So I was talking to another local Mom about choosing schools for our kids. Part of the conversation went like this:

OtherMom: "I've never heard anything good about Natural Friends."

(Then she remembered that my younger daughter attends Natural Friends, and stopped, looking embarrassed.)

Me: "Really? What do you hear about Natural Friends? I want to know!"

OtherMom: "People say it's loosey-goosey, and the kids just do what they want."

There's a part of me that responds "I wish!", and another part that writes a blog post about it.

On the one hand, Natural Friends is loosey-goosey enough to hang in there with my sometimes difficult younger daughter, and that's a good thing for us.

On the other hand, they apparently haven't gotten Alfie Kohn's memo on the subject of homework, which they start assigning nightly in the FIRST flippin' GRADE.

On the third hand, the academics at Natural Friends can be pitiful, especially math. Just today I started working Younger Daughter through Singapore Math 1B, and if she stays at Natural Friends I know I will have to do a great deal more. So far she likes the Singapore Math workbook (knock wood.)

My dream school would be loosey-goosey and laissez-faire in re compliance issues (the classic triumvirate of "sit down, shut up and do what you're told"), but crystal-clear in re academic issues like content knowledge and procedural fluency.

Is there such a school? Probably not. I think the reason is human psychology. The kind of teacher who wants to provide nurturing and tolerance to children tends to be the kind of teacher who isn't very academic. The kind of teacher who cares about academics is often also the kind of teacher who wants to see compliant, on-task kids.

It is a source of constant amazement to me how often schools get these issues exactly wrong; that is, they require unquestioning obedience and endless hours of work (from kids and parents both!) without actually delivering content knowledge. That is the worst possible bargain.

Kid-Friendly schools are schools that put kids and their needs first.

## Monday, February 28, 2011

### Loosey-Goosey

## Thursday, February 24, 2011

### What is Student Engagement?

(from Trailblazers Math, grade 2.) |

Unfortunately, life is not that simple. It is possible to be mentally engaged while sitting quite still (e.g., while watching a movie), and it is also possible to be mentally absent while moving around (e.g., daydreaming while folding laundry.) You can make kids move around, but that doesn't necessarily mean that they're interested in what they're doing, or that they're learning anything in particular. A bad project is less engaging than a good lecture.

## Tuesday, February 22, 2011

### I Have Measured Out My Life with Coffee Spoons

For I have known them all already, known them all:—

Have known the evenings, mornings, afternoons,

I have measured out my life with coffee spoons;

I know the voices dying with a dying fall

Beneath the music from a farther room.

(from

We find that in doing measurement activities, children learn about number. It’s a two-way street. Our approach is not, “Well, we’ll teach the kids about number, and once they understand number, then we can teach them about measurement, because measurement is based on number.” We find it works the other way, too: by doing various measurement activities, which are very engaging for the students, they’re building their number ideas.

(from Math Trailblazers, quoting one of the developers.)

I think the program is pretty good with measurement. Kids like to measure things, and the program builds on that; it builds on their interests.

(from Math Trailblazers, quoting a 3d grade teacher.)

Have known the evenings, mornings, afternoons,

I have measured out my life with coffee spoons;

I know the voices dying with a dying fall

Beneath the music from a farther room.

(from

*The Love Song of J. Alfred Prufrock*, by T. S. Eliot.)We find that in doing measurement activities, children learn about number. It’s a two-way street. Our approach is not, “Well, we’ll teach the kids about number, and once they understand number, then we can teach them about measurement, because measurement is based on number.” We find it works the other way, too: by doing various measurement activities, which are very engaging for the students, they’re building their number ideas.

(from Math Trailblazers, quoting one of the developers.)

I think the program is pretty good with measurement. Kids like to measure things, and the program builds on that; it builds on their interests.

(from Math Trailblazers, quoting a 3d grade teacher.)

"Kids like to measure things?" Really? I've never noticed my kids show any particular interest in measuring. I have noticed, however, that Trailblazers spends an unbelievable amount of time and effort on measurement, from the Bouncing Ball lab to the above worksheet, part of an entire section that has the kids measuring random objects in hands and cubits (forearm lengths). Why? In order to demonstrate what a bad idea it is to use non-standard units!

## Monday, February 21, 2011

### Parent-Teacher Conferences in China

(from Country Driving, by Peter Hessler.)

During the first six weeks of school, Wei Jia distinguished himself by an early interest in English, an unruffled demeanor, and a complete refusal to sit still. In a Chinese classroom, the group is the foundation for every endeavor, and each child always knows his place within that organization ... Peer discipline is crucial — children who misbehave are often asked to stand before the class, where other students help the teacher criticize the guilty party. At the beginning none of this seemed to faze Wei Jia. Having missed kindergarten, he had no concept of school routines; he talked out of turn and he played with pencils at his desk. He lost school assignments and he forgot homework. He wandered the classroom during lessons ...

These infractions, along with a host of others, were described at the first parent-teacher conference. In Chinese schools, such meetings are communal: all of the parents attend at once, and all of them listen as the teacher summarizes each child's performance. The good students are praised, the bad students are criticized, and the listening parents are socialized in much the same way as the children: by the power of the group. There is no greater loss of face than hearing in public that your child does poorly at school. And the bad ones always receive the most attention ... And Wei Jia — he was the fidgeter, the classroom-wanderer, the kid who played with pebbles in the principal's presence.

During the first six weeks of school, Wei Jia distinguished himself by an early interest in English, an unruffled demeanor, and a complete refusal to sit still. In a Chinese classroom, the group is the foundation for every endeavor, and each child always knows his place within that organization ... Peer discipline is crucial — children who misbehave are often asked to stand before the class, where other students help the teacher criticize the guilty party. At the beginning none of this seemed to faze Wei Jia. Having missed kindergarten, he had no concept of school routines; he talked out of turn and he played with pencils at his desk. He lost school assignments and he forgot homework. He wandered the classroom during lessons ...

These infractions, along with a host of others, were described at the first parent-teacher conference. In Chinese schools, such meetings are communal: all of the parents attend at once, and all of them listen as the teacher summarizes each child's performance. The good students are praised, the bad students are criticized, and the listening parents are socialized in much the same way as the children: by the power of the group. There is no greater loss of face than hearing in public that your child does poorly at school. And the bad ones always receive the most attention ... And Wei Jia — he was the fidgeter, the classroom-wanderer, the kid who played with pebbles in the principal's presence.

## Friday, February 18, 2011

### northTOMom on Constructivist Math

(From the comments to The Birds, the Bees and Constructivist Math.)

... for me the key issue is not whether a math program promotes the retention of mathematical facts or concepts, but rather whether or not it stimulates or enables further learning. I think constructivist math programs, by continually frustrating kids, and by denying them basic competence, make it difficult for students to know whether or not they like math or have any real interest in it.

... there are some constructivists who believe that the end—as well as the beginning—of math instruction must always be real world applications. I disagree with this, since to me math is a language, and any pleasure I once derived from it came from this aspect of it.

... for me the key issue is not whether a math program promotes the retention of mathematical facts or concepts, but rather whether or not it stimulates or enables further learning. I think constructivist math programs, by continually frustrating kids, and by denying them basic competence, make it difficult for students to know whether or not they like math or have any real interest in it.

... there are some constructivists who believe that the end—as well as the beginning—of math instruction must always be real world applications. I disagree with this, since to me math is a language, and any pleasure I once derived from it came from this aspect of it.

## Thursday, February 17, 2011

### The Birds and the Bees and Constructivist Math

Years ago, parents could buy little picture books to read to their kids when the tykes asked "Where do babies come from?". Designed for thoroughly embarrassed parents (isn't that all of us?), the books went through the conceptual habits of most of the animal kingdom (insects, fish, birds ...) before arriving at humans. This way, blushing Dad had time to work up to the really difficult stuff, and if he was lucky, the kid might have fallen asleep!

My college biology teacher told us that some genius did a follow-up study. It was very simple: he went around to kids whose parents had dutifully read them the book, and asked the kids "where do babies come from?" He discovered that the kids, understandably, had gotten the different species all mixed up. A typical answer:

"Daddy holds the babies in his mouth until it's time to go to the hospital."

Constructivist math takes a similar approach, with similar consequences. When the kid asks "how can I multiply two big numbers together?", constructivist math behaves like the blushing Dad, loosening his shirt collar with one finger while replying: "Here's an ancient lattice method, and over here is a partial products method, and oh, look! let's measure our armspan!" while never getting around to the method that everyone actually uses.

Since the kids don't really understand any of the methods, they tend to combine them, using steps 1 and 2 of one method, followed by 4 and 5 of another method, and coming up with the wrong answer after a great deal of effort and frustration. I say, cut to the chase! Just teach them the standard algorithm.

My college biology teacher told us that some genius did a follow-up study. It was very simple: he went around to kids whose parents had dutifully read them the book, and asked the kids "where do babies come from?" He discovered that the kids, understandably, had gotten the different species all mixed up. A typical answer:

"Daddy holds the babies in his mouth until it's time to go to the hospital."

Constructivist math takes a similar approach, with similar consequences. When the kid asks "how can I multiply two big numbers together?", constructivist math behaves like the blushing Dad, loosening his shirt collar with one finger while replying: "Here's an ancient lattice method, and over here is a partial products method, and oh, look! let's measure our armspan!" while never getting around to the method that everyone actually uses.

Since the kids don't really understand any of the methods, they tend to combine them, using steps 1 and 2 of one method, followed by 4 and 5 of another method, and coming up with the wrong answer after a great deal of effort and frustration. I say, cut to the chase! Just teach them the standard algorithm.

## Wednesday, February 16, 2011

### Nel Noddings re: Homework

From Critical Lessons: What our Schools Should Teach, by Nel Noddings:

Students need to believe that they should reflect, evaluate, and make authentic decisions. That means perhaps rejecting some of what the adult community advises them to do. It means questioning some practices that seem unhelpful or even damaging. Must there be homework every night? Why? What are students learning from this practice? Is the assigned homework necessary for meaningful understanding of the subject matter? Or is the object to teach docility and obedience to authority?

... If we educators are thoughtful, many of us will admit that much homework is meaningless, even absurd.

Students need to believe that they should reflect, evaluate, and make authentic decisions. That means perhaps rejecting some of what the adult community advises them to do. It means questioning some practices that seem unhelpful or even damaging. Must there be homework every night? Why? What are students learning from this practice? Is the assigned homework necessary for meaningful understanding of the subject matter? Or is the object to teach docility and obedience to authority?

... If we educators are thoughtful, many of us will admit that much homework is meaningless, even absurd.

### No Homework, the Wrong Way

Here's my latest e-mail to the Head of School at Natural Friends.

I read the [newspaper] article about the second-grade mock economy. I liked everything about it until I got here:

"Students also can save money for luxuries, such as a no-homework pass ($65)..."

If the homework was necessary for the child's education, you would never give a pass, right? Conversely, if the homework is not necessary for the child's education, why assign it at all?

Think of the message that the kids are being sent -- "Homework is an unnecessary chore that we assign for no other reason than because we like to make kids do stuff. We know you hate it, so for the right price we're willing to let you off the hook."

Second grade is way too young for homework in any case. It's an extremely rare child of that age who can consistently remember to do homework, so it really becomes Mom's responsibility (nobody criticizes Dad if the homework wasn't done.) Speaking as Mom, I have enough opportunities to fight with my kids, thank you very much, and I don't need the school to provide more.

I hope you will consider abolishing homework for the lower grades. If you can't abolish it, how about letting parents opt out? Thank you. -- FedUpMom.

I read the [newspaper] article about the second-grade mock economy. I liked everything about it until I got here:

"Students also can save money for luxuries, such as a no-homework pass ($65)..."

If the homework was necessary for the child's education, you would never give a pass, right? Conversely, if the homework is not necessary for the child's education, why assign it at all?

Think of the message that the kids are being sent -- "Homework is an unnecessary chore that we assign for no other reason than because we like to make kids do stuff. We know you hate it, so for the right price we're willing to let you off the hook."

Second grade is way too young for homework in any case. It's an extremely rare child of that age who can consistently remember to do homework, so it really becomes Mom's responsibility (nobody criticizes Dad if the homework wasn't done.) Speaking as Mom, I have enough opportunities to fight with my kids, thank you very much, and I don't need the school to provide more.

I hope you will consider abolishing homework for the lower grades. If you can't abolish it, how about letting parents opt out? Thank you. -- FedUpMom.

## Tuesday, February 15, 2011

### Grandparents

We're having a grandparent moment in the blogosphere, from the New York Times' typically navel-gazing Motherlode article to Katie Allison Granju's cheerful confession that her ability to juggle family and career is because of the daily childcare help she receives from her mother-in-law. In the news, we've got the Kelly Williams-Bolar case, in which a single mother claimed her children resided at their grandfather's house. And of course we have a First Family with a First Grandmother in residence.

My husband and I are both descendants of sparse, scattered families. None of my grandparents was a daily (or weekly, or even monthly) presence in my life as a child, and the same is true of my children. None of my siblings or parents lives in the same state that I do, and this is true for my husband, my parents, and my husband's parents as well. Many professional-class families look this way, because professionals follow their careers wherever they might take them, and wind up living far from their family of origin.

What are we missing when we miss daily connections with extended family? We miss continuity and a sense of perspective. It's easier to get caught up in a competitive, destructive pre-professional rat race when your whole world consists of kids competing with each other to build the best college application, and parents who are constantly stressed out by work.

My husband and I are both descendants of sparse, scattered families. None of my grandparents was a daily (or weekly, or even monthly) presence in my life as a child, and the same is true of my children. None of my siblings or parents lives in the same state that I do, and this is true for my husband, my parents, and my husband's parents as well. Many professional-class families look this way, because professionals follow their careers wherever they might take them, and wind up living far from their family of origin.

What are we missing when we miss daily connections with extended family? We miss continuity and a sense of perspective. It's easier to get caught up in a competitive, destructive pre-professional rat race when your whole world consists of kids competing with each other to build the best college application, and parents who are constantly stressed out by work.

## Monday, February 14, 2011

### The Case of Kelly Williams-Bolar

Here's the strange case of a woman who actually did jail time for the crime of falsifying records so that her kids could attend a better public school. There's a decent article about it at the Huffington Post here. The embedded NPR interview is also worth listening to.

Kelly Williams-Bolar, of Akron, Ohio, used her father's home address to enroll her kids in a desirable school district, rather than her neighborhood district. As she explains in the NPR interview, her kids spend a great deal of time at their grandfather's house. And as many posters have pointed out, the grandfather has been paying property taxes that support his district's schools for years.

What a mess our public education system has become. There are so many issues here I scarcely know where to begin. I'll just hint at a few of them:

1.) Race. Kelly Williams-Bolar is black, and lives in a mostly black school district. The district she wanted to send her kids to is mostly white.

2.) Changing family structures. Kelly Williams-Bolar is a single (divorced) mother, and her children's father is hardly mentioned as part of this story. Clearly, her own father is more present to her kids than her ex-husband. It's doubtful that her children will be able to call on their father for help as adults, as Kelly W.-B. has done.

3.) Downward mobility. The grandfather is apparently in better financial shape than the single mother.

4.) What is public about public education? If kids are strictly segregated by race and income, with violators prosecuted, why do we call it "public"?

Readers? Your thoughts?

Kelly Williams-Bolar, of Akron, Ohio, used her father's home address to enroll her kids in a desirable school district, rather than her neighborhood district. As she explains in the NPR interview, her kids spend a great deal of time at their grandfather's house. And as many posters have pointed out, the grandfather has been paying property taxes that support his district's schools for years.

What a mess our public education system has become. There are so many issues here I scarcely know where to begin. I'll just hint at a few of them:

1.) Race. Kelly Williams-Bolar is black, and lives in a mostly black school district. The district she wanted to send her kids to is mostly white.

2.) Changing family structures. Kelly Williams-Bolar is a single (divorced) mother, and her children's father is hardly mentioned as part of this story. Clearly, her own father is more present to her kids than her ex-husband. It's doubtful that her children will be able to call on their father for help as adults, as Kelly W.-B. has done.

3.) Downward mobility. The grandfather is apparently in better financial shape than the single mother.

4.) What is public about public education? If kids are strictly segregated by race and income, with violators prosecuted, why do we call it "public"?

Readers? Your thoughts?

## Thursday, February 10, 2011

### Guest post: George W. Bush, School Superintendent

[From Chris, originally posted at A Blog About School]

When I recently wrote about how our school makes the kids wait outside in the cold every morning, standing in line, until schools starts, northTOmom commented, “I suppose when I complain about our schools in Toronto,” she wrote, “I should be grateful for these small blessings: longish lunches/recesses and fewer arbitrary draconian rules than in the schools of Iowa City! (I thought it was a progressive city!)”

I’m never sure exactly what “progressive” means, especially in the context of education. (One of No Child Left Behind’s key sponsors, after all, was Edward Kennedy.) But, for what it’s worth, Johnson County is one of the bluest counties in America. Barack Obama won seventy-five percent of Iowa City’s popular vote. Iowa City has a reputation as an artsy, intellectual, socially liberal college town; the Advocate even named it America’s third most gay-friendly city. So why do so many features of our public schools seem like they could have been designed by the most authoritarian, anti-intellectual, corporate-captive elements of America’s political spectrum? (Examples here, here, here, and here.)

One could speculate: Maybe it’s because what we think of as progressive educational ideas are just not that widely shared, even among people who consider themselves liberal. Maybe academics, having gotten where they are on the strength of their standardized-test-taking skills, are happy to support test-driven educational policies. Maybe it’s because Iowa City, source of the Iowa Test of Basic Skills and home to ACT and Pearson, is the standardized testing capital of the world.

But those speculations, even if there’s some truth to them, are beside the point. The fact is: What goes on in Iowa City public schools has virtually nothing to do with what the citizens of the Iowa City district want or believe. Turnout in school board elections ranges between three and six percent. Once elected, the school board serves largely to implement policies that the federal and state governments have imposed on it. The school board hires a superintendent to carry out the day-to-day administration of the schools, and he then gives a good deal of discretion to individual principals. By the time the superintendent and principals are making decisions about what actually goes on in the schools, there is very little reason for them to worry about what Iowa Citians think. They are far more likely to concern themselves with the incentives and penalties built into the federal No Child Left Behind Act; if they don’t raise those test scores, they could lose their jobs. So test-prep it is, with all the accompanying emphasis on creating quiet, obedient followers-of-instructions who will be great low-level employees some day. And progressive education -- with its concern for critical thinking, for the humanities, for the autonomy and basic dignity of the kids -- be damned.

In other words, there’s a reason our school district’s policies seem like they could have been designed by George W. Bush and Dick Cheney: because they were. Set aside, for the moment, your own political leanings. Is it really a good idea to impose a nationwide approach to education on every community, regardless of whether that approach conflicts with a community’s own values? If that’s “conservative,” then the meaning of that word sure has changed.

Related post here.

When I recently wrote about how our school makes the kids wait outside in the cold every morning, standing in line, until schools starts, northTOmom commented, “I suppose when I complain about our schools in Toronto,” she wrote, “I should be grateful for these small blessings: longish lunches/recesses and fewer arbitrary draconian rules than in the schools of Iowa City! (I thought it was a progressive city!)”

I’m never sure exactly what “progressive” means, especially in the context of education. (One of No Child Left Behind’s key sponsors, after all, was Edward Kennedy.) But, for what it’s worth, Johnson County is one of the bluest counties in America. Barack Obama won seventy-five percent of Iowa City’s popular vote. Iowa City has a reputation as an artsy, intellectual, socially liberal college town; the Advocate even named it America’s third most gay-friendly city. So why do so many features of our public schools seem like they could have been designed by the most authoritarian, anti-intellectual, corporate-captive elements of America’s political spectrum? (Examples here, here, here, and here.)

One could speculate: Maybe it’s because what we think of as progressive educational ideas are just not that widely shared, even among people who consider themselves liberal. Maybe academics, having gotten where they are on the strength of their standardized-test-taking skills, are happy to support test-driven educational policies. Maybe it’s because Iowa City, source of the Iowa Test of Basic Skills and home to ACT and Pearson, is the standardized testing capital of the world.

But those speculations, even if there’s some truth to them, are beside the point. The fact is: What goes on in Iowa City public schools has virtually nothing to do with what the citizens of the Iowa City district want or believe. Turnout in school board elections ranges between three and six percent. Once elected, the school board serves largely to implement policies that the federal and state governments have imposed on it. The school board hires a superintendent to carry out the day-to-day administration of the schools, and he then gives a good deal of discretion to individual principals. By the time the superintendent and principals are making decisions about what actually goes on in the schools, there is very little reason for them to worry about what Iowa Citians think. They are far more likely to concern themselves with the incentives and penalties built into the federal No Child Left Behind Act; if they don’t raise those test scores, they could lose their jobs. So test-prep it is, with all the accompanying emphasis on creating quiet, obedient followers-of-instructions who will be great low-level employees some day. And progressive education -- with its concern for critical thinking, for the humanities, for the autonomy and basic dignity of the kids -- be damned.

In other words, there’s a reason our school district’s policies seem like they could have been designed by George W. Bush and Dick Cheney: because they were. Set aside, for the moment, your own political leanings. Is it really a good idea to impose a nationwide approach to education on every community, regardless of whether that approach conflicts with a community’s own values? If that’s “conservative,” then the meaning of that word sure has changed.

Related post here.

## Wednesday, February 9, 2011

### Bouncing Ball Math Lab

So far, the Head of School at Natural Friends seems to have decided that what their math program really needs is better PR. To this end, he included a message from the math specialist in the school's bulletin. The math specialist has worked at Natural Friends for many years while the kids were graduating right into remedial math at their next school. She is a lot more likely to be part of the problem than part of the solution, IMHO. Here's the specialist's account of a 4th-grade "math lab":

Teacher 4 holds out a tennis ball a little above his waist height and asks his class, "Do you think you could predict how high this ball would bounce if I dropped it from 1 meter? "

Students suggest, "60 cm." "1 ½ meters.' 'To the ceiling."

"What could we do to make reasonable predictions?"

An animated discussion follows. The students know from past experience that they will have to experiment by dropping their ball a number of times from various heights to be able to make a good prediction. They decide to work in groups of three . Each group gets a ball and agrees to drop it several times from 40 cm, 60 cm and 120cm. They purposely omit dropping it from 100 cm (1 m) because they are intent on predicting the answer to Teacher 4's question before actually measuring it. From the many labs they have done in earlier grades they know that they will need to take at least three trial drops from each height and then find the average in order to get a more accurate result.

And so another Math Lab begins. By now the students are familiar with the process of planning an experiment, collecting data, graphing their data, and finally analyzing their results and testing their predictions.

These fourth graders have just learned how to calculate the mean and they will use this new skill to find the average of the three drops from each height. (In previous labs they usually took the median [the middle number of the three trials] as the average.) This lab will reinforce skills such as measuring, graphing, making 'best fit lines', and working cooperatively. It will also enable students to practice their new ability to find the mean.

There is a lively hum in the class as they students spread around the room and begin to plan their group work. They tape their meter sticks to the wall and practice dropping the ball and reading the results while the ball is in motion. Then they are ready to carry out the experiment, record the data and graph their results..

Later they find a 'best fit line' for their data points, so that they can predict how high the ball would probably bounce if it were dropped from exactly 1 meter. They then test their hypothesis by dropping the ball from 1 meter and compare this with their predictions.

This math lab is one of eight labs fourth graders will do during this academic year. For each lab, students sketch their plan, gather their materials, collect data in a data chart, then graph and analyze the data.

We have found these labs to be an excellent way for students to use and extend the mathematics that they are learning in a meaningful and highly motivated way.

and my response, sent to the Head of School and the math specialist:

I read the description of the 4th grade math lab in today's newsletter, and I have a question. When the kids take an average of three measurements, how do they perform the calculation? Do they add the numbers using the standard addition algorithm, then divide using long division? Or do they just use a calculator? If they're using calculators, they've missed an opportunity to practice their math skills. Over-reliance on calculators is one of the problems that lead to kids graduating from NF without the skills they need. (I see a calculator next to a student's elbow in one of the photos.)

If the kids use calculators for anything more challenging than 2+2, how much math is really being taught here? Kids need to achieve fluency with numbers, which comes -- wait for it -- from working with numbers. I think the calculators are a crutch used by the teacher to avoid confronting the reality of how weak the kids' math skills really are.

I didn't mention it in my e-mail, but I am also deeply skeptical of the picture painted in this description. Were the kids really engaged by the question of how high the ball would bounce? I doubt that either of my daughters would be.

Teacher 4 holds out a tennis ball a little above his waist height and asks his class, "Do you think you could predict how high this ball would bounce if I dropped it from 1 meter? "

Students suggest, "60 cm." "1 ½ meters.' 'To the ceiling."

"What could we do to make reasonable predictions?"

An animated discussion follows. The students know from past experience that they will have to experiment by dropping their ball a number of times from various heights to be able to make a good prediction. They decide to work in groups of three . Each group gets a ball and agrees to drop it several times from 40 cm, 60 cm and 120cm. They purposely omit dropping it from 100 cm (1 m) because they are intent on predicting the answer to Teacher 4's question before actually measuring it. From the many labs they have done in earlier grades they know that they will need to take at least three trial drops from each height and then find the average in order to get a more accurate result.

And so another Math Lab begins. By now the students are familiar with the process of planning an experiment, collecting data, graphing their data, and finally analyzing their results and testing their predictions.

These fourth graders have just learned how to calculate the mean and they will use this new skill to find the average of the three drops from each height. (In previous labs they usually took the median [the middle number of the three trials] as the average.) This lab will reinforce skills such as measuring, graphing, making 'best fit lines', and working cooperatively. It will also enable students to practice their new ability to find the mean.

There is a lively hum in the class as they students spread around the room and begin to plan their group work. They tape their meter sticks to the wall and practice dropping the ball and reading the results while the ball is in motion. Then they are ready to carry out the experiment, record the data and graph their results..

Later they find a 'best fit line' for their data points, so that they can predict how high the ball would probably bounce if it were dropped from exactly 1 meter. They then test their hypothesis by dropping the ball from 1 meter and compare this with their predictions.

This math lab is one of eight labs fourth graders will do during this academic year. For each lab, students sketch their plan, gather their materials, collect data in a data chart, then graph and analyze the data.

We have found these labs to be an excellent way for students to use and extend the mathematics that they are learning in a meaningful and highly motivated way.

and my response, sent to the Head of School and the math specialist:

I read the description of the 4th grade math lab in today's newsletter, and I have a question. When the kids take an average of three measurements, how do they perform the calculation? Do they add the numbers using the standard addition algorithm, then divide using long division? Or do they just use a calculator? If they're using calculators, they've missed an opportunity to practice their math skills. Over-reliance on calculators is one of the problems that lead to kids graduating from NF without the skills they need. (I see a calculator next to a student's elbow in one of the photos.)

If the kids use calculators for anything more challenging than 2+2, how much math is really being taught here? Kids need to achieve fluency with numbers, which comes -- wait for it -- from working with numbers. I think the calculators are a crutch used by the teacher to avoid confronting the reality of how weak the kids' math skills really are.

I didn't mention it in my e-mail, but I am also deeply skeptical of the picture painted in this description. Were the kids really engaged by the question of how high the ball would bounce? I doubt that either of my daughters would be.

Labels:
constructivist math,
curriculum,
private schools,
Trailblazers

## Sunday, February 6, 2011

### Paula Poundstone Re: Projects, Report Cards

I remember waking my mother on a school morning, just before I went to the bus stop, saying, "Mom, it's the school play today, and I'm supposed to be a carrot. Can you get up and make my costume?"

I know my mother used to hope that someday I would experience some of the frustration she had in raising me. I've been paid back in spades. "Mom, my science project is due today and I need to buy a poster board and I need your spleen and we're out of staples."

"Toshia, it's really hard to get you a poster board at the last minute."

"She just told us today."

I found Toshia's report card in her pants pocket when I was putting the laundry pile in the washing machine, because not only was she not going to show it to me, she was going to ruin a whole load of laundry with it. She had turned a D-minus into a D-plus by putting a vertical line through the minus sign. I wasn't so much upset with her as I was fascinated. "Exactly how different was my reaction going to be to a D-minus?" I showed her how to make a D into a B and asked that, in the future, she aim higher and have a little self-respect.

(from There's Nothing in this Book that I Meant to Say.)

I know my mother used to hope that someday I would experience some of the frustration she had in raising me. I've been paid back in spades. "Mom, my science project is due today and I need to buy a poster board and I need your spleen and we're out of staples."

"Toshia, it's really hard to get you a poster board at the last minute."

"She just told us today."

I found Toshia's report card in her pants pocket when I was putting the laundry pile in the washing machine, because not only was she not going to show it to me, she was going to ruin a whole load of laundry with it. She had turned a D-minus into a D-plus by putting a vertical line through the minus sign. I wasn't so much upset with her as I was fascinated. "Exactly how different was my reaction going to be to a D-minus?" I showed her how to make a D into a B and asked that, in the future, she aim higher and have a little self-respect.

(from There's Nothing in this Book that I Meant to Say.)

## Saturday, February 5, 2011

### Paula Poundstone Re: Homework

I hate homework. Sometimes I think it's worse for the family than drugs and alcohol could ever hope to be. I didn't do my own homework. If my kids aren't smart enough to get out of theirs, why should I do it? I get mad at them for not hiding it better.

(from There's Nothing in this Book that I Meant to Say.)

(from There's Nothing in this Book that I Meant to Say.)

## Thursday, February 3, 2011

### What's so Progressive About "Constructivist" Math?

The makers of "constructivist" math curricula like Everyday Math and Trailblazers have marketed themselves very cleverly as promoting progressive education. Then, anyone who criticizes the program can be labeled "anti-progressive" and effectively ignored.

They also crow about their "integrated" approach, which, in theory, makes math "relevant" to other subjects like language arts and social studies, but, in practice, just leads to piles of dull, pointless work that doesn't teach math. The fact that the inventors of these curricula think that math needs to be made "relevant" to other subjects betrays their bias; they don't like or appreciate math on its own terms.

There's nothing "progressive" about 3d-grade homework like "write a multiplication story about 6 x 4". Suggested solution: "We had a birthday party for one of my best friends. I had pizza and ice cream. When we were all done we opened up presents and sang happy birthday. Then her mom gave all 6 of us at the party 4 tokens each to use at the arcade games. That is 24 games that we played."

I'd estimate that the physical act of writing this out would take an average third-grader at least a half-hour. They're supposed to illustrate it too. If you add in time for the inescapable whining, complaining, cajoling, and nagging, you've used up at least an hour of your evening for your kid to learn a math fact that they could have written in numbers in about 30 seconds. (For quicker results, I recommend the FedUpMom solution: take 5 minutes to send the teacher an e-mail explaining why your kid won't be doing the homework.)

What is "progressive" about teaching 5 different methods of subtraction, each more laborious and less universal than the traditional algorithm, and skipping the traditional algorithm altogether, as Everyday Math does? It can't be called "constructivist" either, since the algorithms must be taught by the teacher. Actually, if it was truly constructivist and you just asked the kids to invent their own method, they'd probably do a better job.

I'd like to decouple the issue of Everyday Mathematics and Trailblazers from the progressive vs. traditional ed. debate. I can't stand Everyday Math and Trailblazers, but it's not because I'm a hidebound traditionalist; it's because they are just bad curricula that do a terrible job of teaching math.

They also crow about their "integrated" approach, which, in theory, makes math "relevant" to other subjects like language arts and social studies, but, in practice, just leads to piles of dull, pointless work that doesn't teach math. The fact that the inventors of these curricula think that math needs to be made "relevant" to other subjects betrays their bias; they don't like or appreciate math on its own terms.

There's nothing "progressive" about 3d-grade homework like "write a multiplication story about 6 x 4". Suggested solution: "We had a birthday party for one of my best friends. I had pizza and ice cream. When we were all done we opened up presents and sang happy birthday. Then her mom gave all 6 of us at the party 4 tokens each to use at the arcade games. That is 24 games that we played."

I'd estimate that the physical act of writing this out would take an average third-grader at least a half-hour. They're supposed to illustrate it too. If you add in time for the inescapable whining, complaining, cajoling, and nagging, you've used up at least an hour of your evening for your kid to learn a math fact that they could have written in numbers in about 30 seconds. (For quicker results, I recommend the FedUpMom solution: take 5 minutes to send the teacher an e-mail explaining why your kid won't be doing the homework.)

What is "progressive" about teaching 5 different methods of subtraction, each more laborious and less universal than the traditional algorithm, and skipping the traditional algorithm altogether, as Everyday Math does? It can't be called "constructivist" either, since the algorithms must be taught by the teacher. Actually, if it was truly constructivist and you just asked the kids to invent their own method, they'd probably do a better job.

I'd like to decouple the issue of Everyday Mathematics and Trailblazers from the progressive vs. traditional ed. debate. I can't stand Everyday Math and Trailblazers, but it's not because I'm a hidebound traditionalist; it's because they are just bad curricula that do a terrible job of teaching math.

## Tuesday, February 1, 2011

### Reforming Math 5

(Continuing from Reforming Math 1, Reforming Math 2, Reforming Math 3, and Reforming Math 4.)

Here's the latest from the Head of Natural Friends:

I have read your e-mail several times and the more I have thought about it the more I am convinced that the distance between your position and mine is small.

I share the conviction that computation is an important component of mathematics. I share the conviction that this vital curricular thread (computation) has developmentally appropriate expectations associated with it. For example, multiplication tables 0 to 12 known at the end of fourth grade, and addition, subtraction, multiplication, and division of parts of wholes (fractions, decimals, and percents) mastered at the end of fifth grade.

You seem to object to constructivist, mathematical inquiry only in so far is it is not the whole of the math curriculum (and not primary) or insofar as it is tiring, tedious, time-wasting (and alliterative).

I want you to know that our mathematics specialist shares the conviction that both computation and interesting, constructivist, mathematical inquiry are important elements of a strong mathematics curriculum. I want you to know by way of example that our fourth grade teacher has identified the aforementioned multiplication tables expectation (in writing and at curriculum night) for his class parents this year.

I can not speak to the history of the successful implementation of this point of view at Natural Friends but I can tell you that I am determined that we as a faculty will successfully implement a mathematics curriculum that contains both elements and reflects clearly both rote and more creative expectations going forward.

and my reply:

I expect we agree on goals more than we do on methods.

I told you about NF's current reputation among the surrounding schools, not because I'm asking you to fix the past, (although if you can, be my guest), but because I'm trying to convince you that the status quo should not be allowed to continue.

If I could wave a magic wand and get anything I wanted, I would have you throw out Trailblazers/Connected Math and bring in Singapore Math. Singapore Math is clear, it's concise, and it teaches real math. TB/CM, by contrast, just doesn't teach a long list of important algorithms and concepts (I hope you've had a chance to peruse my list -- the e-mail is titled "Missing Math"), and it wastes a great deal of time and energy on substandard algorithms (like "partial sums" and "partial quotients"). There is also way too much time spent on discussion and writing in English, and not enough time spent learning the symbolic language of mathematics. TB/CM is very weak on the abstract qualities of math; it doesn't go near logic and inference.

Now, I'm not against constructivist inquiry if the kids enjoy it. Of course, kids should be encouraged to ask questions and make sense of what they're learning. If they can exercise their math skills while engaged in an interesting project or game, I'm all for it. But they also need a coherent, complete curriculum. Clearly stated goals (as in your example of the 4th grade) are an important first step.

I'm not a constructivist or traditionalist or drill-and-killer. I'm a pragmatist. I want to know that if Younger Daughter stays at NF through the 6th grade, she will go on to her next school able to handle their math program, without remediation or extra tutoring. I want her to know math, like math, and have justified confidence with it. Can NF deliver all this?

Sincerely,

FedUpMom.

P.S. Speaking of games, here's one that Older Daughter likes. It's about probability.

Can't Stop

And here's a list of math games:

Math Games

Here's the latest from the Head of Natural Friends:

I have read your e-mail several times and the more I have thought about it the more I am convinced that the distance between your position and mine is small.

I share the conviction that computation is an important component of mathematics. I share the conviction that this vital curricular thread (computation) has developmentally appropriate expectations associated with it. For example, multiplication tables 0 to 12 known at the end of fourth grade, and addition, subtraction, multiplication, and division of parts of wholes (fractions, decimals, and percents) mastered at the end of fifth grade.

You seem to object to constructivist, mathematical inquiry only in so far is it is not the whole of the math curriculum (and not primary) or insofar as it is tiring, tedious, time-wasting (and alliterative).

I want you to know that our mathematics specialist shares the conviction that both computation and interesting, constructivist, mathematical inquiry are important elements of a strong mathematics curriculum. I want you to know by way of example that our fourth grade teacher has identified the aforementioned multiplication tables expectation (in writing and at curriculum night) for his class parents this year.

I can not speak to the history of the successful implementation of this point of view at Natural Friends but I can tell you that I am determined that we as a faculty will successfully implement a mathematics curriculum that contains both elements and reflects clearly both rote and more creative expectations going forward.

and my reply:

I expect we agree on goals more than we do on methods.

I told you about NF's current reputation among the surrounding schools, not because I'm asking you to fix the past, (although if you can, be my guest), but because I'm trying to convince you that the status quo should not be allowed to continue.

If I could wave a magic wand and get anything I wanted, I would have you throw out Trailblazers/Connected Math and bring in Singapore Math. Singapore Math is clear, it's concise, and it teaches real math. TB/CM, by contrast, just doesn't teach a long list of important algorithms and concepts (I hope you've had a chance to peruse my list -- the e-mail is titled "Missing Math"), and it wastes a great deal of time and energy on substandard algorithms (like "partial sums" and "partial quotients"). There is also way too much time spent on discussion and writing in English, and not enough time spent learning the symbolic language of mathematics. TB/CM is very weak on the abstract qualities of math; it doesn't go near logic and inference.

Now, I'm not against constructivist inquiry if the kids enjoy it. Of course, kids should be encouraged to ask questions and make sense of what they're learning. If they can exercise their math skills while engaged in an interesting project or game, I'm all for it. But they also need a coherent, complete curriculum. Clearly stated goals (as in your example of the 4th grade) are an important first step.

I'm not a constructivist or traditionalist or drill-and-killer. I'm a pragmatist. I want to know that if Younger Daughter stays at NF through the 6th grade, she will go on to her next school able to handle their math program, without remediation or extra tutoring. I want her to know math, like math, and have justified confidence with it. Can NF deliver all this?

Sincerely,

FedUpMom.

P.S. Speaking of games, here's one that Older Daughter likes. It's about probability.

Can't Stop

And here's a list of math games:

Math Games

Labels:
constructivist math,
curriculum,
private schools,
Trailblazers

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