Discovery Learning; More from Math Coach

Dr. Wayne Wickelgren, author of Math Coach; a Parent's Guide to Helping Children Succeed in Math, has much to say about "discovery learning" and the "new math", often called "fuzzy math" (and which he calls "Standards math").

Here are some of his insights:

"The most pervasive theme echoed throughout the Standards is their emphasis on student exploration and discovery. Instead of presenting information to the class, Standards math teachers ask their students to discover mathematical concepts while solving math problems. "Typically, students break up into small groups of four or so to solve a problem. The teacher circulates among the groups to observe the discussions but otherwise does not interfere with their learning by providing too much information."

"This framework is intended to let each child's natural creativity in math blossom, enabling children to discover important concepts and problem solving methods on their own. . . Teachers encourage students in the groups to do a lot of talking and writing about their thinking process that led to a solution . . ."

"To facilitate discussion, the groups are often working on math problems that are somewhat different from traditional computational or story problems. . . grounded in real-world situations. They are open-ended and contain many parts and many possible answers. . ."

"One example: A middle school math teacher demonstrates a pendulum made from a string and a weight and asks students to construct a pendulum, investigate how it functions, and formulate questions that arise."

"Traditional problems by contrast, have a single correct answer and focus on closely related mathematical ideas and facts."

Dr. Wickelgren explains that hands-on, real-world activities dominates "Standards" math classrooms. Students are never encouraged to memorize addition, subtraction, multiplication, and division facts, but rather to manipulate objects to find the answers, rather than using pencil and paper, repeating the activity each time a set of facts are presented.

"Memorization is regarded as dull for kids and also ineffective as a learning method, as it seems at odds with really understanding the material."

All teachers know the value of manipulating objects to teach the four basic operations, but for a child to have to repeatedly group objects to solve 8 X 6 is standard operating procedure in a "fuzzy math" classroom.

Dr. Wickelgren also describes the organization of the textbooks:

Rather than dividing a year by topics, such as two-digit multiplication, fractions, long division, and decimals, the year is organized into group projects which link to other subjects to create interdisciplinary studies. Rather look at how the textbook is organized:

"A year's worth of mathematics might look like this: A Wagon Train's Journey West, A Genetic Study of Fruit Fly Reproduction, Managing a Supermarket, A Month in the Life of a Real Estate Broker, A Voyage to Mars."

The "fuzzy math" crowd design these activities because they believe that prior to adolescence, children's minds can handle such "concrete" mathematical concepts, mentioned above, "but are not mature enough to handle abstract numbers and operations."

And so your child, being too immature to memorize facts, may be asked to design and create a pretty portfolio with attractive bindings to hold their writings about how they feel about math. All of this is during math class!

Dr. Wickelgren acknowledges such positive features of Standards math as "emphasis on understanding, solving more challenging problems, enriching math curriculum with more probability. . . early study of coordinate geometry". But he also warns of the perils of the "discovery learning", which will need to be discussed in a later post.

[Dr. Wickelgren also acknowledges that the Standards have been modified, but warns that the changes are slow to make their way down to the classroom, especially since there are so many who refuse to see the error in the "new math" approach. Curriculum writers take it very personally. Their "works" are "their babies". ]

Real World Math

There is as great thread discussing "Real World Math" on Kitchen Table Math. If you are confused as to how "real world" activities can be detrimental, see the comments posted by Barry Garelick and subsequent discussion.

Is Your Student Being Taught "Fuzzy" Math?

Parents may wonder if their student's math curriculum is "fuzzy" math. Here are some general identifying marks of "fuzzy" math:

1. Very little practice (You might have someone tell you that new studies show that too much drill kills interest in math. That is not true -- it makes students efficient and confident.) Lack of pencil and paper work -- in the "fuzzies' minds it's bad to do a lot of pencil and paper work.
2. Individual problems on the homework are not actually graded. Students are given credit if they show that they "tried" to do it. It doesn't even matter if they successfully solved the problem.
3. Calculators are used to do what children should be learning to do mentally. Some people may even be so bold as to claim that there are students who will never learn all of these math facts anyway. Calculators are said to be sufficient.
4. (Almost exclusively) student-centered activities. Students work in groups to figure out something, and the teacher may not even be involved at all.
5. There will be little or no instructions, certainly no explicit instructions. Activities are student directed and teacher input is lacking. Students are sent home to figure it out by themselves and the next day the class is asked by the teacher if there were any questions.
6. "Real world math" is what it's all about. It's one of the buzz words. After all, who doesn't want students prepared for the "real world".
7. Students are told to write paragraphs explaining all of the steps that are used to solve the problem. Or students are expected to write about how they feel about math. Or as Walter Willaims referenced, students write on such topics as "If Math were a color, what what that be?" In other words, students are writing their math. So much for the benefit of symbols and digits to help solve a problem efficiently, in the least amount of time.
7. Math books are huge, thick books, and pages are filled with visual "clutter" which distract students' thoughts. (For some "adhd" or "add" students, these pages can be a disaster. It is no wonder it takes them 50 minutes to do a 15 minute assignment.) There is a lot of "non-math" content such as photographs in color and motivational stories which are meant to "inspire" kids to greatness, I suppose, but which have no place in the middle of a math assignment.
8. Patterns, patterns, patterns. Looking for patterns, drawing patterns. Probability will be prevalent by 4th or 5th grade. And much time spent on data analysis projects (finding the mode, the mean, the median) starting in elementary school. What is appropriate for a high school course is inappropriate for elementary chldren. The time spent on one "projects" may be days and will indeed use lots of pencil and paper. Notice here: It's OK for them to do pencil and paper work. It's just not OK for me or you to do pencil and paper work on traditional math practice.
9. And here's one dead give-away that the curriculum takes a "fuzzy" math approach:
Students are given problems in one lesson, for which they are not at all prepared. Students spend much, much time on these problems, only to discover that the concept is taught a lesson or two later So if your student has no idea what is being asked, look ahead and you'll probably find that the concept is coming up. This is called "discovery learning" because students have a wonderful opportunity to "discover" the concept on their own. Imagine your 4th grader being forced to "discover" how to do long division with no input from anyone else!!

I'm sure there are more I've overlooked. One more thing that is obvious: Your student is (perhaps suddenly) discouraged, thinks he/she is not smart, gives up trying. I know one student who had been in my 5th grade class and was an excellent and a very diligent student. What didn't come naturally, she learned by shear determination and perseverance. How sad I was to hear that she was threatening to kill herself because her high school math was so hard for her and she didn't think she was ever going to get it. Her teacher's approach was to assign the algebra/geometry lesson, forcing the students to teach themselves, and then ask if any of the stusdents had any questions or problems. If there were no questions, they proceeded on to the next lesson.)

So, do any of these ring a bell to you? Well, if so, you must rescue your student as fast as possible. Go to Kitchen Table Math for insights how a family rescued their own student. It took lots of hours after school, but the results made it worth it.