fd :height rt 90 FD 25 rt 90]
pu rt 90 FD 35 lt 90

See what happens if you type the following in the command centre.

BAR 100
BAR 3fourths
100 BAR 1half 100
BAR 2thirds 3fourths 100

Battle of the Functions
You can make a game out of all these arithmetic reporters. Put kids in groups of four or five and have them each contribute one new arithmetic procedure in the style of DOUBLE. They may use their own imprecise names for the reporters if they wish (as long as they can explain its function to their peers). Each kid takes turns inventing a number problem consisting of stacked-up reporters and one numerical input. The object of the game is to invent a problem that is difficult, but not impossible to solve in one’s head. Wiseguys are penalized by the rules of the game.