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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 distracts 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 children. 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 that is obvious. Your student is (perhaps suddenlyl) 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 into two parents who faced similar situations and successfully helped their students.
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27 comments:
Catherine, I didn't necessarily mean to post this on your blog. But I guess I'll leave it here.
I've been asked many times to start my own blog with stories of students I have helped and other helpful ideas. I have no grand thoughts for anything phenomenal here. There are many people who have forged a path and set the pace and I'm not trying to compete with you at all. I'm just trying to show that "math trouble" may not be the kids' fault. I'm hoping to encourage parents to get involved in their children' struggles early by making the parents feel they are not alone and their story is one of many.
Concerned Teacher,
This is the perfect place to post. Thank you. In the early KTM days we went through a lot of the same points, but new parents are coming up all of the time. We old-timers forget that as we move on (and our children grow up.)
Also, I think it is enormously helpful to hear from teachers, as well as parents.
SusanS
I'm not a fuzzy math advocate by any means and I agree with most of the warning signs on this list. However, I do not understand why connecting math concepts to real world situations is an indication of a fuzzy math program. My algebra students came alive this year when I showed them how the distance formula is used in programming video games. When I taught middle school, I connected everything from percentages to coordinate pairs to real world examples. Math doesn't have to be abstract and irrelevant. Making real world connections can increase student interest in math which may lead to lower drop out/failure rates.
However, I do not understand why connecting math concepts to real world situations is an indication of a fuzzy math program.
It depends on how one defines "real world". Those who rail against the so-called rote-ridden, formulaic traditional math, point to problems such as work, distance, and mixture problems as irrelevant to students' interests. Other criticism includes that such problems contain all the information that the student needs, they work out neatly, they don't represent the messiness of problems one encounters in the "real world". The solution, in the reformists' mind, is to present students with assignments requiring them to collect data, come to conclusions about such data that they may or may not be prepared to do. For example, in one assignment I saw, students were to throw various types of paper airplanes, measure how far they travelled, how long they were in the air, and other parameters. These data were then given to another group of students who then were to come up with a scheme for rating which plane flew the longest distance. In the documentation of this assignment, it was evident the students were not familiar with the distance = rate*time formula, though some of the brighter kids seem to stumble on it. The whole assignment was one of stumbling and fumbling which passes for discovery and further passes for learning. It is neither. That they were engaged is irrelevant. The assignment had no value because they were unable to make connections to previous learned and (hopefully) mastered material.
What you have done in your algebra class does relate to previous learned and mastered material. And the students enjoyed being able to put what they've learned into practice.
But many of these so-called real world assignments are nothing more than data collection and data mongering with some statistics thrown in. Not much application of previously learned material takes place. Nor discovery. Nor learning. But onlookers ooh and ahh when they see how "engaged" the students are.
Correction to last comment. The paper airplane assignment was not for students to determine which plane flew the longest distance, but which plane flew "the best". A typical "rich open-ended complex problem" that served to do nothing but make the teachers feel good about themselves and the students feel as if they learned something.
"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!!"
Actually, I lived that in 5th grade; my 4th grade teacher didn't teach us much math and in 5th grade we were supposed to know it already. Somehow I had gotten to the age of 10 without realizing that you can ask the teacher for help if you don't know how to do the assignment. One of my clearest and worst memories of elementary school is sitting there, trying every way I could think of to do those long division problems and completely failing. It was one of the things that convinced me I was just bad at math--I was 19 when I figured out that I actually quite like math.
Now I homeschool and use Saxon.
--dangermom
--dangermom
Would you consider posting your story on my new blog sight? I'm just getting started and it is my goal to use stories like yours to help parents whose children face situations just as you did.
http://mathwithouttears.blogspot.com/
I think more and more that fuzzy math isn't all bad. After all, if I take an honest look at how I homeschool my kids a LOT of what they do in fuzzy math, I do with my kids. Of course there's traditional stuff we do too...And we can never find the half-dozen calculators we own so we just don't use those.
Often has me wondering if it's that what's fails in the classroom can work at home or if it's how I drive firmly down the middle between the extremes that makes it work for us.
You should definitely post here!
THANK YOU!
Post as much and as often as you like -- this really is a group undertaking (I think!)
Post as much and as often as you like -- this really is a group undertaking (I think!)
#6, real world paragraphs, is the one that drives me crazy. Not only do you have to (hopefully) actually be able to do the problem, then you have to write an essay.
Math is it's own language.
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.
This one is a KILLER.
C's entire 6th grade year was spent in a TRADITIONAL curriculum & class where the homework was never, EVER collected & corrected & the teacher asked if anyone had questions.
Needless to say, the boys didn't have questions.
Ever.
One time the teacher assigned a bunch of algebra word problems. This was before any of them had ever seen the words "let x equal."
I walked C. & his pal through the problems, 2 of which they had no clue whatsoever how to approach even with me "helping."
The next day I asked them if the teacher had gone over the problems in class.
She hadn't.
I asked whether either of them had raised his hand and said he didn't understand how to do the problem.
No.
That was one of the few things I was able to get changed. I complained about it so much that the teacher finally stopped leaving it up to the kids to ask questions as the structuring principle of the lessons.
I'm very sorry to hear what a hard time your former student is having.
This is a constant source of frustration to me. "Discovery" teaching, when it puts full responsibility on the student to self-teach AND gives kids letter grades, is very harsh.
One of the regulars here (I'm forgetting who at the moment...) has told me she thinks constructivist approaches are particularly difficult for anxious kids.
I'm just trying to show that "math trouble" may not be the kids' fault. I'm hoping to encourage parents to get involved in their children' struggles early by making the parents feel they are not alone and their story is one of many.
That's been my mission for quite some time now.
I may be wrong about this, but I think parents have made some headway at the middle school in terms of conveying the idea that the school should be responsible for teaching.
It's not that things have changed tremendously....but the discourse has changed....
Apparently the superintendent believes in accountability and formative assessment, so these ideas are coming from the administration, too.
The idea that the grade on the student is a grade on the teacher and her principal is still foreign.
That's the next step.
It's not just that the school should be responsible for students passing the state tests.
The school is responsible for the students doing well.
My algebra students came alive this year...
I sure can't improve on what Barry said (Which needs to go up front.)
I would love any and all of the applied-math examples you use in your class, and so would C. I think.
"Real-world" in the constructivist curricula are, to me, almost bizarrely non real-world.
Barry's write....it's just non-stop COUNTING stuff.
Counting stuff and then finding mean, median, and mode.
In my district, the kids are doing mean, median, and mode every single year, year-in and year-out.
Plus they do all this counting and data-corralling on pointless stuff nobody wants any data on, like how many kids wore tennis shoes versus how many kids wore dress-up Sunday school shoes to class (that was a Trailblazers example, from the book).
Gee, there are 12 girls in the class and all 12 wore tennis shoes --- what does this tell us???
Speaking of applied math, this is another thing that gets to me....I LIKE applied math.
If math curricula are going to incorporate real-world math, let's have actual real-world math -- something a real person might do in the real world.
Bring back shop.
Please.
And home ec. Real home ec.
Our kids are required to take Home Ec. There's no shop; shop was banned years ago. Too dangerous!
So the kids take Home Ec.
What do they do in Home Ec?
Bake one set of cookies & hand-sew a sewing kit frog.
Three years of Home Ec, and does my kid know how to sew on a button?
No.
"However, I do not understand why connecting math concepts to real world situations is an indication of a fuzzy math program."
Because that's what these programs say. You don't hear that (level of) talk from a rigorous math curriculum. That doesn't mean that motivating students with real world applications is a bad idea. But it doesn't mean that real world applications should be the vehicle for learning and mastery. That is very wasteful of time and doesn't get the job done. As Barry says, just because the students are engaged, it doesn't mean that the proper learning is taking place.
I've given talks about how math is used for video games and computer-aided design. It's easy enough to talk about the concepts, but what I wanted them to understand is that getting excited about a subject is just the beginning. Fuzzy math thinks that once you get kids excited, the rest is easy. It isn't. After the diet guru gets you all fired up, you still have to eat less and exercise, day after day.
If kids need to have a real world justification for basic things like the distance formula, then they are in for a tough time. [Actually, most computer graphics programs are only interested in comparing distances, in which case you never need to take the square root. In the middle of a loop done millions of times, that can save a lot of time. The signed distance between a point and a plane can also be calculated by using a simple dot product.] There are lots of fascinating things to talk about, but the kids still have to go home and do their homework. Shallow motivation wears off very fast.
In many ways, an emphasis on vocational (real world) applications make students less patient with mastery of the basics required to reach the highest levels of learning. It's the difference between going to vocational school or to an engineering college; the difference between going to Full Sail University or Carnegie Mellon in Computer Science. It's not good for students when schools shoot for the top of a tree rather than for the moon.
"Bring back shop."
Careful. Applied math is not "shop" math. I had the chair of an engineering department at MIT warn me (when I was a student) about "applied hydrodynamics", but he was not talking about vocational school math.
"...something a real person might do in the real world."
A pure mathematician might deal with issues of topology, but an applied mathematician might focus on issues (the math) of solid modeling in a computer program. Those applied issues involve very complex math.
Much of the real world math being done can't even be explained to teachers, let alone kids. So what do schools do? They have kids build bridges out of Popsicle sticks.
Applied math to a mathematician does not mean "application of math to science and engineering." And shop class is another world away from engineering.
While Applied Math means differential equations and fluid mechanics to lots of people, it can also mean combinatorics, graph theory, probability theory, etc. Working on Monte Carlo Markov Chain methods is "modeling" in some sense, but definitely NOT the same sense that building a component analysis model is.
All we applied math folks did was prove theorems. In physics, we used math and didn't prove theorems--but that wasn't applied math, it was applications of math. Still, again, that was nothing like shop class either.
Fuzzy math thinks that once you get kids excited, the rest is easy. It isn't. After the diet guru gets you all fired up, you still have to eat less and exercise, day after day.
This has been taken to a logical extreme by the Project Lead the Way folks.
This is a $100K 4-year program whose SOLE purpose, as far as I can tell, is to entice students into enrolling in 4 years of the math courses their high school already had but no one was taking.
And the premise of Project Lead the Way isn't remedial; it isn't, "We'll persuade your students to take 4 years of math by plugging the gaps."
It's entirely motivational.
"Pre-engineering" is so riveting that students who would have quit the instant they passed the Regents exam for Math A will persist through Math B and pre-calc.
Careful. Applied math is not "shop" math. I had the chair of an engineering department at MIT warn me (when I was a student) about "applied hydrodynamics", but he was not talking about vocational school math.
I'm happy to use whatever term you wish, short of "real-world math" and "everyday math."
I still say bring back shop.
I hadn't quite realized how bad "Exploratories" and "Specials" in the middle school are. These are course the kids are required to take. C. got out of them this year because he was taking Earth Science, which has a lab, and chorus.
The art exploratory--this is REQUIRED--appears to be an entire school year spent photoshopping stuff.
We have fantastic fine arts teachers, and this is what the kids are forced to do.
Why can't they take drawing and painting for a year?
Why do they HAVE to take photographs (with no instruction in photography) and manipulate them with Photoshop?
Next year the Middle School Model will be "implemented" and we'll have Exploratories up the ying yang.
No doubt they will all be INTERDISCIPLINARY because teaching subjects in isolation.
umm...I believe I meant "Barry's right."
Barry's write....it's just non-stop COUNTING stuff.
Ooh, I have one! In a fuzzy math classroom, the seats in each pod of around four seats face each other. Corollary 1: Off-task chatting and games are expedited. Corollary 2: When attention must be given to some point in the classroom, about a quarter of the students must twist 180 degrees to face it--or else ignore it.
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