“Today’s classroom is like none that has come before it. It is diverse in every way imaginable — language, culture, economics, family makeup, and styles of learning. Welcome to a place where this richness is celebrated, nurtured, and encouraged to grow — Welcome to MathLand.”
MathLand, produced by Creative Publications of Mountain View, California, is a 36-week program incorporating a new way of thinking about math. No more boring and ineffective memorization and drilling. MathLand teaches students to “think for themselves.”
The MathLand package comes with a guidebook for teachers, an assessment guide, sample letters to parents, calculators, a videotaped infomercial, and 10 tubs of plastic shapes, dice, and other manipulatives. What it doesn’t come with are student textbooks or worksheets, and that is what has caused the greatest uproar among some parents and educators.
MathLand, like other trendy approaches to elementary education, has zealous defenders. The program also has equally zealous opponents who have established a web page about MathLand (http://www.intres.com/math/).
Their main concern is that the program substitutes the learning of mathematical knowledge for self-esteem, validation and fuzzy concepts. MathLand has no testing, no review, no textbooks, and no building block sequence for mathematical concepts.
WorldNetDaily has obtained a large amount of MathLand materials, including a full curriculum package. Detailed examination of the material shows MathLand’s goals are to: a) substitute new computing methods for traditional ones; b) redefine the concept of “correct” and “incorrect”; c) redefine the role of the teacher; and d) insert a subtle social agenda into the math curriculum.
Old methods vs. new
For an instructor’s text, MathLand’s guidebook contains many of polemical arguments against “rote learning.” Reminding teachers that “The only rules in MathLand are the ones students invent for themselves,” the authors go on to extol the virtues of discovery-based learning and the evils of memorization. They tell us that “Memorized formulas can be easily forgotten.” There are also numerous not-so-subtle criticisms of the traditional method of teaching math. The authors describe the traditional method as the “rules way,” while the MathLand method is the “thinking way.”
The authors are convinced that the MathLand method is not only better, but quicker. “When students are encouraged to think rather than being given rules to follow, the traditional, slowly-paced sequencing of problems over weeks and months is unnecessary,” reads the guidebook.
MathLand’s main criterion for determining the worth of its methods seems to be whether children like it or not. “I like the thinking way best because it is very easy and fun,” reads one student’s comment. “I don’t like the rules way because it is to coplecated (sic),” says another.
MathLand extols diverse approaches to problem-solving — unless that approach happens to use traditional methods. Then coercion steps in. The guidebook includes a “note from a teacher” that reads: “This week some very capable students who were used to using the algorithm struggled a bit as they were forced to use understanding rather than rote procedures.”
MathLand’s assessment guide includes possible responses teachers might hear during student interviews. One student is depicted saying: “My dad says I shouldn’t use the calculator. He says he never uses one.” The sample assessment for this interview reads: “Has negative feelings about the use of the calculator brought on by social forces.”
Certainly, traditional methods have their pitfalls and shortcomings. Are MathLand’s methods more scientific, more deliberative and more defensible? Judge for yourself.
Under the heading “Key Mathematical Ideas for Grade 6,” the text explains that “Equations expressing the relationships between unknowns can be solved through modeling and trial-and-error.” The guidebook continues by explaining that “Trial-and-error is a valid solution technique, allowing all students to approach the problems at some level.”
If trial-and-error is not the mathematics discipline you were hoping for in your child’s education, how about this: “This student solves the problem using a guess-and-check multiplication strategy.”
If this sounds suspiciously like the whole language method of reading, you are not far off. The authors explain that “Division in MathLand is not a separate operation to master, but rather a combination of successive approximations, multiplication, adding up, and subtracting back, all held together by students’ own number sense.”
And if the students’ own “number sense” is inadequate? “Periods of disequilibrium are a necessary and important part of a healthy learning process.”
Parents upset with the lack of student textbooks or testing may be more displeased with the manipulatives that have been substituted for them. The MathLand package comes with spinners, dice, double-six dominoes and playing cards. Either MathLand is a subsidiary of Milton Bradley or it is a suburb of Las Vegas.
The limitations of manipulatives when teaching fractions are obvious. While students can become quite proficient dealing with halves and fourths, they are totally at sea when faced with thirteenths or forty-sevenths. Mixed numbers, reducing, and common denominators are given lip service by MathLand. And for a program so heavy with manipulatives, instruction in the use of traditional tools such as compasses, protractors and slide rules is conspicuously absent.
Right and wrong
MathLand follows in the footsteps of many previous California education trends by blurring the distinction between the concepts of “correct” and “incorrect.” In fact, the actual work of MathLand students, used as illustrations in the guidebook, contains scores of atrocious spelling and grammatical errors.
“Students see that teachers are more interested in their reasons and explanations for solutions and discoveries, not whether or not everyone gets the same solution in the same way,” say the authors.
There are constant admonitions against holding students to strict standards of accuracy. “Don’t worry if the students’ graphs are not exactly accurate,” reads one lesson.
This attitude leads to the fuzzy standards that critics decry. In Unit 9 of MathLand’s 6th grade package, nearly the end of the program, student exercises include: “Write down one of your favorite things to do. Then tell some ways you can think mathematically about it.”
The MathLand dogma is that correctness is reached through discussion and consensus. Not once in all the material does MathLand counsel a teacher on what to do when students agree on an incorrect answer. The author’s advice is to “Let the final conclusion about which answer is right come from the class, through discourse, not from you.”
Teacher’s role
It should come as no surprise that MathLand has adherents among pupils and teachers. Many students prefer it because the traditional method of times tables, algorithms and formulas is hard work. Many teachers prefer it because teaching the traditional way is also hard work. While using MathLand in the classroom cannot be a breeze, it calls more upon a teacher’s classroom management skills than his or her mathematical skills.
In the first week of MathLand, the teacher is told, “This week you are an observer.” In subsequent weeks, he or she is reminded that “In all cases you will be a facilitator and a guide.”
MathLand moves in the direction of having the teacher abdicate his or her authority as the classroom’s expert on the subject matter. An instruction in the guidebook reads: “Do not feel that you must know the answers to every problem before the class begins to discuss them. In fact, not knowing the answers ahead of time can be an advantage as you facilitate the discussion. Let the class debate the solution alternatives and through this debate convince themselves (and you) of the best choices.”
The danger in this approach is obvious. If the teacher does not know the answer ahead of time, and the students are sufficiently convincing, the entire classroom can agree on an incorrect answer or concept without anyone knowing it.
PC math
Finally, the authors apparently cannot help but to force political correctness into the math curriculum. During a survey exercise, designed to give students practice in working with pie graphs and percentages, MathLand instructs teachers to “Encourage them to include more socially significant questions. What world personality do you most admire? What is the worst problem in our school? in our city? in the world?”
The authors provide an actual illustration of the kind of survey they have in mind: “What can we do to help the Earth?” One group must have had a small minority of dissidents. Their survey read: “One-twelfth of our class thinks we need better education.” Lest you become too encouraged by that result, it was the same percentage as those who thought “hairspray is the best way to help our planet.”