kitchen table math, the sequel: 6/14/09 - 6/21/09

## Saturday, June 20, 2009

### The Arlington Algebra Project & e-math instruction

These look like terrific resources:

The Arlington Algebra Project

eMath Instruction

Thanks to Kate!

### Fear of Knowledge

Of the three constructivist theses before us, the most influential is the thesis of fact-constructivism—which is somewhat surprising given that it is also the most radical and the most counterintuitive. Indeed, properly understood, fact-constructivism is such a bizarre view that is it hard to believe that anyone actually endorses it. And yet, it seems that many do.

According to fact-constructivism, it is a necessary truth about any fact that it obtains only because we humans have constructed it in a way that reflects our contingent needs and interests. This view stands opposed to fact-objectivism, according to which many facts about the world obtain entirely independently of human beings.

[snip]

Fact-constructivism would seem to run into an obvious problem. The world did not begin with us humans; many facts about it obtained before we did. How then could we have constructed them? For example, according to our best theory of the world, there were mountains on earth well before there were humans. How, then, could we be said to have constructed the fact that there are mountains on earth.

One famous constructivist, the French sociologist Bruno Latour, seems to have decided to just bite the bullet on this point. When French scientists working on the mummy of Ramses II (who died c. 1213 BC) concluded that Ramses probably died of tuberculosis, Latour denied that this was possible. “How could he pass away due to a bacillus discovered by Robert Koch in 1882?” Latour asked. Latour noted that just as it would be an anachronism to say that Ramses died from machine-gun fire so it would be an anachronism to say that he died of tuberculosis. As he boldly put it: “Before Koch, the bacillus had no real existence.”

Fear of Knowledge: Against Relativism and Constructivism
by Paul Boghossian

### Barry on retrofitting a bad curriculum

However, the question still remains: if you've got a 'lemon,' in the form of an ineffective school or curriculum, then what?

Well, what did you do? You taught your son at home. That's reteaching but can also be called tutoring. I did the same with my daughter. Was it effective? I think so, but I resented having to do it. I got spoiled when my daughter had good teachers in 7th and 8th grades in math. I felt guilty not going through the work with her until I realized that "normal" mean the child understands it by going to school and learning it.

When things are abnormal, after a while it gets to be too much. If there's a good private school around and the parents can afford it, that's the option some seek (as you did).

In terms of other students I tutor, as Anne Dwyer said, if you can identify weak areas that are holding up learning, yes it's effective. In terms of retrofitting a bad curriculum, it's just about impossible as an independent tutor. The parents would have to be willing to have their child take an alternative course. In essence, that's what parents are doing when they send their children to Kumon or Sylvan, etc. Those are schools. So the child is put in the position of going to school twice, and the parents penalized by having their taxes go to waste, and having to shell out more money for the learning centers.

retrofitting a bad curriculum: that is a fantastically useful phrase.

That's a basic public school concept: we'll spend millions on this lousy math curriculum the parents can't stand and we'll "supplement."

Win - win!

Welcome to Grand Canyon

### how many tutors in Palo Alto?

Almost 60 percent of Palo Alto parents supplement their children's math education through private tutors, extra workbooks and other means, mostly because they feel Palo Alto classes aren't challenging enough, according to results of a district survey released this week.

The district conducted an online survey of about 1,200 elementary school parents, and will compare its results with another survey taken next spring, after students have spent a year learning the district's new Everyday Mathematics curriculum.

During the debates over the controversial Everyday Math program, adopted as the district's new curriculum in April, many parents said Everyday Math is confusing and doesn't teach basic math skills. Parents frequently said they would have to supplement their children's math education.

Under the current curriculum, 62.8 percent of parents said their children don't need extra help in math, the survey says. But 57.2 percent said they provide supplemental math work anyway, mostly in the form of extra practice materials like workbooks or software, or regular math tutoring by a sibling or parent.

About 6.5 percent of parents said they hired a private math tutor, and 21.6 percent said their children attend a private math program like Kumon or Score.

A majority of parents who supplement their children's math education — 51 percent — said a "main reason" they do so is because their child needs to be more challenged in math, and 42.9 percent said a main reason was because their child enjoys math.

Former school board member Mandy Lowell, who has been critical of the district's adoption of Everyday Math, said boredom with math has been a "perennial problem" here. Palo Alto students are the sons and daughters of engineers and scientists who enjoy math, and have passed their love for the subject on to their children, she said, but the program focuses more on "supermarket math."

They do what they do.

### Anne Dwyer on what tutoring can achieve (& who needs tutoring & why)

Ok, here's what I see from the trenches.

First, I think I see the big picture because I:
have a special ed student in pre algebra
have a daughter in regular 6th grade math
teach remedial math in college
tutor bright but struggling high school boys in math
have just finished 8 credits of graduate mathematics

I could write a whole long post, but I'd get bored in the middle and delete it. So here goes with the conclusion:

1. Certain school districts (mine) believe in good curricula and qualified teachers. (see the exception below) This combination makes all the difference in the world. The highly qualified teachers know what the students need to learn in math, and will find a way to do the direct instruction. (The exception in my district is, of course, elementary school.)

2. I have tutoring students in other districts who use good curricula but have poorly qualified teachers and students in districts with highly qualified teachers and poor curricula. The boys I am tutoring had a very solid foundation in basic math and are still struggling. The good news is a good tutor can fill in the holes quite easily.
very small.

3. All of my professors at the university that I attend use the direct instruction method. They go over every proof in the book in detail (even though the proof is in the book) and they give solutions to every problem they assign.

### Former Public School Teacher

Non-renewed, forced out.

This means that you are made to feel so uncomfortable in your position that you look for another job and you are unable to even get an interview at another school in one of the 15 largest districts in the country. So you move to another district, lose the "tenure" and then are non-renewed due to budget cuts and mostly disagreement with teaching fuzzy math.

I taught at one of the states way down there on the list of funding. I think it's 49 or 50. I was doing fine until I had a daughter. Then I started looking at every kid like she was my own. I'm not proud of that fact, but at least I finally saw the light. That's when things started going wrong. It also coincided with Everyday Mathematics being adopted by the district. I saw gifted kids in the 6th grade who couldn't multiply and divide. Kids who should have been able to move up to algebra in the 7th grade. I had work to do. I had to re-teach them everything from 4th and 5th grade and do 6th and pre-algebra so they could be where they should be.

When I was anonymous at school I wasn't bothered, but I got so excited by the changes that I started talking about it. The beginning of the end was the first week of October 2006.

I wish that I had quit first instead of them "quitting" me. I am starting to realize that I don't want to work in the system anymore. My daughter does Kumon, because I want other teachers for her besides me. Her Kumon teacher is from India. We will begin ALOHA abacus training, another teacher from India, next month. I hope to begin teaching abacus in the near future.

I know that the emotion and frustration you are reading here are not very productive, but I have been dying inside for a long time.

Signed
Former Public School Teacher
This is an atrocity.

### chemprof on what tutoring can achieve

I'll semi-agree with Kate. A few years ago, we implemented tutoring by the course TAs for students who were really struggling, usually because of inadequate preparation or miserable math skills. We found we had to put in a "miss two sessions and you lose your slot" policy, as struggling students also often blew off the tutoring session, partly I suspect because it was free.

Tutoring can work really well for a student who needs to see the material again, and who comes to the session having looked over her notes and with questions. There, I've seen 30-60 minutes with the tutor each week changing a low C into a mid-range B (or even in one extreme case, a student who had failed twice ending up with an A!) It can be nearly useless for a student who comes with nothing, hasn't looked at anything, and isn't even sure where to start. Of course, I'm also talking about college students, where "taking responsibility for your own learning" is actually appropriate!

I'm very interested in this question - thanks so much for taking the time to comment.

Based entirely in personal experience, I've come to the conclusion that tutoring is 'bad' -- i.e. it's a bad model for learning (& teaching). It's like buying a lemon and then taking it to the shop a whole lot.

However, the question still remains: if you've got a 'lemon,' in the form of an ineffective school or curriculum, then what?

How well can tutoring work when there's no other option?

## Friday, June 19, 2009

### Kate on teaching & tutors in an affluent district

I teach in a district with many wealthy families.

Some of the teachers at my school drive very nice cars. They are all married to someone who makes alot more than we do.

Some parents would hire a tutor whether their child needs it or not. They feel like if they don't, they're not doing everything they can.

I don't think tutors are particularly helpful, for several reasons.

In my experience the main benefit of a tutor is that it compels students who tend to blow off/copy assignments to sit and focus on math for at least an hour a week.

I prefer my students not get tutored because they sometimes cop an attitude in class like they don't have to pay attention, because the tutor will teach it to them later. (This is not very many students...just an obnoxious, overprivileged few.) Overall it sends a message that parents don't trust teachers to get the job done.

All that being said, most of my students don't have tutors. They participate in learning activities and complete the work I ask them to, and we get good results.

Thanks, Kate!

(Back in a bit - I promised myself I would do "first things first" this morning. Sure, I've already broken that promise, but that's why God invented the mid-course correction.)

## Thursday, June 18, 2009

### Scarsdale runs amok

A Scarsdale Education for the Future (pdf file)

It's getting to be time to tell my Holland story.

## Wednesday, June 17, 2009

### are parents rational?

Steve H. needs to hie himself over to Dan Willingham's blog right this minute and share his wit and wisdom re: parents and their ability to think as clearly as a person who has obtained a professional administrative services credential.

### Wolfram Alpha

The long-running debate over whether students should be allowed to wield calculators during mathematics examinations may soon seem quaint.

The latest dilemma facing professors is whether to let students turn to a Web site called WolframAlpha, which not only solves complex math problems, but also can spell out the steps leading to those solutions. In other words, it can instantly do most of the homework and test questions found in many calculus textbooks.

The new tool will be a bane to teaching, some professors say—but others see a blessing.

WolframAlpha was created by Stephen Wolfram, an entrepreneur who invented Mathematica, one of the first computer math engines. His new site debuted last month to much media fanfare and, like Google, provides answers to questions typed into a simple search box. It is free and already boasts millions of searches.

A Calculating Web Site Could Ignite a New Campus 'Math War'
by Jeffrey R. Young

I need WolframAlpha for proofs.

### United States for World Class Math

Just in: a website for people like us who want a seat at the table when it comes to national math standards:

United States Coalition for World Class Math

Check out their Design Principles for K-12 Mathematics Standards:

1. All students should be expected to master foundational concepts and skills – especially in arithmetic – that are prerequisite to an authentic Algebra I course in a logical progression from grade to grade in the elementary and middle school years. The Final Report of the National Mathematics Advisory Panel (NMAP) should be the guiding document describing appropriate mathematical content.

2. The K-7 standards should be designed to prepare as many students as possible for an authentic Algebra I course in Grade 8. K-7 standards should be based on the "Critical Foundations of Algebra" described on pages 17-19 of the NMAP’s Final Report. Standards for authentic Algebra I and Algebra II courses should be based on "The Major Topics of School Algebra" described on pages 15-16 of the NMAP’s Final Report.

3. Standards-based alternatives could be written for less prepared students and alternate paths after algebra and geometry for high school students, depending on student achievement, interests, and career goals. For example:

a. The standards document could outline the possibility of a two-year course spanning Grade 7 and Grade 8 based on Grade 7 standards for students who, at the end of Grade 6, are judged to need more time to master foundational concepts and skills for Algebra I.

b. The standards document could outline a two-year course spanning Grade 8 and Grade 9 based on authentic Algebra I standards for students completing Grade 7 who are judged to need two full years to master Algebra I standards.

4. As emphasized by the National Mathematics Advisory Panel, "a focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided." Placement of the standards should reflect the grade level at which mastery is expected, and standards should not be repeated from year to year.

a. The sequence of the standards should be logical and hierarchical, following the structure of mathematics itself and should be modeled after the strong standards in California, Indiana, and Massachusetts.

b. "Benchmarks for the Critical Foundations" (pages 19-20 in the National Mathematics Advisory Panel’s Final Report) and recommendations from the National Council of Teachers of Mathematics’ Curriculum Focal Points should be used for grade level placement.

c. Concepts and skills, once mastered, should be used in subsequent years with a minimum of review.

5. In order to focus on building solid foundations for the more advanced mathematics – including algebra – that occurs in Grades 8-12, extraneous topics including aspects of geometry such as tessellations, nets, statistical approaches to geometric properties, much of data analysis, probability and statistics, and non-algebraic concepts such as pattern recognition should not be present in the K-7 standards.

6. In Grades K-7, the distribution of content by strand should be stated explicitly as percentages at each grade level and should change as students move up through the grades.

a. Early grades should concentrate on the arithmetic of whole numbers and measurement, with a limited amount of geometry and graphing. Certain aspects of algebra, as well as preparation for algebra, should be present from the earliest grades, as is the case with the California and Massachusetts standards.

b. Students should be expected to acquire automatic recall of basic number facts at least to 10 x 10 and 10 + 10.

c. Students should be expected to understand and use the standard algorithms of whole-number arithmetic in the early elementary grades (i.e., addition, subtraction, multiplication, and long division).

d. Students should be expected to understand and use the standard definitions for operations with fractions in conjunction with the standard algorithms of whole number arithmetic to compute sums, differences, products and quotients of fractions, including fractions expressed as decimals and percents.

e. The algebra strand gains emphasis in the middle grades, focusing on the content specified by the National Mathematics Advisory Panel.

7. The organization of the standards should change at Grade 8.

a. In grades K-7, standards should include multiple strands of mathematics, with their relative weight appropriately adjusted through the grades.

b. For algebra and beyond, standards should be given for a single-subject course sequence (Algebra I, Geometry, Algebra II, Pre-calculus, etc.) and their components re-ordered for alternative integrated mathematics courses. The standards for the Geometry course should require students to do proofs and to understand postulates, theorems and corollaries.

8. Mathematical problems should have mathematical answers.

a. In general, students should learn techniques for problem solving that can be applied to many contexts. Problems should be contextualized in the "real world" only when the context is sensible and relevant and contributes to an understanding of the mathematics in the problem.

b. Standards documents should include example problems. The level of difficulty of these problems should reflect mathematical complexity rather than non-mathematical issues.

9. K-12 math standards should meet the criteria specified by the American Federation of Teachers. They should be:

a. Clear and specific enough to provide the basis for a common core curriculum.
b. Rooted in the content of mathematics.
c. Clear and explicit about the content and the complexity students are to learn.
d. Measurable and objective.
e. Comparable in rigor to the standards of A+ countries, with grade-level specificity.

10. Standards documents should appropriately emphasize the attainment of procedural fluency. Students must be competent in performing all K-7 tasks without using a calculator.

11. Standards documents should only address mathematical content; language pertaining to pedagogy should be excluded.

12. As emphasized by the National Mathematics Advisory Panel, mathematicians should be included in greater numbers, along with mathematics educators, mathematics education researchers, curriculum specialists, classroom teachers, and the general public, in the standard-setting process and in the review and design of mathematical test items for state, NAEP, and commercial tests.

CO Coalition for World Class Math

Common Core Standards: Who Made the List?

### Portfolios and Finals

I need to know if this is common for middle school. Work gets done, stays in portfolios at school and then comes home at the end of the year. It's too late to learn from the material or to question the result. One of those portfolios came home with my son today. It was for a thematic project that covered many subjects and was completed months ago. He had to give himself a rubric grade,so he gave himself a 4 out of 5. I'm sure his friends gave themselves a 5.

I told the principal earlier in the year, in a firm but nice way, that I want all homework and tests graded in a timely fashion and sent home. Apparently, that can't or won't happen. I also asked her about some related impossible 5 issues and grades and she said that it really doesn't matter. The high school won't know about the grades. Ha, ha, ha.

Then there are issues with teachers using grades as weapons against kids. They tell the class who got what grade. This isn't across the board, just selective. The school makes a big deal about their bullying policy, but they should add a section on bullying by teachers. My son didn't want to bring in a note for PE class due to a sore ankle because the gym teacher would call him a baby. He's seen it happen to other kids. That reminds me. That low/high ropes session he went to a while back wasn't about teambuilding. It was about boot camp work versus punishment. It was at a National Guard facility. All of the kids were given stupid names by the drill sergeants and had to do push-ups if they did something wrong. They had to do things in teams just like how new recruits have to do things in teams.

## Tuesday, June 16, 2009

### the unwritten rule

from Revisiting Professional Learning Communities at Work by Richard DuFour, Rebecca DuFour, and Robert Eaker:

Education has developed its own ... tradition of unwritten rules or norms that impact the day-to-day workings of schools across the United States. Like baseball, these norms are not only unwritten, they are largely unexamined. They simply represent "the way we do things here." Someone entering the profession as a new teacher in a traditional school will soon discover the unwritten rules, the way things are to be done. If those rules or norms were written, here is what they might say:

[snip]

Our job is to teach, and the students' job is to learn. [italics mine]
Hence: tutors.

lgm on upstate NY
it's good to be rich
all things PLC

### upstate New York

from lgm:
Here (upstate), the norm is that homework or classwork is checked by the teacher, but if it shows lack of concept/mastery understanding, there is no reteach unless student qualifies for specialist help. If the parent doesn't and the child is unclassified, the child will be dropped in to a lower section at the end of the unit (gr. 4-5) or the year (K-3). When he falls behind far enough he'll qualify for specialist help via RtI. The in-the-know parents just hire the tutor or do it themselves rather than let the student fall that far behind.

Also, is Scarsdale teaching for excellence or 'for the pass'? I notice here that the info needed in math to perform at the '4' level on the grade level state exams is not taught in class. One has to afterschool with a quality curriculum.

Here, 3rd graders do write a 'research paper' in class. The topic is 3rd grade friendly and most can do it. It reminds me more of a five paragraph essay than a paper.

I would like schools to teach kids how to write book reports.

Then I'd like schools to assign book reports.

Thank you very much.

### if you're raising a shy and/or sensitive boy

two words: guitar lessons

Indexed (see: back cover)

## Monday, June 15, 2009

### Optimism

From a post entitled: Teachers can save the economy:

### Barry G on learning physics in high school

We had a bit of physics in 8th and 9th grades. My first real course was as a senior in high school. The teacher was very good and I was totally amazed by the subject. Although it was not calculus-based, it did use trig which we were studying at the time, and math and science merged very nicely. I still remember the lecture on the derivation of the formula for distance of a uniformly accelerating body, relating it to the "area under the curve" which in this case was a straight line, and thus was the area of a triangle. I wondered why he called a straight line a "curve", and the next year in freshman calculus, it again all made sense, when we learned integration.
I can't wait to learn calculus.

Or physics.

Speaking of subjects I intend to learn, The Teaching Company has high school courses. I ordered the chemistry course. * I'm thinking of asking C. to work through as much of it as he can next summer, before he takes chemistry at Hogwarts. (He's taking AP biology next year, when he'll be a sophomore.)

I have Nature of the Earth, too, and Building Great Sentences, which is fantastic. Building Great Sentences is so fantastic that the other night, when Ed and an attorney friend were discussing the critical importance of writing short sentences, I rolled my eyes.

"You don't try to write short sentences?" Ed asked.

"No," I said curtly, leaving the men to wonder why.

While it is true that I personally have not read Strunk & White, I have listened to two lectures from Building Great Sentences, and thus feel confirmed in my view that short sentences are neither here nor there.

*

### Scarsdale tutors

I was just talking to a guy who is related to a Scarsdale grade school teacher.

Scarsdale teachers start tutoring Scarsdale students for pay as early as second grade.

Scarsdale tutors, part 1

## Sunday, June 14, 2009

### Richard on Physics First

I have a quote on my teaching room along the lines of .......

"There are three physics courses taught at most universities: physics with calculus, physics without calculus and physics without physics."

It sounds like Physics First could be a prerequisite for "physics without physics."

Speaking of physics without calculus, is this calculus without calculus?

I've been cruising this course for a long time....

### Damar the starling bird

Cognition and Language Lab

I think I've mentioned a couple of times that I came out of Animals in Translation thinking if there is one critter as smart as people or smarter, it's birds. There might be others, of course. There might be lots of others. But birds were the ones that were hard to ignore.

Funny thing: The Birds was one of my favorite movies when I was a kid.

### Physics First?

"To teach her students about velocity, teacher Ethel Locke set them loose in the halls of Woonsocket High School with marble launchers.
Through trial and error, the students discovered that their marbles achieved the longest arcs if they were launched at an angle halfway between the floor and the ceiling. If they set the launchers at higher or lower angles, gravity pulled the marbles to the floor at shorter distances."

Physics no longer a junior member

"Pausing from the task at hand, Devon confided that he liked physics better than he thought he would. Ordinarily, he said, it 'is not a class you would like.' "

That's because it isn't physics.

How about deriving the equations you need from g=32.174 ft/sec^2 and analytically calculating that angle.?

Does anyone have any experience with Physics First? The story claims that this order has "nearly doubled" the demand for AP science courses in physics, biology, and chemistry. They must have another senior-level AP physics course. This means that kids would take two physics courses in high school?