Consider this 7th grade math problem: A company makes both 3-wheel and 4-wheel scooters. If it has 50 scooter bodies and 160 wheels, calculate how many 3-wheel and 4-wheel scooters it can produce using all of its bodies and wheels.

Let X = 3-wheel scooters.

Let Y = 4-wheel scooters

So, (1): 3X + 4Y = 160 wheels.

And (2): X + Y = 50 scooters.

Rearrange equation (2), subtracting X from both sides, to yield Y = 50 minus X.

Substitute into equation (1) to yield 3X + 4(50 – X) = 160

Simplify to,: 3X + 200 – 4X = 160

Collect: 3X – 4X = 160 – 200

Solving: X = 40 and Y = 10

• removing some advanced math from today’s curriculum would add time to reinforce the fundamentals.
• “Forget the algebra,” she said. “How can a kid who doesn’t understand fractions and can’t multiply solve this problem?“
• We might be more successful if only the math was taught and not the often complex concepts behind it.
• Stop the nonsense. Forget concepts and critical thinking and “delivering math as a community.” Give kids the math knowledge they need in life.

My 7th-grade math text has two pages using models explaining division of fractions that are more confusing than enlightening. All I get from students are deer-in-headlights looks. So, with this problem, 1/4 / 3/8, I teach a simple, straight-forward method.

Invert the divisor, changing 3/8, for instance, into 8/3.

Then multiply.

So 1/4 / 3/8 becomes 1/4 x 8/3 = 8/12 or 2/3.

I see no reason for spending a math period explaining why we do the computation like this. The goal is for kids to divide fractions, not to understand why we divide fractions that way. It’s like in football; you have to know how to block and tackle before you do the razzle-dazzle.

In 1998, the Fordham Foundation began publishing its State of the State Math Standards. The findings were bleak, and the 2005 results were no better. Headed by David Klein, math professor at California State University, Northridge, the study found most states have inadequate math standards.

The average state grade was a “high D.” Three got an A and three a B. Fifteen (including Illinois) received C’s, 18 got D’s and 11 got F’s.

Government funding for organizations such as the education division of the National Science Foundation also are responsible for bad math scores, Klein said. In 1999, for instance, the group recommended 10 “exemplary” and “promising” programs that Klein has labeled some of the worst math education programs in the country.

Klein wrote to urge withdrawal of the programs. His letter was signed by more that 200 mathematicians, including two former presidents of the Mathematical Association of America, seven Nobel laureates and winners of the Fields Medal, the highest award in mathematics. It was ignored.

According to the American School Board Journal, the National Council for Teachers of Math argues for a more conceptual approach using the following reasoning: “We live in a different world. We have different kids. We don’t know how to measure success. We have to learn to connect math to our children and to respect their ideas, and it’s important to think about how we deliver math as a community.”
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Kids who want to be scientists and mathematicians will have ample time for advanced math in 8th grade through high school and college.

What I see is if children understand fuzzy math they will do well in math and science because they understand the big picture the WHY. It is the children that are not math inclined that struggle with fuzzy math. Not all children or people have the same gifts. Why do we have to ram children or people into a SYSTEM that does not appreciate their gifts? A one size fits all SYSTEM doesn’t work.

You are correct that “A one size fits all SYSTEM doesn’t work.”, but that’s what we are given with our current public school system. We have to start funding the child and not the system. If this doesn’t change, and soon, we will doom another generation to being ignorant and unable to keep America great.

I was a Math Major in college. My wife and I homeschool and we deal with the affects of what fuzzy math did to my oldest child. They made A’s, yet still could not figure out math problems without much frustration. Since we started homeschooling and doing Direct Instruction things have changed. They now understand and can solve problems much faster. It was the fuzzy math that was the problem not whether the kid is good in math or not.

Fuzzy math doesn’t teach the how, it only teaches why. As the article points out and from my personal experience, you have to understand how or you don’t care about why.

No one who was not there during the early years of Head Start and FT can know how much your initiative, intellect and commitment contributed to the development of those programs. You simply shook off criticism and attempts at censorship and moved ahead, because you knew you were right and that what you were doing was important for kids. Lest you think that censorship is too strong a word, let me remind you that many in the early education field did not want your program included in FT. As confirming evidence for my personal experience and memory I cite the Head Start consultant meeting held in, I think, September 1966, in which a group of consultants, by their shrill complaints, stopped the full release of a Head Start Rainbow Series pamphlet which described an approach more direct than the approach favored by mainline early childhood educators&shyp;but one that was much less direct than the one you and Carl Bereiter were developingand using. The endorsement of Milton Akers for inclusion of “all” approaches in Head Start and FT Planned Variation made our task much easier. Ziggy, despite what some critics have said, your program’s educational achievement success through the third grade is thoroughly documented in the Abt reports. Your own followup studies have validated the program’s longer term success. I am completely convinced that more extensive studies of multiple outcomes,which the Department of Education has been unwilling to fund, would providea great deal more evidence for your program’s success.