John,

The reason we get beaten by many other countries is a complex issue. I saw an excellent presentation by Zalman Usiskin last year who discussed TIMMS, SIMMS and PISA and how many of the statistics collected were invalid or just comparing apples to oranges.

But one of our problems is that our students spend so little time in school compared to other countries. We have 25% less time for instruction, and this is probably the main reason kids don't practice enough and end up in 9th grade not knowing how to add fractions. We use an agricultural calendar to run our academic years, and we should have given that up 50 years ago.

Unfortunately, that will never happen: the unions won't allow it, because the teachers have entered into a kind of bargain: we'll accept the lousy wages if we get to work an abbreviated day and year. If we really wanted to improve achievement, we have to have more time for students to work, which means abandoning our outmoded calendar.

On another note, there was an interesting study done on "gut instinct" and mathematical achievement. Apparently, the facility to estimate answers was more highly correlated to mathematics achievement than ability to precisely compute numbers. Funny, we spend all these years teaching kids to get precise answers and in the end, it's the ones who just have that "instinct" for numbers that are doing all the achieving.

rmberkman-Please don't bash the teachers. I have no input whatsoever into our school calendar. Many of my friends and colleagues would love a year-round calendar. Change occurs when it begins at the grassroots level. Instead of painting all teachers or unions with one broad brush, please consider that it is not going to advance your cause even if it does help you get something off your chest.

Hi rmberkman,

You bring up some interesting points. I only got to Trig in high school and definitely it wasn't my strong suit. My son is a college freshman, majoring in Mathematics and Physics, and he wants to teach. I definitely find that as he goes farther in Math the more it leaves numbers and is looking at patterns. He's definitely not afraid of math--tutoring in the math lab during the semester and planning on teaching at some point.

I will have to leave you at the idea of leaving an agrarian calendar however. Maybe I should just homeschool, but I use the summers to do enrichment, and a year round calendar simply would not allow my kids to do all the things I plan.

Jennis - you are absolutely right about other countries requiring mastery before moving on to other concepts.

In the US, most states (CA and FL for example) require that 1st graders "master" up to 20 different math concepts. Most US curriculum attempt this by giving a very high overview, a bit of practice and then quickly moving on. Parents are told that if a child does not master a concept, the program will spiral back the following year.

The problem is that most kids cannot truly MASTER the concepts and their foundational knowledge and number sense is compromised. Many can hold it together through the elementary years, but in MS and HS fall apart when algebra is introduced.

The top scoring foreign countries, require that lower elementary students master 3-4 concepts each year. These students have a solid foundation. The long term scores speak for themselves.

My son's LD school is adopting the approach of the foreign schools. The school year is 180 days, just like everyone else. They have 49 minutes of math a day. Since this approach began 3 years ago, test scores have increased based on normative tests.

I agree that time on task would also be helpful. I wish that my guy had 90 minutes or so of math (as would the head of the math dept). But, even within the current school day and school year, there is much that schools can do to improve results.

Just as an FYI - my son's school is working with another LD school and two public schools to see if they can implement this approach with similar results. The early results say that so far, so good.

I'm reading Jo Boaler's wonderful book on mathematics education, "What's Math Got To Do With It?" Boaler is a researcher who has worked in the UK and the US and performed longitudinal studies of children engaged in mathematics education. It's a vital book for understanding where mathematics education is today, and where it should be going. Has anybody read it?

I have only started to master basic mutilpication by reviewing math homework with my children. I too was a math student pushed to each new concept without understanding or passing the previous lesson in the first place. I'm ebarrassed at how poor my skills are and my children struggled too also.
We did use www.jumpmath.org which has been a godsend. They are a charitable orginaztion to promote numeracy. "JUMP Math believes that all children can be led to think mathematically, and that with even a modest amount of attention every child will flourish. By demonstrating that even children who are failing math or are labelled as slow learners can excel at math, we hope to dispel the myths that currently prevail. We offer educators and parents complete and balanced materials as well as training to help them reach all students".

I tried looking the book up, and it's not released in the US until June 30th. Did you get an advance copy?

Can you talk about what interests you in the book?

Ah, I forgot - yes, I did get an advanced copy because I met Dr. Boaler at a mathematics conference. What I like about the book is that it is non-hysterical and very reasoned, which seems to be lacking in a lot of discussions about education, especially in mathematics. She cites relevant data, provides references and never stoops to the smears or misrepresentations that seem to be characteristic of the people who are taking part in the "math wars," which is a silly label to begin with.

rmberkman,

You do realize, hysteria sells. And truthfully, when people are talking about their life's work (the teachers), or their offspring (the parents), it does get a little hysterical.

My kids are 10 years apart. My son's the college freshman and my daughter is in 2nd grade. My son is already a Math/Physics major, absolutely in love with his subjects, but he was definitely torn in high school whether to follow that path or his love of film and editing. He decided for himself, he could edit "for fun" and he'd follow a math/physics path to a career.

My daughter has the benefit of an additional adult in her life (her brother), and I'll continue to help open her eyes to math the only way I can--through cooking and recipes, through architecture and building design, and through sitting with piles of flashcards and some math web sites. I definitely don't vilify math, and truthfully the only time my son gets hives is if anyone mentions Arithmetwist, but that's another story :)

Great question! My daughter asked me this question when she turned seven. I think Mathematics is a way life and it should be taught as it relate to all aspects of life. Most people use it from the time they wake up until they close their eyes sleeping.

Our state teacher of the year was selected based on the non traditional way she taught Mathematics. She brought shop, bank, business, hospital, gas station, government, and all sciences into her Mathematics classroom.

I practice the same way when I am helping my daughter in any problem in Maths and it makes more sense to her than memorizing the time table and others.

Thanks for sharing!

I'm one of "Imported scientist" from Asia.
I was a little surprised that American engineering students were not really good at Math. I ended up get a job and live here and I beleive that is partly because US fail to teach kids to math and science..
Now, I have a kid in a kindergarten. At first, I was worried about she might not learn enough math. Then, I got totally confused when I looked at their math curriculum. The level of math they said they will teach in each grade level is not low and it has some hard math concepts very early. Which make me wonder, is US math education improved? Then, I reallized what she learned in her class is not really much. So, at this point, I got totally confused. And some of comments I get here is really helpful for me to understand situation - "They taught introduce difficulat concept ealry, but not really expect students master it.".. This feels funny.
In my opionnin, math is a language for science and engineering (Mathamatician will have differnt opionin, since they will need more depth. Actully my husband is a mathamatician). Like every other langugate, understanding is not enough to master it. You have to practice it and use it. What is the best way to do it, I don't know.
At this moment, all my concern is how much math my kids need to know to have enough to compete globally when they grow up. Whether or not, I can trust their school to do the job or I have to teach them beyong what school teaches..

Msbear,
I think you are saying exactly what my son's school is saying. Understanding is not mastery. Mastery is necessary. We teach a lot of complicated stuff early - and maybe the kids do not really learn it.

Thus the foundation of sand.

Thank you for sharing your prospective - because the Asian countries do score better and do approach math differently. I think that the US can learn from this.

Life is not always about working harder (although hard works helps). It is also about working smarter. And based on what I have learned from consultants working at my son's school, we don't approach math in a "smart" way.

BTW - since your child is young, and you are concerned about her mastering the "basics", you may be interested in this software: www.symphonylearning.com/

My son's school is using this as a diagnostic and teaching tool to insure that the students have a solid number sense, master operations, and build fluency.

Thanks for your input - it is very helpful.

This Jo Boaler book is very interesting, and when you set it alongside other books about the cognitive aspects of mathematics, a lot of our current practice falls short. As it turns out, "computational fluency" is not about repeating an algorithm over and over again - it is the ability to work flexibly with numbers. For example, it is being able to see 92 - 68 and say, "Okay, 90 = 60 = 30, and 2 - 8 = -6, so the answer is 24" or "92 - 68 is the same as 94 - 70, so the answer is 24" or "68 to 70 is 2, + 20 = 90 + 2 = 24" or a number of other ways. Memorizing quickly forgotten algorithms is the wrong path to learning computation, yet we still pretty much teach it that way year in and year out, and kids get the wrong message about what mathematics is about and how creative it really is.

Hi, I am a Kindergarten teacher. Several years ago, I was terrified about teaching math. I struggled with math myself throughout my entire educational learning experience. I was so delighted when my Principal signed on for an extremely talented Math Consultant to come in and work with our staff. Math finally became fun and I couldn't wait to get back to the classroom and teach math in a new way. We moved from teaching math from the abstract to the concrete in all grade levels with scaffolding to help move to the abstract. This works because not only did our math improve, but we are now a Nationally Distinguished Title I School. Every year we review our test scores per grade level from Kindergarten through the 5th grade to analyze where each teacher was the strongest and the weakest. This helps educators to put more emphasis on weaker skills for the following year. It also helps us to communicate with colleagues to find gaps in our teaching looking from K-5th to see where we are missing the boat!

I love math. I have always been good at it yet I am learning more every day. There are great and interesting web-sites about math and they are showing different methodology. My husband has found many live examples on You Tube about how to use math in extraordinary ways. I have found them intriguing. My daughters school also teaches more of a pattern based method of math. I just makes more sense. They use Math Consultants at my daughters school. From what I can understand, they gradually go through the curriculum in 3 week steps. If at any time the teacher or students struggle they can contact the consultants for expert help. As they master each concept they move onto the next.

Check out the clips on this web-site that my daughter school uses for teaching the students and they encourage parents to use it too.

www.schultzcenter.org/mathvideos.shtml

We, as a nation, are falling behind in many areas. We have to think outside the box to help our children succeed. They are the future and if it means a new innovative way of learning then, so be it. It is hard to bend our already formed opinions and techniques but, this stuff works. How can we teach forward thinking if don't open our minds to the possibilities. Due to the population of other counties like India and China their top 1% students out number all of our students combined. No wonder so many companies are trying to outsource work and projects. We have to give our kids a competative edge. I want my children to be successful in our future world as we become more of a global society. I am very interested in how other countries are approaching learning. I am trying to learn quickly so that I can pass it on.

Kids today are not learning as they learned fifty years ago. Not even close. Most (almost all) public school systems advance middle school children to the next grade irrespective of their performance. NONE of the countries who are kicking our tails in international tests do this. They ENSURE that the students nail their calculation skills--basic math operations, including with decimals and fractions--before they are advanced, and before they're able to use calculators.

Don't minimize the importance of developing these skills: they lead to the instinct for numbers that makes more complex problem-solving possible. The repetition of adding fractions with unlike denominators, or doing long division, is vital.

Anyone who makes excuses for other countries' outperforming us should look hard at the data: our kids don't get basic math; the issue is not about 21st century unpreparedness. Further, even if countries weed out worst-performing students, the fact remains that even our best kids cannot compete with their best.

Fifty percent of my incoming ninth-graders cannot add fractions; it has been this way for years. They have been advanced through middle school with no real REQUIREMENT--just "expectations" and "benchmarks"; more sensible countries laugh at this. They know, as many of our teachers and parents do know, that such a policy sabotages each subsequent classroom, putting in it kids who are not ready to learn what that teacher is supposed to be teaching. Thus, even prepared kids lose ground. By the end of eighth grade, the result is catastrophic.

An added result is that there is an unwarranted sense of security on the part of parents as well as students, that each must be doing okay, since they are being promoted. Thus, the one strong bit of leverage which schools held over parent behavior has been thrown out.

But, those who accept social promotion (though they refuse to call it that) myopically focus on just one kid--the one who might've been kept back--and refuse to consider the consequences to an entire curriculum, an entire school system.

We're teaching as we did fifty years ago? I wish.

John Ennis

This conversation has gotten quite lively, which confirms two things: first, people are actually interested in math and how it is taught, and people are still frustrated about how math is taught.

I'll address a few of the comments, since I started this thread, in no particular order:

• Math Consultants: this is one of the most important things a school can do to improve the level of mathematics instruction in a school. Beyond a single methods course that teachers take as part of their degrees, most teachers have little or no training in the teaching of mathematics. Their focus is usually on language arts and social studies. With so little understanding of the theory and practice of teaching mathematics in elementary school, it is no wonder children get a very rudimentary understanding of mathematics when they enter middle school.

• Mastery and understanding are not mutually exclusive; the research shows that both are necessary to develop mathematical competency. Our problem in this country is not that we lean too far in one area or another, but that we don't have enough time to do both. We have the shortest school day and school year of any industrialized country in the world. Our school year is 1/3 shorter than Japan, Singapore, China and Korea. Think about this: each year, our students spends 33% less time than other countries mastering algorithms, engaging in problem solving, and learning computational facts (and much more time during the summer to forget all that information!) Our lagging performance will not change unless our children spend more time in school.

On "outsourcing" to India: the fact is, we export technical jobs to other countries for the same reason that we have "call centers" there, which is that it is much cheaper. Why pay someone in the US $10 per hour to answer phones when you can do it in Bangalore for $2? It's the same with writing computer code: a software designer in the US earns $50 to $75,000 a year; in India, you can hire one for about $25,000. Since software is a universal language and there are no shipping costs associated with sending it across continents, companies choose the place where labor is cheapest. If there is a problem here, it is capitalism which is to blame.

But it does sound like schools are stepping up to the plate and doing their part to help children progress in mathematics.

The fact that our school day and school year in the US is shorter, is a HUGE math problem in itself. Most schools in the US devote one period a day to math - typically 45 minutes to an hour for 180 days.

Mastery and understanding takes time on task. If we are spending 30% less time on the task, it is not surprising that overall achievement is lower than other nations. Curriculum aside - this time discrepancy could be an enormous factor in the over all lower math scores in the US.

But - there is a lot of Resistance to extending learning time.

I'm not sure if we can have it both ways - shorter time at school and higher scores. There is only so much excellent teaching and hard work can do.

If I were to solve the problem, I would try to identify the major drivers of successful performance and work on these aspects of our educational system first. I'd like to find out what variables make the biggest difference, which help to move other factors forward more quickly, which are easy and cheap to implement. The issue needs to be considered as a system - and with all stakeholders working together to solve the problem. I'm don't think this is happening yet and until it does, thoughtful, sustained change won't happen. (in math or any other area of education)

I was reading the information about mathematics being taught in other countries and the need of extending school hours and the school days. This is being discussed heavily right now in my district. As a teacher, I feel frustrated because we are comparing students in the U.S. to students in other countries. It is true that students in other countries have a more well-developed foundation in math due to the extensive time on task of learning math, however; we must remember that not all students are allowed to attend school in other countries. Only the students who are very bright with usually high IQ's attend school. Compared to U.S. schools where everyone attends school, thank goodness, because the laws demand it, we are asking teachers to do almost the impossible. Because not all students learn the same way, or at the same pace, U.S. teachers find teaching very difficult. In many cases we are continually dealing with issues such as single parent families, drug babies, ADD, ADHD, obsessive compulsive disorders, emotionally disturbed, handicapped, down sydrome, and the list goes on and on. Not only do we have to make an educational plan for every child within the classroom, but we also have to make sure they pass the yearly test because our jobs are on the line. It is no wonder students in other countries do better in testing areas because they have completely cut out most of the kids which most teachers find difficulty teaching in the first place. People may say whatever they want about our educational system in the U.S., but as far as I am concerned their is great teaching going on everyday across the country! Sadly, it is true we are lagging behind when it comes to outsourcing jobs in the U.S. to overseas workers. But let's face it, we are not comparing apples to apples and oranges to oranges.

I partly agree with energizer comments. It may not be fair to compare US to Asian country. But teacher in Asian country also faces students with broad capability. In my experience(I'm Asian), about 3rd grade some of students clearly starting to fall behind in math. Over US, teachers have advantages because they can just iignore these group. Education policy does not really interested in this group (they are not bright, who cares attitude), and parents of these students felt shameful, do not even think about raise their voice to teachers. I do not want to generalize this to all Asian country and this is more than 20 years ago. This is very sad situation and I'm glad my kids are not growing up under that circumstances.

However, in US I feel like things reversed. Need of bright kids(or sometime regular kids) may be ignored and they are not challenged enough, especially in math. If they are not challenged enough, math skill will not be improved and the worst part of it is they even do not know their math skill is not enough for some carriers (How do they know, if they got A in math in all of their K-12 years and meet the all the milestones).

And another problems is in reality, it does not matter whether comparison is fair or not, there is huge gap between in math performance in international students in US students. Trust me on this, I'm teaching Engineering in University. Whatever reason is after K-12 math education, math skills of our kids are not developed enough and this is not because they are less capable of, but because how US school teaches and VALUES math..

Well said

I read Jo Boaler's book, based on the recommendations in this post. I was right with her until I read the chapter on Ability Grouping. Her arguments against AG assume that high level and low level students are eager to work together towards the same goal. She assumes all children and parents are motivated. Its just not so. I like her ideas of group problem solving instead of just rote learning, but there really needs to be a mix of both.

I have noticed that schools broadly cover many math concepts in a school year, without mastery of any. The math consultant idea and year round schedule are possible solutions to this problem.

Two things must be admitted: 1) our kids, by every measure available, do not know basic math as they did in past generatations (high school graduates not knowing basic calculations, on a large scale, is a new phenomenon), and 2) our best students can't compete with the world's best--this is a separate issue from the question of whether their AVERAGE students are better because of dropping the worst-performing kids from the mix.

The elephant under the rug, in all the discussion about methods and theory, is the impossibility of holding kids to a standard of performance, when, if performance and learning are not adequate, students are nevertheless advanced to the next grade.

That is the most stark difference between how we taught when we were more successful, and how we teach now. The list of reasons other countries outperform us must have this at the top.

John